Tag: Innovation

Innovation: Faster, Higher, Stronger
Proposed GNSS Navigation Messages for Improved Performance

By Wentao Zhang and Yang Gao

INNOVATION INSIGHTS by Richard Langley

TIME-TO-FIRST-FIX, commonly known by the initialism TTFF, is the elapsed time between the powering on or starting up of a GNSS receiver and when it successfully computes either a two-dimensional (height constrained) or three-dimensional position fix and sets its clock to the correct time. A three-dimensional fix requires simultaneous receiver measurements on the signals from a minimum of four satellites along with the satellites’ positions (ephemerides) and the offsets between the individual satellite clocks and the GNSS system time.

TTFF depends crucially on the availability and timeliness of the satellite ephemerides and clock information when a receiver starts up and, accordingly, there are three types of start-up with correspondingly different TTFF.

A cold start (sometimes also called a factory start) occurs when the receiver has no knowledge of its current position, time or the positions of the satellites and their clock offsets. The receiver must do a blind search of the sky trying different possible Doppler frequency shifts and pseudorange delays for all the satellites in the constellation. Once satellites are found and tracked, the ephemerides and clock information must be collected. This is repeated in each satellite’s navigation message every 30 seconds. In addition, the information on the offset between GNSS system time and UTC must be collected along with the ionospheric delay correction parameters and the almanac (an approximate ephemeris for all active satellites in the constellation) to be used for faster subsequent signal acquisition. This data is only transmitted once in the 12.5-minute-long navigation message. Therefore, the TTFF for a cold start can take up to 12.5 minutes and even longer especially if the GNSS signals are hard to acquire such as in obstructed environments.

A warm start, or what we might call normal operation, occurs when the receiver has some a priori information on its position, the time and the approximate locations of the satellites. Typically, this means knowing the receiver position to within a few hundred kilometers, time to within 10 minutes or so, and a reasonably fresh almanac. Armed with that information, a receiver knows which satellites should be visible to it and can quickly acquire and track satellite signals and obtain the satellite ephemeris and clock information. Since that information is repeated every 30 seconds, TTFF for a warm start can be 30 seconds or less.

A hot start occurs when a receiver is powered on after being off and stationary for a short interval and it therefore has a very good estimate of its position and the current time and valid satellite ephemeris and clock data. TTFF for a hot start, therefore, is typically only a few seconds. This mode of receiver operation would also apply to scenarios where all signals are temporarily lost in road or rail tunnels or where a number of signals are momentarily blocked by obstructions causing a break in position fixing.

Fast first fixes were traditionally only possible when a receiver had a clear view of the sky and could readily acquire the navigation messages. Pseudorange measurements can be made, however, even if satellite signals are somewhat attenuated in strength to the point that navigation messages cannot be acquired. Position fixing in this case would be possible if the receiver could obtain the navigation information from elsewhere. Over the past decade or so, assisted GNSS techniques have been developed to provide frequently refreshed navigation information over cellular telephone networks, for example. But would there be a way to achieve fast first fixes autonomously without reliance on these assisted techniques? Not with the signals presently being transmitted by either the mature or nascent constellations, it seems, but in this month’s column, we look at proposed changes to the way navigation messages are formulated that could result in a future satellite navigation system providing faster fixes effectively giving receivers higher sensitivity and stronger performance.

“Innovation” is a regular feature that discusses advances in GPS technology and its applications as well as the fundamentals of GPS positioning. The column is coordinated by Richard Langley of the Department of Geodesy and Geomatics Engineering, University of New Brunswick. He welcomes comments and topic ideas. Email him at lang @ unb.ca.

Despite some differences in their structures, different GNSS broadcast navigation (NAV) messages usually consist of two parts: immediate (primarily ephemeris) and non-immediate (primarily almanac) data. The immediate data is repeated at a much shorter interval than the non-immediate data, and expires much sooner than the non-immediate data. Taking GPS as an example, the civilian navigation (CNAV) messages consist of five subframes with each lasting six seconds, as depicted in FIGURE 1. The first three subframes provide the ephemeris, with the content repeated every 30 seconds and updated every two hours, while the last two subframes provide the almanac for each satellite in 25 pages, with the content updated nominally every six days (according to the GPS Interface Specifications document), but updates are actually daily.

FIGURE 1. Frame structure of GPS CNAV messages.

Depending on the accuracy of receiver time and the availability of previously collected ephemerides (the immediate data) when powered on, GNSS user equipment (UE) might experience cold, warm or hot starts, among which the warm start is the most common case. In the widely accepted definition for warm start, no valid ephemeris is available, but the receiver time is roughly known at startup.

As depicted in FIGURE 2, the position fix sequence by a standalone GNSS UE normally consists of signal acquisition, tracking, bit synchronization, frame synchronization, ephemeris downloading, measurements taking and position computation. In performing a regular warm start, signal acquisition usually takes only a few hundred milliseconds for a GPS device in open-sky environments. However, under weak signal conditions, signal acquisition might take much longer (say a few tens of seconds). Once the signal is acquired, the tracking loop is activated, and immediately after the signal is pulled in the process of data-bit synchronization is started. This process takes a few hundred milliseconds to several seconds depending on signal strength and algorithm efficiency. In a stable tracking status, the navigation bits are collected sequentially one by one. Collecting a complete copy of a GPS ephemeris takes about 18 seconds in open-sky environments but may take minutes or even forever in weak signal environments due to an increased bit error rate (BER). As soon as the ephemeris downloading from three to four satellites is completed and the measurements are made, the user position fix usually can be obtained immediately. Therefore, in weak signal environments, the obstacles to fast time-to-first-fix (TTFF) are primarily signal acquisition and ephemeris downloading, and in open-sky environments the obstacle mainly lies in the time needed for ephemeris downloading.

FIGURE 2. Typical sequence of position fix process in standalone GPS user equipment (Msr=measurements).

For a GNSS UE in an open-sky environment on the Earth’s surface, the minimum received signal level for GPS L1 is around -130 dBm according to the interface specifications. For other GNSS signals, the nominal received signal levels are approximately the same.

However, in some extreme cases, such as urban canyon, foliage and indoor environments, the signals finally arriving at a receiver’s antenna could be heavily attenuated by 30 dB or even more. Working under such conditions requires GNSS UE to have high-sensitivity capability.

When the GNSS signal strength drops to a certain level, it causes immediate difficulties in the GNSS receiver tracking loop and for ephemeris downloading. Firstly, the parameters of the tracking loop, designed for normal signal strengths, are no longer optimum for either obtaining enough gain for signal detection or for maintaining signal tracking. Secondly, BER increases with decreasing signal strength. When the signal carrier-to-noise-density ratio drops below 27 dB-Hz, even if signal tracking is maintained, the increased BER would make it difficult for successful decoding of NAV messages.

Sensitivity improvements for a GNSS receiver can involve contributions from the antenna, the RF front end and baseband signal processing. In the signal processing, to obtain adequate processing gain in signal-to-noise ratio for signal detection, combined coherent and non-coherent integrations are needed. An approximate relationship for calculating such processing gain is given in Equation (1). Considering that non-coherent integration is subject to squaring loss, for a fixed total integration period (T_I), increasing the coherent period (T_c) is more efficient for achieving higher processing gain. However, without knowing the navigation bits, the coherent integration is limited within a 1-bit period or 20 milliseconds for GPS signals.

(1)

To improve sensitivity to -160 dBm, coherent integration over multiple bits is desired. Therefore, valid navigation bits as well as the bit boundaries are needed for data wipe-off. For this purpose, previously collected navigation bits can be directly used if they are still valid or fresh navigation messages from different sources, including ephemeris and almanac, can be used to recover the navigation bits.

GNSS Assistance Technologies

The existing efforts for improving TTFF and sensitivity for GNSS UE include developing assistance systems and implementing new algorithms for UE. The concept of AGPS goes back to the late 1990s when lots of patents were filed and then granted in early 2000s. Seeing the challenges of TTFF and sensitivity for standalone GPS devices, the general idea from the patents is to provide assistance information to GNSS UE, such as time, rough location, a list of visible satellites, the Doppler shift of each satellite, ephemerides and so on, in a way to speed up each stage in the process of a position fix (Figure 2). With a series of AGPS specifications embodied in the 3GPP and Open Mobile Alliance standards since 2001, AGPS-enabled products have become quite popular in the GNSS marketplace.

The assistance data definitely brings enhanced performance in TTFF and sensitivity for GNSS UE, but it is a challenge when network connectivity is not available. A technology often referred to as ephemeris extension (EE) was introduced by Global Locate and SiRF, which enables fast TTFF and high sensitivity for GNSS UE even without network connectivity. According to the descriptions of the long-term orbit used by Broadcom and InstantFix used by CSR, both are based on orbit determination theory and provide alternative ephemerides with a validity period extending to a few days, rather than two hours for the regular GPS ephemerides. As of today, a variety of EE products are available from many companies and research institutes, and EE has become a standard feature for GNSS products in the market place.

Limitations of Existing GNSS Assistance Technologies

In spite of the benefits to TTFF and improved sensitivity, the assisted GNSS (AGNSS) and EE technologies have obvious limitations, as detailed in TABLE 1. Building and maintaining the AGNSS infrastructure require significant efforts and continuous cost. Any AGNSS-capable UE, unlike standalone GNSS UE, are tied to good signals from the subscriber cellular phone networks to get assistance data on time, which substantially limit their areas of operation. The EE technologies consist of server-based and client-based modes. Client-based EE is good for standalone UE, but the accuracy is subject to the validity of the embedded Earth orientation parameters (EOPs), and the quantity and quality of the local data collection. Server-based EE is able to provide better accuracy, but it also needs support from the global infrastructure for data collection and is subject to network connectivity. Table 1 clearly indicates that AGNSS and EE can only be beneficial under certain prerequisite conditions, such as with network connectivity and data availability. In other words, even with the above-described technologies, fast TTFF and high sensitivity may still not be obtainable when those prerequisite conditions are not met, which is not uncommon in practical use.

TABLE 1. Comparison of assisted GNSS (AGNSS) and extended ephemeris in improving time-to-fist-fix (TTFF) and sensitivity.

Suggested New GNSS NAV Messages

The fundamental cause of the problem related to TTFF and sensitivity, in our view, lies in the congenital weakness of the design of the existing GNSS NAV messages. Taking GPS as an example, the contents of GPS subframes 1–3 are updated every two hours, although the ephemeris is valid for up to four hours. It is challenging for standalone GPS UE working in weak signal environments to catch up with such frequent ephemeris updates. Working properly during the past two hours does not mean that the UE can work properly in the next two hours if ephemerides are not downloaded in time. The NAV messages received two hours ago cannot be used for data aiding in the subsequent two hours to improve tracking sensitivity. For startups under normal signal conditions, the UE, if missing the start of subframe 1, have to wait 30 seconds to get to the next subframe 1 to download a complete copy of the ephemeris. Successful startups four hours ago also do not help much to reduce the TTFF in the subsequent startups, as time is needed again for ephemeris downloading.

For other GNSSs, some specifications of their NAV messages are listed in TABLE 3. According to these specification, the downloading of Galileo ephemerides takes at least 30 seconds, and if the start of the first ephemeris page is missed, it will take at least 50 seconds to get a complete copy. So, from this perspective, the Galileo TTFF for standalone devices is expected to be longer than that for GPS. As to BeiDou, given the high degree of similarity between BeiDou D1 and GPS CNAV messages, it is expected that for standalone BeiDou UE, TTFF is also similar to standalone GPS UE. For GLONASS, the downloading takes just about10 seconds, and it will take about 30 seconds to get a complete copy of the ephemeris if the start of the first ephemeris string is missed. Therefore, in this regard, the GLONASS TTFF for standalone devices is expected to be the fastest among the GNSSs. It is worth noting that the GLONASS ephemeris, unlike that of other GNSSs, comprises Cartesian coordinates, velocity components and solar/lunar gravitational accelerations at the reference time, with the content valid over about 0.5 hours. Upon receiving the ephemeris, the UE is to calculate the satellite orbit by numerically integrating the motion equations that include the second zonal geopotential coefficients through a fourth-order Runge-Kutta method. Since the designed NAV messages for GPS, GLONASS, BeiDou and Galileo are all valid for only short periods (see Table 3), they are all subject to the aforementioned limitations.

TABLE 3. Comparison of the NAV messages for GPS/GLO/BD(D1)/GAL(F/NAV)/New GNSS.

The common weaknesses in the NAV messages of GPS, GLONASS, BeiDou and Galileo described above can be overcome and fast TTFF and high sensitivity can be facilitated through the design of new NAV messages, when the following guidelines are followed:
- Update interval, as short as possible
- Repeat interval, as high as possible
- Length of ephemeris content, as short as possible
- Ephemeris life expectancy, as long as possible
Let’s take a closer look at the GPS CNAV messages in terms of the above four guidelines. In the GPS CNAV messages, the primary content includes:
- Satellite clock
- Satellite ephemeris
- Ionosphere information
- UTC parameters
- Almanac
Two types of atomic clocks, rubidium and cesium, with stabilities of 10^-12 to 10^-13 are used on the GPS satellites. Given such stabilities, it is possible to have the clock parameters updated at an interval much longer than two hours, without introducing significant errors in the pseudorange observations. For the Keplerian parameters in the GPS ephemerides, they are derived from the fitting of four-hour orbit curves. The orbit, represented by the Keplerian parameters plus perturbation corrections, gives the overall best fitting of the whole orbit segment. If fitting over a longer orbit curve, it would be harder for the fitted orbit to agree well with each small portion of the original orbit. A set of Keplerian orbital parameters can be a good approximation of a short orbit segment (say four hours), but can hardly be the case over a long period (say 24 hours). Frequent updating of the ephemeris content is therefore indispensable in order to guarantee the orbit accuracy using this approach. As a result, there is not much room for extending the ephemeris update interval or equivalently to lower the update frequency.

GPS CNAV messages include ionosphere information using the Klobuchar model, UTC parameters for relating GPS Time to UTC, and the almanac providing the rough orbits for all GPS satellites in service. According to the GPS Interface Specifications, all these messages will be updated at least once every six days, but they are typically updated on a daily basis.

Based on the above analysis, it can be concluded that, in GPS CNAV messages, the only part that changes frequently is the ephemeris (primarily the Keplerian parameters). To facilitate fast TTFF and high sensitivity, we should reduce the update frequency of the GPS CNAV message. For that, the key is to find a way to minimize the update frequency of the ephemerides.

Taking a close look at the satellite orbit may help us find a hint. For a satellite in space, given the initial conditions (position, r, velocity, , and so on) in Equation (2) at time t₀, the succeeding orbit, r(t), can be obtained by integrating the accelerations, , in Equation (3), as illustrated in Equation (4).

(2)

(3)

(4)

To ensure the accuracy of the derived orbit, r(t), the forces exerted on the satellites that result in the acceleration, (t), should be well modeled. The forces are both gravitational and non-gravitational.

Standard gravitational force models embedded in UE can be independently used for years without introducing significant accuracy loss. As to the force of solar radiation, it is related to the reflectivity and attitude of the solar panels of the satellite, which can also be well modeled by some slow-varying and satellite-dependent parameters. If a set of such solar radiation parameter(s) along with some satellite initial conditions (position and velocity) can be provided with a certain period (say one day), the satellite orbit can be derived in the UE through some embedded force models.

By now, we have found what we are looking for — namely, the solar radiation parameter(s) together with the satellite initial condition at a reference time, which can be the ideal content for our new ephemeris that can deliver a long orbit even if updated at a low frequency.

Consider that, at any epoch, the satellite position and velocity expressed in Cartesian form (r, ) can also be identically expressed in Keplerian form through the set of standard elements as is currently done with GPS.

The initial condition expressed in Keplerian form may give a better idea of what the orbit looks like and may have advantages for message encoding and sanity checks when it is adopted as the ephemeris content.

The above fundamental analysis leads us to propose the new GNSS NAV messages provided in TABLE 2, which comply with the previously mentioned guidelines and therefore should be able to inherently facilitate fast TTFF and provide UE with high sensitivity.

Note that the EOP data in the above table, used for relating coordinates in an Earth-centered Earth-fixed (ECEF) frame and those in an Earth-centered inertial (ECI) frame, are slowly varying parameters. The update interval for each part of the new NAV messages in Table 2 is one day, but for the almanac part, the update interval can be possibly extended to a few days similar to that currently used for GPS. In the ephemeris part, the proposed messages contain the six basic Keplerian elements and one solar radiation parameter for a selected reference time (t₀). Once the ephemeris is downloaded, the six Keplerian elements can be immediately transformed to Cartesian position, r(t₀), and velocity, (t₀), in the ECEF frame, and further converted to the initial condition in the ECI frame to derive the entire orbit through Equation (4).

TABLE 2. Proposed content of new GNSS navigation messages.

Compared to the current GPS ephemeris, Table 2 contains many fewer parameters, so it is possible to have the new GNSS ephemeris and clock data packed in only two subframes, assuming that the data rate, word structure and subframe length are the same as for GPS CNAV messages. For the remaining parts listed in Table 2, they can be packed into multiple pages of 2 subframes in a similar way as the pages of subframes 4 and 5 in GPS CNAV messages. Therefore, we have the frame structure of the proposed new GNSS NAV messages as depicted in FIGURE 3. Considering that the contents of the first two subframes play a primary role in TTFF, the pages of subframes 3 and 4 are not further discussed here.

FIGURE 3. Frame structure of the new GNSS NAV messages.

Advantages of the New NAV Messages

The content of the new NAV messages have been proposed in the last section, but the detailed format design is beyond the scope of this article. In TABLE 3, a comparison of the new NAV messages to the current GPS, GLONASS (GLO), BeiDou (BD) and Galileo (GAL) messages is presented. For the convenience of comparisons, the same data rate (50 bits per second [bps]) and the same length of subframe (6 seconds) as for the GPS CNAV messages have been used for the new GNSS NAV messages.

Compared to other GNSS NAV messages, the new NAV messages have a smaller size, but the contained ephemeris has a longer life and, as a whole, the new NAV messages just need to be updated once every 24 hours. To help understand the advantages of the new NAV messages, we have made several comparisons.

Standalone UE, New GNSS vs. GPS. For any new GNSS that deploys the new NAV messages, the UE just need to download the ephemeris from the satellites once in a whole day, whereas current GPS UE need to do it 12 times. In each downloading, it takes about 18 seconds for current GPS UE compared to about 12 seconds for the new GNSS UE. So there is no doubt that, from the TTFF perspective, the new NAV messages have incomparable advantages over the current GPS ones. Once a complete copy of the new NAV messages is downloaded, it can be used for data aiding in tracking loops for the rest of the whole day, even without network connections in weak signal environments. However, for current standalone GPS UE, they have to be in a strong signal environment to acquire fresh NAV messages every two hours. Otherwise there could be no position fix available in the next two hours due to the stale NAV bits and expired ephemerides. So, from a sensitivity point of view, a GNSS with the new NAV messages (referred to as new GNSS below) will also have incomparable advantages over GPS.

Assisted UE, New GNSS vs. GPS. There are three purposes for assistance information for mobile devices: 1) to expedite signal acquisition; 2) to save time in ephemeris downloading; and 3) to have navigation bits for data aiding in the tracking loops. For assisted GPS UE and assisted GNSS UE with the new NAV messages, there is not much difference in the first aspect, as the assistance data, such as a satellite vehicle list, Doppler frequency, code phase, location and time, are common to both. For the second and third purposes, the assistance data sent from the assisting network to the UE are only needed once per day using the new NAV messages because they are updated only once per day. For assisted GPS UE, the assistance data are needed once every 2 hours, which means that GPS UE need frequent network connectivity and more network bandwidth for data transportation. In addition, as the size of a GPS frame is larger than the frame of the proposed new NAV messages, the time delay in transporting the assistance data will be longer in a GPS assistance network.

New GNSS, Standalone vs. Assisted. When the new GNSS NAV messages are deployed, as the messages are only needed to be downloaded once a day, the assisted UE mostly show advantage in sensitivity and the required time for signal acquisition. Since signal acquisition is difficult only when the signal becomes weaker than a certain level, the performance of standalone and assisted new GNSS UE is expected to be comparable under normal signal conditions. Under weak signal conditions, as long as the NAV messages are received once a day, the performance in tracking sensitivities for both standalone and assisted UE is also expected to be comparable.

Feasibility Considerations

Since the proposed update interval for the new NAV messages is 24 hours, a period much longer than that currently used by all constellations, some immediate concerns may arise, such as:
- Is the orbit/clock derived from the ephemeris good enough for 24 hours?
- Is the calculation load for deriving satellite orbits affordable for a UE?
The advancement in orbit determination and EE technologies can help relieve the worry on the first concern. For the JPL predicted orbit and clock states, it is claimed that the user range error (URE) of around one meter for one day and URE of less than 10 meters for seven-day predictions can be obtained.

For a future GNSS that deploys the proposed new NAV messages, an orbital determination center (ODC) on the ground should be able to provide orbit predictions better than or at least comparable to those already obtained. Every 24 hours, as the intermediate results of the orbit predictions are obtained in the ODC, the new ephemeris data can be extracted and packed as one part of the new NAV messages. Once uploaded to the satellites and broadcast to GNSS UE on the ground, they can be used in deriving satellite orbits. The accuracies of the orbits/clock finally derived by GNSS UE will be subject to the accuracy of ephemeris, clock coefficients, EOPs and force models embedded in UE.

The EOP data, describing the irregularities of the Earth’s rotation, are needed for coordinate transformations between ECEF and ECI, so the up-to-date EOP data carried in the new NAV messages ensures no accuracy loss in such transformations. For the force models embedded in GNSS UE, accuracy is not a problem as long as they are the same as that used by the ODC.

As to the satellite clock, it is desired that, even if the clock coefficients are updated once per day, the accuracy of the predicted clock is still sufficient for navigation. For the current spaceborne clocks on GPS satellites, they are primarily rubidium atomic clocks with stability not better than about 10^-13. The advancement of atomic clock technologies is fast, especially in recent years, and the era of rubidium, cesium and hydrogen maser clocks is evolving to ytterbium and even optical atomic clocks. As of today, atomic clocks as stable as 10^-18have been operated in laboratory settings. A project called the Space Optical Clock aims to put a lattice optical clock with a stability of 10^-16on the International Space Station by 2020. So it is foreseeable that new GNSSs should be able to deploy atomic clocks with stability several orders better than those currently deployed. At the stability of 10^-16, the clock will only introduce millimeter-level errors in ranging in a 24-hour period. With such a stable satellite clock, there should be no accuracy concerns with clock data being updated once per day.

Once the broadcast ephemeris is received by a UE, numerical integration can be started to derive the satellite orbit. During the numerical integration, the calculation load is primarily dependent on the following factors: 1) the length of numerical integration; 2) the numerical integration step size; 3) the order of the integrator; and 4) the complexity of local force models. Regarding the run-time necessary for orbital numerical integration on an embedded system, some published results indicate that a three-day prediction (numerical integration) takes only around 0.6 seconds on a 600-MHz processor with floating point unit. So a 12-hour integration would take only about 0.1 seconds on the same platform. As of 2014, for the popular high-end smartphones on the market, the speed of embedded processors ranges from 1.2 to 2.5 GHz with dual- or quad-cores. Considering the drastically growing computation power of mobile processors and the potential of further algorithm optimizations in orbital integration, the calculation load of numerical integration for a 12-hour interval is not at all an issue on a mobile device today, much less in the future.

The GPS system designers four decades ago might not have realized that GPS would become so popular in the 21st century. Fast TTFF and high sensitivity have become standard requirements. The growing power of the application processors has also been beyond the imagination of people 40 years ago. So in their design, fast TTFF and high sensitivity might not have been given too much attention. The GPS modernization program is an attempt to meet the growing expectation on the system performance in the applications for today and the near future. In view of this, there is no reason not to give special considerations to inherently support fast TTFF and high-sensitivity applications when investigating and designing a new GNSS. Certainly, such efforts can be found both in recently launched GPS (Block IIF) and Galileo satellites, such as the pilot channels, but navigation under weak signal conditions for future standalone GPS and Galileo devices is still susceptible to the frequent change of NAV messages (see Table 3).

Conclusions

In this article, we have analyzed the benefits and limitations of the existing technologies (AGNSS and EE) widely adopted to improve TTFF and sensitivity performance, and pointed out the weakness in current GNSSs. Instead of seeking solutions in the user terminal, this article proposes to deploy new NAV messages on future GNSSs, with the contents updated once a day, to inherently facilitate fast TTFF and high sensitivity in the standalone GNSS UE. A future GNSS that uses such new NAV messages will have significant advantages for both standalone and assisted UE.

Acknowledgment

This article is based, in part, on the paper “New GNSS Navigation Messages for Inherent Fast TTFF and High Sensitivity” presented at the 2015 Pacific PNT Meeting of The Institute of Navigation, held in Honolulu, Hawaii, April 20–23, 2015.

WENTAO ZHANG is a Ph.D. student in the Department of Geomatics Engineering at the University of Calgary. His research interest lies in different location technologies, and he is focusing his research on potential new GNSS navigation messages in an attempt to inherently improve time-to-first-fix and receiver sensitivity.

YANG GAO is a professor in the Department of Geomatics Engineering at the University of Calgary. His research expertise includes both theoretical aspects and practical applications of satellite-based positioning and navigation systems. His research focuses on high-precision GNSS positioning and multi-sensor integrated navigation systems.

FURTHER READING
- Authors’ Conference Paper
“New GNSS Navigation Messages for Inherent Fast TTFF and High Sensitivity” by W. Zhang and Y. Gao in Proceedings of The Institute of Navigation 2015 Pacific PNT Meeting, Honolulu, Hawaii, April 20–23, 2015, pp. 131–141.
- Assisted GNSS
A-GPS: Assisted GPS, GNSS, and SBAS by F. van Diggelen, published by Artech House, Boston and London, 2009.

“First AGPS–Now BGPS: Instantaneous Precise Positioning Anywhere” by I. Petrovski, H. Hojo and T. Tsujii in GPS World, Vol. 19, No. 11, Nov. 2008, pp. 42–48.

“Assistance When There’s No Assistance — Long-Term Orbit Technology for Cell Phones, PDAs” by D. Lundgren and F. van Diggelen in GPS World, Vol. 16, No. 10, Oct. 2005, pp. 32–36.

“Assisted GPS: Using Cellular Telephone Networks for GPS Anywhere” by R. Bryant in GPS World, Vol. 16, No. 5, May 2005, pp. 40–45.

“Assisted GPS: A Low-Infrastructure Approach” by J. LaMance, J. DeSalas and J. Järvinen in GPS World, Vo. 13, No. 3, March 2002, pp. 46–51.
- Satellite Orbits
Satellite Orbits: Models, Methods and Applications by O. Montenbruck and E. Gill, published by Springer-Verlag, Berlin and Heidelberg, 2000.

“The Orbits of GPS Satellites” by R.B. Langley in GPS World, Vol. 2, No. 3, March 1991, pp. 50–53.
- Predicted Orbits and Clocks
Predicted GNSS Ephemeris, Rx Networks Inc., Vancouver, Canada.

Multiple GNSS Assistance Services for u-blox GNSS Receivers: User Guide, UBX-13004360 – R02, u-blox AG, Thalwil, Switzerland, March 2015.

“Predicted Orbit & Clock States,” Global Differential GPS System, Jet Propulsion Laboratory, Pasadena, Calif., Nov. 14, 2013.

“SiRF InstantFix II Technology” by W. Zhang, V. Venkatasubramanian, H. Liu, M. Phatak and S. Han in Proceedings of ION GNSS 2008, the 21st International Technical Meeting of the Satellite Division of The Institute of Navigation, Savannah, Ga., Sept. 16–19, 2008, pp. 1840–1847.

Long Term Orbits (LTO™), Technical Brief, Broadcom Corp., Irvine, Calif., 2007.
- Assisted GNSS Standards
Enabler Release Definition for Secure User Plane Location (SUPL), Candidate Version 3.0, OMA-ERELD-SUPL-V3_0-20140916-C, Open Mobile Alliance Ltd., San Diego, Calif., September 2014.

“GNSS Test Standards for Cellular Location: Multi-Constellations Working in a Dense Urban Future” by P. Anderson, E. Anyaegbu and R. Catmur in GPS World, Vol. 24, No. 5, May 2013, pp. 27–37.

Universal Mobile Telecommunications System (UMTS); LTE; Universal Terrestrial Radio Access (UTRA) and Evolved UTRA (E-UTRA) and Evolved Packet Core (EPC); User Equipment (UE) conformance specification for UE positioning; Part 1: Conformance test specification (3GPP TS 37.571-1 version 9.0.0 Release 9), European Telecommunications Standards Institute, Sophia Antipolis, France, 2012.
- GNSS Interface Control Documents
BeiDou Navigation Satellite System Signal in Space Interface Control Document, Open Service Signal, Version 2.0, China Satellite Navigation Office, Dec. 2013.

Navstar GPS Space Segment / Navigation User Interfaces, Interface Specification, IS-GPS-200 Revision H, Global Positioning Systems Directorate, Systems Engineering and Integration, Los Angles, Calif., Sept. 2013.

European GNSS (Galileo) Open Service Signal in Space Interface Control Document, Ref : OS SIS ICD, Issue 1.1, European Union, September 2010.

GLONASS Interface Control Document, Navigation Radiosignal in Bands L1, L2, Edition 5.1, Russian Institute of Space Device Engineering, Moscow, 2008.
October 8, 2015
Innovation: Getting There by Tuning In

Using HD Radio Signals for Navigation

By Ananta Vidyarthi, H. Howard Fan and Stewart DeVilbiss

INNOVATION INSIGHTS by Richard Langley

THE YEAR WAS 1906. On Christmas Eve of that year, Canadian inventor Reginald Fessenden carried out the first amplitude modulation (AM) radio broadcast of voice and music. He used a high-speed alternator capable of rotating at up to 20,000 revolutions per minute (rpm). Connected to an antenna circuit, it generated a continuous wave with a radio frequency equal to the product of the rotation speed and the number of magnetic rotor poles it had. With 360 poles, radio waves of up to about 100 kHz could be generated. However, Fessenden typically used a speed of 10,000 rpm to produce 60 kHz signals. By inserting a water-cooled microphone in the high-power antenna circuit, he amplitude-modulated the transmitted signal. On that Christmas Eve, he played phonograph records, spoke and played the violin with radio operators being amazed at what they heard.

Fessenden had earlier worked with spark-gap transmitters, as these were standard at the time for the transmission of Morse code, or telegraphy, the wireless communication method already in use. But they couldn’t generate a continuous wave and couldn’t produce satisfactory AM signals. But as telegraphy was the chief means of communication, they remained in use for many years along with high-powered alternators and the Poulsen arc transmitter, which could also generate continuous waves.

Although other experimental AM broadcasts were carried out using alternators or arc transmitters, voice transmissions — and in particular sound broadcasting — didn’t take off until the invention of amplifying vacuum tubes. Just before World War I, it was found that they could be used in an oscillator circuit to produce continuous waves, which could be easily modulated to make an AM transmitter. Such transmitters could be used for point-to-point communications but also for broadcasting, and a number of experimental broadcasting stations were established in Europe and North America during and just after the war. Tubes were also instrumental for improvements in receiver technology. “Where there was one licensed station in America in 1920, there were nearly 600 stations just five years later, and the number of radio receivers went from thousands of crystal sets to millions of vacuum-tube circuits.” — from The Science of Radio by Paul J. Nahin, one of my favorite writers on electronics and mathematics.

AM radio broadcasting used frequencies in the long-wave, medium-wave and short-wave frequency bands, and still does. But AM signals often have low audio quality due to bandwidth limitations imposed by regulators and interference from other stations, atmospheric disturbances and electrical noise. So, over the past decade or so, many broadcasters have abandoned long-wave and medium-wave frequencies and moved to the frequency modulation or FM broadcast band with its superior signal capability.

However, this migration pattern might be slowed or stopped if digital broadcasting were to be fully embraced on the AM broadcast bands. A digital technique developed by the iBiquity Digital Corporation is gradually being adopted by broadcasters in the United States and elsewhere. The technique provides FM-quality sound in the medium-wave band by supplementing existing AM signals or replacing them altogether. It can also supply data about the transmitting station and its broadcast. Some 240 AM radio stations in the U.S. already use the technology. (It can also be used in the FM band to provide CD-like quality.)

But these digital signals in the AM broadcast band might serve an additional purpose beyond improving the listening experience. In this month’s column, our authors tell us about some extensive simulation work they have carried out to demonstrate the feasibility of using digital radio signals for navigation. In the future, you may be able to turn on your radio and tune in to get to where you’re going.

“Innovation” is a regular feature that discusses advances in GPS technology and its applications as well as the fundamentals of GPS positioning. The column is coordinated by Richard Langley of the Department of Geodesy and Geomatics Engineering, University of New Brunswick. He welcomes comments and topic ideas. Email him at lang @ unb.ca.

It is well known that the GPS signals are weak and are therefore subject to interference and blockage due to obstruction. Signals of opportunity (SOO), on the other hand, which are designed for other purposes such as communication, may also be used for navigation and have relatively greater signal power than GPS. They are plentiful and relatively more resistant to blockage and jamming compared to GPS. Many authors have presented methods and algorithms utilizing SOO such as AM and FM broadcast signals, TV broadcast signals and 3G/4G wireless communication signals (see Further Reading for examples). These signals are robust and have very good received power levels compared with GPS, and are capable of penetrating through buildings. In addition, these signals are readily available and there is no need for any additional installation of transmitting devices or infrastructure.

In this article, we present the results of a study using AM HD Radio, digital radio in the 540–1700 kHz band of the frequency spectrum, with known transmitter locations, to locate and track receiver locations that are otherwise unknown. HD Radio, originally meaning hybrid-digital radio, is a trademarked term for iBiquity Digital Corporation’s digital radio technology. Unlike analog AM radio signals, digital radio signals are well structured and more immune to co-channel interference, and hence could be better adapted for navigation. In addition, with the proliferation of software-defined radios (SDRs), digital AM radio may eventually replace analog AM radio.

The challenges of navigation using digital radio signals include narrow signal bandwidths, long symbol durations and lack of synchronization among transmitters. Therefore, digital radio signals are not an ideal choice for accurate position estimation, similar to many other SOO that aren’t designed for navigation. Nevertheless, in this work, we have designed algorithms to overcome such difficulties to obtain a good level of location accuracy, making it a feasible alternative for SOO navigation.

Signal Format of Digital AM Radio

Digital AM signals have a well-defined structure called in-band-on-channel (IBOC) that can be exploited for localization purpose. It employs sophisticated digital radio waveforms, which can deliver compact-disc-like sound quality, free of interference and noise, to radio listeners. It uses the existing AM and FM analog broadcasting bands and channel schemes to transmit digital signals. The IBOC digital radio transmitter system encodes analog audio into binary form for transmission.

The design provided by IBOC AM radio has two service modes with two new waveform types: hybrid (denoted by MA1) and all-digital (denoted by MA3). The hybrid waveform retains the analog AM signal, while the all-digital waveform completely replaces the analog AM signal. In the hybrid service mode, the bandwidth of the analog audio signal waveform can be 5 kHz or 8 kHz. The digital signal is transmitted on both sides of the analog host signal in the primary and secondary sidebands. It is also transmitted on the tertiary sidebands, which are 20 dB beneath the analog signal as shown in FIGURE 1.

FIGURE 1. Logical channels and sidebands on the frequency spectrum; hybrid mode with 5-kHz analog signal bandwidth. (After iBiquity.)

For the 8-kHz configuration, the secondary sidebands are also beneath the analog host signal. The greatest system enhancements are realized with the all-digital system, as shown in FIGURE 2. In this system, the analog signal is replaced with the all-digital primary sidebands whose power is increased relative to the hybrid system levels. Secondary and tertiary sideband powers are also increased to the level of the hybrid waveform. Reference subcarriers are also provided to convey system control information. The end result is a higher power digital signal with an overall bandwidth reduction.

FIGURE 2. Logical channels and sidebands on the frequency spectrum; all-digital mode. (After iBiquity.)

Digital radio offers distinct advantages over analog, including mitigation of transmission artifacts and improved audio quality. These changes provide a more robust digital signal that is less susceptible to adjacent channel interference, thereby reducing the noise in the system. An overview of the AM digital system for both the service modes, MA1 and MA3, is given in the following paragraphs. However, in the simulation study we carried out, we used the all-digital AM (MA3) mode. The all-digital AM system has a smaller bandwidth than the hybrid signal. If reasonable localization results can be obtained with it, then we can predict that better localization results may be obtained with the hybrid signal.

IBOC uses an orthogonal frequency-division multiplexing (OFDM) waveform for signal modulation. Each OFDM subcarrier channel has a spacing of 181.7 Hz. The hybrid MA1 service mode comprises 163 subchannels indexed from -81 to 81 over a total bandwidth of 29.4 kHz as shown in Figure 1. The all-digital MA3 service mode has only 105 subchannels indexed from -52 to 52 over a total bandwidth of 18.9 kHz as shown in Figure 2. Therefore, when compared to the all-digital mode, hybrid mode contains more training symbols per OFDM symbol duration. The training symbols are important since these symbols are known and will be used to perform correlation to estimate the signal time of arrival. We predict that since the hybrid mode contains more training symbols than the all-digital mode, detection accuracy will be higher for the hybrid mode. Hence, choosing the all-digital MA3 service mode for the localization will be more challenging, and this is another reason for our decision to use MA3. Demonstrating the capability of the all-digital MA3 service mode for localization would imply that the hybrid mode could be used for the same, with at least the same or better performance.

Interleaving in time and frequency is used to mitigate the effects of burst errors. The interleaver output is according to a structured matrix (not shown here). Each interleaver matrix consists of information associated with a specific portion of the transmitted spectrum, and consists of eight interleaver blocks, with each block of size of 32 × 25. Hence, each block has 800 symbols to be filled, out of which 50 are known training symbols. Since this work entirely relies on training symbols, understanding interleaving is important so we know exactly where the training symbols are in a signal data stream. From the interleaving matrix, the positions of all training symbols are given, which have a periodic appearance of every 16 rows.

The OFDM subcarrier mapping transforms interleaver output into scaled 16 quadrature amplitude modulation (QAM) and 64 QAM and binary phase-shift keying (BPSK) symbols and then maps them to specific OFDM subcarriers. The inputs to OFDM subcarrier mapping are according to the interleaver matrices, which map respective symbols to the primary, secondary, tertiary, Primary IBOC Data Service (PIDS) and reference subcarriers. One row of each active interleaver matrix and one bit of the system control vector are mapped into each OFDM symbol (every T_s seconds) to produce one output vector X, where T_s = 5.805 × 10^-3seconds.

OFDM signal generation takes the complex frequency domain OFDM symbol X as generated above and outputs a time-domain representation of the digital signal. Let X_n be the vector X for the nth OFDM symbol, and X_n[k] be the kth element of X_n, which is the complex scaled constellation points for the subcarrier mapping for the nth symbol, where k = 0, 1,…, L-1 is the subcarrier index in the frequency-domain input to the signal generation for transmission. The input vector X is transformed into a shaped time-domain baseband pulse y_n(t) defining the nth OFDM symbol as

where n = 0, 1, …, ∞, . Note that n indexes consecutive OFDM symbols, L = 105 is the maximum number of OFDM subcarriers, T_s and ∆f are the OFDM symbol period and OFDM subcarrier spacing, respectively, and W(t) is the time-domain pulse shaping function.

Time of Arrival Acquisition

Since the training symbols are known, a local copy can be generated at a receiver to correlate with the received digital AM signal to measure signal time of arrival (TOA). Measuring TOA accurately from a correlation peak is crucial, since any error in TOA measurement directly affects localization accuracy. The relatively narrow bandwidths and hence long symbol durations of the digital AM radio signals pose a challenge as they give rise to potentially large timing errors, thereby greater localization errors. To improve the location accuracy, strong digital AM signal levels are used to our advantage so methods such as curve fitting and time averaging can be performed. Moreover, unlike the structures of the civil GPS signals, which are all known, only the training symbols and their positions in the digital AM signals are known. Other data in the digital AM signals are random and cannot be used for correlation. Therefore, using long correlation vectors will help in detecting peaks as there will be more training symbols.

Sampling. Correlation is performed, of course, after sampling. So we first discuss how to choose an appropriate sampling frequency. After correlation, if we detect the peak and record it as TOA only at the corresponding sampling instant, a maximum distance error of c/2f_s can occur between two adjacent samples, where c is the speed of light and f_s is the sampling frequency. At the Nyquist sampling frequency, say 40 kHz, this error could be as large as 3,750 meters. Sampling at a frequency much higher than the Nyquist can help to improve accuracy, but this improvement diminishes as the sampling frequency increases beyond a certain value, because the narrow signal bandwidth makes the peak of its correlation function rounded, so detection of the actual peak becomes less accurate. In our simulations, we found that this point of diminishing returns is at about f_s = 10 MHz, at which the error between two adjacent samples is 15 meters, much better than that at the Nyquist sampling rate. This high sampling rate is easily doable with today’s digital technologies. However, this 15-meter error is the ranging error between one transmitter and one receiver. Five or more transmitters have to be considered for the location algorithm presented in a later section. Then, the ranging error of 15 meters may magnify to the order of a few kilometers as location errors. Clearly, there is a need to detect TOA of a correlation peak between two adjacent samples; that is, we need interpolation to achieve a smaller TOA error.

Interpolation. To calculate the TOA between two adjacent samples, we interpolate by curve fitting the correlation data and estimate the TOA by solving polynomial functions. It was observed that the correlation peak is asymmetric, so the correlation curve is shaped differently to the left and right of the peak value. This is illustrated in FIGURE 3. Therefore, we need to fit two different curves on each side of the correlation peak. By a trial-and-error process, we determined that a quadratic polynomial is sufficient to fit the correlation values close to the peak. Therefore two simple quadratic functions are fitted for the correlation data points to the left and right of the peak.

FIGURE 3. Asymmetric correlation peak denoting different slopes on either side.

FIGURE 4 shows curve fitting for the correlation of a received signal and a local signal sampled at 10 MHz. The maximum time error due to sampling is T_samp/2, which equals 5 ×10^-8 seconds. This translates into a distance error of 15 meters and localization error of a few kilometers as mentioned before. From Figure 4, it is seen that the intersection point, which is taken as the measured TOA, is much closer to the actual TOA resulting in a much smaller distance error.

FIGURE 4. Enlarged views of Figure 3 near the peak.

Based on the HD Radio documentation, a normal signal-to-noise ratio (SNR) is calculated to be 52 dB. However, in case of adverse channel conditions, lower SNR levels of 30 dB and 10 dB have also been considered. Our simulations show that, with additive white Gaussian noise, the TOA estimation errors are affected by SNR very little above 10 dB, and are improved by an order of magnitude compared with no curve fitting. To make sure the TOA estimation error for the 10 dB SNR case can be used for the purpose of localization, we carried out a Monte Carlo simulation. Twenty-one different random signals were simulated, and the TOA measurement errors after curve fitting were recorded at different delays. The ensemble average of these TOA estimation errors was within 2 ×10^-9 seconds. These results confirm that a 10 dB SNR signal can be very well used for localization. Thus, we used an SNR of 10 dB for all the simulations discussed later in this article.

Differential Time-Difference of Arrival

Once all the TOAs from different transmitters are obtained, they are sent to a processing station, which could be one of the receivers. Due to lack of synchronization in digital AM radio transmitters as well as unknown clock offsets in digital AM radio receivers, the obtained TOAs are not aligned, so they cannot be directly used for location determination. A technique called differential time-difference of arrival (dTDOA), which is similar to GPS double differencing and was published by the authors elsewhere (see Further Reading), is employed here to overcome this problem.

Consider the case where there are two transmitters, A and B, and two receivers, C and D, as shown in FIGURE 5.

FIGURE 5. Principle of differential time-difference of arrival (dTDOA).

When transmitter A is transmitting, its signal is received at different time instances by receivers C and D due to different propagation delays. The internal clock of each receiver records the correlation peak with respect to its local time at the corresponding receivers. TOAs of the signal from transmitter A at both receivers C and D are recorded as and , which also contain the unknown transmitter A clock time offset. Differencing these two TOAs , the unknown transmitter A clock time offset is cancelled. But this TDOA is unsynchronized, so it cannot be used for location determination. Then we find the similar unsynchronized TDOA from transmitter B, . To eliminate the unknown receiver clock offsets we difference the two TDOAs, resulting in a dTDOA:

Thus, by using a minimum of two transmitters and two receivers, a dTDOA cancels receiver clock offsets and transmitter clock offsets, thus avoiding the need of precise clock synchronization. The number of independent dTDOA equations required to solve for the locations of n receivers is given by (m-1)(n-1) where m is the number of transmitters, and n is the number of receivers. For two receivers, there are four unknowns in a two-dimensional positioning plane, so we need a minimum of five transmitters to obtain four independent equations to solve for four unknown location parameters. If one of the receivers is permanently stationary with a known location such as in differential GPS, then we only need three transmitters to solve for two unknown horizontal location parameters, or four transmitters for three unknown location parameters in 3-D .

The above dTDOA equations, when expressed in terms of receiver locations, are non-linear. The non-linear over-determined or exact system of equations can be solved using iterative procedures, such as non-linear least squares or the Levenberg-Marquardt (LM) technique. In the simulations we ran, we found that the LM method was more robust than the Gauss-Newton method because it was capable of converging to the solution in the global minimum even if the initial guess was relatively far away. But a reasonable initial estimate of the solution can help with faster convergence. If the initial estimate is too far away, the solution often converges to a local minimum instead of the global minimum.

Therefore, a good initial estimate of the solution is crucial. An approximate initial estimate can be calculated in several ways. For example we can solve linearized equations based on the non-linear dTDOA equations. Or we can use a simple table lookup if we have some a priori knowledge of roughly where the receivers are located.

Once the initial locations are found, the next step is to track the locations of the receivers when they are moving. A Kalman filter should be used for tracking. A Kalman filter can also incorporate the non-linear dTDOA equations with TOA measurement as input for close coupling between localization and tracking. Or, for simplicity, short of using a Kalman filter, the previous locations can be fed into the LM method to find the next locations. The LM method for this kind of tracking has faster convergence than for repeated initialization, so the next locations can be calculated quickly.

Time Averaging. Due to error in tracking, the computed locations are not exact but are usually around the actual location. Time averaging is then used to further improve tracking performance. Time averaging can also be used to smooth the TOA measurements or the locations computed from dTDOA equations as input to a Kalman filter.

Repeated use of the LM method, as shown in FIGURE 6, for estimating a stationary receiver’s coordinates always forms an error ellipsoid because of the noise and computation error. The estimated points are depicted by black points in Figure 6. The small yellow circle in the middle corresponds to the actual location. By simulation, it was found that averaging all the possible estimated locations produced a location much closer to the actual location, as depicted by the red cross in Figure 6. Obviously the more points to average — that is, the larger the time-averaging window — the more accurate the averaged location will be. In general, such time averaging can improve location and tracking performance by an order of magnitude.

FIGURE 6. Image depicting time averaging of a stationary receiver’s location.

For a moving receiver, there is a trade off in choosing the time-averaging window. The larger the time-averaging window, the better the averaged location accuracy, but the larger the resulting time delay in the averaged location. This time delay is also affected by how frequently we update the tracked locations. Receiver velocity and the Doppler effect also affect the choice of the time-averaging window.

Simulation Results

We performed a comprehensive computer simulation study. The primary aim of this simulation study was to prove that the accuracy of digital AM signals for navigation can be improved using the methods introduced in the previous sections, despite the narrow bandwidth of the signals, thereby making digital AM a viable choice for navigation. A number of factors will affect the performance of navigation using digital AM signals including the sampling frequency, SNR, time-averaging window and location update frequency. In this simulation study, these factors have been taken into consideration.

To simulate a realistic environment, we chose the city of Chicago, where there are many digital AM transmitters providing good coverage to the city. We chose the six best transmitters in Chicago based on the power of the signal and location. The working range of the receivers is large enough to perform a detailed study of all the navigation techniques. The locations of the radio station transmitters are shown in FIGURE 7. All figure axes are in kilometers. Colored dots are transmitter locations; colored circles are their ranges. Green tracks are the chosen routes for a fast-moving receiver. Short brown tracks are those of the other receiver, somewhere in the same zone and traveling slowly.

FIGURE 7. Transmitter locations and two different routes considered for simulation with two receivers. (Map courtesy of Google.)

We simulated two receivers moving along the chosen green and brown routes, but we will only show the navigation results of the faster moving receiver along the green routes. A minimum of five transmitters is needed. The entire simulation was done in Matlab. The time-domain digital AM received signals were modeled according to the specifications described previously. Delays corresponding to transmitter and receiver locations were calculated and simulated into the signals received at the two receivers. An SNR of 10 dB was used for all received signals. Along Route 1 (upper left corner of Figure 7), five transmitter signals can be received, whereas along Route 2 (center right in Figure 7), six transmitter signals are received. Simulation conditions and results for these two routes are given in TABLES 1 and 2.

TABLE 1. Simulation parameters and results of Route 1 (five-transmitter zone).

TABLE 2. Simulation parameters and results of Route 2 (six-transmitter zone).

In addition, the tracking results for the fast-moving receiver are laid on top of photo maps of the routes, and are shown in FIGURES 8 and 9. The worst-case situation happens when, for example, transition of zones or handover of transmitters happen, for which no specific additional measures were taken in the simulations as shown in Figure 8.

FIGURE 8. Worst-case result for five-transmitter tracking. (Photo map courtesy of Google.)

However, the typical tracking result in Figure 9 happens most of the time. Clearly, the more transmitters that can be used, the better the accuracy results. Use of more than two receivers or use of a stationary receiver with a known location can reduce this demand on the number of transmitters.

FIGURE 9. Typical six-transmitter tracking result. (Photo map courtesy of Google.)

The fast sampling frequency, the curve fitting and the time-averaging window are the most important factors affecting the accuracy of this work, and are easily adjustable. In our simulations we used a time-averaging window of 1 second. We expect that the accuracy would further improve as the time-averaging window is increased, but this would result in increased latency. The velocity of the receiver is one limiting factor in choosing the time-averaging window. For a receiver traveling at a maximum speed of 145 kilometers per hour, a time-averaging window of 1 second corresponds to 20.14 meters of tracking lag. Any greater tracking lag may become intolerable. In general, our simulations show that curve fitting alone and time averaging alone each improved localization accuracy by an order of magnitude. When curve fitting and time averaging were combined, the localization accuracy was improved by two orders of magnitude. If a Kalman filter were used for tracking, we would expect further accuracy improvement.

Other challenges that deserve further study to make this concept a mature technology include multipath propagation and its mitigation, incorporation of estimating digital AM carrier phase, and incorporation of a Kalman filter for tracking. Further increased location accuracy is expected by incorporation of these techniques.

Acknowledgment

This article is based, in part, on the paper “A Navigation Solution Using HD Radio Signals” presented at the 2015 International Technical Meeting of The Institute of Navigation, Dana Point, Calif., Jan. 26–28, 2015.

ANANTA VIDYARTHI graduated from Anna University, India, in 2009 with a B. Tech. degree in electronics and communication engineering. She came to the University of Cincinnati in the fall of 2009 and earned her M.S. degree in 2012 in electrical engineering. Currently, she is working with Cummins Inc. in Columbus, Ind.

H. HOWARD FAN graduated from the University of Illinois in Urbana-Champaign with a Ph.D. in electrical engineering in 1985. He has been on the faculty of the University of Cincinnati since then, where he is a professor of electrical engineering and computing systems. His research interests are in digital signal processing, system identification, signal processing for communications, interference mitigation, direction finding, and navigation and location.

STEWART DEVILBISS graduated from Ohio State University with a Ph.D. in electrical engineering in 1994. Since 2007 he has served as the technical advisor for the Navigation and Communication Branch at the Sensors Directorate of the Air Force Research Laboratory, headquartered at Wright-Patterson Air Force Base, Ohio. His primary research interest is in technologies to improve navigation robustness and accuracy.

FURTHER READING

• Authors’ Conference Paper

“Navigation Solution Using HD Radio Signals” by A. Vidyarthi and H.H. Fan in Proceedings of ION ITM 2015, the 2015 International Technical Meeting of The Institute of Navigation, Dana Point, Calif., Jan. 26–28, 2015, pp. 285–292.

• HD Radio

The IBOC Handbook: Understanding HD Radio Technology by D.P. Maxson. Published by Focal Press, Burlington, Mass., 2013.

HD Radio Air Interface Design Description – Layer 1 AM, Doc. No. SY_IDD_1012s, Revision E. Published by iBiquity Digital Corporation, Columbia, Md., March 22, 2005.

HD Radio AM Transmission System Specifications, Doc. No SY_SSS_1082s, Revision F. Published by iBiquity Digital Corporation, Columbia, Md., Aug. 24, 2011.

• Differential Time-Difference of Arrival

“Asynchronous Differential TDOA for Non-GPS Navigation Using Signals of Opportunity” by C. Yan and H.H. Fan in Proceedings of ICASSP 2008, the IEEE 2008 International Conference on Acoustics, Speech and Signal Processing, Las Vegas, Nev., March 31–April 4, 2008, pp. 5312–5315, doi: 10.1109/ICASSP.2008.4518859.

• Positioning Using Analog AM Signals of Opportunity

“Opportunistic Navigation: Finding Your Way with AM Signals of Opportunity” by J. McEllroy, J.F. Raquet and M.A. Temple in GPS World, Vol. 18, No. 7, July 2007, pp. 44–49.

“Phase Measurements Using Direct Conversion AM Radio Navigation” by A. Dinh, R. Mason, R. Palmer and K. Runtz in Proceedings of WESCANEX 97, the IEEE 1997 Conference on Communications, Power and Computing, 22–23 May 1997, pp. 280–285, doi: 10.1109/WESCAN.1997.627154.

• Positioning Using TV Signals of Opportunity

“Cooperative position location with signals of opportunity” by C. Yang, T. Nguyen, D. Venable, M. White and R. Siegel in Proceedings of NAECON 2009, the IEEE 2009 National Aerospace and Electronics Conference, Dayton, Ohio, July 21–23, 2009, pp. 18–25, doi: 10.1109/NAECON.2009.5426658.

“Prime Time Positioning: Using Broadcast TV Signals to Fill GPS Acquisition Gaps” by M. Martone and J. Metzler in GPS World, Vol. 16, No. 9, Sept. 2005, pp. 52–60.

“A New Positioning System Using Television Synchronization Signals” by M. Rabinowitz and J. J. Spilker, Jr. in IEEE Transactions on Broadcasting, Vol. 51, No. 1, March 2005, pp. 51–61, doi: 10.1109/TBC.2004.837876.

• Positioning Using 3G Cellar Signals of Opportunity

“A Signals of Opportunity Based Cooperative Navigation Network” by M.A. Enright and C.N. Kurby in Proceedings of NAECON 2009, the IEEE 2009 National Aerospace and Electronics Conference, Dayton, Ohio, July 21–23, 2009, pp. 213–218, doi: 10.1109/NAECON.2009.5426626.

September 4, 2015
Innovation: Carrier-Phase RF Ranging
Precise, Accurate and Multipath-Resistant Distance and Speed Measurements

In this month’s column, we take a look at a short-distance two-way ranging system using a 5.8-GHz carrier to supply not only precise and accurate distance measurements but also complementary measurements of speed.

By Bradley D. Farnsworth, E.J. Kreinar and David W.A. Taylor

INNOVATION INSIGHTS by Richard Langley

THERE IS A LONG HISTORY of determining distances using radio waves with a large number of techniques being developed over the years for positioning, navigation, situational awareness and other purposes.

Of course, we are all familiar with the latest and greatest distance-measuring technology: GPS and its GNSS brethren. The distance to each observable satellite is determined by measuring the time it takes for the radio signal to travel from the transmitting antenna of the satellite to the receiver’s antenna and then, using the speed of light in a vacuum (which is also the speed of radio waves), converting the signal travel time into a distance. Distances can be determined from either the signal’s modulation (the pseudorandom noise codes) or the carrier phase. Both approaches require modeling and estimation to account for various errors or biases.

GPS is an example of one-way ranging. Other systems, notably radar, are two-way systems relying on reflections (passive ranging) or transponders (active ranging) to return a signal to the point of transmission.

Radar was developed during Word War II although radio-ranging technologies and techniques existed before the war started (to measure the height of the ionosphere, for example) and allowed radar’s rapid development and use during the war.

Besides ranging to terrestrial objects, radar has been used extraterrestrially. Independent experiments in the United States and Hungary in 1946 resulted in the first detections of radar reflections from the moon. Radar has been used subsequently to range to other solar system bodies as well.

Also developed during World War II were several radio-based systems for aircraft navigation. An outgrowth of these were the Loran-C and Omega hyperbolic positioning systems. They operated with networks of coordinated transmitters using frequencies at the low end of the radio spectrum. With widespread GPS availability, Omega was shut down in September 1997 followed by the North American Loran-C chains in 2010. Other chains are threatened with closure. However, there is an ongoing debate about bringing Loran-C back to North America in the form of Enhanced Loran (eLoran) as an autonomous backup for GPS. The United Kingdom has already implemented an eLoran network. Among other improvements, eLoran uses range measurements from multiple transmitters to determine position fixes.

The first terrestrial electromagnetic-distance-measurement or EDM device using microwave signals was the Tellurometer. Developed for surveying in 1954, it initially used a 3-GHz carrier modulated by frequencies near 10 MHz and was capable of accurately measuring distances up to at least 50 kilometers (line of sight).

Ranging can be performed with virtually any radio signal, and viable positioning techniques have been developed to use so-called signals of opportunity such as AM, FM and TV signals. And purpose-designed systems have been developed using ultra-wideband and other short-distance radio technologies.

An issue with any radio-based ranging system is multipath where, in addition to a direct line-of-sight signal, interfering signals are received after being reflected off nearby structures. Multipath degrades the system’s achievable precision and accuracy. Better performance can be obtained by using measurements on the signal’s carrier rather than on its modulation, and the higher the carrier frequency, generally the smaller will be the multipath error in the distance measurement. In this month’s column, we take a look at a short-distance two-way ranging system using a 5.8-GHz carrier to supply not only precise and accurate distance measurements but also complementary measurements of speed.

“Innovation” is a regular feature that discusses advances in GPS technology and its applications as well as the fundamentals of GPS positioning. The column is coordinated by Richard Langley of the Department of Geodesy and Geomatics Engineering, University of New Brunswick. He welcomes comments and topic ideas. Email him at lang @ unb.ca.

Reliable measurements of distance and speed are a critical aid to integrated positioning and navigation systems. Several different sensor technologies can provide such measurements including a variety of radio frequency (RF) ranging techniques. Previous work by the authors based on round-trip time-of-flight RF ranging using the baseband code phase of direct sequence spread spectrum (DSSS)-modulated signals achieves centimeter-level distance estimation performance. This DSSS ranging implementation approaches the Cramér-Rao lower bound in a benign RF channel (the theoretical lower bound on the variance or corresponding standard deviation of any unbiased estimator of a deterministic parameter — the best we can ever expect to achieve). A distance measuring radio (DMR) produced by our company is shown in FIGURE 1.

FIGURE 1. Distance measuring radio. The dimensions of the radio are 160 × 69 × 13.3 millimeters with a mass of 180 grams. (Image: Bradley D. Farnsworth, E.J. Kreinar and David W.A. Taylor)

Our baseband ranging capability has been demonstrated on a direct conversion radio operating in the unlicensed 5.8-GHz industrial, scientific and medical (ISM) band with approximately 20 MHz RF signal bandwidth, and has been previously implemented in the 2.4 GHz and 915 MHz ISM bands. The system uses an 11-megachip-per-second chipping rate and a symbol rate of about 687 kHz per channel (16 chips per symbol). This method has been implemented with both binary phase-shift keying (BPSK) and quadrature phase-shift keying (QPSK) modulation. The same signal that is used for ranging is also used for data communications. A decentralized asynchronous carrier-sense multiple access with collision avoidance (CSMA/CA) networking layer supports networked operation.

The DMR performs real-time digital signal processing on a Kintex-7 field-programmable gate array (FPGA) baseband processor to compute ranging observables on the received baseband packet structure. A round-trip measurement duration under three milliseconds allows for approximately 350 measurements per second for a single pair of DMRs. Measurements do not require a priori synchronization of the remote radios nor high-performance reference oscillators, as remote oscillator behavior is observed in the ranging operation. The measurement is highly compatible with frequency agility techniques. A system of ranging radios provides networked operation for measurements between multiple platforms.

The primary limitation of DSSS code-phase ranging is degraded accuracy and reliability in challenging multipath environments. This is somewhat mitigated by a “quality factor” observation on the characteristics of the received DSSS baseband signal, which can be used to de-weight or exclude corrupted baseband ranging measurements from an integrated navigation or positioning filter. However, it is desirable to provide a ranging measurement that has improved robustness against multipath corruption in all environments.

Multipath Effects on Carrier Phase

The carrier phase of the DSSS ranging signal in space can be used as an additional ranging measurement. Each 5.8-GHz RF carrier-wave cycle has a length of about 52 millimeters. Phase measurements on the received carrier phase in a round-trip ranging exchange are proportional to the propagation distance of the RF signal over the air. These measurements of the carrier phase can be made precisely, and they are inherently more tolerant to multipath than baseband phase measurements.

Consider a simplified two-ray RF channel model, where there is a direct RF line-of-sight (LOS) path and a multipath (MP) reflection. The two signals will have a phase difference between MP and LOS of θ_m and an amplitude ratio of MP to LOS of α, which lumps together the attenuation due to the additional path length of the MP signal, the reflection coefficient of the reflecting surface, the difference in antenna gain at the incidence angles and other factors. The received signal will be a superposition of the two signals with a phase difference between this composite and the original LOS of θ_c. This phase difference is the multipath-induced error on the received carrier phase. The worst-case error will occur when there is a small difference in total path length. In this case, the LOS and MP are inseparable by the DSSS receiver, and the error is bounded by Equation 1. The error is reduced for MP with much longer path length due to both a reduced amplitude coefficient α of the MP signal, as well as separation by the DSSS receiver due to the baseband spreading codes.

(1)
The multipath carrier-phase error bounds are ±90 degrees for α ≤ 1, which is satisfied when there is an RF LOS signal present. In practice, α is typically much less than 1. For a more practical case of α = 0.1, the maximum carrier-phase error is less than ±6 degrees. At 5.8 GHz RF, ±6 degrees corresponds to about 0.1 millimeters. A plot of this response for various values of α is shown in FIGURE 2.

FIGURE 2. Carrier-phase error due to multipath interference for various values of relative multipath amplitude. (Image: Bradley D. Farnsworth, E.J. Kreinar and David W.A. Taylor)

As a physical interpretation, the carrier-phase error goes to zero when there is zero phase difference between LOS and MP signals as the signals happen to be in phase already, and at ±180 degrees where the MP signal is in phase with the LOS signal but with inverted polarity, and serves to reduce the magnitude of the received signal, which is the case in a deep multipath fade. MP signals arrive at a dynamic receiver with an unpredictable distribution of relative phase to the LOS signal due to platform motion. This resistance to multipath is highly desirable for use in an RF ranging system. The following sections will present a ranging method that leverages this useful behavior.

Carrier-Phase Ranging Measurement

Each DMR round-trip ranging exchange consists of transmission and reception of a packet between two cooperating DMR devices, typically termed “originator” and “transponder” with roles determined by software configuration. For baseband ranging, the code phase is computed on the oversampled shape of the DSSS correlator output and exchanged in the round-trip measurement. The number of elapsed baseband clock periods between receive and transmit on the transponder and between transmit and receive on the originator are also observed to compute a round-trip coarse time. These measurements, plus a calibration offset due to cabling and other systematic delays, are used to perform baseband ranging.

Two additional observations are required for carrier-phase ranging: the carrier phase of the received DSSS signal in space and the carrier-frequency offset of the received carrier with respect to the local oscillator on the receiving radio. These observables are exchanged in a round-trip transaction, generating carrier-phase range (CPR), the magnitude of carrier-phase velocity (CPV) and clock-offset measurements. This section will describe the background of the CPR and CPV measurements.

Assuming the communicating DMRs operate with identical carrier frequencies, the round-trip carrier-phase ranging measurement is a function of the RF carrier wavelength λ_C = c/f_C and the received phase on each DMR (φ_O and φ_T) in units of radians. The measurement is ambiguous by N_amb half-wavelengths, as shown in Equation 2.

(2)
The frequency offsets measured at each receiver (S_O and S_T) in units of hertz will reflect the Doppler-based velocity offset between the two receivers, as shown in Equation 3.

(3)
While the velocity measurement is absolute, the carrier-phase ranging measurement is ambiguous within a half-wavelength in a round-trip measurement. There are several ways to overcome this limitation including using the velocity measurement to “unwrap” sequential carrier-phase observations, using baseband phase measurements to establish absolute offsets, by aiding the measurement with a strapdown inertial measurement unit (IMU) and by other means. The primary error source for carrier-phase ranging in practice is the solution of integer ambiguity, not the actual phase measurements. The quality of the phase measurements becomes the limiting factor when the integer ambiguity is resolved perfectly. An analysis of the Cramér-Rao lower bound (CRLB) for carrier-phase ranging and carrier-frequency velocity measurements along with measured performance is presented in the following section.

Measurement Performance Bounds

The CRLB for estimation of phase and frequency of a sinusoid based on a number of data samples in additive white Gaussian noise has been previously treated in the literature and can be interpreted to provide a best case, lower bound on how well the measurements could perform. The CRLBs for carrier-frequency and phase estimation are computed in terms of the sinusoid’s signal-to-noise ratio, SNR, the number of observed samples of the phase of the signal N_S and the sample rate of the measurement system f_S.

The CRLB for the standard deviation of carrier-phase ranging measurements is presented in Equation 4 in units of radians. In general, the standard deviation of carrier-phase measurements improves with the square root of N_S and the square root of SNR.

(4)
The CRLB for carrier-phase estimation can be used to compute the CRLB for carrier-phase ranging by scaling each measurement by λ_C

(5)
This CRLB can be interpreted for the carrier-phase ranging observable generation process used in this DMR system. N_S can be expanded to Equation 6, with N_C = 12 chips out of a 16-chip pseudorandom noise code, α = 400 symbols typically tracked (assuming 100 symbrols are consumed in automatic gain control out of a 512-symbol preamble), and f_Sample/f_Chip = 44 MHz/11 MHz = 4. [Note different use of the character α here than in the section on multipath.] This gives N_S = 400 · 12 · 4 = 19,200 in a typical usable DMR preamble as currently implemented.

(6)
FIGURE 3 shows the CRLB for carrier-phase ranging measurement evaluated over a range of SNR and with a varying number of symbols used in the ranging preamble, with typical α = 400 in the current implementation. Evaluating the phase CRLB at a conservatively low SNR = 10 dB and typical N_S = 19,200 on a 5.8-GHz RF carrier yields a lower bound of about 27 micrometers standard deviation for a round-trip carrier-phase ranging measurement.

FIGURE 3. Cramér-Rao lower bound for carrier-phase ranging with different numbers of symbols used in the ranging preamble. (Image: Bradley D. Farnsworth, E.J. Kreinar and David W.A. Taylor)

The CRLB for the standard deviation of carrier-frequency-offset measurements is presented in Equation 7 in units of hertz. In general, the standard deviation of carrier-frequency observation improves with N_S^3/2 and the square root of SNR.

(7)
The CRLB for carrier-frequency estimation can be used to compute the CRLB for carrier-phase velocity by scaling each measurement by λ_C to convert to meters per second, and reducing the standard deviation by the square root of 2 due to the two independent phase measurements being conducted in the round-trip experiment as shown in Equation 8.

(8)
Evaluating the round-trip carrier-phase velocity CRLB at a conservatively low SNR = 10 dB and typical N_S = 19,200 on a 5.8-GHz RF carrier yields a lower bound of about 10 centimeters per second velocity standard deviation. FIGURE 4 shows the CRLB for velocity measurement evaluated over a range of SNR and with varying number of symbols used in the ranging preamble.

FIGURE 4. Cramér-Rao lower bound for carrier-phase velocity with different numbers of symbols used in the ranging preamble. (Image: Bradley D. Farnsworth, E.J. Kreinar and David W.A. Taylor)

These CRLB levels predict that excellent CPR with precision much better than millimeter level and CPV precision much better than a meter per second should be achievable with the designed system assuming a perfect carrier-frequency generation circuit operating in additive white Gaussian noise. The practical limiting factor for these measurements at high SNR is typically the phase-noise performance of the reference oscillators themselves.

Measurement Results

CPR measurements have been implemented in our DMRs and tested in a variety of environments. In a static data collection, CPR demonstrates a stationary precision of approximately 0.1 millimeters at one sigma as shown in the histogram in FIGURE 5. The red line indicates the best-fit to a Gaussian curve of the measurement data, showing very well behaved data.

FIGURE 5. Histogram showing carrier-phase range precision. (Image: Bradley D. Farnsworth, E.J. Kreinar and David W.A. Taylor)

A static collection of CPV measurements demonstrates a precision of approximately 15 centimeters per second at one sigma as shown in the histogram of CPV data in FIGURE 6, which also has the best fit Gaussian distribution overlaid. The performance of these measurements approaches the CRLB.

FIGURE 6. Histogram showing carrier-phase velocity precision. (Image: Bradley D. Farnsworth, E.J. Kreinar and David W.A. Taylor)

To further quantify the accuracy of CPR, a test was conducted comparing CPR to the distance measured by a survey-grade total station laser rangefinder. The transponding radio was mounted on a tripod and moved to varying distances away from the originating radio, which was located near the total station. FIGURE 7 shows the distance-measurement results. The blue dots are the baseband distance measurements and the red dots are the unwrapped carrier-phase range distance measurements. The mean distance and scatter within each stationary period were used to evaluate the precision and accuracy of CPR versus the total station rangefinder values.

FIGURE 7. Distance determined from baseband ranging (blue) and carrier-phase ranging (red) data collected during a test with varying distances between originating and transponding radios and using a total station to provide ground-truth. (Image: Bradley D. Farnsworth, E.J. Kreinar and David W.A. Taylor)

FIGURE 8 shows the outcome of the laser-based total station ground-truth validation of the carrier-phase distance measuring performance in an outdoor LOS environment. The red lines indicate the ±8 millimeter experimental accuracy of the laser ground-truth test setup. The error from each surveyed point is within the uncertainty of the test, with an experimental precision of 0.6 millimeters at one sigma indicated by the vertical error bars on each data point.

FIGURE 8. Range comparison between CPR and a total station. (Image: Bradley D. Farnsworth, E.J. Kreinar and David W.A. Taylor)

System Integration

CPR and CPV measurements have been successfully integrated into a pedestrian tracking dual boot-mounted inertial system. In this configuration, one industrial-grade microelectromechanical systems IMU operating at 400 Hz (three-axis accelerometer, three-axis gyro and three-axis magnetic compass) is mounted on the heel of each boot, and a DMR with CPR/CPV capability is attached to the medial side of each boot. The DMRs perform inter-boot ranging and velocity measurements at 360 Hz throughout system operation. The walking motion generates a very high-dynamic, high-multipath environment that is challenging for RF systems.

FIGURE 9 shows four strides of walking data collected in this configuration. Periodic walking motion is clearly visible on CPR and CPV as the range between boots increases up to 0.6 meters at the extents of strides and passes near zero during foot crossings. CPV measurements are internally consistent with CPR. The first difference of CPR is equivalent to the independent Doppler-based CPV measurement. A significant benefit of the CPV measurement as opposed to the first difference of CPR is that CPV is an absolute measurement with no integer ambiguity.

FIGURE 9. CPR and CPV data for four strides from boot-mounted distance measuring radios. (Image: Bradley D. Farnsworth, E.J. Kreinar and David W.A. Taylor)

For this system, IMU data is integrated using both interpreted zero-velocity updates (ZUPTs) and ranging measurements to determine dead-reckoning motion of each individual boot. The high-precision, multipath-tolerant CPR and CPV measurements are used to constrain inter-boot position and velocity in a centralized extended Kalman filter (CEKF). CPR and CPV residuals from the CEKF are shown in FIGURE 10 and FIGURE 11, representing measurement accuracy in a challenging, high-dynamic environment. All system errors including antenna phase response, integrated IMU errors, and others are included in these histograms, so the true CPR and CPV measurement errors are likely significantly lower, even for this high-multipath environment. This is why we believe our results are a good estimate of the system’s accuracy capability.

FIGURE 10. Histogram showing carrier-phase range accuracy. (Image: Bradley D. Farnsworth, E.J. Kreinar and David W.A. Taylor)

FIGURE 11. Histogram showing carrier-phase velocity accuracy. (Image: Bradley D. Farnsworth, E.J. Kreinar and David W.A. Taylor)

While the overall CPR measurement accuracy of about 11 millimeters is two orders of magnitude worse than the stationary measurement precision of 0.1 millimeters, it should be noted that this includes all measurement biases in the system and various error sources.

CPV achieves an in-system measurement accuracy of 0.31 meters per second, which is approximately a factor of two degraded from the stationary, LOS collection (0.15 meters per second). In this sense, CPV is shown to be an extremely robust measurement in the presence of multipath and non-ideal antenna patterns throughout actual walking motion.

Conclusions

This article presents a new method to perform highly precise, accurate and multipath-resistant measurements of distance and velocity using a small portable radio. Measurements that are as accurate as a laser require only milliseconds to complete and are insensitive to multipath interference. This opens up a wide range of applicability as an aiding sensor to integrated navigation systems. Performance has been demonstrated in the high-dynamic and high-multipath environment between the boots of a walking pedestrian, and similar performance is expected in industrial and military applications. By employing a conventional communications link, measurements of CPR and CPV should be scalable to longer distances with the availability of the measurements roughly comparable to the availability of the communications link.

CPR and CPV achieve stand-alone measurement precision of much better than 1 millimeter standard deviation, and about 15 centimeters per second velocity respectively at a rate of hundreds of measurements per second. In-system performance of CPR and CPV measurement residuals demonstrates 1-centimeter CPR accuracy and 30 centimeters per second CPV accuracy. The measurements presented in this article are typically 100 times more precise than typical baseband round-trip RF measurements in a similarly challenging RF environment.

Acknowledgments

The work described in this article was sponsored by ENSCO Inc.

Manufacturers

The distance measuring radio is manufactured by ENSCO Inc. The inertial measurement unit used in the boot test was a Memsense LLC model H3, while the total station used for calibration was a Leica Geosystems AG model TS30.

BRADLEY D. FARNSWORTH is the chief engineer for positioning, navigation and timing (PNT) at ENSCO Inc., Springfield, Va. He holds several U.S. patents and has expertise in real-time signal processing, autonomous systems and mixed-signal design. He received his B.S. summa cum laude and M.S. degrees in electrical engineering from Case Western Reserve University, Cleveland, Ohio.

E.J. KREINAR is with ENSCO Inc. and holds B.S. and M.S. degrees in electrical engineering from Case Western Reserve University. He has expertise in optimal estimation using Kalman filters, real-time signal processing and autonomous systems.

DAVID W.A. TAYLOR is the director of technology development and business area lead for PNT at ENSCO Inc., where he leads R&D programs developing sensors and systems for national security applications. He holds several U.S. patents and is an expert in GPS-denied navigation technologies. Taylor holds a B.S. in physics from Rhodes College, Memphis, Tenn. and a Ph.D. in geophysics from Virginia Polytechnic Institute and State University (Virginia Tech), Blacksburg, Va.

FURTHER READING
- Authors’ Conference Paper on which the Article is Based
“Precise, Accurate, and Multipath-Resistant Networked Round-Trip Carrier Phase RF Ranging” by B.D. Farnsworth, E.J. Kreiner and D.W.A. Taylor in Proceedings of ITM 2015, the 2015 International Technical Meeting of The Institute of Navigation, Dana Point, Calif. January 26–28, 2015, pp. 651–656.
- Radio Frequency Ranging
“Where Are We? Positioning in Challenging Environments Using Ultra-Wideband Sensor Networks” by Z. Koppanyi, C.K. Toth and D.A. Grejner-Brzezinska in GPS World, Vol. 26, No. 3, March 2015, pp. 44–49.

“Hybrid Positioning: A Prototype System for Navigation in GPS-Challenged Environments” by C. Rizos, D.A. Grejner-Brzezinska, C.K. Toth, A.G. Dempster, Y. Li, N. Politi, J. Barnes, H. Sun and L. Li in GPS World, Vol. 21, No. 3, March 2010, pp. 42–47.

RF Ranging for Location Awareness by S.M. Lanzisera and K. Pister, Technical Report No. UCB/EECS-2009-69, Dept. of Electrical Engineering and Computer Sciences, University of California at Berkeley, Berkeley, Calif., May 19, 2009.

“Opportunistic Navigation: Finding Your Way with AM Signals of Opportunity” by J. McEllroy, J.F. Raquet and M.A. Temple in GPS World, Vol. 18, No. 7, July 2007, pp. 44–49.

“GPS + LORAN-C: Performance Analysis of an Integrated Tracking System” by J. Carroll in GPS World, Vol. 17, No. 7, July 2006, pp. 40–47.

“Prime Time Positioning: Using Broadcast TV Signals to Fill GPS Acquisition Gaps” by M. Martone and J. Metzler in GPS World, Vol. 16, No. 9, September 2005, pp. 52–60.
- Direct Sequence Spread Spectrum Radio Frequency Ranging
“High-Precision 2.4 GHz DSSS RF Ranging” by B.D. Farnsworth and D.W.A. Taylor in Proceedings of ITM 2011, the 2011 International Technical Meeting of The Institute of Navigation, San Diego, Calif., January 24–26, 2011, pp. 178–183.

“High Precision Narrow-Band RF Ranging” by B.D. Farnsworth and D.W.A. Taylor in Proceedings of ITM 2010, the 2010 International Technical Meeting of The Institute of Navigation, San Diego, Calif., January 25–27, 2010, pp. 161–166.
- Estimating Phase and Frequency of Noisy Signals
Phase and Frequency Estimation: High-Accuracy and Low-Complexity Techniques by Y. Liao, Master’s thesis, Dept. of Electrical and Computer Engineering, Worcester Polytechnic Institute, Worcester, Mass., May 2011.

Equation images: Bradley D. Farnsworth, E.J. Kreinar and David W.A. Taylor
June 8, 2015

Innovation: Where Are We?

Positioning in Challenging Environments Using Ultra-Wideband Sensor Networks

By Zoltan Koppanyi, Charles K. Toth and Dorota A. Grejner-Brzezinska

INNOVATION INSIGHTS by Richard Langley — **INNOVATION INSIGHTS** by Richard Langley

QUICK. WHO WAS THE FIRST TO PREDICT THE EXISTENCE OF RADIO WAVES? If you answered James Clerk Maxwell, you are right. (If you didn’t and have an electrical engineering or physics degree, it’s back to school for you.) In the mid-1800s, Maxwell developed the theory of electric and magnetic forces, which is embodied in the group of four equations named after him. This year marks the 150th anniversary of the publication of Maxwell’s paper “A Dynamical Theory of the Electromagnetic Field” in the Philosophical Transactions of the Royal Society of London.

Interestingly, Maxwell used 20 equations to describe his theory but Oliver Heaviside managed to boil them down to the four we are familiar with today. Maxwell’s theory predicted the existence of radiating electromagnetic waves and that these waves could exist at any wavelength. Maxwell had speculated that light must be a form of electromagnetic radiation. In his 1865 paper, he said “This velocity [of the waves] is so nearly that of light, that it seems we have strong reason to conclude that light itself (including radiant heat, and other radiations if any) is an electromagnetic disturbance in the form of waves propagated through the electromagnetic field according to electromagnetic laws.”

That electromagnetic waves with much longer wavelengths than those of light must be possible was conclusively demonstrated by Heinrich Hertz who, between 1886 and 1889, built various apparatuses for transmitting and receiving electromagnetic waves with wavelengths of around 5 meters (60 MHz). These waves were, in fact, radio waves. Hertz’s experiments conclusively proved the existence of electromagnetic waves traveling at the speed of light. He also famously said “I do not think that the wireless waves I have discovered will have any practical application.” How quickly he was proven wrong.

Beginning in 1894, Guglielmo Marconi demonstrated wireless communication over increasingly longer distances, culminating in his bridging the Atlantic Ocean in 1901 or 1902. And, as they say, the rest is history. Radio waves are used for data, voice and image one-way (broadcasting) and two-way communications; for remote control of systems and devices; for radar (including imaging); and for positioning, navigation and time transfer. And signals can be produced over a wide range of frequencies from below 10 kHz to above 100 GHz.

Conventional radio transmissions use a variety of modulation techniques but most involve varying the amplitude, frequency and/or phase of a sinusoidal carrier wave. But in the late 1960s, it was shown that one could generate a signal as a sequence of very short pulses, which results in the signal energy being spread over a large part of the radio spectrum. Initially called pulse radio, the technique has become known as impulse radio ultra-wideband or just ultra-wideband (UWB) for short and by the 1990s a variety of practical transmission and reception technologies had been developed.

The use of large transmission bandwidths offers a number of benefits, including accurate ranging and that application in particular is being actively developed for positioning and navigation in environments that are challenging to GNSS such as indoors and built-up areas. In this month’s column, we take a look at the work being carried out in this area by a team of researchers at The Ohio State University.

“Innovation” is a regular feature that discusses advances in GPS technology and its applications as well as the fundamentals of GPS positioning. The column is coordinated by Richard Langley of the Department of Geodesy and Geomatics Engineering, University of New Brunswick. He welcomes comments and topic ideas. Email him at lang @ unb.ca.

GNSS technology provides position, navigation and timing (PNT) information with high accuracy and global coverage where line-of-sight between the satellites and receivers is assured. This condition, however, is typically not satisfied indoors or in confined environments. Emerging safety, military, location-based and personal navigation applications increasingly require consistent accuracy and availability, comparable to that of GNSS but in indoor environments.

Most of the existing indoor positioning systems use narrowband radio frequency signals for location estimation, such as Wi-Fi, or telecommunication-based positioning (including GSM and UMTS mobile telephone networks). All these technologies require dedicated infrastructure, and the narrowband RF systems are subject to jamming and multipath, as well as loss of signal strength while propagating through walls. In contrast, using ultra-wideband (UWB) signals can, to some extent, remediate those problems by offering better resistance against interference and multipath, and they feature better signal penetration capability. Due to these properties, the use of UWB has the potential to support a broad range of applications, such as radar, through-wall imagery, robust communication with high frequency, and resistance to jamming. Furthermore the impulse radio UWB (IR-UWB), the subject of this article, can be an efficient standalone technology or a component of positioning systems designed for multipath-challenged, confined or indoor environments, where GNSS signals are compromised.

IR-UWB positioning can be useful in typical emergency response applications such as fires in large buildings, dismounted soldiers in combat situations, and emergency evacuations. In such circumstances, the positioning/navigation systems must determine not only the exact position of any individual firefighter or soldier to facilitate their team-based mission, but also navigate them back to safety. Under these scenarios, a temporary ad hoc network has to be quickly deployed, as the existing infrastructure is usually non-functional, damaged or destroyed at that point. The UWB-based systems may easily satisfy these criteria: (1) nodes placed in the target area can rapidly establish the network geometry even if line-of-sight between nodes is not available, (2) the communication capability allows for sharing measurements, and (3) the node positions may be calculated based on these measured ranges in a centralized or distributed way. Once the node coordinates have been determined, the tracking of the moving units can start. Obviously, the resistance against jamming makes this solution attractive for military applications.

Ad Hoc Network Formation for Emergency Response

Quick deployment
Sufficient positioning accuracy
Robustness against interference (jamming)
Signal penetration through solid structures

Generally, positioning systems, both local and global, require an infrastructure, which defines the implementation of a coordinate frame. For example, the national reference frames and their realizations support conventional land surveying, or the satellite and the GPS tracking subsystems, as well as the beacons in Wi-Fi systems. UWB positioning also follows the same logic; the network infrastructure defines a local coordinate system and allows for range measurements between the network nodes and the tracked unit(s).

Ad Hoc Sensor Network: Ad hoc networks are temporary, and thus, the node coordinates are not expected to be known or measured a priori; consequently, they are calculated based on measuring the ranges between the units in the initial phase, and can be updated subsequently if the network configuration changes.

Anchored Networks: The network nodes’ coordinates are known. If only local coordinates are known, then to connect to a global coordinate frame, at least one node’s global coordinates and a direction vector must be known to anchor and orient the network.

Anchor-Free Networks: No node coordinates are known, thus the localization problem is underdetermined. Nevertheless, the problem is still solvable, if it is extended with additional constraints.

Tracking: Once a network is established, static/moving objects can be positioned in the network coordinate system.

Ultra-Wideband Ranging

At the beginning of the 21st century, the Federal Communications Commission (FCC) introduced new regulations that enabled several commercial applications and initiated research on UWB application to PNT. The current FCC rules for pulse-based positioning or localization implementations require the applied bandwidth be between 3.1 and 10.6 GHz and the bandwidth to be higher than 500 MHz or the fractional bandwidth to be more than 0.2.

The typical IR-UWB ranging system consists of multiple transceiver units, including the transmitter and the receiver components. The transmitter emits a very short pulse (high bandwidth) with low energy, and the receiver detects the signal after it travels through the air, interacting with the environment. After reaching objects, the emitted pulse is backscattered as several signals, which likely reach the receiver at different times. In contrast, conventional RF signals are longer in duration, thus the backscattered waves overlap each other at the receiver, forming a complex waveform, and may not be distinguishable individually. Due to the shortness of the UWB signals, measurable peaks are nicely separated, representing different signal paths.

The wave shape of the impulse response of the transmission medium highly depends on the environment complexity due to multipath. Detections in the received wave are determined by a peak-detecting algorithm. Note that the travel time is generally determined from the first detection, as it is assumed to be from the shortest path, although other peak detection algorithms also exist.

In the experiments discussed in this article, a commercial UWB radio system was used. This sensor’s bandwidth is between 3.1 and 5.3 GHz, with a 4.3-GHz center frequency. Three methods are available to obtain ranges: (1) coarse range estimation, based on the received signal strength with dynamic recalibration; (2) precision range measurement (PRM), which uses the two-way time-of-flight technique; and (3) the filtered range estimates (FRE) method that refines the PRM solution using Kalman filtering. In our investigations, PRM data were used in static situations, when both the unit to be positioned and the reference units were static (such as when determining network node coordinates), and FRE was logged in kinematic scenarios.

Localization in a UWB Network

Commercial UWB products usually provide capabilities for all three applications: communication, ranging and radar imaging. In positioning applications, identical units are used for both the rovers — that is, the units to be localized — and the static nodes of the network. The general terminology, however, is that the rover unit with unknown position is called the receiver, and units deployed at known locations are called transmitters. We will also use the terms rover and stations. The positions are typically defined in a local coordinate system. The usual ranging methods used in RF technologies, including signal strength and fingerprinting, time of arrival, angle of arrival, and time difference of arrival, are also applicable to UWB systems. TABLE 1 lists the ranging methods and typical performance levels; the achievable accuracies are based on external references. Note that the accuracy depends on the sensor hardware and network configuration, applied bandwidth, signal-to-noise ratio, peak detection algorithm, experiment circumstances, formation and the environment complexity.

TABLE 1. Typical accuracy of the different UWB localization techniques. Note that the results depend on the hardware, antenna, applied bandwidth, experiment circumstances and geometric configuration; * denotes indoor environment with area coverage of a few times 10 × 10 meters, with line-of-sight conditions, and ** refers to the maximum error in the outdoor test area of about 100 × 100 meters).

Signal Strength. The received signal strength (RSS) requires modeling of the signal loss, which is a challenging problem since signals at different frequencies interact with the environment in different ways, and thus the resulting accuracy is generally inadequate for most applications. The fingerprinting approach is also applied to UWB positioning; the signal-strength vector received from the transmitters identifies a location by the best match, where the vector-location pairs are measured in a calibration/training phase and stored in a database.

Time of Flight. The time-of-flight method requires the synchronization of the clocks of the UWB units, which is difficult, in particular, in the low-cost systems. Therefore, most UWB systems are based on the two-way time-of-flight method, which eliminates the unknown clock delay between the sensors, although it also has its own challenges. The range between two units is obtained by measuring the time difference of the transmitted and received pulses plus knowing the fixed response time of the responding unit.

Computing Position in a Network. Once the ranges are known in a network environment, the position is determined by circular lateration. The principle for the 2D case with three stations is shown in FIGURE 1. Note that each range determines a circle around the known stations (stations 1, 2 and 3 in the figure), thus, if the stations’ coordinates are known, the unknown position can be calculated as the intersection of these circles. The problem is treated as a system of non-linear equations; note that the lateration requires at least three or four nodes in an adequate spatial distribution for 2D and 3D positioning, respectively. The measured ranges, characterized by the error terms usually modeled with a normal distribution, are depicted by the dotted parallel circles around the solid “perfect” range in Figure 1. Note that this is an optimization problem, which can be solved with direct numerical approximation, such as gradient methods, or by solving the respective linear system after linearizing the problem with close initial position values.

Time Difference and Angle of Arrival. The time difference of arrival (TDoA) approach is useful when the time synchronization is not established. The unknown time delays are eliminated by subtracting the travel times between the rover and the stations, and the response time of the responding unit must be known. The location estimation is similar to the time of arrival case, but rather than the intersection of the circles, hyperbolic function curves representing constant TDoA values are used to determine the rover position. Also, if errors are present in the measurements, the position calculation becomes an optimization problem instead of finding the root of an equation. The TDoA can be combined with the angle of arrival (AoA). This method assumes that the set of UWB antennas are arranged in an array, and the angle can be calculated as the time difference of the first and the last detection from different antennas of the array.

Calibration

The ranges obtained by UWB sensors could be further improved by calibration — for example, by estimating antenna and hardware delays. In our outdoor tests, the joint calibration model (see Two Calibration Models box) was used, and coefficients of various model functions were estimated. During these tests, the UWB units were placed at the corners of a 15 × 15 meter area (see FIGURE 2).

At two diagonal corners, two UWB units with a 1.5-meter vertical separation were installed on poles, while at the two other corners only one unit was used. These six units formed the nodes or the stations of the network. In all cases, a GPS antenna was fixed to the top of the poles to provide reference data. A pushcart with two UWB units, a logging laptop computer, a GPS antenna and a receiver formed the rover system. The reference solution was obtained by using the GPS measurements, with the accuracy around 1 centimeter after kinematic post-processing using precise satellite orbit and clock data. During calibration, the pushcart was collecting stationary data at points 1 to 12, marked on a 5 × 5 meter grid, as shown in Figure 2.

Two Calibration Models

Individual sensor calibration is the approach where the sensor delays are determined separately, for example, , where is the measured range between stations A and B, and are the calibration functions, and is the corrected range.
Joint calibration model is the approach where the calibration function does not provide the offset per station, but rather gives the relative offset between the two stations, where .

The calibration model as a function of the measured distance can be constant, linear or a higher-order polynomial.

After acquiring range data between the rover and network stations, three types of joint calibration functions were investigated: constant, linear and polynomial models. The coefficients of these functions were estimated from the measured ranges and GPS-provided reference positions at all grid points. The estimated functions with respect to the six network nodes are shown in FIGURE 3. Our hypothesis was that the accuracy is assumed to depend on the rover-station distance, and thus, the detected discrepancies between the rover and reference points are expected to be higher if the distance is larger. The results indicate that a constant correction (that is, an antenna delay) is generally sufficient, indicating that the calibration may be applicable to similar installations. In some cases, a linear trend (a distance dependency) may be recognized due to slight data changes, but the observed regression lines are either increasing or decreasing, which clearly rejects the distance-dependency hypothesis. The linear and second-order polynomial functions likely model only local effects. The corrections provided by these functions depend on the environment, and consequently, are valid only in that configuration and where they were observed.

Error surfaces, derived as the approximation of a second-order surface from the residuals at the grid points between the receiver and the six station units, show that the discrepancies can be as large as 0.5 meter. Calibrated results using the constant model show that all the discrepancies are less than 10 centimeters with an empirical standard deviation of 3.6 centimeters. This suggests that, at least, the constant-model-based calibration is needed.

Tracking Outdoors and Indoors

If the coordinates of the network nodes and the calibration parameters are known, the location of the moving rover can be calculated with circular lateration. The experiment described in this section is based on the same field test as presented earlier. For assessing the outdoor tracking performance, a random trajectory of the pushcart inside and outside of the rectangle defined by nodes was acquired (see FIGURE 4). The reference trajectory was obtained by GPS and the UWB trajectory was calculated with circular lateration.

TABLE 2 presents a statistical comparison of the coordinate component differences between the GPS reference and the UWB trajectory based on calibrated ranges. The mean of the X and Y coordinate differences are around 0 centimeters, and their standard deviations are 9.7 and 13.2 centimeters, respectively, with the largest differences being less than half a meter in both coordinate components. Note that the vertical coordinates have large errors due to the small vertical angle, which translates to weak geometric conditions for error propagation.

TABLE 2. Statistical results for the coordinate components.

Indoor UWB positioning is more challenging than outdoor, as propagation through walls modifies the RF signals resulting in attenuations and delays. Furthermore, the geometric error propagation conditions (that is, the shape of the network) may also reduce the quality of positioning. In the indoor tests, a personal navigation system demonstration prototype built in our lab (shown in FIGURE 5) was used as a rover. During the tests, the person was moving at a normal pace, and the rover unit recorded the ranges from the reference stations. Concerning the network, two point types are defined: (1) network nodes depicted by a double circle in the figure, which are used in the tracking phase; and (2) reference points marked by a single circle, which support the validation of the positioning results.

Since no reference solution was available during the indoor testing, the calibration method’s consistency was evaluated based on the relative or internal accuracy metric, which is the a posteriori reference standard deviation error:

where v is the vector of residual errors and r=dim(A^TA) – rank(A^TA) is the degrees of freedom of the network with A being the design matrix describing the geometry of the network. The m₀ values are shown in FIGURE 6. This parameter describes the statistical difference of the measurements from the assumed model (circular lateration). The average m₀ is 7.6 centimeters without calibration, and higher if any of the outdoor calibration models are used.

FIGURE 6. The indoor test results showing values of m0 at the epochs.

To estimate the absolute or external accuracy without a reference trajectory, points 1002 and 1004 were used as checkpoints with known coordinates. Obviously, these points were not part of the network. The UWB rover unit was placed at these points, and data were acquired in a static mode. The coordinates were continuously calculated after measuring at least three ranges. TABLE 3 presents the statistical results. Note that the average is not 0, thus the result is biased, indicating that the signal penetration and/or multipath effects are present in this complex indoor environment. Also, note that no calibration was performed, as no indoor calibration results were available, and using the outdoor calibration models only decreased the positioning accuracy. In addition, the standard deviations indicate the average m₀ is consistent with the external error for point 1002, while this hypothesis is rejected for point 1004.

TABLE 3. Differences between the UWB position estimations and the correct coordinates at points 1002 and 1004.

Taking a closer look at the results of point 1004, the ambiguity problem of the circular lateration can be observed. The random measurement error can be large enough to cover two possible intersections in circular lateration, thus the estimator may oscillate between two solutions. Two main causes for this ambiguity are a weak network configuration and the large ranging errors (see FIGURE 7).

Ad Hoc UWB Sensor Network

We have also carried out tests on an indoor ad hoc sensor network using different coordinate estimation methods. Indoor distance measurements typically do not follow a normal or Gaussian error distribution but rather a Gaussian mixture distribution, which demands the use of a robust estimation method. Our results showed that the maximum likelihood estimation technique performs better than conventional least squares for this type of network.

Conclusion

Ultra-wideband technology is an effective positioning method for short-range applications with decimeter-level accuracy. The coverage area can be extended with increasing network size. The technology can be used independently or as a component of an integrated positioning/navigation system. GPS-compromised outdoor situations and indoor applications can be supported by UWB in permanent and ad hoc network configurations. While UWB technology is relatively less affected by environmental conditions, signal propagation through objects or other non-line-of-sight conditions can reduce the reliability and accuracy.

Acknowledgments

This article is based, in part, on the paper “Performance Analysis of UWB Technology for Indoor Positioning,” presented at the 2014 International Technical Meeting of The Institute of Navigation, held in San Diego, Calif., Jan. 27–29, 2014.

Manufacturer

The experiments discussed in the article used a Time Domain Corp. PulsON 300 UWB radio system.

ZOLTAN KOPPANYI received his B.Sc. degree in civil engineering in 2010 and his M.Sc. in land surveying and GIS in 2012, both from Budapest University of Technology and Economics (BME), Hungary. He also received a B.Sc. in computer science from the Eötvös Loránd University, Budapest, in 2011. He is a Ph.D. student at BME and was a visiting scholar at the Ohio State University (OSU), Columbus, in 2013. His research area is human mobility pattern analysis and indoor navigation.

CHARLES K. TOTH is a research professor in the Department of Civil, Environmental and Geodetic Engineering at OSU. He received an M.Sc. in electrical engineering and a Ph.D. in electrical engineering and geo-information sciences from the Technical University of Budapest, Hungary. His research expertise covers broad areas of 2D/3D signal processing; spatial information systems; high-resolution imaging; surface extraction, modeling, integrating and calibrating of multi-sensor systems; multi-sensor geospatial data acquisition systems, and mobile mapping technology.

DOROTA A. GREJNER-BRZEZINSKA is a professor in geodetic science, and director of the Satellite Positioning and Inertial Navigation (SPIN) Laboratory at OSU. Her research interests cover GPS/GNSS algorithms, GPS/inertial and other sensor integration for navigation in GPS-challenged environments, sensors and algorithms for indoor and personal navigation, and Kalman and non-linear filtering.

“Ultra-Wideband Range Estimation: Theoretical Limits and Practical Algorithms” by I. Guvenc, S. Gezici, and Z. Sahinoglu in Proceedings of ICUWB2008, the 2008 Institute of Electrical and Electronics Engineers International Conference on Ultra-Wideband, Hannover, Germany, September 10–12, 2008, Vol. 3, pp. 93–96, doi: 10.1109/ICUWB.2008.4653424.

• Received Signal Strength Fingerprinting

“Increased Ranging Capacity Using Ultrawideband Direct-Path Pulse Signal Strength with Dynamic Recalibration” by B. Dewberry and W. Beeler in Proceedings of PLANS 2012, the Institute of Electrical and Electronics Engineers / Institute of Navigation 2012 Position, Location and Navigation Symposium, Myrtle Beach, S.C., April 23–26, 2010, pp. 1013–1017, doi: 10.1109/PLANS.2012.6236843.

“Indoor Ultra-Wideband Location Fingerprinting” by H. Kröll and C. Steiner in Proceedings of IPIN 2010, the 2010 International Conference on Indoor Positioning and Indoor Navigation, Zurich, September 15–17, 2010, pp. 1–5, doi: 10.1109/IPIN.2010.5648087.

• Ultra-Wideband Time-of-Arrival and Angle-of-Arrival“Ultra-Wideband Time-of-Arrival and Angle-of-Arrival Estimation Using Transformation Between Frequency and Time Domain Signals” by N. Iwakiri and T. Kobayashi in Journal of Communications, Vol. 3, No. 1, January 2008, pp. 12–19, 10.4304/jcm.3.1.12-19.

• Maxwell’s Equations

“The Long Road to Maxwell’s Equations” by J.C. Rautio in IEEE Spectrum, Vol. 51, No. 12, December 2014, North American edition, pp. 36–40 and 54–56, doi: 10.1109/mspec.2014.6964925.

A Student’s Guide to Maxwell’s Equations by D. Fleisch, Cambridge University Press, Cambridge, U.K., 2008.

March 5, 2015

GPS Reflections Group Honored with Water Prize

The GPS Reflections Group of University of Colorado-Boulder has been awarded the prestigious Prince Sultan Bin Abdulaziz International Creativity Prize for Water. The prize is awarded biannually to acknowledge innovative work that contributes to the sustainable availability of water and the alleviation of the global problem of water scarcity.

The awards will be presented in a ceremony in Riyadh, Saudi Arabia, on December 16, concurrently with the 6th International Conference on Water Resources and Arid Environments (ICWRAE 6), December 16-18, 2014.

Professors Kristine Larson and Eric Small developed a new method to measure water at the Earth’s surface. The research team discovered that standard geodetic GPS instruments are sensitive to hydrological influences. They subsequently developed a cost-effective technique, GPS Interferometric Reflectometry (GPS-IR), to measure soil moisture, snow depth, and vegetation water content around GPS antennas. GPS-IR has the advantage of relying on an existing GPS infrastructure installed by surveyors and geoscientists that covers an increasingly large portion of the global surface.

Larson has written for GPS World magazine (see Innovation: How Deep Is That White Stuff?), and her team’s sea-level work has been reported here before.

Larson and Small collaborated with scientists at the University Corporation for Atmospheric Research and the National Atmospheric and Oceanic Administration, also in Boulder.

The team uses the GPS-IR technique to analyze data streams from existing GPS networks in near real-time. Data from hundreds of operational GPS sites are downloaded and processed, yielding estimates of hydrologic variables within 24 hours.

Scientists and government agencies can access this information at the team’s web portal and use the data to improve monitoring and forecasting of hydrologic variables.

November 12, 2014
Innovation: Ionospheric Modeling Using GPS
Greater Fidelity Using a 3D Approach

By Wei Zhang, Attila Komjathy, Simon Banville, and Richard B. Langley

INNOVATION INSIGHTS by Richard Langley

MAY YOU LIVE IN INTERESTING TIMES. So goes the purported Chinese proverb and curse. When it comes to the ionosphere, an interesting time might indeed be a curse for most users of GPS. The ionosphere – that region of the upper atmosphere where free electrons exist in sufficient numbers to affect the propagation of radio waves – owes its existence primarily to the extreme ultraviolet (EUV) and x-ray photons emitted by the sun. They ionize atoms and molecules in the upper atmosphere, freeing the outer electrons. Mostly the ionosphere is well behaved but it can get quite interesting when it is disturbed by space weather events such as solar flares or coronal mass ejections.

The signals from the GPS satellites are perturbed as they transit the ionosphere. Pseudorange measurements are increased in value (an additional delay) and carrier-phase measurements are decreased (a phase advance). If not fully modeled or otherwise accounted for, the perturbations can decrease the accuracy of GPS positioning, navigation, and timing (PNT). For highest PNT accuracies, observations are made at the two frequencies transmitted by all GPS satellites and because the ionosphere’s effect on radio signals is dispersive, a linear combination of the measurements removes almost all of the ionospheric perturbations. On the other hand, the ionosphere’s effect on single frequency observations must be corrected using a model. Most commonly, the model assumes that all of the electrons in the ionosphere can be compressed into a thin shell at a certain height above the receiver. This permits the computation of an estimate of the vertical ionospheric delay. Then, a mapping function is used to predict the slant delay, the delay contributing to a GPS measurement. The approach works reasonably well, particularly if near-real-time values of vertical delay can be provided to users as is done by the Wide Area Augmentation System and other satellite-based augmentation systems. However, this two-dimensional approach ignores the fact that the electron content of the ionosphere is actually spread out in the vertical direction and so has certain inaccuracies, which can increase when the ionosphere is disturbed.

In an effort to improve ionosphere modeling with potential application to single-frequency GNSS users, a couple of my current graduate students together with a former student, have investigated a three-dimensional approach to ionospheric modeling using empirical orthogonal functions or EOFs to describe the vertical structure of the ionosphere. EOFs reduce the dimensionality of a data set or an empirical model consisting of a large number of interrelated variables, while retaining as much of the variance present in the data set as possible. This is achieved by transforming to a new set of variables, the orthogonal functions, which are uncorrelated (orthogonal), and which are ordered so that the first few retain most of the variation present in all of the original variables. Only three functions are required to account for more than 99 percent of the variability in the International Reference Ionosphere – 2007, for example.

In this month’s column we look at the performance of this 3D approach to modeling the ionosphere including times when the ionosphere is particularly interesting.

“Innovation” is a regular feature that discusses advances in GPS technology and its applications as well as the fundamentals of GPS positioning. The column is coordinated by Richard Langley of the Department of Geodesy and Geomatics Engineering, University of New Brunswick. He welcomes comments and topic ideas.

Ionospheric modeling plays an important role in improving the accuracies of positioning and navigation, especially for current civil aircraft navigation and mass-market single-frequency users. Measurement-driven models are considered to be among the best candidates for real-time single-frequency positioning owing to their real-time applicability and relatively higher accuracy compared to empirical models, such as the GPS broadcast (also known as Klobuchar) and NeQuick models. A good example of a real-time positioning application is satellite-based augmentation systems (SBAS), including the Wide Area Augmentation System (WAAS), the European Geostationary Navigation Overlay Service (EGNOS), the Japanese MSTAT Satellite-based Augmentation System (MSAS), and the Indian GPS Aided Geo Augmented Navigation system (GAGAN). Because the ionosphere can be the largest error source in single-frequency positioning, the accuracy of ionospheric modeling is critical for single-frequency applications.

Several organizations have been routinely providing ionospheric products to correct errors caused by the ionosphere in the form of ionospheric maps — that is, vertical total electron content (vTEC) at grid points (including regional and global products), such as those from WAAS and the International GNSS Service (IGS), with various processing time delays ranging from near real time to a couple of weeks. Among the earliest works of ionosphere modeling, the University of New Brunswick-Ionospheric Modeling Technique (UNB-IMT) was developed in the mid-1990s. This technique was demonstrated to effectively derive both regional and global total electron content (TEC) maps. However, most of the models, including the current version of UNB-IMT, approximate the ionosphere using a single thin-shell approach with an altitude set at, for example 350 km, which may introduce additional modeling errors up to several TEC units (1 TECU = 10¹⁶ electrons/m²), corresponding to meter-level errors of measurement delay or advance at the GPS L1 frequency.

To overcome any downside of such models, three-dimensional (3D) ionospheric tomographic modeling methods have been proposed and implemented by several groups since the late 1990s. Different from the two-dimensional (2D) single thin-shell ionospheric models, where the parameters to be estimated are associated with TEC, the modeled variables in the tomographic model are related to electron density functions. Therefore, we may expect more complex structures of electron densities (such as those observed during ionospheric storms or in the highly variable equatorial anomaly) to be revealed by the models. A commonly accepted modeling approach is to describe the ionospheric horizontal (longitudinal and latitudinal) variability by a spherical harmonic (SH) expansion up to a specific degree and its vertical dimension modeled by empirical orthogonal functions (EOFs).

However, SH models are not ideal for capturing local variability in the ionosphere because each basis function of spherical harmonics exists over the entire geographic region of interest, such as the entire globe in the case of global modeling. In other words, localized measurements will have influence on the estimated state across the whole globe. As alternative approaches, wavelet, finite element (meshes/pixels), and local-basis-function models have been proposed and implemented to capture the localized information content in the measurements and pass this information on to the end user. On the other hand, the inversion process can occasionally become singular as many of the parameters to be estimated tend to be ineffective and less meaningful. This is especially the case when our goal is to obtain better accuracies with higher order wavelet bases or smaller meshes/pixels. Due to the potential computing and transmitting burden, the two modeling techniques may have more difficulties associated with real-time applications, such as real-time single-frequency positioning, although they have advantages for capturing localized structures in the ionosphere.

Aiming for potential real-time applications of 3D tomographic models, we have extended the UNB-IMT from 2D to 3D by modeling the vertical dimension of the ionosphere using EOFs. In this article, we discuss our approach and report on some initial tests including comparing its performance with the 3D SH approach.

The 2D UNB-IMT was demonstrated to work with various network sizes: regional, baseline-by-baseline, and even single standalone stations. Therefore, it is expected that this technique will help in capturing localized ionospheric structures above small regional networks or above a single standalone station. Additional benefits may be expected for disturbed ionospheric conditions. For assessing the two modeling techniques, a small regional network was chosen to perform station-by-station and batch processes. The performance of both methods with the two processing scenarios has been compared by analyzing the post-fit residuals and vTECs of the state estimation process, as well as the repeatability of estimates of differential code biases (DCBs) for both quiet and disturbed ionospheric conditions.

3D UNB-IMT

Because of the limited number of ionospheric parameters to be estimated, the 2D UNB-IMT was considered suitable for real-time applications, such as real-time single-frequency precise point positioning (PPP) and SBASs. In fact, it can be proven that the modeling method of the current 2D UNB-IMT is identical to the original planar fit of WAAS in nature if the locations of reference stations tend to collocate with WAAS ionospheric grid points (IGPs). Although additional parameters are involved, we believe the 3D UNB-IMT approach with its potential for improved modeling accuracy is still suitable for real-time applications. In this section, we will introduce the 3D UNB-IMT modeling strategy and demonstrate its applicability with a regional network and single standalone stations.

Model Description. In order to clearly present the technique demonstrated in our recent work, we first briefly review the 2D UNB-IMT. Linear polynomial functions were initially proposed for describing the spatial variability of the ionosphere. We model the observed slant TEC (sTEC) between a satellite and a receiver from carrier-phase and pseudorange (code) observations at some epoch as the product of a bilinear polynomial representing the vTEC at the thin-shell ionospheric pierce point (IPP) of the signal raypath and a mapping function that projects the vTEC to sTEC plus receiver and satellite instrumental biases (DCBs). The input variables are the geographic longitude of the IPP referenced to the solar-geomagnetic coordinate system (in other words, the difference between the longitude of the IPP and the longitude of the mean sun) and the difference between the geomagnetic latitude of the IPP and the geomagnetic latitude of the station. We consequently have three polynomial coefficients to estimate for each station: a constant term, one to describe the longitude variations, and one for the latitude variations.

The mapping function used in the model is the standard geometric mapping function, which computes the secant of the zenith angle of the signal geometric ray path at the IPP at a specified shell height. Because of the dependence of the ionosphere on solar radiation and the geomagnetic field, the solar-geomagnetic reference frame is used to compute the TEC over each station in this technique. Since the ionosphere changes more slowly in the sun-fixed reference frame than in the Earth-fixed one, such a reference frame is ideal for producing more accurate TEC estimates.

The initial version of UNB-IMT ignored the non-linear spatial variation of the ionosphere. Non-linear terms are expected to be able to absorb more complex variability of the ionosphere and thus more properly describe the ionosphere in disturbed conditions. Regarding this issue, the drawbacks of some modeling methods based on linear models have been reported: for example, the highly variable ionosphere might be absorbed by the estimated DCBs, making the repeatability of the estimated DCBs (day-to-day variability) correlated with the variability of the ionosphere. To enhance the performance of UNB-IMT, especially under disturbed ionospheric conditions, UNB researchers extended the linear version of UNB-IMT to a quadratic one and assessed it by using a wide-area regional network in North America. This modified approach reduced the post-fit residuals significantly by better modeling the ionospheric variations with the help of the additional second order (non-linear) terms.

To better use a priori information in the development of 3D UNB-IMT, we separate the TEC into a background reference or “known” part and a perturbation or to-be-modeled part. The background reference part of TEC could be calculated from an a priori source of electron density, such as any kind of ionospheric model, including empirical and theoretical ionospheric models. The density, as a function of latitude, longitude, height, and time, is integrated along the raypath between the receiver and a satellite.

Then, the perturbation part of the electron density is modeled by the inner product of EOFs and polynomial functions with associated estimated coefficients to depict the variability of the ionosphere in the vertical and horizontal directions respectively. And this part is similarly integrated along the raypath and added to the reference part along with the DCBs.

Empirical Orthogonal Functions. The EOF method is a method of choice for analyzing the variability of a single field (with only one scalar variable). Variability of the ionosphere with respect to height is needed for the 3D models. The method finds the spatial patterns of variability based on historical data sets (as reflected in empirical or theoretical models). In other words, the modes of variability decomposed by the method are primarily “data modes,” and not necessarily physical or actual real-time models. Due to its noted ability in describing the background ionosphere, the data sets output from the empirical Ionospheric Reference Ionosphere 2007, were utilized to form the EOFs in our technique.

Thus, the data sets of electron densities are realized by uniform sampling at the following variant time scale intervals and specific geographic locations:
- Solar cycle: [1998:1:2008] (year)
- Season of year: [Dec., Mar., Jun., Sep.] (month)
- Time of day: [1:1:24] (hour)
- Day of month: [1:9:28] (day of month)
- Geographic latitude: [30:5:60] (degree)
- Geographic longitude: [280:5:300] (degree),
where the numbers separated by colons correspond to minimum:increment:maximum. The data sets cover the whole spatial area of interest. The data sets of a whole solar cycle in typical equinox and solstice months are used to ensure that the EOFs span the range of profile variations that include the variation in solar EUV and x-ray output. Each electron density profile with respect to height at these locations and time points is sampled in the vertical dimension at [100:2:2000] (km). Figure 1 shows the first three third-order normalized EOFs based on the data sets. The first three eigenvalues account for 92.22, 6.69, and 0.78 percent of the total respectively. Provided the solution is nonsingular, the choice of the highest order of EOFs is a trade off between processing time and modeling accuracy as to the specific network and capability of computer(s). In our current work, the highest order of three was chosen. In this case, the neglected vertical variation of the ionosphere corresponding to higher order EOFs is 0.31 percent.

FIGURE 1. The normalized first three dominant EOFs extracted from the IRI-2007 empirical model.

Once the modeling approach has been constructed, the following task is to estimate the coefficients. Considering the potential real-time applications, a Kalman filter is employed to solve the TEC observation equation. To be specific, the following settings are used. The correlation time is set to five minutes, which correspond to the WAAS update interval for ionospheric grid points. The uncertainty of the dynamic model, 0.008 TECU2/second, is chosen to characterize the potential rapid change of the ionosphere.

Finally, the estimated coefficients provided by the Kalman filter are then used to reconstruct the electron density field.

Testing the Approach

In this section, we report on tests of the 3D UNB-IMT and compare its performance with that of the 3D SH approach. Because of the advantages of sensitivity of 2D UNB-IMT, especially with the single-station processing strategy, it is expected that this technique will help in better capturing localized ionospheric structures above small regional networks or above a single standalone station compared to the 3D SH approach. Additional benefits may be expected for disturbed ionospheric conditions.

For assessing the two modeling techniques, a small regional network of four IGS reference stations located from geographic latitude 39.0° N to 48.1° N and longitude 66.7° W to 77.6° W was chosen to perform single-station and multi-station (network) processing. The stations are GODZ in Greenbelt, Maryland; UNBJ and FRDN in Fredericton, New Brunswick; and VALD in Val d’Or, Quebec. Figure 2 shows the locations of the reference stations chosen for the modeling. The dual-frequency GPS data used for the tests was obtained from October 13–25 (day of year (doy) 286–298) in 2011 with the sampling time interval of 30 seconds. The corresponding values of the interplanetary magnetic field Bz component; the planetary geomagnetic index, Kp; the auroral electrojet index, AE; and the disturbance storm-time index, Dst on these days are shown in FIGURE 3. It is seen that a severe ionospheric storm triggered by a coronal mass ejection from the sun occurred late on October 24 (doy 297), 2011, and continued through the entire day of October 25 (doy 298), 2011. The other days seem relatively quiet. Thus, we chose October 16, 2011, as a typical day with quiet ionospheric conditions and October 25, 2011, as a typical day with disturbed ionospheric conditions in the following tests. The performance of both methods (3D UNB-IMT and SH model) with the two processing scenarios will be compared by analyzing the post-fit residuals and TEC of the state estimation process for both quiet and disturbed ionospheric conditions.

FIGURE 2. The network of the four stations used in the evaluation procedures.

All four reference stations in the small network have the ability to provide both C/A- and P-code pseudorange measurements. In our tests, the P-code observable is used to extract TEC through leveling the corresponding carrier-phase measurements. We used a 15°-elevation-angle cut-off in our study.

Single Station Experiment. The estimated parameters of 2D and 3D UNB-IMT have different physical meanings due to the different modeling strategies. In theory, the 3D UNB-IMT can reproduce the electron densities for any location (horizontal and vertical) at any epoch. Figure 4 shows an example of the electron density profile produced by the linear 3D UNB-IMT in the zenith direction of station FRDN at 12:00 UT on October 16 (doy 289), 2011. Therefore, we will have to integrate electron densities into TEC for the 3D UNB-IMT modeling results if we want to compare how the two approaches have modeled the ionosphere side by side. For the purpose of sensitivity comparison, the results from 2D and 3D UNB-IMT are compared in terms of post-fit residuals as well as time series of estimated vTEC in the single-station processing scenario. As discussed above, we use the GPS data from station FRDN only for October 16 and 25, 2011, in this subsection. The post-fit residuals are calculated as the difference between the measured and estimated biased sTEC.

FIGURE 4. The electron density profile produced by linear 3D UNB-IMT overhead FRDN at 12:00 (UT) on October 16 (doy 289) in 2011.

From the top to bottom panels, Figure 5 shows the estimated vTEC in the zenith direction over the station, post-fit residuals, estimated satellite and receiver DCBs, and unbiased sTEC with respect to local mean solar time series obtained with linear 2D (left-hand panels) and 3D (right-hand panels) UNB-IMT approaches respectively. We use a different color for each satellite to see individual improvement of satellites in terms of post-fit residuals, estimated DCB, and unbiased sTEC. As for the potential improvement of 3D UNB-IMT, we supposed, if the 2D model with single-shell assumption does not depict the variability of the ionosphere quite well (especially the vertical variability of the ionosphere), we should expect to see an improvement from the 3D model in terms of post-fit residuals. As seen in this figure, the 3D UNB-IMT improves the results in terms of post-fit residuals. The means and standard deviations of the residuals with the 2D and 3D UNB-IMT are shown in Table 1.

FIGURE 5. Sensitivity test (the panels from the top to the bottom correspond to: estimated vertical TEC, post-fit residuals, satellite and receiver DCB, slant TEC with respect to local time) between linear 2D (the left-hand panels) and 3D (the right-hand panels) models at FRDN on October 16 (doy 289) in 2011.

TABLE 1. The means and standard deviations of the residuals under the quiet (Q, October 16, 2011) and disturbed or storm (S, October 25, 2011) ionospheric conditions with linear (L) and quadratic (Q) modeling approaches. Units = TECU.

The 3D UNB-IMT with three times as many parameters is allowed to “accommodate” more (vertical) variations of the ionosphere. The benefits are also manifest in the improvement of the estimated vTEC and estimated satellite and receiver DCBs. In terms of estimated vTEC, the smooth variation of TEC may be expected at mid-latitudes during quiet ionospheric conditions without any ionospheric anomaly. The unmodeled variation of TEC in 2D UNB-IMT seen in the post-fit residuals is also manifest as “artificial small jumps” in the vTEC panel. In other words, the 3D UNB-IMT is able to better represent the measurements from low-elevation-angle satellites owing to the EOFs replacing the mapping function. It is the typical case when a satellite comes into or goes out of view of the receiver. The estimated DCBs are relatively constant over the entire day. But it is also found from the estimated DCBs that the results from 2D UNB-IMT have slightly more variability. Both effects seem to be related to the unmodeled errors. The post-fit residuals in the 3D UNB-IMT are closer to the zero mean Gaussian distribution.

Then, we further evaluated the performance of 2D and 3D UNB-IMT under significantly disturbed conditions. Figure 6 shows the results with the same modeling strategies as demonstrated in Figure 5 but on October 25, 2011. Similar conclusions can be drawn from Figure 6, where better results in terms of post-fit residuals are obtained with 3D UNB-IMT (Table 1). In terms of estimated vTEC, the results from both strategies under the disturbed conditions look more irregular than those under the quiet conditions and deviate a little from the sine-wave-like daily variation. Some actual variation of the ionosphere during disturbed conditions may be captured and correctly illustrated as the bumps for both approaches. Furthermore, the unmodeled errors may also be explained as artificial small jumps/bumps in vTEC curves (revealed by the magnitude of post-fit residuals). It is seen that 3D linear UNB-IMT explains more variation of the ionosphere than 2D linear UNB-IMT. However, some residual unmodeled errors may still exist with the 3D model.

FIGURE 6. Sensitivity test (the panels from the top to the bottom correspond to: estimated vertical TEC, residuals, satellite and receiver DCB, slant TEC with respect to local time) between linear 2D (the left-hand panels) and 3D (the right-hand panels) models at FRDN on October 25 (doy 298) in 2011.

As concluded by other investigators, a higher order model could explain more spatial (non-linear) variations of the ionosphere, especially for geomagnetic storm conditions. The results with 2D and 3D quadratic UNB-IMT approaches are shown in Figure 7. In the post-fit residual panels, it can be seen that the residuals with 3D quadratic UNB-IMT are mostly within ±2 TECU except for several small spikes that happened between 0:00 and 4:00 local mean solar time and reflect that not all the electron density variations had been correctly represented by the model used. But it is clear that the 3D quadratic UNB-IMT can significantly improve the modeling precision compared to the 2D quadratic/linear UNB-IMT and 3D linear UNB-IMT. The magnitude of the post-fit residuals shown in this panel is even comparable with the results for the quiet condition shown in Figure 5. In terms of vTEC, a few spurious spikes are occasionally found when processing the data from the four stations with the 3D quadratic model and single-station processing strategy. Other data sources, such as data from incoherent backscatter measurements, may be needed to confirm if the spikes are caused by the instability of the model or actual ionospheric structures. Still, the vTEC curves with 3D quadratic UNB-IMT look smoother than 2D UNB-IMT. In terms of estimated DCBs, it is found that the results with 3D quadratic UNB-IMT approach exhibit relatively fewer perturbations than the other three approaches tested.

FIGURE 7. Sensitivity test (the panels from the top to the bottom correspond to: estimated vertical TEC, residuals, satellite and receiver DCB, slant TEC with respect to local time) between quadratic 2D (the left-hand panels) and 3D (the right-hand panels) models at FRDN on October 25 (doy 298) in 2011.

As we found for the 2D modeling approaches, the single thin-shell assumption with a fixed ionospheric shell height may introduce additional modeling errors. That is mainly because the layer with highest electron density (F2 layer) is not always located at a fixed height. Especially in disturbed ionospheric conditions, such as the case shown in Figures 6 and 7, the layer height would change significantly. Some methods have been proposed and tested with the help of more reliable “true” heights from other resources, such as ionosondes. However, due to the limited number of the instruments deployed and limited information provided (only information from overhead), the applications with these methods would have to be limited to the specific area covered by stations or networks equipped with the instruments. In addition, as to real-time application, the data processing time delay of ionosondes might be another technical issue these methods have to face. Compared with these methods, one benefit of the 3D UNB-IMT is its potential for real-time application for any size of network. Another benefit is its vertical modeling capability to depict vertical variation of electron density so the improved results would also be expected for disturbed ionospheric conditions. It is clearly seen from Figures 6 and 7 that the lowest vTECs around 4:00 LT reach down to 0 TECU with the 2D linear/quatratic UNB-IMT, which are considered as unphysical results. It is confirmed that small biases still exist in the results with the 2D model likely due to the improper shell height chosen (fixed at 350 km for the results shown in this article).

Multi-Station Experiment. When using the modeling scheme for a network solution, we will generally have two possible processing scenarios. One is processing the data of all the stations as a batch, and the other is processing station by station (or baseline by baseline).

The advantages and disadvantages of the batch process can be summarized as follows. It has more redundancies in the Kalman filter to estimate a more stable and reliable set of satellite and receiver DCBs. Due to more measurements as an input (state) of the Kalman filter, the convergence time would be shorter in terms of the estimated DCBs. It would be of benefit for real-time applications if we have limited a priori information about the estimated ionospheric parameters and/or DCBs. However, the batch solution seems to be less sensitive to localized information content than the station-by-station solution. The overall effect of the batch solution is smoothing over the network, reducing the size of some small perturbations. Theoretically, localized measurements should not have significant influence on the estimated state across an extended area or even the entire globe. In other words, the batch solution may be beneficial for relatively small local-area networks, but may not be ideally suited for networks as large as wide-area ones. Another straightforward disadvantage of the batch process is its relatively longer processing time, which might be a downside if it is used for real-time applications.

In the multi-station experiment, we tested the 3D UNB- IMT with a small regional network of four IGS reference stations (Figure 2) to investigate its performance with localized ionospheric variations. We performed tests with two scenarios: batch and station-by-station. Due to space restrictions, we cannot thoroughly report the results we obtained here. Please see the conference paper listed in Further Reading for the full details. Overall, the results we obtained in terms of post-processing residuals were similar to those in the single station experiment. We also found that the 3D UNB-IMT with EOFs seems to be able to better model the measurements with low elevation angles than the 2D UNB-IMT with a mapping function.

Comparing 3D UNB-IMT with SH Model. We have compared the results using the batch processing strategy with those from the SH model. The reason for this approach is that we intended to compare the results of the two processing strategies (UNB-IMT and SH) with identical conditions. That is, both methods processed the data using a batch scheme and estimated both ionospheric parameters and DCBs simultaneously, instead of using some other source or processed results. Therefore, in this case, we can compare the results side by side and evaluate the effectiveness of the estimated ionospheric parameters.

Based on the data from the network of the four stations, the sensitivity of the SH models is lower than that of 3D UNB-IMT, although the number of ionospheric parameters of the SH models is comparable or even larger than that of 3D UNB-IMT. In other words, the ionospheric parameters in 3D UNB-IMT to describe the variability of the ionosphere are more effective and meaningful to such a network scale than those in the 3D SH model.

Given the nature of its basis functions, the SH model is an excellent tool for global modeling, but it has some shortcomings for localized variability modeling. As to larger regional networks with longer baselines, such as those used for WAAS, which covers North America, the difference of the sensitivities between the batch and the station-by-station solutions should be larger than the results we have obtained. However, we cannot conclude that the sensitivity of 3D UNB-IMT is better than that of the 3D SH model with the batch processing strategy for such large regional networks before more tests are conducted. Still, it is clearly seen in our tests that the 3D SH model is not always ideal for regional networks in terms of sensitivity.

We reached similar conclusions for October 25, 2011, where the residuals spread more widely compared with quiet-condition residuals. In the storm conditions, the residuals of the quadratic 3D UNB-IMT spread relatively less than those of other modeling strategies. This is especially the case for the several hours at the beginning of the day, which corresponds to the peak of the Dst and Kp indices shown in Figure 3. The quadratic 3D UNB-IMT seems to have the capacity to handle the ionospheric spatial and temporal variation even during severe storm conditions.

FIGURE 3. Interplanetary magnetic field Bz component, Kp index, AE index, and Dst index during October 13–25 (doy 286–298) in 2011; nT = nanoteslas (Data from World Data Center for Geomagnetism, Kyoto and Goddard Space Flight Center Space Physics Data Facility).

Repeatability of Estimated DCBs. The DCBs not only have influence on the quality (accuracy) of the vTEC estimation, but their repeatability can also provide information to evaluate ionospheric models. This implies that the ionospheric models that have the capability to estimate/eliminate more accurate DCBs, independent of ionospheric variability, are preferable. We carried out a number of tests to evaluate the repeatability of estimated DCB values using the 2D and 3D UNB-IMT approaches as well as the 3D SH technique under both quiet and disturbed ionospheric conditions. For quiet ionospheric conditions, the performance of all the tested models looks comparable, although the quadratic 3D UNB-IMT performs slightly better than the others. As to the disturbed conditions, the quadratic 2D/3D UNB-IMT seems be able to provide more stable DCBs than the other models. However, the improvement of the extension from 2D to 3D is slight for the quadratic models, although it is significant for the linear models. The performance of the 3D SH model looks fairly poor compared to 3D UNB-IMT for regional modeling. Consult the conference paper for further details.

Conclusions and Future Research

In the work described in this article, we extended the UNB-IMT from 2D to 3D and compared the performance between them in station-by-station and batch processing scenarios for both quiet and storm ionospheric conditions. We used the data from a small regional network of dual-frequency GPS receivers. The DCBs and ionospheric delays were estimated at the same time by a Kalman filter. The newly developed approach was evaluated by analyzing the post-fit residuals, TEC of the state estimation process, and the repeatability of estimates of DCBs.

In the single-station processing, the improvement of 3D UNB-IMT has been demonstrated in both quiet and disturbed ionospheric conditions in terms of post-fit residuals. The 3D UNB-IMT with more parameters allows the depiction of more complex (vertical) variability of the ionosphere. The 3D UNB-IMT is able to better deal with the measurements from low-elevation-angle satellites owing to EOFs replacing the mapping function. The artificial jumps with 2D UNB-IMT when satellites come into or go out of view of the receiver have been properly handled by the 3D UNB-IMT. In addition, the time series of estimated DCBs with 3D UNB-IMT exhibit less perturbation than the results with 2D UNB-IMT.

As to the multi-station (network) processing, it is confirmed that the station-by-station solution is more sensitive to localized information than the batch solution. Based on the results from our research, station-by-station processing with 3D UNB-IMT is suggested to increase chances to catch localized ionospheric structures.

The repeatability of estimated DCBs was investigated as another indicator to evaluate the viability ofionospheric models.

Before the 3D UNB-IMT is tested in the positioning domain for single-frequency positioning, it is worth validating the model with other data sources. In addition, the potential benefits of 3D UNB-IMT during extremely disturbed ionospheric conditions is worth investigating further.

Acknowledgments

We would like to thank the IGS and the Crustal Dynamics Data Information System for providing the GPS data, and we acknowledge the financial contribution of the Natural Sciences and Engineering Research Council of Canada for supporting the first and last authors. This article is based on the paper “Eliminating Potential Errors Caused by the Thin Shell Assumption: An Extended 3D UNB Ionospheric Modelling Technique” presented at the 26th International Technical Meeting of the Satellite Division of The Institute of Navigation, Nashville, Tennessee, September 16–20, 2013.

WEI ZHANG received his M.Sc. degree in space science in 2009 from the School of Earth and Space Science of Peking University, China. He is currently an M.Sc.E. student in the Department of Geodesy and Geomatics Engineering at University of New Brunswick (UNB) under the supervision of Dr. Richard B. Langley.

ATTILA KOMJATHY is a principal investigator at the California Institute of Technology Jet Propulsion Laboratory and an adjunct professor at UNB, specializing in remote sensing techniques using GPS. He received his Ph.D. from the Department of Geodesy and Geomatics Engineering of UNB in 1997.

SIMON BANVILLE works for the Geodetic Survey Division of Natural Resources Canada on real-time precise point positioning (PPP) using global navigation satellite systems. He is also in the process of completing his Ph.D. degree at UNB under the supervision of Dr. Langley.

FURTHER READING

• Authors’ Conference Paper

“Eliminating Potential Errors Caused by the Thin Shell Approximation: An Extended 3D UNB Ionospheric Modelling Technique” by W. Zhang, R.B. Langley, A. Komjathy, and S. Banville in Proceedings of ION GNSS+ 2013, the 26th International Technical Meeting of the Satellite Division of The Institute of Navigation, Nashville, Tennessee, September 16–20, 2013, pp. 2447–2462.

• 2D Ionosphere Modeling

“SBAS Ionospheric Modeling with the Quadratic Approach: Reducing the Risks” by H. Rho, R. Langley, and A. Komjathy in Proceedings of ION GNSS 2005, the 18th International Technical Meeting of the Satellite Division of The Institute of Navigation, Long Beach, California, September 13–16, 2005, pp. 723–734.

Global Ionospheric Total Electron Content Mapping Using the Global Positioning System by A. Komjathy, Ph.D. dissertation, Technical Report No. 188, Department of Geodesy and Geomatics Engineering, University of New Brunswick, Fredericton, New Brunswick, Canada, 1997.

“Improvement of a Global Ionospheric Model to Provide Ionospheric Range Error Corrections for Single-frequency GPS Users” by A. Komjathy and R. Langley in Proceedings of the 52nd Annual Meeting of The Institute of Navigation, Cambridge, Massachusetts, January 22–24, 1996, pp. 557–566.

• 3D (4D) Ionosphere Modeling

“Comparison of 4D Tomographic Mapping Versus Thin-shell Approximation for Ionospheric Delay Corrections for Single-frequency GPS Receivers over North America” by D.J. Allain and C.N. Mitchell in GPS Solutions, Vol. 14, No. 3, 2009, pp. 279–291, doi: 10.1007/s10291-009-0153-0.

“Regional 4-D modeling of the Ionospheric Electron Density” by M. Schmidt, D. Bilitza, C. Shum, and C. Zeilhofer in Advances in Space Research, Vol. 42, No. 4, 2008, pp. 782–790, doi: 10.1016/j.asr.2007.02.050.

“History, Current State, and Future Directions of Ionospheric Imaging” by G.S. Bust and C.N. Mitchell in Reviews of Geophysics, Vol. 46, No. 1, RG1003, March 2008, doi: 10.1029/2006RG000212.

“Development of the Global Assimilative Ionospheric Model” by C. Wang, G. Hajj, X. Pi, I.G. Rosen, and B. Wilson in Radio Science, Vol. 39, No. 1, RS1S06, February 2004, doi: 10.1029/2002RS002854.

Contributions to the 3D Ionospheric Sounding with GPS Data by M. García-Fernández, Ph.D. dissertation, Research Group of Astronomy and Geomatics, Universitat Politècnica de Catalunya, Barcelona, Spain, 2004. Available online in three parts:

http://www.tesisenred.net/bitstream/handle/10803/7015/01Mgf01de03.pdf?sequence=1

http://www.tesisenred.net/bitstream/handle/10803/7015/01Mgf01de03.pdf?sequence=2

http://www.tesisenred.net/bitstream/handle/10803/7015/01Mgf01de03.pdf?sequence=3.

• Ionospheric Reference Models

“The NeQuick Model Genesis, Uses and Evolution” by S.M. Radicella in Annals of Geophysics, Vol. 52, No. 3/4, June/August 2009, pp. 417–422, doi: 10.4401/ag-4597.

“International Reference Ionosphere 2007: Improvements and New Parameters” by D. Bilitza and B. Reinisch in Advances in Space Research, Vol. 42, No. 4, 2008, pp. 599–609, doi: 10.1016/j.asr.2007.07.048.

• Space Weather and the Ionosphere

“GNSS and the Ionosphere: What’s in Store for the Next Solar Maximum” by A.B.O. Jensen and C. Mitchell in GPS World, Vol. 22, No. 2, February 2011, pp. 40–48.

“Space Weather: Monitoring the Ionosphere with GPS” by A. Coster, J. Foster, and P. Erickson in GPS World, Vol. 14, No. 5, May 2003, pp. 42–49.

“GPS, the Ionosphere, and the Solar Maximum” by R.B. Langley in GPS World, Vol. 11, No. 7, July 2000, pp. 44–49.

• Empirical Orthogonal Functions

“Empirical Orthogonal Functions and Related Techniques in Atmospheric Science: A Review” by A. Hannachi, I.T. Jolliffe, and D.B. Stephenson in International Journal of Climatology, Vol. 27, No. 9, July 2007, pp. 1119–1152, doi: 10.1002/joc.1499.

“Empirical Orthogonal Functions: The Medium is the Message” by A.H. Monahan, J.C. Fyfe, M.H.P. Ambaum, D.B. Stephenson, and G.R. North in Journal of Climate, Vol. 22, No. 24, December 2009, pp. 6501–6514, doi: 10.1175/2009JCLI3062.1.

A Manual for EOF and SVD Analyses of Climatic Data by H. Bjornsson and S. Venegas, Report No. 97-1, Department of Atmospheric and Oceanic Sciences and Centre for Climate and Global Change Research, McGill University, Montreal, February 1997.
February 1, 2014
Innovation: The Devil Is in the Details

Looking Closely at Received GPS Carrier Phase

By Johnathan York, Jon Little, and David Munton

The stability of a received GPS signal determines how well the receiver can track the signal and the accuracy of the positioning results it provides. While the satellites use a very stable oscillator and modulation system to generate their signals, just how stable are the resulting phase-modulated carriers? In particular, do received signals always conform to the published system specifications? In this month’s column we take a look at a specially designed receiver for analyzing GPS carrier phase and some of the interesting results that have been obtained.

INNOVATION INSIGHTS by Richard Langley

A RADIO WAVE, OR ANY ELECTROMAGNETIC WAVE FOR THAT MATTER, may be generally characterized by four parameters: amplitude, frequency, phase, and polarization. If the values of amplitude, frequency, and polarization remain constant, then the wave is a pure oscillation or “tone” and can be represented as a sine wave.

An unvarying tone doesn’t convey any information. However, the wave can be modulated by varying one or more of its characteristic parameters in a controlled fashion. In this way information, whether it be audio, images, or data, can be transmitted from one place to another. The sine wave is therefore referred to as a “carrier” (of the modulation). A continuous wave is a wave that is not interrupted.

Of course, radio waves are not only used for communicating. They’re also used for navigation, radar, and many other purposes including the jamming of other radio signals. The modulating signal may either be continuously varying (analog) or have a fixed number of values of one or more of the parameters (digital) — two values in the case of binary modulation.

Amplitude modulation is commonly used for broadcasting and communications. If a continuous wave is interrupted by keying the transmitter on and off using a code of some kind, such as Morse code, information can be sent. For speech and music transmission, an audio waveform is modulated onto the carrier.

Frequency modulation is used for very high frequency (VHF) high-fidelity broadcasts and for communications in the VHF and ultra-high-frequency ranges of the radio spectrum. The instantaneous carrier frequency changes with the frequency and amplitude of the modulating waveform.

Phase modulation is typically used for data transmissions and, as we know, this is how the pseudorandom noise codes and the navigation message modulate the signal carriers of GPS and other global navigation satellite systems. (While the polarization of a wave can be modulated to transmit information, this is not very common.) The stability of a received GPS signal — both the carrier and its modulations — determines, in part, how well the receiver can track the signal and the accuracy of the positioning results it provides.

While the satellites use a very stable oscillator and modulation system to generate their signals, just how stable are the resulting phase-modulated carriers? In particular, do received signals always conform to the published system specifications? In this month’s column we take a look at a specially designed receiver for analyzing GPS carrier phase and some of the interesting results that have been obtained.

“Innovation” features discussions about advances in GPS technology, its applications, and the fundamentals of GPS positioning. The column is coordinated by Richard Langley, Department of Geodesy and Geomatics Engineering, University of New Brunswick.

By Johnathan York, Jon Little, and David Munton

All global navigation satellite systems (GNSS) rely on well-defined data messages modulated onto stable carrier signals. The transmission of signals that adhere to published interface specifications (ISs) is what permits a GPS or GLONASS signal to be transmitted from a satellite and to be decoded at our receiver. This process is one that most of us never need to consider, and is part of the background magic that make GNSS so powerful.

Still, signals are generated and received by real hardware — hardware that can be subject to the harsh space environment or a challenging ground environment. And once these signals are generated, they propagate to the user along a path through a dynamic medium that includes the ionosphere — a dilute plasma that introduces a well-known time-delay and phase change into the signal. The net result is is an effect on the signal that depends on both time and space.

An interesting question is the following: How do we know that the signal we plan to send (as documented in an IS) is actually the signal that we receive? A pragmatic answer is that GNSS positioning works. If there is a difference between the IS-defined signal and the received signal, the impact is not seen by most users. Another answer is that satellite vendors test (and then test again) their equipment prior to launch, providing a high level of certainty that the ISs are being adhered too. In this article, we will describe our work in providing a third way of answering the question — by monitoring signals — motivated by our desire to see “all the bits, all the time.” We have seen some interesting effects in our observations, and we will discuss our attempts to detect and characterize these effects.

Background

For our purposes, we will be looking strictly at the L1 C/A-code signal. The reasons for this will become clear shortly. The standard textbook form of the noiseless signal is

(1)

where P is the signal power, c_CA(t) is the C/A-code modulation stream of plus and minus ones, n_Nav(t) is the navigation bitstream that is modulated onto the signal, and the cos(ωt) factor represents the fundamental carrier frequency, with ω being the angular frequency (ω=2πf). For the GPS L1 signal, f = 1575.42 MHz. The GPS receiver processes this signal (in the presence of noise) into the observables (such as range, phase, or Doppler frequency shift), or the positions and velocities that we need.

One of the research problems that we find interesting is determining how to monitor the details of the signal in Equation (1) or of any other GNSS signal. Why would this be of interest? To us this is interesting because we have seen events where the signal does not behave as expected. In fact, these events were first noted by the Federal Aviation Administration’s (FAA’s) Wide Area Augmentation System (WAAS) receivers, and were later noted again in ionospheric observations. By being able to monitor the signal at a very detailed level, we can hope to gain insight into the origins of these events.

We are not alone in wanting to validate that the signal and data being produced by a GNSS receiver is valid. A standard approach to monitoring the GNSS signal would be to use an autonomous receiver method, known as receiver autonomous integrity monitoring or RAIM. However, in this approach, the integrity of the navigation solution is evaluated based on the range and phase observables produced by the receiver, and we obtain no insight into the behavior of the actual signal — only the receiver’s behavior in processing the received signals. Another option is to directly observe each satellite’s signal using a high-gain antenna. This approach provides significant insight into the behavior of the signal but is expensive and is really only effective on one satellite at a time. A system, which is close in spirit to our approach, is the Ohio University GPS Anomalous Event Monitor (GAEM). GAEM consists of two high-quality commercial receivers, which serve as independent triggers for an RF capture system. When the receivers detect an anomaly, the RF capture system is able to provide 20 seconds of raw RF data for study.

Using an Inexpensive Software Receiver

The observations we will discuss in the rest of this paper were made using what we term the Global Navigation Satellite System Complex Ambiguity Function receiver, or GCAF. The GCAF is a prototype receiver, and is well suited to some of the detailed analysis we have described.

Briefly, the GCAF receiver is a single-channel, single-frequency (L1) GPS receiver, which uses firmware installed on a field programmable gate array (FPGA) to process the incoming GPS signal. FIGURE 1 is a labeled photograph of the GCAF. RF down-conversion occurs in the module at lower left. The down-converted signal is passed to an FPGA-based software receiver, shown at lower right. All of the processing to produce the complex correlation curves is done in the software receiver. The aggregator, shown at upper right, simply provides an Ethernet interface to the outside.

FIGURE 1. The GCAF receiver.

The incoming signal is correlated against a replica of the expected L1 C/A-code signal, generating samples of the correlation curve. The difference between the GCAF and many standard commercial GPS receivers is that the GCAF samples the C/A-code correlation curve at 512 points (lags) at a 1-kHz rate. Each correlation sample is complex, consisting of in-phase (I) and quadrature (Q) components, with the software that processes the receiver raw data designed to maintain the signal in the I-component, and noise in the Q-component. As a result, the GCAF engine not only tracks the signal where it is expected to appear, but also at nearby offset phases and Doppler shifts simultaneously, and this ability substantially eliminates dependence on the tracking loop behavior and allows the observation of the characteristics of the received signal, rather than inferring them from observations of tracking loop behavior. See the sidebar, for more details on the receiver’s operation.

Since the GCAF provides access to the high-rate complex correlation values, we can “decode” the navigation modulation sequence, n_Nav(t), from the incident signal by tracking the correlation peak phase and watching for phase changes. These phase changes correspond to distinct changes in the carrier phase. FIGURE 2 shows results from measurements collected with the GCAF while observing space vehicle number (SVN) 26 / pseudorandom noise code number (PRN) 26 on August 22, 2009. The top plot shows the amplitude of the in-phase component of the incident signal in blue, and that of the quadrature component in red. The amplitude is in arbitrary units, while the time along the bottom is in milliseconds–so the entire snapshot is only 0.6 seconds long.

FIGURE 2. Amplitude and phase of the detrended L1 C/A-code carrier of SVN26 (PRN26) recorded on August 22, 2009, at 10:16:30 GPS Time.

These results in Figure 2 are as we expect, with the dominant energy appearing in the I-component. Clearly visible in the I-component is the navigation bitstream, which appears as a series of 180° phase changes in the carrier signal (hence changing the sign of the amplitude). The lower plot in Figure 2 shows the results of a “squaring” detector applied to the complex signal. Effectively this doubles any phase changes, since (e^jφ)² = e^j(2φ). This nicely converts the navigation bitstream transitions to 2 × 180°, or 360°, which removes them from the signal. (This is the approach pioneered by one of the first commercial GPS receivers, the Macrometer, for providing correlation-free L1 phase observations by removing both the code and navigation message phase transitions.) What the lower plot in Figure 2 conveys is the absence of any transitions other than the expected ones of 180°.

However, not all of our measurements are quite this typical. In some cases we observe what we term “carrier-phase signal events” (CPSEs). FIGURE 3 shows a typical example of such a CPSE taken on SVN48 (PRN21) on March 13, 2010. In the upper plot, note the sudden change in amplitude in the quadrature component near -100 milliseconds. In the lower plot, note the sudden changes in the carrier phase that occur at the same times as the amplitude changes. In this case, the squaring detector shows clear evidence of a transition that was not anticipated, and appears to be of approximately 90° and persist for approximately 175 milliseconds.

FIGURE 3. Decoded navigation bitstream on SVN45 (PRN21) taken on March 13, 2010, at 20:28:54 GPS Time.

Of course, the single-channel nature of the GCAF does not permit an unambiguous identification of where in the signal chain a CPSE is introduced. The introduction of events might occur within the satellite transmission chain, or be produced within the propagation environment, or possibly be a quirk of the receiver itself. However, the types of events we observe seem a very unlikely failure mode for the GCAF. In the case of the example shown in Figure 2, the only place in the system where a signal at the exact Doppler-shifted frequency of the SV is in the numerically controlled oscillator (NCO) of the carrier-tracking loop. The GCAF tracking loop is updated at a rate slower than many of these events and manual examination of telemetry from the tracking loops in specific instances indicates no anomalous or discontinuous tracking behavior during the events examined. If events are generated by the local receiver environment, one possible mechanism would be a small multipath source at a position so as to induce a phase shift at a greater magnitude than the direct signal. This appears unlikely as events occur at many times of day (and therefore multipath geometries), and have onsets and durations that are difficult to explain with a reasonable multipath reflector.

As a prototype instrument, the GCAF does have practical limitations. One of these limitations is that observations are divided into 5-minute intervals, at which point the signal is reacquired and data collected for another 5-minute interval. This is an operational limitation, which serves to improve robustness and bound individual output file sizes to 1 gigabyte each, and as a result, limits the durations of the CPSE that we can observe.

Event Detection

The simple squaring detector discussed above is not sufficient to provide a robust detection mechanism for the type of CPSEs we might see. In fact, we wanted a metric that would not rely on a pre-definition of what we might see in the signal, but which would flag changes in signal phase that might be interesting. To develop this metric, we borrowed ideas from the field of metrology, specifically work that characterizes noise types in oscillators. We ended up focusing on the modified Allan variance. While we will not detail the derivation of our metric here, we will discuss the results.

The basic idea is to consider the phase, ϕ, of the GPS signal, averaged over sequential periods of duration τ. We choose τ to satisfy τ > 1 millisecond, since this is the basic chipping period of the L1 C/A-code signal. For the n-th period, τ, we denote this averaged phase by <ϕ_n>. By considering the impact of noise, specifically receiver thermal noise and clock stability, we can formulate a probabilistic bound of the form:

(2)

The interpretation of this result is that for a given averaging period τ the interval-to-interval variation in the average phase should never be too large. The right-hand side of Equation (2) provides a threshold for the phase variations over three consecutive periods, and is determined by the receiver thermal noise and clock stability. This bound, which is probabilistic in nature, applies with a false alarm rate of once in 10 years. If the metric exceeds this threshold, we declare that a phase event may have occurred within the three intervals.

There is still the practical question of what averaging intervals τ need to be chosen. We have chosen to use a discrete set of τ that range from a few milliseconds to several seconds. This enables us to identify CPSEs that might occur rapidly (that is, at millisecond levels) or more slowly (at second levels). FIGURE 4 provides an example of the metric response to three consecutive CPSEs that are associated with SVN48 (PRN07). The upper plot shows the results of the squaring detector applied to the phase. Clearly evident are three rapid phase changes of about 20°. The next plot shows the result of the detection metric, which shows three double peaks in the vicinity of the phase changes. The third plot shows the I- (blue) and Q- (green) signal components. The bottom plot shows the NCO offset, which is a useful diagnostic.

FIGURE 4. A CPSE observed on SVN48 (PRN07) on September 15, 2010, at 19:21:42 GPS Time. (Click to enlarge.)

Observations of Signal Events

The examples we have shown so far reflect what we refer to as two-sided discontinuities; that is, a sudden change in phase, followed by a return to close to the original value. FIGURE 5 shows a similar type of CPSE, in which we only see one side of the change. We have seen this type of event quite commonly on SVN62 (PRN25). If there is a return to the original phase, it may be beyond our observation period. Note that the apparent slope in Figure 5 is an artifact of a linear detrending process acting across the discontinuity. FIGURE 6 shows an example of a different type of CPSE that we occasionally see, one in which a change in the slope of the phase occurs (corresponding to a change in frequency). The figure shows a single inflection in the phase rather than a rapid change in the phase value.

FIGURE 5. A CPSE observed on SVN62 (PRN25) on January 16, 2011, at 16:26:03 GPS Time with a magnitude of about 40°. (Image: Authors)

FIGURE 6. A CPSE observed on SVN38 (PRN08) on September 29, 2009, at 18:26:20 GPS Time. (Click to enlarge.)

Over the entire GPS constellation, we see events with rapid phase changes most frequently associated with the signals from three SVNs: 45 (an original Block IIR satellite), 48 (a Block IIR-M satellite), and 62 (a Block IIF satellite). This is most clearly shown in FIGURE 7, which contains a histogram of the number of events with rapid phase changes we have seen, broken out by SVN. For this histogram, we have chosen to count only those events that have well-defined phase discontinuities. Other SVNs, for example SVN34 (a Block IIA satellite), will show CPSEs on occasion, but the signals from this set of three SVNs are the ones that we have come to observe most closely. Until recently, SVN62 was the newest SV, and so we have been heavily weighting our observations on this SV.

FIGURE 7. Histogram of event counts for SVNs 45, 48, and 62 (PRNs 21, 07, and 25) covering the periods from mid-2009 until mid-August 2011. (Data: Authors)

Is There an Impact on Users?

To conclude, it is worth assessing what the potential impact of signal events on user equipment might be. We first began to investigate the detailed carrier-phase structure when we learned that the FAA WAAS system found that the carrier phase from SVN45 behaved differently than the rest of the GPS constellation, and that similar effects were seen in SVN34 (PRN04) and SVN35 (PRN05). What was observed were short-duration irregularities (< 1 minute) in which the carrier phase changed rapidly. These events were noticed simultaneously across multiple receivers. These observations led to our use of the GCAF to investigate the carrier phase. It is clear that the CPSEs can have an impact on specialized equipment.

But what about more standard user equipment? Given the types of events that we have observed, particularly those in which the phase changes suddenly and by a large amount, it is natural to ask how this might impact position and navigation users. A momentary 90-degree phase shift that lasts tens to hundreds of milliseconds might have varying effects on receivers depending on the duration of the event, the design of the carrier tracking loop in the receiver, and the instantaneous noise environment at each receiver.

If the CPSE is shorter than the inverse of the receiver carrier tracking loop bandwidth, then the receiver might perceive the CPSE as a very brief loss of signal since the tracking loop will not be able to respond quickly enough. Observables formed from a second or more of raw values are likely to experience a small reduction in signal strength. As a result, short events are likely to go undetected by a traditional receiver that is primarily performing navigation.

However, CPSEs that persist longer than the inverse of the receiver carrier-tracking-loop bandwidth could be interpreted by the receiver in a variety of ways, including a combination of cycle slip(s), navigation bit polarity inversion, or rapid carrier-phase changes.

Summary

We have been engaged in a detailed examination of the GPS L1 C/A-code signal for several years. In examining the signals, we have found that there are times when the signal exhibits an unexpected transition in phase. Looking across the GPS constellation, we find that these events tend to vary by satellite, both in rate and in behavior. While the impact from these events on most user equipment is small, the fact that the behavior is unique by SV is interesting. The type of detailed signal monitoring we have described is useful in two ways: it provides a means of observing effects that might otherwise pass unnoticed, and it gives us the capability to look for events in the future that might have a more obvious impact.

Acknowledgment

This article was stimulated by our research paper “A Non-Traditional Approach to Analysis of Signal Structure Anomalies Observed in PRN 21” presented at ION GNSS 2010, the 23rd International Technical Meeting of the Satellite Division of The Institute of Navigation in Portland, Oregon, September 21–24, 2010.

Manufacturer

The GCAF receiver uses a Xilinx, Inc., Spartan-3 FPGA.

The Global Navigation Satellite System Complex Ambiguity Function Receiver

The signal from the GCAF’s antenna passes through an amplifier stage, and then to an analog front end, where the signal is downconverted from the L1 frequency, 1575.42 MHz, directly to in-phase and quadrature IF signals. The signal is then passed to a Flexible Low-power Wideband Receiver (FLWR). The FLWR is a low-cost FPGA-based digitizing receiver designed and built by the Applied Research Laboratories at the University of Texas. Notably, the FPGA implementing the C/A-code replica generation and computation of the fast numeric theoretic transform (FNT) is an inexpensive 400 kilo-gate FPGA. The receiver is a two-channel, 10-bit, direct sample receiver, operating at 100 megasamples per second. The FLWR was built to operate as part of an array of antennas, and so connects to an aggregator. In the application discussed in this article, the aggregator simply serves as an interface between the receiver and a host computer. The C/A-code replica generator and the FNT computation of the correlation functions are written as Verilog firmware and loaded onto this receiver. Command and control and data collection occur over a USB port on the aggregator board, which is connected to a local computer.

The host computer receives the time-domain correlation curves from the FPGA and stores them on disk for future processing. The time-domain correlation curve data is also processed by software in the host computer in order to provide feedback to the code and carrier local replica generators on the FPGA. In this way, the tracking loops are closed through the host computer via USB approximately every 100 milliseconds. Because the prototype GCAF provides hundreds of correlator output lags and a rapid dump period, the GCAF is able to track the peak very loosely. That is, unlike a traditional three-lag correlator, which must constantly track the correlation peak in order to produce meaningful data, the GCAF tracking loop needs remain only in the vicinity of the peak. Because the FNT-based GCAF is bit-accurate to traditional early/prompt/late correlators at each lag, there is potential to produce geodetic-quality observables in this loose tracking mode. This stands in contrast to the coarse quality typical of FFT-based loose-tracking approaches. In many cases, this property may make redundant the early/prompt/late-style correlator typically found alongside FFT-based correlators.

Specifically, our prototype implementation has a sufficient number of correlator lags and a sufficiently high dump rate such that it is necessary to remain only within ±25 microseconds of the code peak and ±50 Hz of the carrier peak. The loose-tracking capability of GCAF has interesting implications for signal quality (and anomaly) monitoring. Commercially available atomic frequency standards have time drift rates of 0.2 microseconds per month, and absolute frequency accuracies of well below 1 Hz at the GPS L1 frequency. This level of accuracy means that the GCAF can perform open-loop tracking of GNSS signals when the receiver and satellite positions are known. Open-loop tracking is very useful for anomaly diagnosis and monitoring, as it observes the signals as received from the satellite, as opposed to observing their effects on a tracking loop.

Johnathan York received a Ph.D. degree in electrical engineering from the University of Texas at Austin. He has worked at the University of Texas Applied Research Laboratories (ARL:UT) since 2001, working primarily with high-throughput real-time digital signal processing applications.

Jon Little is a senior engineering scientist at ARL:UT. He holds a B.S. degree (1988) and an M.S. degree (1990) from Auburn University, Auburn, Alabama. He has worked extensively with the design and development of GPS ground systems and receivers.

David Munton received a B.S. degree in physics from Sonoma State University in Rohnert Park, California, and a Ph.D. degree in physics from The University of Texas at Austin. He has worked as a research scientist at ARL:UT since 1993. His GNSS research interests include precise positioning and three-frequency measurement combinations.

FURTHER READING

◾ Carrier-Phase Events and Monitoring

“A Non-Traditional Approach to Analysis of Signal Structure Anomalies Observed in PRN 21” by J. Little, J. York, A. Farris, and D. Munton in Proceedings of ION GNSS 2010, the 23rd International Technical Meeting of the Satellite Division of The Institute of Navigation, Portland, Oregon, September 21–24, 2010, pp. 2190–2198.

“Carrier-Phase Anomalies Detected on SVN-48” by B.W. O’Hanlon, M.L. Psiaki, S.P. Powell, and P.M. Kintner. Jr., in GPS World, Vol. 21, No. 6, June 2010, p. 27.

“GNSS Watch Dog: A GPS Anomalous Event Monitor” by Z. Zhu, S. Gunawardena, M. Uijt de Haag, F. van Graas, and M. Braasch in Inside GNSS, Vol. 3, No. 7, Fall 2008, pp. 18–28.

◾ GCAF Receiver

“A Fast Number-theoretic Transform Approach to a GPS Receiver” by J. York, J. Little, D. Munton, and K. Barrientos in Navigation: The Journal of The Institute of Navigation, Vol 57, No. 4, Winter 2010, pp. 297–307.

“A Complex-Ambiguity Function Approach to a GPS Receiver” by J. York, J. Little, D. Munton, and K. Barrientos in Proceedings of ION GNSS 2009, the 22nd International Meeting of the Satellite Division of The Institute of Navigation, Savannah, Georgia, September 22–25, 2009, pp. 2637–2645.

◾ GPS Interface Specification

Navstar GPS Space Segment / Navigation User Interfaces, Interface Specification, IS-GPS-200 Revision E, prepared by Science Applications International Corporation, El Segundo, California, for Global Positioning System Wing, June 2010.

Global Navigation Satellite System GLONASS, Interface Control Document, Navigational Radio Signal in Bands L1, L2 (Edition 5.1), prepared by Russian Institute of Space Device Engineering, Moscow, 2008.

◾ Receiver Autonomous Integrity Monitoring

“The Integrity of GPS” by R.B. Langley in GPS World, Vol. 10, No. 3, March 1999, pp. 60–63.

◾ GPS Signal Components

“Minding Your Is and Qs” by R.B. Langley, a sidebar in “Open Source GPS–A Hardware/Software Platform for Learning GPS: Part II, Software” by C. Kelley and D. Baker in GPS World, Vol. 17, No.2, February 2006, p. 56.

◾ Modified Allen Variance

“Allan Variance and Clock Stability” by R.B. Langley, a sidebar in “New IGS Clock Products: A Global Time Transfer Assessment” by J. Ray and K. Senior in GPS World, Vol. 13, No. 11, November 2002, p. 48.

The Science of Timekeeping by D.W. Allan, N. Ashby, and C. Hodge, Agilent (formerly Hewlett-Packard) Application Note AN1289, Agilent Technologies Inc., Santa Clara, California, 1997 and 2000.

July 1, 2012
GeoMobile Innovations Announces ArcPad Boot Camp May 14/15 in Portland

GeoMobile Innovations announced that expert ArcPad Mobile GIS instructor Craig Greenwald is back for a ArcPad Bootcamp on May 14/15th in Portland Oregon.

This 2-day hands-on ArcPad 10 Bootcamp is a must for new ArcPad users or users migrating to ArcPad 10. It is also great for GIS administrators who manage and support field crews using ArcPad.

Immediately become productive with ArcPad 10’s core functions with hands-on field and office exercises. Dig into the enhanced ArcGIS Desktop data management tools and enrich your field experience with free ArcGIS Online basemaps and Bing Maps. Learn how to use ArcPad Studio to create custom toolbars, data entry forms, and task lists, tailored to your specific projects and workflows – all with no programming required.

When: May 14-15, 2011, 8:30 a.m. to 4 p.m.

Cost: $795 for 2 days – includes course materials and media to take home.

Location: Metro Regional Center in Portland, OR, 600 NE Grand Ave., Portland, OR 97232

Registration: Download more information about the ArcPad Bootcamp and a registration form.

April 6, 2012
Innovation: Digging into GPS Integrity
Charting the Evolution of Signal-in-Space Performance by Data Mining 400,000,000 Navigation Messages

By Liang Heng, Grace Xingxin Gao, Todd Walter, and Per Enge

There are four important requirements of any navigation system: accuracy, availability, continuity, and integrity. In this month’s column we take a look at one particular aspect of GPS integrity: that of the signal in space and find out how trustworthy is the satellite ephemeris and clock information in the broadcast navigation message.

INNOVATION INSIGHTS by Richard Langley

BUT THE GREATEST OF THESE IS INTEGRITY. There are four important requirements of any navigation system: accuracy, availability, continuity, and integrity.

Perhaps the most obvious navigation system requirement, accuracy describes how well a measured value agrees with a reference value, typically the true value. In the case of GPS, we might talk about the accuracy of a range measurement. A receiver actually measures a pseudorange — a biased and noisy measure of the geometric range between the receiver and the satellite. After correcting for satellite ephemeris and satellite clock errors (the primary so-called signal-in-space errors), receiver clock errors, and atmospheric effects, we can get an estimate of the geometric range. How well we account for these errors or biases, will determine the accuracy of the corrected pseudorange measurement and ultimately, the accuracy of a derived position.

A navigation system’s availability refers to its ability to provide the required function and performance within the specified coverage area at the start of an intended operation. In many cases, system availability implies signal availability, which is expressed as the percentage of time that the system’s transmitted signals are accessible for use. In addition to transmitter capability, environmental factors such as signal attenuation or blockage or the presence of interfering signals might affect availability.

Ideally, any navigation system should be continuously available to users. But, because of scheduled maintenance or unpredictable outages, a particular system may be unavailable at a certain time. Continuity, accordingly, is the ability of a navigation system to function without interruption during an intended period of operation. More specifically, it indicates the probability that the system will maintain its specified performance level for the duration of an operation, presuming system availability at the beginning of that process.

The integrity of a navigation system refers to its trustworthiness. A system might be available at the start of an operation, and we might predict its continuity at an advertised accuracy during the operation.

But what if something unexpectedly goes wrong? If some system anomaly results in unacceptable navigation accuracy, the system should detect this and warn the user. Integrity characterizes a navigation system’s ability to provide this timely warning when it fails to meet its stated accuracy. If it does not, we have an integrity failure and the possibility of conveying hazardously misleading information. GPS has built into it various checks and balances to ensure a fairly high level of integrity. However, GPS integrity failures have occasionally occurred.

In this month’s column we take a look at one particular aspect of GPS integrity: that of the signal in space and find out how trustworthy is the satellite ephemeris and clock information in the broadcast navigation message.

The Navstar Global Positioning System is so far the most widely used space-based positioning, navigation, and timing system. GPS works on the principle of trilateration, in which the measured distances from a user receiver to at least four GPS satellites in view, as well as the position and clock data for these satellites, are the prerequisites for the user receiver to fix its exact position. For most GPS Standard Positioning Service (SPS) users, real-time satellite positions and clocks are derived from ephemeris parameters and clock correction terms in navigation messages broadcast by GPS satellites. The GPS Control Segment routinely generates navigation message data on the basis of a prediction model and the measurements at more than a dozen monitor stations. The differences between the broadcast ephemerides/clocks and the truth account for signal-in-space (SIS) errors. SIS errors are usually undetectable and uncorrectable for stand-alone SPS users, and hence directly affect the positioning accuracy and integrity. Nominally, SPS users can assume that each broadcast navigation message is reliable and the user range error (URE) derived from a healthy SIS is at the meter level or even sub-meter level. In practice, unfortunately, SIS anomalies have happened occasionally and UREs of tens of meters or even more have been observed, which can result in an SPS receiver outputting a hazardously misleading position solution. Receiver autonomous integrity monitoring (RAIM) or advanced RAIM is a promising tool to protect stand-alone users from such hazards; however, most RAIM algorithms assume at most one satellite fault at a time. Knowledge about the SIS anomalies in history is very important not only for assessing the GPS SIS integrity performance but also for validating the fundamental assumption of RAIM.

A typical method for calculating SIS UREs is to compare the broadcast ephemerides/clocks with the precise, post-processed ones. Although this method is very effective in assessing the GPS SIS accuracy performance, few attempts have been made to use it to assess the GPS SIS integrity performance because broadcast ephemeris/clock data obtained from a global tracking network sometimes contain errors caused by receivers or data conversion processes and these errors usually result in false SIS anomalies. In this article, we introduce a systematic methodology to cope with this problem and screen out all the potential SIS anomalies in the past decade from when Selective Availability (SA) was turned off.

GPS SIS Integrity

The integrity of a navigation system refers — just as it does to a person — to its honesty, veracity, and trustworthiness. In the case of GPS, this includes the integrity of the ephemeris and clock data in the broadcast navigation messages. We refer to this as signal-in-space integrity.

GPS SIS URE. As indicated by the name, GPS SIS URE is the pseudorange modeling inaccuracy due to operations of the GPS ground control and the space vehicles. Specifically, SIS URE includes satellite ephemeris and clock errors, satellite antenna performance variations, and signal imperfections, but not ionospheric or tropospheric delay, multipath, or any errors due to user receivers. SIS URE is dominated by ephemeris and clock errors because antenna variations and signal imperfections are at a level of millimeters or centimeters.

In broadcast navigation messages, there is a parameter called user range accuracy (URA) that is intended to be a conservative representation of the standard deviation (1-sigma) of the URE at the worst-case location on the Earth. For example, a URA index value of 0 means that the 1-sigma URE is expected to be less than 2.4 meters, and a URA index value of 1 means that the 1-sigma URE is expected to be greater than 2.4 meters but less than 3.4 meters, and so on. In the past several years, most GPS satellites have a URA index value of 0. A nominal URA value, in meters, can be computed as X = 2^(1+N/2), where N is the index value, for index values of 6 or less. For 6 < N < 15, X = 2^(N-2).

GPS SPS SIS Integrity. In the SPS Performance Standard (PS), as well as the latest version of the Interface Specification (IS-GPS-200E), the GPS SPS SIS URE integrity standard assures that for any healthy SIS, there is an up-to-10−5 probability over any hour of the URE exceeding the not-to-exceed (NTE) tolerance without a timely alert during normal operation. The NTE tolerance is currently defined to be 4.42 times the upper bound (UB) on the URA value broadcast by the satellite. Before September 2008, the NTE tolerance was defined differently, as the maximum of 30 meters and 4.42 times URA UB. The reason for the “magic” number 4.42 here is the Gaussian assumption of the URE, although this assumption may be questionable. (4.42 sigma corresponds to a probability level of 99.999 percent (1 – 10^–5)).

In this article, a GPS SPS SIS anomaly is defined as a threat of an SIS integrity failure; that is, a condition during which an SPS SIS marked healthy results in a URE exceeding the NTE tolerance. Because the definition of the NTE tolerance is different before and after September 2008, we consider both of the two NTE tolerances for the sake of completeness and consistency.

Methodology

The SIS anomalies are screened out by comparing broadcast ephemerides/clocks with precise ones. As shown in Figure 1, the whole process consists of three steps: data collecting, data cleansing, and anomaly screening.

Figure 1. Framework of the whole process. XYZB values refer to the coordinates of satellite position and satellite clock bias.

In the first step, the navigation message data files are downloaded from the International GNSS Service (IGS). In addition, two different kinds of precise ephemeris/clock data are downloaded from IGS and the National Geospatial-Intelligence Agency (NGA), respectively. The details about these data sources will be discussed in the next section.

Since each GPS satellite can be observed by many IGS stations at any instant, each navigation message is recorded redundantly. In the second step, a data-cleansing algorithm exploits the redundancy to remove the errors caused on the ground. This step distinguishes our work from that of most other researchers because the false anomalies due to corrupted data can be mostly precluded.

The last step is computing worst-case SIS UREs as well as determining potential SIS anomalies. The validated navigation messages prepared in the second step are used to propagate broadcast orbits/clocks at 15-minute intervals that coincide with the precise ones. A potential SIS anomaly is claimed when the navigation message is healthy and in its fit interval with the worst-case SIS URE exceeding the SIS URE NTE tolerance.

Data Sources

We obtained broadcast navigation message data and precise ephemeris and clock data from publicly available sources.

Broadcast Navigation Message Data. Broadcast GPS navigation message data files are available at IGS Internet sites. All the data are archived in Receiver Independent Exchange (RINEX) navigation file format, which includes not only the ephemeris/clock parameters broadcast by the satellites but also some information produced by the ground receivers, such as the pseudorandom noise (PRN) signal number and the transmission time of message (TTOM).

The IGS tracking network is made up of more than 300 volunteer stations all over the world (a map is shown in Table 1) ensuring seamless, redundant data logging. Since broadcast navigation messages are usually updated every two hours, no single station can record all navigation messages. For the ease of users, two IGS archive sites, the Crustal Dynamics Data Information System (CDDIS) and the Scripps Orbit and Permanent Array Center (SOPAC), provide two kinds of ready-to-use daily global combined broadcast navigation message data files, brdcddd0.yyn and autoddd0.yyn, respectively, where ddd is the day of year yy. Unfortunately, these files sometimes contain errors that can cause false anomalies.

Table 1. Comparison of IGS and NGA precise ephemeris/clock data.

Therefore, we devised and implemented a data-cleansing algorithm to generate the daily global combined navigation messages, which are as close as possible to the navigation messages that the satellites actually broadcast, from all available navigation message data files of all IGS stations. The data-cleansing algorithm is based on majority vote, and hence all values in our data are cross validated. Accordingly, we name our daily global combined navigation messages “validated navigation messages,” as shown in Figure 1.

Precise Ephemeris and Clock Data. Precise GPS ephemerides/clocks are generated by some organizations such as IGS and NGA that routinely post-process observation data. Precise ephemerides/clocks are regarded as “truth” because of their centimeter-level accuracy.

Table 1 shows a side-by-side comparison between IGS and NGA precise ephemeris/clock data, in which the green- and red-colored text implies pros and cons, respectively. For NGA data, the only con is that the data have been publicly available only since January 4, 2004. As a result, for the broadcast ephemerides/clocks before this date, IGS precise ephemerides/clocks are the only references. Nevertheless, care must be taken when using IGS precise ephemerides/clocks due to the following three issues.

The first issue with the IGS precise ephemerides/clocks is the relatively high rate of bad/absent data, as shown in the third row of Table 1. For a GPS constellation of 27 healthy satellites, 1.5 percent bad/absent data means no precise ephemerides or clocks for approximately 10 satellite-hours per day. This issue can result in undetected anomalies (false negatives).

The second issue is that, as shown in the fourth row of Table 1, IGS switched to IGS Time for its precise ephemeris/clock data on 22 February, 2004. The IGS clock is not synchronized to GPS Time, and the differences between the two time references may be as large as 3 meters. Fortunately, the time offsets can be extracted from the IGS clock data files. Moreover, a similar problem is that IGS precise ephemerides use a frame aligned to the International Terrestrial Reference Frame (ITRF) whereas broadcast GPS ephemerides are based on the World Geodetic System 1984 (WGS 84). The differences between ITRF and the versions of WGS 84 used since 1994 are on the order of a few centimeters, and hence a transformation is not considered necessary for the purpose of our work.

The last, but not the least important, issue with the IGS precise ephemerides is that the data are provided only for the center of mass (CoM) of the satellite. Since the broadcast ephemerides are based on the satellite antenna phase center (APC), the CoM data must be converted to the APC before being used. Both IGS and NGA provide antenna corrections for every GPS satellite. Although the IGS and the NGA CoM data highly agree with each other, the IGS satellite antenna corrections are quite different from the NGA’s, and the differences in z-offsets can be as large as 1.6 meters for some GPS satellites. The reason for these differences is mainly due to the different methods in producing the antenna corrections: the IGS antenna corrections are based on the statistics from more than 10 years of IGS data, whereas the NGA’s are probably from the calibration measurements on the ground. In order to know whose satellite antenna corrections are better, the broadcast orbits for all GPS satellites in 2009 were computed and compared with three different precise ephemerides: IGS CoM + IGS antenna corrections, IGS CoM + NGA antenna corrections, and NGA APC. Generally, the radial ephemeris error is expected to have a zero mean. However, the combination “IGS CoM + IGS antenna corrections” results in radial ephemeris errors with a non-zero mean for more than half of the GPS satellites. Therefore, the NGA antenna corrections were selected to convert the IGS CoM data to the APC.

Data Cleansing

Figure 2 shows a scenario of data cleansing. Owing to accidental bad receiver data and various hardware/software bugs, a small proportion of the navigation data files from the IGS stations have defects such as losses, duplications, inconsistencies, discrepancies, and errors. Therefore, more than just removing duplications, the generation of validated navigation messages is actually composed of two complicated steps.

Figure 2. A scenario of data cleansing: In the figure, the GPS satellite PRN32 started to transmit a new navigation message at 14:00. Receiver 1 had not observed the satellite until 14:36, and hence the TTOM in its record was 14:36. Additionally, Receiver 1 made a one-bit error in ∆n (4.22267589140 × 10-9 11823 × 2−43 π). Receiver 2 perhaps had some problems in its software: the IODC was unreported and both the toc and ∆n were written weirdly. Receiver n used an incorrect ranging code, PRN01, to despread and decode the signal of PRN32; fortunately, all the parameters except TTOM were perfectly recorded. Moreover, the three receivers interpreted URA (SV accuracy) differently. A computer equipped with our data cleansing algorithms is used to process all the data from the receivers. The receiver-caused errors are removed and the original navigation message is recovered.

First step. Suppose that we want to generate the validated navigation messages for day n. In the first step, we apply the following operations sequentially to each RINEX navigation data file from day n − 1 to day n + 1:

1) Parse the RINEX navigation file;

2) Recover least significant bit (LSB);

3) Classify URA values;

4) Remove the navigation messages not on day n;

5) Remove duplications;

6) Add all remaining navigation messages into the set O.

The reason why the data files from day n − 1 to day n + 1 are considered is that a few navigation messages around 00:00 can be included in some data files on day n − 1, and a few navigation messages around 23:59 can be included in some data files on day n + 1. The LSB recovery is used here to cope with the discrepant representations of floating-point numbers in RINEX navigation files. The URA classifier is employed to recognize and unify various representations of URA in the files. The duplication removal is applied because some stations write the same navigation messages repeatedly in one data file, which is unfavorable to the vote in the second step.

Second Step. At the end of the first step, we have a set O that includes all the navigation messages on day n. The set O still has duplications because a broadcast navigation message can be reported by many IGS stations. However, as shown in Figure 2, duplications of a broadcast navigation message may come with different errors and are not necessarily identical. Several other examples of such problems can be found in our journal paper listed in Further Reading. Fortunately, most orbital and clock parameters are seldom reported incorrectly, and even when errors happen, few stations agree on the same incorrect value. In our work, these parameters are referred to as robust parameters. On the contrary, some parameters, such as TTOM, PRN, URA and issue of data clock (IODC), are more likely to be erroneous and when errors happen, several stations may make the same mistake. These parameters are referred to as fragile parameters. The cause of the fragility is either the physical nature (for example, TTOM, PRN) or the carelessness in hardware/software implementations (for example, URA, IODC).

Majority vote is applied to all fragile parameters (except TTOM, which is determined by another algorithm described in our journal paper) under the principle that the majority is usually correct. Meanwhile, the robust parameters are utilized to identify the equivalence of two navigation messages — two navigation messages are deemed identical if and only if they agree on all the robust parameters, although their fragile parameters could be different. Therefore, the goal of duplication removal and majority vote is a set P, in which any navigation message must have at least one robust parameter different from any other and has all fragile parameters confirmed by the largest number of stations that report this navigation message.

After the operations above, we have a set P in which there are no duplicated navigation messages in terms of robust parameters and all fragile parameters are as correct as possible. A few navigation messages in P still have errors in their robust parameters. These unwanted navigation messages feature a small number of reporting stations. Finally, the navigation messages confirmed by only a few stations being discarded and the survivors are the validated broadcast navigation messages, stored in files sugldddm.yyn. For further details of our algorithms, see our journal paper.

Anomaly Screening

The validated broadcast navigation messages prepared using the algorithm described in the previous section were employed to propagate broadcast satellite orbits and clocks. For each 15-miniute epoch, t, that coincides with precise ephemerides/clocks, the latest transmitted broadcast ephemeris/clock is chosen to calculate the worst-case SIS URE – the maximum SIS URE that a user on Earth can experience.

Finally, a potential GPS SIS anomaly is claimed when all of the following conditions are fulfilled.
- The worst-case SIS URE exceeds the NTE tolerance;
- The broadcast navigation message is healthy; that is,
  - The RINEX field SV health is 0, and
  - The URA UB ≤ 48 meters;
- The broadcast navigation message is in its fit interval; that is, ∆t = t − TTOM ≤ 4 hours;
- The precise ephemeris/clock is available and healthy.
Results

A total of 397,044,414 GPS navigation messages collected by an average of 410 IGS stations from June 1, 2000 (one month after turning off SA), to August 31, 2010, have been screened. The NGA APC precise ephemerides/clocks and the IGS CoM precise ephemerides/clocks with the NGA antenna corrections were employed as the truth references. Both old and new NTE tolerances were used for determining anomalies.

Before interpreting the results, it should be noted that there are some limitations due to the data sources and the anomaly-determination criteria. First, false anomalies may be claimed because there may be some errors in the precise ephemerides/clocks or the validated navigation messages. Second, some short-lived anomalies may not show up if they happen to fall into the 15-minute gaps of the precise ephemerides/clocks. Third, some true anomalies may not be detected if the precise ephemerides/clocks are temporarily missing. The third limitation is especially significant for the results before January 3, 2004, because only the IGS precise ephemerides/clocks are available, which feature a high rate of bad/absent data. (For example, the clock anomaly of Space Vehicle Number (SVN) 23/PRN23 that occurred on January 1, 2004 is missed by our process because the IGS precise clocks for PRN23 on that day were absent.) Last but not least, users might not experience some anomalies because a satellite was not trackable at that time, or the users were notified via a Notice Advisory to Navstar Users (NANU). (A satellite may indicate that it is unhealthy through the use of non-standard code or data. The authors’ future work will include using observation data to verify the potential anomalies found in the results presented here.) Therefore, all the SIS anomalies claimed in this article are considered to be potential and under further investigation.

Potential SIS Anomalies. A total of 1,256 potential SIS anomalies were screened out under SPS PS 2008 (or 374 potential SIS anomalies under SPS PS 2001). Figure 3 shows all these anomalies in a Year-SVN plot. It can be seen that during the first year after SA was turned off, SIS anomalies occurred frequently for the whole constellation.

Figure 3. Potential SIS anomalies from June 1, 2000, to August 31, 2010. The horizontal lines depict the periods when the satellites were active (not necessarily healthy). The color of the lines indicates the satellites’ block type, as explained by the top left legend.

Moreover, 2004 is apparently a watershed: before 2004, anomalies occurred for all GPS satellites (except two satellites launched in 2003, SVN45/PRN21 and SVN56/PRN16) whereas after 2004, anomalies occurred much less frequently and more than 10 satellites have never been anomalous. Figure 4 further confirms the improving GPS SIS integrity performance in the past decade, no matter which SPS PS is considered.

Figure 4. Number of potential SIS anomalies per year. The SIS performance was improved during the past decade. There were 0 anomalies in 2009 according to SPS PS 2001 and this number is represented by 0.1 in the figure.

Therefore, it is possible to list all potential SIS anomalies from January 4, 2004, to August 31, 2010, in a compact table: Table 2. Most anomalies in the table have been confirmed by NANUs and other literature. The table reveals an important and exciting piece of information: never have two or more SIS anomalies occurred simultaneously since 2004. Accordingly, in the sense of historical GPS SIS integrity performance, it is valid for RAIM to assume at most one satellite fault at a time.

Table 2. List of potential anomalies from January 4, 2004, to August 31, 2010.

Validated Navigation Messages. For the purpose of comparison and verification, the IGS daily global combined broadcast navigation message data files brdcddd0.yyn and autoddd0.yyn were used to propagate broadcast satellite orbits and clocks as well. The NGA APC precise ephemerides/clocks were employed for the truth references. The SPS PS 2008 NTE tolerance was used for determining anomalies. The other criteria for anomaly screening that are the same as in the previous section were still applied.

All the potential SIS anomalies for 2006–2009 were found based on the three kinds of daily combined broadcast navigation messages. Table 3 shows a comparison of the total hours of the anomalies per year. It can be seen that brdcddd0.yyn and autoddd0.yyn result in approximately 11 times more false anomalies than true ones. Moreover, all potential anomalies derived from sugldddm.yyn are confirmed by brdcddd0.yyn and autoddd0.yyn, which indicates that our sugldddm.yyn does not introduce any more false anomalies than brdcddd0.yyn and autoddd0.yyn.

Table 3. Total hours of anomalies per year computed from three different kinds of daily global combined broadcast navigation messages.

Conclusion

In this article, the GPS SIS integrity performance in the past decade was assessed by comparing the broadcast ephemerides/clocks with the precise ones. Thirty potential anomalies were found. The fundamental assumption of RAIM is valid based on a review of the GPS SIS integrity performance in the past seven years.

Acknowledgments

The authors gratefully acknowledge the support of the Federal Aviation Administration. This article contains the personal comments and beliefs of the authors, and does not necessarily represent the opinion of any other person or organization.

The authors would like to thank Mr. Tom McHugh, William J. Hughes FAA Technical Center, for his valuable input to the data-cleansing algorithm. This article is based on the paper “GPS Signal-in-Space Integrity Performance Evolution in the Last Decade: Data Mining 400,000,000 Navigation Messages from a Global Network of 400 Receivers” to appear in the Institute of Electrical and Electronics Engineers (IEEE) Transactions on Aerospace and Electronic Systems..

Liang Heng is a Ph.D. candidate under the guidance of Professor Per Enge in the Department of Electrical Engineering at Stanford University.

Grace Xingxin Gao is a research associate in the GPS Research Laboratory of Stanford University.

Todd Walter is a senior research engineer in the Department of Aeronautics and Astronautics at Stanford University.

Per Enge is a professor of Aeronautics and Astronautics at Stanford University, where he is the Kleiner-Perkins, Mayfield, Sequoia Capital Professor in the School of Engineering. He directs the GPS Research Laboratory, which develops satellite navigation systems based on GPS.

FURTHER READING

• Authors’ Research Papers

“GPS Signal-in-Space Integrity Performance Evolution in the Last Decade: Data Mining 400,000,000 Navigation Messages from a Global Network of 400 Receivers” by L. Heng, G.X. Gao, T. Walter, and P. Enge in Transactions on Aerospace and Electronic Systems, the Institute of Electrical and Electronics Engineers, accepted for publication.

“GPS Signal-in-Space Anomalies in the Last Decade: Data Mining of 400,000,000 GPS Navigation messages” by L. Heng, G.X. Gao, T. Walter, and P. Enge in Proceedings of ION GNSS 2010, the 23rd International Technical Meeting of The Satellite Division of the Institute of Navigation, Portland, Oregon, September 21–24, 2010, pp. 3115–3122.

“GPS Ephemeris Error Screening and Results for 2006–2009” by L. Heng, G.X. Gao, T. Walter, and P. Enge in Proceedings of ION ITM 2010, the 2010 International Technical Meeting of the Institute of Navigation, San Diego, California, January 24–26, 2010, pp. 1014–1022.

• Earlier Work on Assessing GPS Broadcast Ephemerides and Clocks

“GPS Orbit and Clock Error Distributions” by C. Cohenour and F. van Graas in Navigation, Vol. 58, No. 1, Spring 2011, pp. 17–28.

“Statistical Characterization of GPS Signal-in-Space Errors” by L. Heng, G.X. Gao, T. Walter, and P. Enge in Proceedings of ION ITM 2011, the 2011 International Technical Meeting of the Institute of Navigation, San Diego, California, January 24–26, 2011, pp. 312–319.

“Broadcast vs. Precise GPS Ephemerides: A Historical Perspective” by D.L.M. Warren and J.F. Raquet in GPS Solutions, Vol. 7, No. 3, 2003, pp. 151–156, doi: 10.1007/s10291-003-0065-3.

“Accuracy and Consistency of Broadcast GPS Ephemeris Data” by D.C. Jefferson and Y.E. Bar-Sever in Proceedings of ION GPS-2000, the 13th International Technical Meeting of the Satellite Division of The Institute of Navigation, Salt Lake City, Utah, September 19–22, 2000, pp. 391–395.

“The GPS Broadcast Orbits: An Accuracy Analysis” by R.B. Langley, H. Jannasch, B. Peeters, and S. Bisnath, presented in Session B2.1-PSD1, New Trends in Space Geodesy at the 33rd COSPAR Scientific Assembly, Warsaw, July 16–23, 2000.

• Signal-in-Space Anomalies

“GNSS: The Present Imperfect” by D. Last in Inside GNSS, Vol. 5, No. 3, May 2010, pp. 60–64.

“Investigation of Upload Anomalies Affecting IIR Satellites in October 2007” by K. Kovach, J. Berg, and V. Lin in Proceedings of ION GNSS 2008, the 21st International Technical Meeting of the Satellite Division of The Institute of Navigation, Savannah, Georgia, September 16–19, 2008, pp. 1679–1687.

Global Positioning System (GPS) Standard Positioning Service (SPS) Performance Analysis Report No. 58, July 31, 2007, Reporting Period: 1 April – 30 June 2007.

Discrepancy Report, DR No. 55, “GPS Satellite PRN18 Anomaly Affecting SPS Performance” by N. Vary, FAA William J. Hughes Technical Center, Pomona, New Jersey, April 11, 2007.

“GPS Receiver Responses to Satellite Anomalies” by J.W. Lavrakas and D. Knezha in Proceedings of the 1999 National Technical Meeting of The Institute of Navigation, San Diego, California, January 25–27, 1999, pp. 621–626.

• GPS Integrity and Receiver Autonomous Integrity Monitoring

“Prototyping Advanced RAIM for Vertical Guidance” by J. Blanch, M.J. Choi, T. Walter, P. Enge, and K. Suzuki in Proceedings of ION GNSS 2010, the 23rd International Technical Meeting of the Satellite Division of The Institute of Navigation, Portland, Oregon, September 21–24, 2010, pp. 285–291.

“The Integrity of GPS” by R.B. Langley in GPS World, Vol. 10, No. 3, March 1999, pp. 60–63.

• International GNSS Service Ephemerides and Clocks

“On the Precision and Accuracy of IGS Orbits” by J. Griffiths and J.R. Ray in Journal of Geodesy, Vol. 83, 2009, pp. 277–287, doi: 10.1007/s00190-008-0237-6.

“The International GNSS Service: Any Questions?” by A.W. Moore in GPS World, Vol. 18, No. 1, January 2007, pp. 58–64.

International GNSS Service Central Bureau website.

• National Geospatial-Intelligence Agency Ephemerides and Clocks

“NGA’s Role in GPS” by B. Wiley, D. Craig, D. Manning, J. Novak, R. Taylor, and L. Weingarth in Proceedings of ION GNSS 2006, the 19th International Technical Meeting of the Satellite Division of The Institute of Navigation, Fort Worth, Texas, September 26–29, 2006, pp. 2111–2119.

National Geospatial-Intelligence Agency, Geoint Sciences Office, Global Positioning System Division website.

• Antenna Phase Center Corrections

“Generation of a Consistent Absolute Phase-center Correction Model for GPS Receiver and Satellite Antennas” by R. Schmid, P. Steigenberger, G. Gendt, M. Ge, and M. Rothacher in Journal of Geodesy, Vol. 81, No. 12, 2007, pp. 781–798, doi: 10.1007/s00190-007-0148-y.

“The Block IIA Satellite: Calibrating Antenna Phase Centers” by G.L. Mader and F.M. Czopek in GPS World, Vol. 13, No. 5, May 2002, pp. 40–46.

• GPS Interface and Performance Specifications

Navstar GPS Space Segment / Navigation User Interfaces, Interface Specification, IS-GPS-200 Revision E, prepared by Science Applications International Corporation, El Segundo, California, for Global Positioning System Wing, June 2010.

Global Positioning System Standard Positioning Service Performance Standard, 4th edition, by the U.S. Department of Defense, Washington, D.C., September 2008.

Global Positioning System Standard Positioning Service Performance Standard, 3rd edition, by the U.S. Department of Defense, Washington, D.C., October 2001.
November 1, 2011
Innovation: Collective Detection

Enhancing GNSS Receiver Sensitivity by Combining Signals from Multiple Satellites

By Penina Axelrad, James Donna, Megan Mitchell, and Shan Mohiuddin

A new approach to enhancing signal sensitivity combines the received signal power from multiple satellites in a direct-to-navigation solution.

INNOVATION INSIGHTS by Richard Langley

ALTHOUGH I HAVE MANAGED the Innovation column continuously since GPS World’s first issue, it wasn’t until the second issue that I authored a column article. That article, co-written with Alfred Kleusberg, was titled “The Limitations of GPS.” It discussed some of the then-current problems of GPS, including poor signal reception, loss of signal integrity, and limited positioning accuracy.

In the ensuing 20 years, both signal integrity and positioning accuracy have improved significantly. Advances in the GPS control segment’s capabilities to continuously monitor and assess signal performance, together with receiver-autonomous integrity monitoring and integrity enhancement provided by augmentation systems, have reduced worries about loss of signal integrity. The removal of Selective Availability and use of error corrections provided by augmentation systems, among other approaches, have improved positioning accuracy.

But the problem of poor reception due to weak signals is still with us. In that March/April 1990 article, we wrote “[GPS] signals propagate from the satellites to the receiver antenna along the line of sight and cannot penetrate water, soil, walls, or other obstacles very well. … In surface navigation and positioning applications, the signal can be obstructed by trees, buildings, and bridges. … [In] the inner city streets of urban areas lined with skyscrapers, the ‘visibility’ of the GPS satellites is very limited. In such areas, the signals can be obstructed for extended periods of time or even [be] continuously unavailable.”

Poor signal reception in other than open-sky environments is still a problem with conventional GPS receivers. However, extending signal integration times and using assisted-GPS techniques can give GPS some degree of capability to operate indoors and in other restricted environments, albeit typically with reduced positioning accuracy. An antenna with sufficient gain is needed and capable systems are available on the market. The pilot channels of modernized GNSS signals will also benefit signal acquisition and tracking in challenging environments.

In this month’s column, we look at a completely different approach to enhancing signal sensitivity. Rather than requiring each satellite’s signal to be acquired and tracked before it can be used in the navigation solution, the new approach — dubbed “collective detection” — combines the received signal power from multiple satellites in a direct-to-navigation-solution procedure. Besides providing a quick coarse position solution with weak signals, this approach can be used to monitor the signal environment, aid deeply-coupled GPS/inertial navigation, and assist with terrain and feature recognition.

“Innovation” features discussions about advances in GPS technology, its applications, and the fundamentals of GPS positioning. The column is coordinated by Richard Langley, Department of Geodesy and Geomatics Engineering, University of New Brunswick.

Growing interest in navigating indoors and in challenging urban environments is motivating research on techniques for weak GPS signal acquisition and tracking. The standard approach to increasing acquisition and tracking sensitivity is to lengthen the coherent integration times, which can be accomplished by using the pilot channels in the modernized GPS signals or by using assisted GPS (A-GPS) techniques. These techniques operate in the traditional framework of independent signal detection, which requires a weak signal to be acquired and tracked before it is useful for navigation. This article explores a complementary, but fundamentally different, approach that enhances signal sensitivity by combining the received power from multiple GPS satellites in a direct-to-navigation-solution algorithm. As will be discussed in the following sections, this collective detection approach has the advantage of incorporating into the navigation solution information from signals that are too weak to be acquired and tracked, and it does so with a modest amount of computation and with no required hardware changes. This technology is appropriate for any application that requires a navigation solution in a signal environment that challenges traditional acquisition techniques. Collective detection could be used to monitor the signal environment, aid deeply coupled GPS/INS during long outages, and help initiate landmark recognition in an urban environment. These examples are explained further in a subsequent section. In order to understand how the collective detection algorithm works, it is instructive to first consider the traditional approach to acquisition and tracking.

Acquisition Theory and Methods

In a typical stand-alone receiver, the acquisition algorithm assesses the signal’s correlation power in discrete bins on a grid of code delay and Doppler frequency (shift). The correlation calculations take the sampled signal from the receiver’s RF front end, mix it with a family of receiver-generated replica signals that span the grid, and sum that product to produce in-phase (I) and quadrature (Q) correlation output. The correlation power is the sum of the I and Q components, I2 + Q2. Plotting the power as a function of delay and frequency shift produces a correlogram, as shown in FIGURE 1. It should be noted that both correlation power and its square root, the correlation amplitude, are found in the GPS literature. For clarity, we will always use the correlation power to describe signal and noise values.

If a sufficiently powerful signal is present, a distinct peak appears in the correlogram bin that corresponds to the GPS signal’s code delay and Doppler frequency. If the peak power exceeds a predefined threshold based on the integration times and the expected carrier-to-noise spectral density, the signal is detected. The code delay and Doppler frequency for the peak are then passed to the tracking loops, which produce more precise measurements of delay — pseudoranges — from which the receiver’s navigation solution is calculated. When the satellite signal is attenuated, however, perhaps due to foliage or building materials, the correlation peak cannot be distinguished and the conventional approach to acquisition fails.

The sensitivity of traditional tracking algorithms is similarly limited by the restrictive practice of treating each signal independently. More advanced tracking algorithms, such as vector delay lock loops or deeply integrated filters, couple the receiver’s tracking algorithms and its navigation solution in order to take advantage of the measurement redundancy and to leverage information gained from tracking strong signals to track weak signals. The combined satellite detection approach presented in this article extends the concept of coupling to acquisition by combining the detection and navigation algorithms into one step.

Collective Detection

In the collective detection algorithm, a receiver position and clock offset grid is mapped to the individual GPS signal correlations, and the combined correlation power is evaluated on that grid instead of on the conventional independent code delay and Doppler frequency grids. The assessment of the correlation power on the position and clock offset grid leads directly to the navigation solution. The mapping, which is key to the approach, requires the receiver to have reasonably good a priori knowledge of its position, velocity, and clock offset; the GPS ephemerides; and, if necessary, a simplified ionosphere model. Given this knowledge, the algorithm defines the position and clock offset search grid centered on the assumed receiver state and generates predicted ranges and Doppler frequencies for each GPS signal, as illustrated in FIGURE 2. The mapping then relates each one of the position and clock offset grid points to a specific code delay and Doppler frequency for each GPS satellite, as illustrated in FIGURE 3. Aggregating the multiple delay/Doppler search spaces onto a single position/clock offset search space through the mapping allows the navigation algorithm to consider the total correlation power of all the signals simultaneously. The correlation power is summed over all the GPS satellites at each position/clock-offset grid point to create a position domain correlogram. The best position and clock-offset estimates are taken as the grid point that has the highest combined correlation power. This approach has the advantage of incorporating into the position/clock-offset estimate information contained in weak signals that may be undetectable individually using traditional acquisition/tracking techniques.

It should be noted that a reasonable a priori receiver state estimate restricts the size of the position and clock-offset grid such that a linear mapping, based on the standard measurement sensitivity matrix used in GPS positioning, from the individual signal correlations, is reasonable. Also, rather than attempt to align the satellite correlations precisely enough to perform coherent sums, noncoherent sums of the individual satellite correlations are used. This seems reasonable, given the uncertainties in ranging biases between satellites, differences and variability of the signal paths through the ionosphere and neutral atmosphere, and the large number of phases that would have to be aligned.

Applications

The most obvious application for collective detection is enabling a navigation fix in circumstances where degraded signals cause traditional acquisition to fail. The sweet spot of collective detection is providing a rapid but coarse position solution in a weak signal environment. The solution can be found in less time because information is evaluated cohesively across satellites. This is especially clear when the algorithm is compared to computationally intensive long integration techniques.

There are several ways that collective detection can support urban navigation. This capability benefits long endurance users who desire a moderate accuracy periodic fix for monitoring purposes. In some circumstances, the user may wish to initiate traditional tracking loops for a refined position estimate. However, if the signal environment is unfavorable at the time, this operation will waste valuable power. The collective detection response indicates the nature of the current signal environment, such as indoors or outdoors, and can inform the decision of whether to spend the power to transition to full GPS capabilities.

In urban applications, deeply integrated GPS/INS solutions tolerate GPS outages by design. However, if the outage duration is too long, the estimate uncertainty will eventually become too large to allow conclusive signal detection to be restored. Running collective detection as a background process could keep deeply integrated filters centered even in long periods of signal degradation. Because collective detection approaches the acquisition problem from a position space instead of the individual satellite line-of-sight space, it provides inherent integrity protection. In the traditional approach, acquiring a multipath signal will pollute the overall position fix. In collective detection, such signals are naturally exposed as inconsistent with the position estimate.

Another use would be to initialize landmark correlation algorithms in vision navigation. Landmark correlation associates street-level video with 3D urban models as an alternative to (GPS) absolute position and orientation updates. This technique associates landmarks observed from ground-level imagery with a database of landmarks extracted from overhead-derived 3D urban models. Having a coarse position (about 100 meters accuracy) enhances initialization and restart of the landmark correlation process. Draper Laboratory is planning to demonstrate the utility of using collective detection to enable and enhance landmark correlation techniques for urban navigation.

In all of these applications, collective detection is straightforward to implement because it simply uses the output of correlation functions already performed on GPS receivers.

Simulations and Processing

The new algorithm has been tested using live-sky and simulated data collected by a Draper Laboratory wideband data recorder. A hardware GPS signal simulator was used to simulate a stationary observer receiving 11 equally powered GPS signals that were broadcast from the satellite geometry shown in FIGURE 4. The data recorder and the signal simulator were set up in a locked-clock configuration with all of the simulator’s modeled errors set to zero. No frequency offsets should exist between the satellites and the receiver. A clock bias, however, does exist because of cable and other fixed delays between the two units. The data recorder houses a four-channel, 14-bit A/D module. It can support sample rates up to 100 MHz. For this work, it was configured to downconvert the signal to an IF of 420 kHz and to produce in-phase and quadrature samples at 10 MHz.

Results and Discussion

To combine satellites, a position domain search space is established, centered on the correct location and receiver clock bias. A grid spacing of 30 meters over a range of ± 900 meters in north and east directions, and ± 300 meters in the vertical. In the first simulated example, the correlation power for all the satellites is summed on the position grid using a single 1-millisecond integration period. In this case, the true carrier-to-noise-density ratio for each signal is 40 dB-Hz. The results are shown in FIGURE 5. The plots in the left panel show the individual signal correlations as a function of range error. The four plots in the upper-right panel show several views of the combined correlation as a function of position error. The upper-left plot in the panel shows the correlation value as a function of the magnitude of the position error. The upper-right plot shows the correlation as a function of the north-east error, the lower-left the north-down error, and the lower-right the east-down error. Notice how the shape of the constant power contours resembles the shape of the constant probability contours that would result from a least-squares solution’s covariance matrix. The final plot, the bottom-right panel, shows a 3D image of the correlation power as a function of the north-east error. It is clear in these images that in the 40 dB-Hz case each satellite individually reaches the highest correlation power in the correct bin and that the combined result also peaks in the correct bin. In the combined satellite results, each individual satellite’s correlation power enters the correlogram as the ridge that runs in a direction perpendicular to the receiver-satellite line-of-sight vector and represents a line of constant pseudorange.

FIGURE 6 shows a similar set of graphs for a simulator run at 20 dB-Hz. The plots in the left panel and the four plots in the upper-right panel show the individual and combined correlations, as in Figure 5. In the lower-right panel, the 3D image has been replaced with correlations calculated using 20 noncoherent 1-millisecond accumulations. The indistinct peaks in many of the individual correlations (left panel) suggest that these signals may not be acquired and tracked using traditional methods. Those signals, therefore, would not contribute to the navigation solution. Yet in the combined case, those indistinct peaks tend to add up and contribute to the navigation solution. These results indicate the feasibility of using the information in weak signals that may not be detectable using traditional methods and short acquisition times. The situation is further improved by increasing the number of noncoherent integration periods.

Impact of Reduced Geometry. Of course, it is a bit unrealistic to have 11 satellites available, particularly in restricted environments, so we also considered three subsets of four-satellite acquisitions, under the same signal levels. FIGURE 7 compares the position domain correlograms for the following 20 dB-Hz cases: (1) a good geometry case (PRNs 3, 14, 18, 26), (2) an urban canyon case where only the highest 4 satellites are visible (PRNs 15, 18, 21, 22), and (3) a weak geometry case where just a narrow wedge of visibility is available (PRNs 18, 21, 26, 29). As expected, the correlation power peak becomes less distinct as the satellite geometry deteriorates. The pattern of degradation, morphing from a distinct peak to a ridge, reveals that the position solution remains well constrained in some directions, but becomes poorly constrained in others. Again, this result is expected and is consistent with the behavior of conventional positioning techniques under similar conditions.

Focusing on Clock Errors. In some real-world situations, for example, a situation where a receiver is operating in an urban environment, it is possible for the position to be fairly well known, but the clock offset and frequency to have substantial uncertainty. FIGURE 8 shows how the combined satellites approach can be used to improve sensitivity when viewed from the clock bias and frequency domain. The figure presents example 1-millisecond correlograms of clock bias and clock drift for three 20 dB-Hz cases: (1) a single GPS satellite case; (2) a four-satellite, good geometry case; and (3) an 11-satellite, good geometry case. The assumed position solution has been offset by a random amount (generated with a 1-sigma of 100 meters in the north and east components, and 20 meters in the up component), but no individual satellite errors are introduced. These plots clearly show the improved capability for acquisition of the clock errors through the combining process.

Live Satellite Signals. FIGURE 9 shows combined correlograms derived from real data recorded using an outdoor antenna. The first example includes high-signal-level satellites with 1.5-second noncoherent integration. The second example includes extremely attenuated satellite signals with a long noncoherent integration period of six seconds.

The plots in the upper-left and upper-right panels show combined correlograms as a function of the north-east position error for satellite signals with carrier-to-noise-density ratios of 48 dB-Hz or higher. The plots in the lower-left and lower-right panels show combined correlograms resulting from much weaker satellites with carrier-to-noise-density ratios of roughly 15 to 19 dB-Hz, using a coherent integration interval of 20 milliseconds and a noncoherent interval of six seconds. FIGURE 10 shows one of the individual single-satellite correlograms. In this attenuated case, the individual satellite power levels are just barely high enough to make them individually detectable. This is the situation in which collective detection is most valuable.

Conclusions

The example results from a hardware signal simulator and live satellites show how the noncoherent combination of multiple satellite signals improves the GPS position error in cases where some of the signals are too weak to be acquired and tracked by traditional methods. This capability is particularly useful to a user who benefits from a rapid, but coarse, position solution in a weak signal environment. It may be used to monitor the quality of the signal environment, to aid deeply coupled navigation, and to initiate landmark recognition techniques in urban canyons. The approach does require that the user have some a priori information, such as a reasonable estimate of the receiver’s location and fairly accurate knowledge of the GPS ephemerides. Degradation in performance should be expected if the errors in these models are large enough to produce pseudorange prediction errors that are a significant fraction of a C/A-code chip. Absent that issue, the combined acquisition does not add significant complexity compared to the traditional approach to data processing. It can be used to enhance performance of existing acquisition techniques either by improving sensitivity for the current noncoherent integration times or by reducing the required integration time for a given sensitivity. Further development and testing is planned using multiple signals and frequencies.

Acknowledgments

The authors appreciate the contributions of David German and Avram Tewtewsky at Draper Laboratory in collecting and validating the simulator data; Samantha Krenning at the University of Colorado for assistance with the simulator data analysis and plotting; and Dennis Akos at the University of Colorado for many helpful conversations and for providing the Matlab software-defined radio code that was used for setting up the acquisition routines. This article is based on the paper “Enhancing GNSS Acquisition by Combining Signals from Multiple Channels and Satellites” presented at ION GNSS 2009, the 22nd International Technical Meeting of the Satellite Division of The Institute of Navigation, held in Savannah, Georgia, September 22–25, 2009.

The work reported in the article was funded by the Charles Stark Draper Laboratory Internal Research and Development program.

Manufacturers

Data for the analyses was obtained using a Spirent Federal Systems GSS7700 GPS signal simulator and a GE Fanuc Intelligent Platforms ICS-554 A/D module.

PENINA AXELRAD is a professor of aerospace engineering sciences at the University of Colorado at Boulder. She has been involved in GPS-related research since 1986 and is a fellow of The Institute of Navigation and the American Institute of Aeronautics and Astronautics.

JAMES DONNA is a distinguished member of the technical staff at the Charles Stark Draper Laboratory in Cambridge, Massachusetts, where he has worked since 1980. His interests include GNSS navigation in weak signal environments and integrated inertial-GNSS navigation.

MEGAN MITCHELL is a senior member of the technical staff at the Charles Stark Draper Laboratory. She is involved with receiver customization for reentry applications and GPS threat detection.

SHAN MOHIUDDIN is a senior member of the technical staff at the Charles Stark Draper Laboratory. His interests include GNSS technology, estimation theory, and navigation algorithms.

FURTHER READING

• Background
“Noncoherent Integrations for GNSS Detection: Analysis and Comparisons” by D. Borio and D. Akos in IEEE Transactions on Aerospace and Electronic Systems, Vol. 45, No. 1, January 2009, pp. 360–375 (doi: 10.1109/TAES.2009.4805285).

“Impact of GPS Acquisition Strategy on Decision Probabilities” by D. Borio, L. Camoriano, and L. Lo Presti in IEEE Transactions on Aerospace and Electronic Systems, Vol. 44, No. 3, July 2008, pp. 996–1011 (doi:10.1109/TAES.2008.4655359).

“Understanding the Indoor GPS Signal” by T. Haddrell and A.R. Pratt in Proceedings of ION GPS 2001, the 14th International Technical Meeting of the Satellite Division of The Institute of Navigation, Salt Lake City, Utah, September 11–14, 2001, pp. 1487–1499.

“The Calculation of the Probability of Detection and the Generalized Marcum Q-Function” by D.A. Shnidman in IEEE Transactions on Information Theory, Vol. 35, No. 2, March 1989, pp. 389–400 (doi: 10.1109/18.32133).

• Weak Signal Acquisition and Tracking
“Software Receiver Strategies for the Acquisition and Re-Acquisition of Weak GPS Signals” by C. O’Driscoll, M.G. Petovello, and G. Lachapelle in Proceedings of The Institute of Navigation 2008 National Technical Meeting, San Diego, California, January 28-30, 2008, pp. 843–854.

“Deep Integration of Navigation Solution and Signal Processing” by T. Pany, R. Kaniuth, and B. Eissfeller in Proceedings of ION GNSS 2005, the 18th International Technical Meeting of the Satellite Division of The Institute of Navigation, Long Beach, California, September 13–16, 2005, pp. 1095–1102.

“Deeply Integrated Code Tracking: Comparative Performance Analysis” by D. Gustafson and J. Dowdle in Proceedings of ION GPS 2003, the 16th International Technical Meeting of the Satellite Division of The Institute of Navigation, Portland, Oregon, September 9–12, 2003, pp. 2553–2561.

“Block Acquisition of Weak GPS Signals in a Software Receiver” by M.L. Psiaki in Proceedings of ION GPS 2001, the 14th International Technical Meeting of the Satellite Division of The Institute of Navigation, Salt Lake City, Utah, September 11–14, 2001, pp. 2838–2850.

• General Combining Techniques
“Coherent, Non-Coherent, and Differentially Coherent Combining Techniques for the Acquisition of New Composite GNSS Signals” by D. Borio, C. O’Driscoll, and G. Lachapelle, in IEEE Transactions on Aerospace and Electronic Systems, Vol. 45, No. 3, July 2009, pp. 1227–1240.

“Comparison of L1 C/A-L2C Combined Acquisition Techniques” by C. Gernot, K. O’Keefe, and G. Lachapelle in Proceedings of the European Navigation Conference ENC-GNSS 2008, Toulouse, France, April 23–25, 2008, 9 pp.

Performance Analysis of the Parallel Acquisition of Weak GPS Signals by C. O’Driscoll, Ph.D. dissertation, National University of Ireland, Cork, 2007; available on line: <http://plan.geomatics.ucalgary.ca/papers/phd_thesis_cillian_odriscoll_jan07.pdf>.

• Coherent Combining of Signals from Multiple Satellites
“GPS PRN Code Signal Processing and Receiver Design for Simultaneous All-in-View Coherent Signal Acquisition and Navigation Solution Determination” by R. DiEsposti in Proceedings of The Institute of Navigation 2007 National Technical Meeting, San Diego, California, January 22–24, 2007, pp. 91–103.

January 1, 2010