Tersus GNSS Inc. has launched Tersus Oscar, its new generation GNSS real-time kinematic (RTK) system.
Oscar is an all-in-one GNSS receiver that can be used as rover or base system. Paired with a Tersus TC20 controller or A11 mobile terminal, Oscar can more efficiently meet customer application requirements for the optimal surveying solution, according to Xiaohua Wen, founder and CEO of Tersus GNSS.
“Last year, we launched the David GNSS receiver,” Xiaohua said. “This year, we are very excited to introduce an advanced version of David; we named it Oscar.”
Oscar supports calibration-free tilt compensation function, meaning a leveling pole is no longer required. Configuration is made easy with a 1.3-inch interactive screen. With an internal high-performance multi-constellation and multi-frequency GNSS board, the Oscar GNSS receiver can provide high accuracy and stable signal detection, the company said.
The high-performance antenna can speed the time to first fix and improve anti-jamming performance. The built-in large capacity battery can support up to 10 hours of fieldwork.
A radio module in the package supports long-distance communication. With its rugged housing material, Oscar is protected from harsh environments.
In this month’s column, we travel along the road of PPP development, examine its current status and look at where it might go in the near future
By Sunil Bisnath, John Aggrey, Garrett Seepersad and Maninder Gill
Innovation Insights with Richard Langley
PPP. It’s one of the many acronyms (or initialisms, if you prefer) associated with the uses of global navigation satellite systems. It stands for precise point positioning. But what is that? Isn’t all GNSS positioning precise? Well, it’s a matter of degree.
Take GPS, for example. The most common kind of GPS signal use, that implemented in vehicle “satnav” units; mobile phones; and hiking, golfing and fitness receivers, is to employ the L1 C/A-code pseudorange (code) measurements along with the broadcast satellite orbit and clock information to produce a point position.
Officially, this is termed use of the GPS Standard Positioning Service (SPS). It is capable of meter-level positioning accuracy under the best conditions. There is a second official service based on L1 and L2 P-code measurements and broadcast data called the Precise Positioning Service (PPS).
In principle, because the P-code provides somewhat higher precision code measurements and the use of dual-frequency data removes virtually all of the ionospheric effect, PPS is capable of slightly more precise (and accurate) positioning. But because the P-code is encrypted, PPS is only available to so-called authorized users.
While meter-level positioning accuracy is sufficient for many, if not most applications, there are many uses of GNSS such as machine control, surveying and various scientific tasks, where accuracies better than 10 centimeters or even 1 centimeter are needed. Positioning accuracies at this level can’t be provided by pseudoranges alone and the use of carrier-phase measurements is required. Phase measurements are much more precise than code measurements although they are ambiguous and this ambiguity must be estimated and possibly resolved to the correct integer value.
Traditionally, phase measurements (typically dual-frequency) made by a potentially moving user receiver have been combined with those from a reference receiver at a well-known position to produce very precise (and accurate) positions. If done in real time (through use of a radio link of some kind), this technique is referred to as real-time kinematic or RTK.
A disadvantage of RTK positioning is that it requires reference station infrastructure including a radio link (such as mobile phone communications) for real-time results. Is there another way? Yes, and that’s PPP. PPP uses the more precise phase measurements (along with code measurements initially) on at least two carrier frequencies (typically) from the user’s receiver along with precise satellite orbit and clock data derived, by a supplier, from a global network. Precision, in this case, means a horizontal position accuracy of 10 centimeters or better.
In this month’s column, we travel along the road of PPP development, examine its current status, and look at where it might go in the near future.
In a 2009 GPS World “Innovation” article co-authored by Sunil Bisnath, the performance and technical limitations at the time of the precise point positioning (PPP) GPS measurement processing technique were described and a set of questions asked about the potential of PPP, especially with regard to the real-time kinematic (RTK) measurement processing technique.
Since the 2009 article, we’ve seen a significant amount of research and development (R&D) activity in this area. Many scientific papers discuss PPP and making use of PPP — a search on Google Scholar for “GNSS PPP” delivers nearly 7,000 results, and for “GPS PPP” more than 15,000 results! Will PPP eventually overtake RTK as the de facto standard for precise (that is, few centimeter-level) positioning? Or, in light of PPP R&D developments, should we be asking different questions, such as will multiple precise GNSS positioning techniques compete or complement each other or perhaps result in a hybrid approach?
In almost a decade, have we seen much in the way of positioning performance improvement, where “performance” can refer to positioning precision, accuracy, availability and integrity? Or, to some users, has the Achilles’ heel of PPP — the initial position solution convergence period — only been reduced from, for example, 20 minutes to 19 minutes? From such a perspective, all of this PPP research might not appear to have produced much tangible benefit. Advances have been made from this research and we will explore them here. Also, aside from many researchers working diligently on their own PPP software, there are now a number of well-established PPP-based commercial services — a number that has grown and been affected by the wave of GNSS industry consolidation over the decade. Consequently, there is much more to this story.
This month’s article summarizes the current status of PPP performance and R&D, and discusses the potential future of the technique. In the first part of the article, we will present brief explanations of conventional dual-frequency PPP, recent research and implementations, and application of the evolved technique to low-cost hardware. We will conclude the article with a rather dangerous attempt at near-term extrapolation of potential upcoming developments and conceivable implications.
Conventional PPP
The concept of PPP is based on standard, single-receiver, single-frequency point positioning using pseudorange (code) measurements, but with the meter-level satellite broadcast orbit and clock information replaced with centimeter-level precise orbit and clock information, along with additional error modeling and (typically) dual-frequency code and phase measurement filtering. Back in 1995, researchers at Natural Resources Canada were able to reduce GPS horizontal positioning error from tens of meters to the few-meter level with code measurements and precise orbits and clocks in the presence of Selective Availability (SA). Subsequently, the Jet Propulsion Laboratory introduced PPP as a method to greatly reduce GPS measurement processing time for large static networks. When SA was turned off in May 2000 and GPS satellite clock estimates could then be more readily interpolated, the PPP technique became scientifically and commercially popular for certain precise applications.
Unlike static relative positioning and RTK, conventional PPP does not make use of double-differencing, which is the mathematical differencing of simultaneous code and phase measurements from reference and remote receivers to greatly reduce or eliminate many error sources. Rather, PPP applies precise satellite orbit and clock corrections estimated from a sparse global network of satellite tracking stations in a state-space version of a Hatch filter (in which the noisy, but unambiguous, code measurements are filtered with the precise, but ambiguous, phase measurements). This filtering is illustrated in FIGURE 1, where measurements are continually added in time in the range domain, and errors are modeled and filtered in the position domain, resulting in reduced position error in time.
FIGURE 1. Illustration of conventional PPP measurement and error modeling in state-space Hatch filter, resulting in reduced position error in time.
The result is the characteristic PPP initial convergence period seen in FIGURE 2, where the position solution is initialized as a sub-meter, dual-frequency code point positioning solution, quickly converging to the decimeter-level in something like 5 to 20 minutes, and a few centimeters after ~20 minutes when geodetic-grade equipment is used (at station ALGO, Algonquin Park, Canada, on Jan. 2, 2017). For static geodetic data, daily solutions are typically at the few millimeter-level of accuracy in each Cartesian component.
FIGURE 2. Conventional geodetic GPS PPP positioning performance characteristics of initial convergence period and steady state for station ALGO, Algonquin Park, Canada, on Jan. 2, 2017.
The primary benefit of conventional PPP is that with the use of state-space corrections from a sparse global network, there is the appearance of precise positioning from only a single geodetic receiver.
Therefore, baseline or network RTK limitations are removed in geographically challenging areas, such as offshore, far from population centers, in the air, in low Earth orbit, and so on, and without the need for the requisite terrestrial hardware and software infrastructure. PPP is now the de facto standard for precise positioning in remote areas or regions of low economic density, which limit or prevent the use of relative GNSS, RTK or network RTK, but allow for continuous satellite tracking. These benefits translate into the main commercial applications of offshore positioning, precision agriculture, geodetic surveys and airborne mapping, which also are not operationally bothered by initial convergence periods of tens of minutes.
For urban and suburban applications, RTK and especially network RTK allow for near-instantaneous, few-centimeter-level positioning with the use of reference stations and regional satellite (orbit and clock) and atmospheric corrections. The use of double-differencing and these local or regional corrections allows sufficient measurement error mitigation to resolve double-differenced phase ambiguities. All of this additional information is not available to conventional PPP, limiting its precise positioning performance, but which is considered in PPP enhancements.
Progress on PPP Convergence Limitations
Over the past decade or so, PPP R&D activity can be categorized as follows:
Integration of measurements from multiple GNSS constellations, transitioning from GPS PPP to GNSS PPP;
Resolution of carrier-phase ambiguities in PPP user algorithms — in an effort to increase positional accuracy and solution stability, but foremost in an effort to reduce the initial convergence period; and
Use of a priori information to reduce the initial convergence and re-convergence periods and improve solution stability, making use of available GNSS error modeling approaches.
Unlike relative positioning, which makes use of measurements from the user receiver as well as the reference receiver, PPP only relies on measurements from the user site. This situation results in weaker initial geometric strength, and so the addition of more unique measurements is welcome. To make use of measurements from all four GNSS constellations (GPS, GLONASS, Galileo and BeiDou), user-processing engines must account for differences in spatial and temporal reference systems between constellations and numerous equipment delays between frequencies and modulations. The former can be done so that any number of measurements from any number of constellations can be processed to produce one unique PPP position solution. The latter requires a great deal of calibration, especially for heterogeneous tracking networks and user equipment (antenna, receiver and receiver firmware), most notably for the current frequency division multiple access GLONASS constellation.
FIGURE 3 shows typical multi-GNSS float (non-ambiguity-fixed) horizontal positioning performance at multi-GNSS station GMSD in Nakatane, Japan, on March 24, 2017. As with all modes of GNSS data processing, more significant improvement with additional constellations can be seen in sky-obstructed situations.
FIGURE 3. Typical conventional multi-GNSS PPP float horizontal positioning accuracy for station GMSD, Nakatane, Japan, March 24, 2017 (G: GPS, R: GLONASS, E: Galileo and C: BeiDou).
Related to multi-constellation processing is triple-frequency processing afforded by the latest generation of GPS satellites and the Galileo and BeiDou constellations. More frequencies mean more measurements, although with the same satellite-to-receiver measurement geometry as dual-frequency measurements. Again, additional signals require additional equipment delay modeling, in this case especially for the processing of GPS L1, L2 and L5 observables.
For processing of four-constellation data available from 20 global stations in early 2016, FIGURE 4 shows the average reduction of float (non-ambiguity-fixed) horizontal error from dual- to triple-frequency processing of approximately 40% after the first five minutes of measurement processing. In terms of positioning, this result, for this time period with a limited number of triple-frequency measurements, means a reduction in average horizontal positioning error from 43 to 26 centimeters within the first five minutes of data collection.
FIGURE 4. Average dual- and triple-frequency static, float PPP horizontal solution accuracy for 20 global stations. Data collected from tracked GPS, GLONASS, Galileo and BeiDou satellites in early 2016.
PPP with ambiguity resolution, or PPP-AR, was seen as a potential solution to the PPP initial solution convergence “problem” analogous to AR in RTK. Various researchers put forward methods, in the form of expanded measurement models, to isolate pseudorange and carrier-phase equipment delays to estimate carrier-phase ambiguities. These methods remove receiver equipment delays through implicit or explicit between-satellite single-differencing and estimate satellite equipment delays in the network product solution either as fractional cycle phase biases or altered clock products.
FIGURE 5 illustrates the difference between a typical GPS float and fixed solution (for station CEDU, Ceduna, Australia, on June 28, 2017). Initial solution convergence time is reduced, and stable few-centimeter-level solutions are reached sooner. For lower quality data, ambiguity fixing does not provide such quick initial solution convergence. Fixing is dependent on the quality of the float solution; and, for PPP, the latter requires time to reach acceptable levels of accuracy. Therefore, depending on the application, PPP-AR may or may not be helpful.
FIGURE 5. Typical float (red) and fixed (pink) GPS PPP horizontal solution error at geodetic station CEDU, Ceduna, Australia, on June 28, 2017.
To consistently reduce the initial solution convergence period, PPP processing requires additional information, as is the case for network RTK, in which interpolated satellite orbit, ionospheric and tropospheric corrections are needed since double-differenced RTK baselines over 10 to 15 kilometers in length contain residual atmospheric errors too large to effectively and safely resolve phase integer ambiguities. For PPP, uncombining the ionospheric-free code and phase measurements from the conventional model is required, to directly estimate slant ionosphere propagation terms in the filter state.
In this form, the model can allow for very quick re-initialization of short data gaps by using the pre-gap slant ionospheric (and zenith tropospheric) estimates as down-weighted a priori estimates post-gap — making these estimates bridging parameters in the estimation filter. Expanding this approach, external atmospheric models can be used to aid with initial solution convergence.
FIGURE 6 illustrates, for a large dataset, that applying a spatially and temporally coarse global ionospheric map (GIM) to triple-frequency, four-constellation float processing can reduce one-sigma convergence time to 10 centimeters horizontal positioning error from 16 to 6 minutes. If local ionospheric (and tropospheric) corrections are available and AR is applied, PPP (sometimes now referred to as PPP-RTK) can produce RTK-like results with a few minutes of initial convergence to few-centimeter-level horizontal solutions.
FIGURE 6. Averaged horizontal error from 70 global sites in mid-2016 using four-constellation, triple-frequency processing.
PPP Processing with Low-Cost Hardware
As the impetus for low-cost, precise positioning and navigation for autonomous and semi-autonomous platforms (such as land vehicles and drones) continues to grow, there is interest in processing such low-cost data with PPP algorithms. For example, it has been shown that with access to single-frequency code and phase measurements from a smartphone, short-baseline RTK positioning is possible. It has also been shown that similar smartphone data can be processed with the PPP approach. From the origins of PPP, it may be argued that single-frequency processing and many-decimeter-level positioning performance is not “precise.” But we will avoid such semantic arguments here (but see “Insights”), and focus on the use of high-performance measurement processing algorithms to new low-cost hardware. We are currently witnessing great changes in the GNSS chip market: single-frequency chips for tens-of-dollars or less; and boards with multi-frequency chips for hundreds-of-dollars. And these chips will continue to undergo downward price pressure with increases in capability, and be further enabled for raw measurement use in a wider range of applicable technology solutions. There are now a number of low-cost, dual-frequency, multi-constellation products on the market, with additional such products as well as smartphone chips coming soon.
To process data from such products with a PPP engine, modifications are required to optimally account for single-frequency measurements in the estimation filter, optimize the measurement quality control functions for the much noisier code and phase measurements compared to data from geodetic receivers, and optimize the stochastic modeling for the much noisier code and phase measurements. The single-frequency measurement model can be modified to either make use of the Group and Phase Ionospheric Calibration linear combination (commonly referred to as GRAPHIC) or ingest data from an ionospheric model. Due to the use of low-cost antennas, as well as the low-cost chip signal processing hardware, code and phase measurements suffer from significant multipath and noise at lower signal strengths; therefore, outlier detection functions must be modified. Also, the relative weighting of code and phase measurements must be customized for more realistic low-cost data processing.
FIGURE 7 compares the carrier-to-noise-density ratio (C/N0) values from ~1.5 hours of static GPS L1 signals collected from a geodetic receiver with a geodetic antenna, a low-cost receiver chip with a patch antenna, and a tablet chip and internal antenna, as a function of elevation angle. Received signal C/N0 values can be used as a proxy for signal precision. The three datasets were collected at the same time in mid-September 2017 in Toronto, Canada, with the receivers and antennas within a few meters of each other. The shading represents the raw estimates output from each receiver, while the solid lines are moving-average filtered results.
FIGURE 7. Carrier-to-noise-density ratios of ~1.5 hour of static GPS L1 signals from a geodetic receiver with a geodetic antenna, a low-cost receiver chip with a patch antenna, and a tablet chip and internal antenna, as a function of elevation angle.
Keeping in mind the log nature of C/N0, the high measurement quality of the geodetic antenna and receiver are clear. The low-cost chip and patch antenna signal strength structure is similar, but, on average, 3.5 dB-Hz lower. And the tablet received signal strength is lower still, on average a further 4.0 dB-Hz lower, with greater degradation at higher signal elevation angles and much greater signal strength variation.
The PPP horizontal position uncertainty for these datasets is shown in FIGURE 8. Note that reference coordinates have been estimated from the datasets themselves, so potential biases, in especially the low-cost and tablet results, can make these results optimistic. Given that only single-frequency GPS code and phase measurements are being processed, initial convergence periods are short and horizontal position error reaches steady state in the decimeter range. The geodetic and the low-cost results are comparable at the 2-decimeter level, whereas the tablet results are worse, at the approximately 4-decimeter level. Initial convergence of the geodetic solution is superior to the others, driven by the higher quality of its code measurements. The grade of antenna plays a large role in the quality of these measurements, for which there are physical limitations in design and fabrication. While geodetic antennas can be used, this is not always feasible, given the mass limitations of certain platforms or the cost limitations for certain applications.
FIGURE 8. Horizontal positioning error (compared to final epoch solutions) for geodetic, low-cost and tablet data processed with PPP software customized for single-frequency and less precise measurements.
Comments Regarding the Near Future
The PPP GNSS measurement processing approach was originally designed to greatly reduce computation burden in large geodetic networks of receivers by removing the need for network baseline processing. The technique found favor for applications in remote areas or regions with little terrestrial infrastructure, including the absence of GNSS reference stations. Given PPP’s characteristic use of a single receiver for precise positioning, various additional augmentations have been made to remove or reduce solution initialization and re-initialization interval to near RTK-like levels. But, to what end?
This question can be approached from multiple perspectives. From the theoretical standpoint, there is the impetus to maximize performance — millimeter-level static positioning over many hours, and few-centimeter-level kinematic positioning in a few minutes — by augmenting PPP in any way necessary. There is the academic exercise of maximizing performance without the need for local or regional reference stations – apparent single-receiver positioning, or truly wide-area augmentation. In terms of engineering problems, we can work to do more with less, that is, decimeter-level positioning with ultra-low-cost hardware, or the same with less, that is, few-centimeter-level positioning with low-cost hardware. And from the practical or commercial aspect, the great interest is for the implementation of evolved PPP methods for applications that can efficiently and effectively make use of the technology.
In terms of service providers, be it regional or global, commercial or public, there is momentum to provide enhanced correction products that are blurring the lines across the service spectrum from constellation-owner tracking to regional, terrestrial augmentation. A public GNSS constellation-owner, through its constellation tracking network, can provide PPP-like corrections and services. A global commercial provider with or without regional augmentation can provide similar services. The key is providing multi-GNSS state-space corrections for satellite orbits, satellite clocks, satellite equipment delays (fractional phase biases), zenith ionospheric delay and zenith tropospheric delay at the temporal and spatial resolution necessary for the desired positioning performance at reasonable cost, that is, subscription fees that particular markets can bear.
Given these correction products, PPP users have a greater ability to access a wide array of positioning performance levels for various new applications, be it few-decimeter-level positioning on mobile devices to few-centimeter-level positioning for autonomous or semi-autonomous land, sea and air vehicles. PPP can be used for integrity monitoring and perhaps safety-of-life applications where low-cost is a necessity and relatively precise positioning for availability and integrity purposes is required. For safety critical and high-precision applications, such as vehicle automation, PPP can be used alongside, or in combination with, RTK for robustness and independence with low-cost hardware. Such a parallel and collaborative approach would require a hybrid user processing engine and robust state-space corrections from a variety of local, regional and global sources, as we are seeing from some current geodetic hardware-based commercial services.
Near-future trends should also include more low-cost, multi-sensor integration with PPP augmentation. Optimized navigation algorithms and efficient user processing engines will be a priority as the capabilities of low-cost equipment continue to increase and low-cost integrated sensor solutions are required for mass-market applications. Analogous to meter-level point position GNSS, lower hardware costs should drive markets to volume sales, PPP-like correction services, and GNSS-based multi-sensor integration into more navigation technology solutions for various industry and consumer applications.
Clearly, the future of PPP continues to be bright.
SUNIL BISNATH is an associate professor in the Department of Earth and Space Science and Engineering at York University, Toronto, Canada. For over twenty years, he has been actively researching GNSS processing algorithms for a wide variety of positioning and navigation applications.
JOHN AGGREY is a Ph.D. candidate in the Department of Earth and Space Science and Engineering at York University. He completed his B.Sc. in geomatics at Kwame Nkrumah University of Science and Technology, Ghana, and his M.Sc. at York University. His research currently focuses on the design, development and testing of GNSS PPP software, including functional, stochastic and error mitigation models.
GARRETT SEEPERSAD is a navigation software design engineer for high-precision GNSS at u-blox AG and concurrently is completing his Ph.D. in the Department of Earth and Space Science and Engineering at York University. His Ph.D. research focuses on GNSS PPP and ambiguity resolution. He completed his B.Sc. in geomatics at the University of the West Indies in Trinidad and Tobago. He holds an M.Sc. degree in the same field from York University.
MANINDER GILL is a geomatics designer at NovAtel Inc. and concurrently is completing his M.Sc. in the Department of Earth and Space Science and Engineering at York University. His M.Sc. research focuses on GNSS PPP and improving positioning accuracy for low-cost GNSS receivers. He holds a B.Eng. degree in geomatics engineering from York University.
FURTHER READING
• Comprehensive Discussion of Technical Aspects of Precise Point Positioning
“Precise Point Positioning” by J. Kouba, F. Lahaye and P. Tétreault, Chapter 25 in Springer Handbook of Global Navigation Satellite Systems, edited by P.J.G. Teunissen and O. Montenbruck, published by Springer International Publishing AG, Cham, Switzerland, 2017.
• Earlier Precise Point Positioning Review Article
“Precise Point Positioning Using IGS Orbit and Clock Products” by J. Kouba and P. Héroux in GPS Solutions, Vol. 5, No. 2, October 2001, pp. 12–28, doi: 10.1007/PL00012883.
“Precise Point Positioning for the Efficient and Robust Analysis of GPS Data from Large Networks” by J.F. Zumberge, M.B. Heflin, D.C. Jefferson, M.M. Watkins and E.H. Webb in Journal of Geophysical Research, Vol. 102, No. B3, pp. 5005–5017, 1997, doi: 10.1029/96JB03860.
“Reduction of PPP Convergence Period Through Pseudorange Multipath and Noise Mitigation” by G. Seepersad and S. Bisnath in GPS Solutions, Vol. 19, No. 3, March 2015, pp. 369–379, doi: 10.1007/s10291-014-0395-3.
“Global and Regional Ionospheric Corrections for Faster PPP Convergence” by S. Banville, P. Collins, W. Zhang and R.B. Langley in Navigation, Vol. 61, No. 2, Summer 2014, pp. 115–124, doi: 10.1002/navi.57.
“A New Method to Accelerate PPP Convergence Time by Using a Global Zenith Troposphere Delay Estimate Model” by Y. Yao, C. Yu and Y. Hu in The Journal of Navigation, Vol. 67, No. 5, September 2014, pp. 899–910, doi: 10.1017/S0373463314000265.
“External Ionospheric Constraints for Improved PPP-AR Initialisation and a Generalised Local Augmentation Concept” by P. Collins, F. Lahaye and S. Bisnath in Proceedings of ION GNSS 2012, the 25th International Technical Meeting of the Satellite Division of The Institute of Navigation, Nashville, Tennessee, Sept. 17–21, 2012, pp. 3055–3065.
“Integer Ambiguity Resolution on Undifferenced GPS Phase Measurements and Its Application to PPP and Satellite Precise Orbit Determination” by D. Laurichesse and F. Mercier, J.-P. Berthias, P. Broca and L. Cerri in Navigation, Vol. 56, No. 2, Summer 2009, pp. 135–149.
“Resolution of GPS Carrier-phase Ambiguities in Precise Point Positioning (PPP) with Daily Observations” by M. Ge, G. Gendt, M. Rothacher, C. Shi and J. Liu in Journal of Geodesy, Vol. 82, No. 7, July 2008, pp. 389–399, doi: 10.1007/s00190-007. Erratum: doi: 10.1007/s00190-007-0208-3.
“Isolating and Estimating Undifferenced GPS Integer Ambiguities” by P. Collins in Proceedings of ION NTM 2008, the 2008 National Technical Meeting of The Institute of Navigation, San Diego, California, Jan. 28–30, 2008, pp. 720–732.
• Precise Positioning Using Smartphones
“Positioning with Android: GNSS Observables” by S. Riley, H. Landau, V. Gomez, N. Mishukova, W. Lentz and A. Clare in GPS World, Vol. 29, No. 1, January 2018, pp. 18 and 27–34.
Lear Corporation, a global supplier of automotive seating and electrical systems, has entered into a definitive agreement to acquire Israel-based EXO Technologies, a developer of GPS technology providing high-accuracy solutions for autonomous and connected vehicle applications.
EXO Technologies has operations in San Mateo, California, and Tel Aviv, Israel. Financial terms of the transaction were not disclosed.
EXO Technologies has developed core technology that addresses the need for high-accuracy positioning in a vehicle. Its proprietary technology works with existing GPS receivers to provide centimeter-level accuracy anywhere on the globe without the need for terrestrial base-station networks.
EXO Technologies offers a software-based GPS approach — PICO pinpoint positioning software — that enhances GNSS receivers. By correcting satellite orbit error and clock error, it eliminates the inherent error sources within navigation messages. Its algorithms reduce complementary errors and construct a full positioning solution.
The integration of EXO’s technology with Lear’s vehicle and connectivity expertise will enable a superior vehicle positioning solution, the companies say.
“EXO has developed technology that is essential for the future of connected and autonomous vehicles,” said Nuri Golan, EXO co-founder and CEO. “We are extremely excited to join the Lear family where we will provide unparalleled solutions for vehicle-to-vehicle, autonomous driving and other applications.”
“Lear is a leader in automotive connectivity solutions including Vehicle-to-Vehicle and Vehicle-to-Infrastructure communications,” said Matt Simoncini, Lear’s president and chief executive officer. “The acquisition of EXO Technologies will provide Lear with a differentiated technology to significantly improve GPS accuracy and reliability, thereby enhancing vehicle safety and enabling autonomous driving.
“The combination of EXO Technologies with Lear’s existing resources further strengthens our connectivity capabilities,” Simoncini said. “We see excellent growth opportunities for our E-Systems business as the proliferation of connected and autonomous vehicles will drive increased demand for improved accuracy and reliability in vehicle positioning.”
A dense reference network facilitates low-cost carrier-phase differential GNSS positioning with rapid integer-ambiguity resolution. This could enable precise lane-keeping for automated vehicles in all weather conditions.
Strong demand for low-cost precise positioning exists in the mass market. Carrier-phase differential GNSS (CDGNSS) positioning, accurate to within a few centimeters even on a moving platform, would satisfy this demand were its cost significantly reduced. Low-cost CDGNSS would be a key enabler for many demanding consumer applications.
Centimeter-accurate positioning by CDGNSS has been perfected over the past two decades for applications in geodesy, precision agriculture, surveying and machine control. But mass-market adoption of this technology will demand much lower user cost — by a factor of 10 to 100 — yet still require rapid and accurate position fixing. To reduce cost, mass-market CDGNSS-capable receivers will have to make do with inexpensive, low-quality antennas whose multipath rejection and phase center stability are inferior to those of antennas typically used for CDGNSS.
Moreover, there will be a strong incentive to use single-frequency receivers, whereas almost all receivers used for CDGNSS in surveying and similar applications are multi-frequency. Despite these user-side disadvantages, mass-market precise positioning will be expected to demonstrate convergence and accuracy performance rivaling that of the most demanding current precise positioning applications: Users will be dissatisfied with techniques requiring more than a few tens of seconds to converge to a reliable sub-decimeter solution.
Meeting this challenge calls for innovation targeting both the rover (user) equipment and the reference network. Here we examine the challenge from the point of view of the reference network and offer demonstration results for a low-cost end-to-end system.
The recent trend in precise satellite-based positioning has been toward precise point positioning (PPP), whose primary virtue is the sparsity of its reference network. But standard PPP requires several tens of minutes or more to converge to a sub-10-centimeter 95 percent horizontal accuracy. Faster convergence can be achieved by recasting the PPP problem as one of relative positioning, thereby exposing integer ambiguities to the end user.
This technique, known as PPP-RTK or PPP-AR, is mathematically similar to traditional network real-time kinematic (NRTK) positioning. As the network density is increased, sub-minute or even instantaneous convergence is possible with dual-frequency high-quality receivers. Even single-frequency PPP-RTK is possible, with convergence times of approximately 5 minutes for a 40-kilometer network spacing.
For PPP-RTK and NRTK, convergence time is synonymous with the time required to resolve the integer ambiguities that arise in double-difference (DD) carrier-phase measurements, referred to here as time to ambiguity resolution, or TAR. As reference networks become denser, they can better compensate for spatially-correlated variations in signal delay introduced by irregularities in the ionosphere and, to a lesser extent, in the neutral atmosphere. Improvement is manifest as reduced uncertainty in the atmospheric corrections that the network sends to the user. Reduced uncertainty in the atmospheric corrections is key to reducing TAR.
Prior work has established an analytical connection between uncertainty in the ionospheric corrections (denoted σi ) and TAR. The existing literature does not, however, offer a satisfactory model for the dependence of σι on network density.
The prevailing model is based on single-baseline CDGNSS, which is inapt for PPP-RTK and NRTK. Moreover, prior work does not address the effect of network-side multipath on the accuracy of the corrections data, which becomes increasingly important as low-cost and poorly-sited reference stations are used to densify the network.
Here, we examine the relationship between ionospheric uncertainty and probability of correct ambiguity resolution, and present the results of an empirical investigation of the relationship between network density and the total uncertainty in network correction data. We developed a simple analytical model relating error variance in network corrections to network density. Our analysis and experiments indicate that for rapid TAR in challenging urban environments with low-cost receivers, network density must be significantly increased. We report on the design and deployment of a dense network in Austin, Texas, and demonstrate a new system that taps into the network to provide reliable vehicle lane-departure warning.
AMBIGUITY RESOLUTION
Reducing the ionospheric uncertainty σι allows a strong prior constraint to be applied in the ionosphere-weighted model, thereby increasing P( = z), the probability that the estimated and true integer ambiguity vectors are equivalent. It is instructive to consider single-epoch ambiguity resolution (AR), for two reasons.
First, for stationary users with low-cost equipment, multipath errors dominate in the carrier-phase measurement and are strongly correlated over 100 seconds or more. Thus, if single-epoch AR fails then a static user may have to wait an unacceptably long time for multipath errors to decorrelate enough to permit AR. In any case, singe-epoch performance is a strong predictor of multi-epoch performance over an interval short enough (a few tens of seconds) to satisfy impatient mass-market users.
Second, a convenient and accurate analytical model (by Dennis Odijk and PJG Teunissen) for single-epoch AR reveals the dependency of P( = z) on scenario parameters of practical interest: the standard deviation of ionospheric correction errors, the number of visible satellites, the standard deviation of undifferenced carrier- and code-phase measurement errors (including multipath-induced errors), a satellite geometry factor, the number p of free parameters to be estimated (p=3 for negligible tropospheric error, p=4 to estimate a single additional tropospheric parameter), and the number of carrier frequencies broadcast by each of the satellites (1, 2 or 3) along with each carrier’s wavelength.
The model is highly accurate for single-epoch AR, but only approximate for multiple epochs, with accuracy degrading as the data interval lengthens. The model’s inaccuracy results from its assumption that overhead satellites remain static from epoch to epoch, which yields pessimistic results for even fairly short data capture intervals (for example, 30 seconds). Fully accounting for satellite motion in an analytical model for P( = z) is an open problem, which is why studies that wish to account for satellite motion resort to simulation.
Figures 1 and 2 show single-epoch, single-frequency results from the analytical P( = z) model for parameters approximately reflecting the mass-market use case. The most important conclusion to draw from these figures is that for single-epoch, single-frequency AR to be even moderately reliable (PT⩾0.9) over the next few years, the ionospheric uncertainty σι must be held under 2 millimeters. This will relax somewhat as more Galileo and MEO BeiDou satellites come online, but signal blockage in built-up areas will raise the effective elevation mask angle significantly above the 15 degrees assumed here, reducing the number of available satellites. Thus, sub-2-mm ionospheric uncertainty remains desirable for urban environments even as GNSS constellations become fully populated.
Figure 1. Single-epoch single-frequency ambiguity fixing. Blue traces (left axis) indicate the probability P(z^=z) of correctly resolving all integer ambiguities with a single epoch of data as a function of the number of satellites m. Each trace represents P(z^=z) for a different value of ionospheric uncertainty σι. Green bars (right axis) represent the probability mass function P(m) for the number of satellites above an elevation mask angle of 15 degrees, assuming 31 GPS, 14 Galileo, and 3 WAAS satellites (projected mid 2017). Each blue trace is marked with the total probability of correct integer resolution PT, a function of both the trace itself and P(m). Other parameters of the scenario: geometry factor fg=2.5, standard deviation of undifferenced phase measurements σϕ=3mm, standard deviation of undifferenced pseudorange measurements σρ=50cm, and number of estimated parameters p=3.Figure 2 . Total probability of a correct fix for the scenario of Figure 1 as a function of ionospheric uncertainty σι.
Figures 3 and 4 offer results for a dual-frequency (L1-L2) single-epoch scenario. All other scenario parameters are held as for the single-frequency scenario except that, in an attempt to be somewhat more pessimistic, P(m) is based only on GPS satellites. It is assumed that from each satellite the user can extract dual-frequency measurements. As with the single-frequency case, it is evident that dual-frequency PT is strongly dependent on σι. The dual-frequency case is more forgiving, but substantial performance improvement can still be had by reducing σι to under 2 mm.
Figure 3. As Figure 1 except for dual-frequency (L1-L2) measurements and the probability mass function P(m) corresponds only to a constellation of 31 GPS satellites. The elevation mask angle is again taken to be 15 degrees. It is assumed that dual-frequency measurements can be obtained from every GPS satellite.Figure 4. Total probability of a correct fix for the scenario of Figure 3 as a function of ionospheric uncertainty σι.
Corrections Uncertainty and Network Density. A key question arises in connection with σi: How is related to reference network density? One expects to decrease with increased network density, but what is the exact relationship?
Dennis Odijk’s work adopts a linear relationship between σi and the distance l between the user and the nearest reference station:
σi = βl, 0.3 ≤ β ≤ 3 mm/km
Parameter β depends on ionospheric activity; Odijk recommends determining β empirically. Similarly, his other work adopts a linear relation, with β = mm/km. But there appears to be no justification for applying this linear model to ionospheric corrections provided to a user by a network of reference receivers. The linear trend corresponds to individual single-baseline solutions involving a single master reference station without network aiding; it is not representative of how σi varies for a rover within a reference network.
Instead of determining how σi varies throughout a reference network, it will be more useful to consider the spatial variation in the variance of aggregate error in network-provided corrections. The aggregate error variance, denoted , can be modeled as the sum of variances associated with (1) residual ionospheric delay error, (2) residual neutral atmospheric (hereafter tropospheric) error, and (3) error due to carrier-phase multipath at the reference network stations:
This model assumes that precise orbital ephemerides are used to eliminate spatially-correlated errors due to satellite ephemeris errors and that the contribution to from reference station carrier-phase thermal noise is negligible compared to reference station carrier-phase multipath error.
Focusing therefore on σv , consider its relationship to reference network density γ, expressed in stations per unit area. This relationship depends on the assumed model for the DD ionospheric and tropospheric delays. Let a denote the master reference station and let S = {s1, s2, …, sN} denote the set of all secondary stations available in the network. Then, for pivot satellite i and alternate satellite j , suppose that the true combined DD atmospheric delay at secondary station s∈S can be accurately modeled as follows, where xs, ys, and zs represent the secondary station’s east, north, and up displacement from the master: (1)
Dai et al. refer to this model as a linear interpolation model or first-order surface model. The quantities and are the model parameters for the satellite pair i, j.
Map showing trends in σv across a simulated reference network assuming a linear model for combined DD ionospheric and tropospheric delays and independent errors due to multipath at each station. The master station is marked in black; secondary reference stations are marked in white. Blue denotes low σv. Red denotes high σv.
For the linear model in (1), one can show that if stations are sufficiently uniformly distributed (i.e., no station clumping), then the average value of σv across a network, denoted , is approximately related to the network density γ by (3)
where q is a parameter related to the variance of the uncorrelated errors , s∈S. This approximation becomes highly accurate as γ increases. [See full paper for details.]
It is clear from (3) that, for the linear model (1),can be driven to an arbitrarily small value by increasing the network density γ, and this is true despite the presence of multipath in the reference station carrier-phase measurements. Whether (3) applies in practice depends on whether (1) can be considered an accurate model for , at least over a compact region. The following section examines this question empirically. It further seeks to identify, for an example dense reference network, the density γ beyond which further reduction inno longer matters (would no longer improve ) because rover multipath dominates.
ANALYSIS OF A DENSE REFERENCE NETWORK
We examined σι as a function of network density using data from several organizations providing GNSS reference station observations: National Geodetic Survey Continuously Operating Reference Stations, UNAVCO, and the California Real Time Network. This combination allowed analysis of a hypothetical reference network of 23 high-quality GNSS receivers with an overall network density of approximately 8 nodes/1,000 km2, or an average inter-station spacing of 14 km. The relative positions of the sites selected to comprise this reference network, located between Los Angeles and Pomona, California, are depicted graphically below.
Depiction of the placement of the 23 GNSS reference stations. Horizontal positions are relative to the master station, LONG of CRTN, in kilometers. The color map indicates the height of each station above the WGS 84 geoid in meters.
DD carrier-phase observations from GPS L1 C/A signals spanning GPS weeks 1850 through 1859 were used for the analysis. A minimum satellite elevation mask was enforced at 20 degrees. Any satellite not above the elevation mask and providing carrier-phase observations at both the beginning and end of each processing window was excluded. A step size of 10 minutes was used. The longest available sub-window, meeting the above requirements and providing a minimum of 6 satellite vehicles (1 pivot satellite and 5 others), was selected for processing.
To facilitate batch processing, integer ambiguities were assumed to be resolved correctly when the mean standard deviation of carrier-phase residuals for that solution was less than one quarter wavelength of the GPS L1 frequency. In application, this constraint resulted in rejecting only 0.6 percent of all solutions.
Network Corrections Estimation. Estimation of network corrections made use of least-squares estimation applied to carrier-phase residuals measured between master station LONG, denoted a hereafter, and secondary reference stations s∈S, where S is now taken to be the set of all stations other than LONG. Consider the following model for the DD carrier-phase measurement, expressed in meters, between master station a, secondary station s∈S, pivot satellite i, and alternate satellite j:
(4)
Here, λ is the carrier wavelength; is the DD carrier-phase measurement, in cycles; is the DD range; is the DD integer ambiguity; is the DD combined atmospheric delay, which includes tropospheric and ionospheric delays; and is the DD carrier-phase measurement error, which is dominated by carrier-phase multipath error at a and s.
Experimental analysis ofas a function of network density proceeded as follows. A subset of secondary stations Sk ⊂S was chosen, together with a, to act as the kth test network. A large number K of subsets Sk of various geographic size and density were analyzed. Let {S\Sk} denote the set of secondary stations not in the kth test network. For each Sk, k = 1, 2,…, K, all secondary stations in {S\Sk} were designated, one at a time, to act as a test station, or rover. Atmospheric delays estimated by the kth network for test station s∈{S\Sk} were then differenced from actual delays measured by s to evaluate the quality of the atmospheric delay estimates.
Details of the atmospheric delay estimation procedure for the kth test network are as follows. For each s∈Sk, a DD measurement residual was formed for each pivot satellite i and alternate satellite j as
(5)
where was assumed known to sub-millimeter accuracy and was assumed to have been resolved correctly. The true DD atmospheric error contributing to (5) was assumed to vary linearly with geometry over sufficiently short baselines as modeled in (2). The DD multipath error term was assumed to be zero mean, and the component due solely to s was assumed to be uncorrelated with all corresponding components .
Under these assumptions, can readily be estimated via least squares. Let be the vector containing the residuals for |Sk|x1. This residuals vector can be modeled as
(6)
where H is an |Sk|x4 matrix whose rows are of the form [xs ys zs1]. The 4 x 1 vector contains the parameters of the hyper-plane to be estimated at each epoch. The |Sk|x1 vector wijcontains DD measurement errors.
An estimate from a least-squares solution of (6) was used to produce a network correction for a test secondary station s∈{S\Sk}, acting as rover, at location xs, ys, zs :
(7)
The subscript l on the atmospheric correction indicates that the correction is based on a linear model for DD atmospheric errors; it is used to distinguish the correction from those produced by a quadratic model later on. The correction was applied at test station s∈{S\Sk} to produce a corrected DD phase measurement
This procedure was repeated at each epoch for each satellite pair i, j visible to each test station s∈{S\Sk} of the kth test network, k = 1, 2,…K.
If the assumed models hold, then in the limit as the network density increases, can be modeled as
(8)
where is DD phase measurement error due only to multipath at s. In other words, as network density increases, application of the network correction eliminates not onlybut also , the component of the DD phase measurement error due to multipath at the master.
Linear least-squares compared to quadratic-least squares estimation. To evaluate the assumption that DD tropospheric and ionospheric errors vary proportional to relative position, c1 was estimated with the full set of secondary stations S for single epochs at 300 second intervals. The probability distributions of the contributions of those parameters (e.g., cxlxs and not simply cxl) are shown below. For comparison, equivalent values are calculated for a quadratic least-squares estimate of the following form:
(9)
Here, the subscript q of denotes a quadratic model for DD atmospheric delays. The distributions of comparable terms from (9) are also shown in the next two figures. These data represent the collection of all satellites above the elevation mask angle. It is noted that when all satellites are considered together, the expected value of these terms is very near zero.
Probability densities of the terms estimated at the station location for SPMS of UNAVCO. As indicated by the legend, the linear components are shown for a linear least-squares estimation as well as the linear components for a quadratic least-squares estimation. These data represent the probability densities for all GPS satellites combined.
Probability densities of the terms calculated at the station location for SPMS of UNAVCO.
The next two figures show the same data as the two above, but with each GPS satellite plotted separately. It is noted that the linear parameters, when considering only a particular satellite, are not necessarily zero-mean. This is hypothesized to be a manifestation of the satellite orbit reflected in the tropospheric and ionospheric errors. It is interesting to note that the quadratic terms shown in the second figure below largely exhibit zero mean behavior despite non-zero mean for the associated linear terms.
Probability densities of the terms for every GPS satellite observed, calculated at the station location for SPMS of UNAVCO, where each plot line represents a different GPS satellite. This figure is intended to qualitatively illustrate the non-zero mean nature of these linear terms when considered for individual satellites.
Probability densities of the terms for every GPS satellite observed, calculated at the station location for SPMS of UNAVCO, where each plot line represents a different GPS satellite. This figure is included to qualitatively illustrate the largely zero mean nature of these quadratic terms when considered for individual satellites.Probability densities of the difference between linear least-squares and quadratic least-squares network correction estimates for representative reference stations. The red vertical lines denote boundaries between which 68.27% of the probability distribution is contained; displayed as a comparative proxy to lσ of the Gaussian-distribution (these distributions are non-Gaussian). Recall that CGDM has a distance to the master station of 15.1km, BGIS is at 21.6km, and LORS is at 23.1km.
The figure above shows the probability distributions of the difference between (7) and (9) (i.e., ) at three representative reference station positions. It can be noticed that despite the increasing baseline distance of LORS and BGIS as compared to CGDM, there is no apparent correlation in these estimation errors. Notice that CGDM and LORS have very similar distributions despite their difference in baselines. BGIS and LORS, with similar baselines, exhibit very different distributions. There is no apparent correlation found between reference station positions and these error terms. Additionally, these distributions are zero-mean for all s∈S (to within 0.5 mm in each case) with 68.27% boundaries positioned between 1.5-5.5 mm. Because these errors appear indistinguishable from multipath, it is concluded, for this specific network and time period, that linear least-squares estimation is sufficient for estimating tropospheric and ionospheric errors. This is fortunate, because the linear model for atmospheric DD delays provides an averaging effect on multipath present at the reference stations which minimizes the introduction of multipath errors into the estimates produced.
Uncorrected carrier-phase residuals. The figure below shows the expected values for DD carrier-phase residual standard deviations for all s∈S through use of uncorrected observations. These data were produced by averaging the standard deviation of the DD carrier-phase residuals calculated at each epoch across all satellites present in the solution. The fitted curve indicates a linear growth of DD carrier-phase residuals with β = 0.62 mm/km. Additionally, the mm-level scatter of these data points suggest that position biases of the resolved reference station positions are also mm-level. If the linear fit is shifted down by approximately 4 mm (e.g., taking the minimum data points as those with very little position bias) and extrapolated to 0 km, one can consider this as providing a rough estimate of DD multipath at the reference stations; 4.7 mm (DD) or 3.3 mm (single-difference equivalent).
Standard deviation of uncorrected DD carrier-phase residuals versus baseline distance between each of the 22 reference stations and the master reference station.
Uncorrected Carrier-Phase Residuals. Figure 5 shows the expected values for DD carrier-phase residual standard deviations for all secondary stations, based on observations that were not corrected for atmospheric delay. These data were produced by averaging the standard deviation of the DD carrier-phase residuals calculated at each epoch across all satellites present in the solution. The fitted curve indicates a linear growth of DD carrier-phase residuals with distance to the master. The mm-level scatter of these data points suggest that biases of the resolved reference station positions are also mm-level.
Figure 5. Standard deviation of uncorrected DD carrier-phase residuals versus baseline distance between each of the 22 reference stations and the master reference station.
Network-Corrected Residuals. Figure 6 displays similar data to Figure 5, except that the carrier-phase residuals are those that remain after network corrections are applied. Each data point corresponds to a particular subset of secondary stations together with the master, and a particular rover selected at random from the remaining stations. Both the size and specific selection of secondary stations comprising each subset were randomly selected. In all, 70 different network configurations and more than 3.67 million NRTK solutions were analyzed.
Figure 6. Standard deviation of carrier-phase residual remainders (the carrier-phase residuals which remain after application of network corrections) versus average network density. The fitted curve is simply a polynomial fit of these data; it is not based on any theoretically anticipated behavior.
Figure 6 shows that carrier-phase residuals after application of network corrections are considerably reduced compared to those original magnitudes seen in Figure 5. With increasing network density, the DD residuals’ deviation asymptotically approaches a minimum value of about 4 mm, which corresponds to an undifferenced deviation of 2 mm. This floor is due to multipath at the rover. Deviations in excess of this floor are caused by residual ionospheric errors and, to a lesser extent, neutral atmospheric errors.Attributing the excess deviation entirely to residual ionospheric errors, and assuming these are uncorrelated with multipath, one can estimate from Figure 6 the undifferenced ionospheric uncertainty. For example, for a 50-km inter-station distance, σι=(℘(142 – 42))/2=6.7mm. To achieve the σι<2 mm recommended earlier for fast and reliable AR, station separation should be no more than 22 km, which we round down to a recommended value of 20 km to provide a margin of station redundancy.
NETWORK DEPLOYMENT
We have developed and deployed a low-cost reference network testbed in Austin, Texas, with site hosting courtesy of the Texas Department of Transportation. The Longhorn Reference Network boasts a dozen stations, with plans for 20 (Figure 7). The network’s average inter-station spacing is far shorter than the 20-km spacing recommended earlier. The tighter spacing provides redundancy and flexibility of experimentation. The low-cost reference stations are deployed in environments with greater multipath and signal blockage than those of the high-quality stations studied earlier. Such non-ideal signal environments are to be expected in a dense low-cost reference network, for which choice of station siting is driven largely by opportunity.
Figure 7. Overview of the planned Austin area reference network (Google Maps).
The reference station design, pictured in Figure 8 and diagrammed in Figure 9, is novel. Each station is a self-contained, solar-powered node supporting a software-defined dual-frequency, dual-antenna GNSS receiver with an always-on cellular connection to university servers for data collection and software maintenance.
Figure 8. Low-cost reference station in the Longhorn Reference Network.Figure 9. Reference station components.
Live Vehicle Demonstration. In partnership with Radiosense, an Austin-based precise positioning startup, we have developed and demonstrated a low-cost vehicle lane departure warning system that receives corrections from our dense reference network. The system takes in lane widths from an external database and infers a safe driving corridor within each lane by analyzing the behavior of human drivers on the same road. A vehicle’s proximity to the lane boundary is displayed in real time to the driver and passengers.
For robustness against cycle slips and to provide a baseline against which to compare future improvements, the system currently employs single-epoch CDGNSS positioning without aiding from additional sensors. In choosing a single-epoch approach, the system naively discards information regarding the underlying integer ambiguities at the beginning of each measurement epoch. Still, the system performs well with the typical number of overhead signals in a light urban environment: correct and internally-validated solutions were available in over 92 percent of measurement epochs. When a second rover antenna is included to combat multipath with spatial diversity, this percentage improves to 96. Such good single-epoch performance suggests that, when armed with additional sensor aiding and proper integer ambiguity persistence, reliable and accurate vehicle positioning can be maintained in more challenging environments.
Demonstration setup. The live demonstration followed a predetermined route in the vicinity of the University of Texas campus. The 1-mile route (Figure 10) passed through both open-sky and partially-blocked environments.
Figure 10. Demonstration route.
Prior to the demonstration, the vehicle was driven several times on the same route collecting GNSS measurements to precisely map typical driving trajectories on the route. The ensemble of trajectories was used to build a centimeter-accurate model of the lane center along the route. The sensing equipment employed during this mapping phase is no different than that used during the demonstration, making feasible eventual crowd-sourcing, wherein end-user vehicles generate and update the centerline models.
The demonstration vehicle was outfitted with two dual-frequency GNSS antennas mounted with magnetic bases onto the roof. The first antenna, designated primary, operated as the rover in a single-baseline CDGNSS solution against the master reference station of the Longhorn Reference Network, as illustrated in Figure 11. This baseline provided the geo-referenced, centimeter-accurate vehicle position. The other antenna, designated secondary, was paired with the primary antenna to produce a constrained-baseline CDGNSS solution providing sub-degree-accurate vehicle heading. The secondary antenna also served as a backup when the primary antenna produced a result that did not pass the precise positioning engine’s internal validity testing.
Figure 11. GNSS antenna configuration. A single-baseline precise position solution between the primary antenna and the master reference station provides precise vehicle position. A constrained-baseline 2D attitude solution between the primary and secondary antennas provides heading.
The GNSS antennas were connected to a low-cost, dual-frequency front-end in the trunk of the vehicle (FIGURE 12)which downconverted and digitized the incoming signals and subsequently fed them to a low-cost single-board computer running the precise positioning engine. A cellular modem received real-time measurements from the master reference station, while a WiFi router streamed real-time solutions to several Android devices in the vehicle for real-time visualization of precise within-lane position.
Figure 12. Low-cost, dual-frequency rover system in the trunk of the vehicle.
Demonstration Results. Figures 13, 14 and 15 show snapshots of the Android application and a still frame of the side of the vehicle in three different scenarios. The large rectangle indicates vehicle position with respect to the modeled lane center, changing color from green, when the vehicle is within the safe driving corridor, to yellow as the vehicle nears the edge of the lane, and finally to red if the vehicle breaks the lane boundary. One could imagine wrapping a control loop around these signals to enable last-moment lane-keeping.
Figure 13. Vehicle position relative to lane edge (left) synchronized in time with video still frame (right), centered safely within the lane, as depicted by green rectangle.Figure 14. Vehicle nearing lane edge, as depicted by yellow rectangle.Figure 15. Vehicle crossing lane edge, as depicted by red rectangle.
Figure 16 reveals the precision with which the positioning engine was able to locate the vehicle’s driver-side antenna in four repeated passes along the test route. The variation between the four yellow traces is primarily due to driver non-repeatability; actual measurement precision is at the centimeter scale. A small bias in the traces’ registration to the picture is present because Google Earth imagery is only registered to the International Terrestrial Reference Frame with meter-level accuracy.
Figure 16. Four repeated traces of driver’s side antenna as vehicle made a turn.
Figure 17 shows a time history of the vertical deviation from the route mean, in meters. The zoomed view of the vertical deviation shown in Figure 18 allows one to appreciate the precision of the positioning engine: the vertical trajectory is smooth at the centimeter level. Figure 19 shows the DD residuals in carrier phase and pseudorange for GPS PRN 30 during the four loops in Figure 17. One-sigma undifferenced phase and pseudorange deviations are 3.4 mm and 42 cm, respectively.
Figure 17. Time history of the vertical deviation from the route mean, in meters.Figure 18. Zoomed view of the time history of the vertical deviation from the route mean, showing the centimeter-level precision in the 3.3 Hz positioning data.Figure 19. Double-difference carrier phase (top) and pseudorange (bottom) residuals for GPS satellite 30 at frequency L1 over the full time interval shown in Figure 17.
The figures demonstrate that the precise positioning engine fed by reference data from the Longhorn Reference Network maintained centimeter-accurate knowledge of the vehicle’s position during almost the entire trajectory, despite passing between a large football stadium and parking garage, each of which introduced significant signal blockage and multipath.
For the data shown in Figure 17, 96 percent of the 3.3-Hz measurement epochs resulted in a correct and internally-validated positioning solution. The majority of the remaining solutions were correct but did not pass internal validation. For only 0.6 percent of solutions were the carrier-phase integer ambiguities resolved incorrectly, but all of these incorrect solutions were caught and excluded by the validation algorithm.
Furthermore, the number of overhead signals during the time in which this particular dataset (set A) was taken was average, as seen in the upper plot of Figure 20. 16 signals above 15 degrees elevation were available during this time. In contrast, the number of overhead signals for a second dataset taken 8 days prior (set B) was much worse, with only 12 signals above 15 degrees elevation, as seen in the lower plot.
Figure 20. The number of signals above a 15-degree elevation mask. Each plot spans an entire day. The black arrows denote the time of day in which two different datasets, A and B, were taken. The dashed red line represents the mean number of signals above the mask over both days. Dataset A was taken during a nominal time when 16 signals were available, while dataset B was taken during a worst-case time when only 12 signals were available.
For insight into the performance of the positioning engine as a function of the number of overhead satellites, Table 1 details the performance of these two datasets (as well as a third dataset) in terms of the percentage of epochs that passed the positioning engine’s internal validation testing, based on a ratio test with a fixed threshold of 2.0. Results are shown for single- and dual-antenna positioning solutions and for dual-antenna vehicle heading solutions.
Table 1. The performance of each dataset in terms of the percentage of solutions that passed validation testing.
A large drop-off in positioning performance occurs when the number of overhead signals is reduced below 16, while the constrained-baseline heading determination performance remains good throughout. Fortunately, it will not be long until even more signals are available. Within the next 8 months, the Galileo constellation will add six fully operational satellites. These will bring the number of GPS L1, GPS L2C, Galileo E1, and SBAS signals that are above 15 degrees elevation to 16 or more 95 percent of the time, enabling high-reliability single-epoch CDGNSS positioning.
CONCLUSIONS
For a sufficiently dense reference network, linear least squares estimation can be applied to the task of reducing uncertainties due to tropospheric and ionospheric delays for the purposes of providing improved positioning accuracy as well as faster time to ambiguity resolution for carrier-phase differential positioning. High network density allows use of a strong linear model for atmospheric delays, which has the virtue of suppressing network-side multipath errors in the provided corrections.
A network of 23 high-quality reference stations in the vicinity of Los Angeles, California, was studied to determine what network density is sufficient to make all network-side error sources negligible compared to rover receiver multipath. A density of three stations per 1,000km2, or an average inter-station spacing of 20 km, was found to drive network-side ionospheric, tropospheric, and multipath errors well below rover receiver multipath.
These findings motivate a significant densification of permanent reference networks, at least in built-up areas where signal blockage and multipath are common, to support mass-market applications for which low user (rover receiver) cost and rapid convergence to a reliable sub-decimeter position are a priority. In a light urban setting, and with the kind of satellite coverage that will soon become the norm, we demonstrated vehicle lane departure warning in a field test that produced highly reliable instantaneous sub-decimeter positioning.
ACKNOWLEDGMENTS
This work was supported in part by Samsung Research America, by the Data-Supported Transportation Operations and Planning Center (D-STOP), a Tier 1 USDOT University Transportation Center, and by the Texas Department of Transportation under the Connected Vehicle Problems, Challenges and Major Technologies project.
Centimeter Positioning with a Smartphone-Quality GNSS Antenna
By Kenneth M. Pesyna, Jr., Robert W. Heath, Jr. and Todd E. Humphreys, the University of Texas at Austin
The smartphone antenna’s poor multipath suppression and irregular gain pattern result in large time-correlated phase errors that significantly increase the time to integer ambiguity resolution as compared to even a low-quality stand-alone patch antenna. The time to integer resolution — and to a centimeter-accurate fix — is significantly reduced when more GNSS signals are tracked or when the smartphone experiences gentle wavelength-scale random motion.
GNSS chipsets are now ubiquitous in smartphones and tablets. Yet the underlying positioning accuracy of these consumer-grade GNSS receivers has stagnated over the past decade. The latest clock, orbit, and atmospheric models have improved ranging accuracy to a meter or so, leaving receiver-dependent multipath and front-end-noise-induced variations as the dominant sources of error in current consumer devices. Under good multipath conditions, 2-to-3-meter-accurate positioning is typical; under adverse multipath, accuracy degrades to 10 meters or worse.
Yet outside the mainstream of consumer GNSS receivers, centimeter — even millimeter — accurate GNSS receivers can be found. These high-precision receivers are used routinely in geodesy, agriculture, and surveying. Their exquisite accuracy results from replacing standard code-phase positioning techniques with carrier phase differential GNSS (CDGNSS) techniques. Currently, the primary impediment to performing CDGNSS positioning on smartphones lies not in the commodity GNSS chipset, which actually outperforms survey-grade chipsets in some respects, but in the antenna, whose chief failing is its poor multipath suppression. Multipath, caused by direct signals reflecting off the ground and nearby objects, induces centimeter-level phase measurement errors, which, for static receivers, have decorrelation times of hundreds of seconds. The large size and strong time correlation of these errors significantly increases the initialization period — the so-called time-to-ambiguity-resolution (TAR) — of GNSS receivers employing CDGNSS to obtain centimeter-level positioning accuracy.
Prior work on centimeter-accurate positioning with low-cost mobile devices has focused on external devices, or “pucks,” which contain a GNSS antenna and chipset. These devices interface with the smartphone via Bluetooth or a wired connection. Such solutions, which enjoy the better sensitivity and multipath suppression offered by their comparatively large, high-quality GNSS antennas, do not provide insight into the feasibility of CDGNSS on a stand-alone smartphone platform.
This article demonstrates that centimeter-accurate CDGNSS positioning is indeed possible based on data sampled from a smartphone-quality GNSS antenna. This result has far-reaching significance for precise mass-market positioning. We offer an empirical analysis of the average gain and carrier phase multipath error susceptibility of smartphone-grade GNSS antennas. We also demonstrate that, for low-quality GNSS antennas such as those in smartphones, wavelength-scale random antenna motion substantially improves the time to integer ambiguity resolution.
This article focuses on single-frequency CDGNSS rather than multiple-frequency CDGNSS or other carrier-phase-based techniques, such as precise-point positioning (PPP), for three reasons. First, virtually all smartphones are equipped with single-frequency GNSS antennas tuned to the L1 band centered at 1575.42 MHz, and single-frequency CDGNSS will likely forever remain the cheapest option. Second, as compared to PPP, CDGNSS converges much faster to centimeter accuracy, which will be important for impatient smartphone users.
Finally, as centimeter-accurate GNSS moves into the mass market, GNSS reference stations will proliferate so that the vast majority of users can expect to be within a few kilometers of one. In this so-called short baseline regime, the differential ionospheric delay between the reference and mobile receivers becomes insignificant, obviating differential delay estimation via multi-frequency measurements. Of course, the additional signal measurements produced by multiple-frequency receivers would lead to faster convergence times and improved robustness, but for many applications, single-frequency measurements will be adequate.
Test Architecture
We used the test architecture shown in Figure 1 to collect data from a smartphone-grade antenna and higher quality antennas, process these data through a software-defined GNSS receiver, and compute a CDGNSS solution on the basis of the carrier phase measurements output by the GNSS receiver.
Figure 1. Test architecture designed for an in-situ study of a smartphone-grade GNSS antenna. The analog GNSS signal is tapped off after the phone’s internal bandpass filter and low-noise amplifier and is directed to a dedicated RF front-end for downconversion and digitization. Data are stored to file for subsequent post-processing by a software GNSS receiver and CDGNSS filter.
The architecture has been designed such that the antenna is left undisturbed within the phone; data are collected by tapping off the analog signal immediately after the phone’s internal bandpass filter and low-noise amplifier. This analog signal is directed to an external radio frequency (RF) front-end and GNSS receiver. Use of an external receiver permits well-defined GNSS signal processing unencumbered by the limitations of the phone’s internal chipset and clock.
The clock attached to the external front-end was an oven-controlled crystal oscillator (OCXO), which has much greater stability than the low-cost oscillators used to drive GNSS signal sampling within smartphones. However, it was found that reliable cycle-slip-free GNSS carrier tracking only required a 40-ms coherent integration (pre-detection) interval, which is within the coherence time of a low-cost temperature-compensated crystal oscillator (TCXO) at the GPS L1 frequency.
Although only a single model of smartphone was tested using this architecture — a popular mass-market phone — the results are assumed representative of all smartphones from the same manufacturer.
Using this architecture, many hours of raw high-rate (∼6 MHz) digitized intermediate frequency samples were collected and stored to disk for post processing. Also stored to disk were high-rate data from a survey-grade antenna, which served as the reference antenna for CDGNSS processing. An in-house software-defined GNSS receiver, known as GRID, was used to generate, from these samples, high-quality carrier phase measurements. GRID is a flexible receiver that can be easily adapted to maintain carrier lock despite severe fading. Complex baseband accumulations output from GRID allowed detailed analysis of the signal and tracking loop behavior to ensure that no cycle slips occurred. The generated carrier phase measurements were subsequently passed to a CDGNSS filter, a model for which is described in the next section.
CDGNSS Processing
The CDGNSS filter described in this section ingests double-differenced carrier phase measurements output from GRID and processes them to produce (1) the centimeter-accurate trajectory estimate of the mobile antenna, (2) a time history of phase residuals, (3) carrier phase integer ambiguity estimates, (4) theoretical integer ambiguity resolution success bounds, and (5) empirical integer ambiguity resolution success rates. These outputs are used to analyze the performance of the smartphone-grade antenna and compare its performance to higher-quality antennas.
CDGNSS Filter Model. The filter’s state has a real-valued component xk that models the mobile antenna’s relative center of motion, its instantaneous offset from this center of motion, and its velocity at each time epoch k:
. (1)
The filter’s state also has an integer-valued component that models the CDGNSS phase ambiguities:
(2)
where NSV is the total number of satellites tracked. Such integer ambiguities are inherent to carrier phase differential positioning techniques; their resolution has been the topic of much past research and is required to produce a CDGNSS positioning solution.
Dynamics and Measurement Models. The real-valued state component xk is assumed to evolve as a mean-reverting second-order Gauss-Markov process. This process models the time-correlated and mean-reverting motion a smartphone experiences when held or moved gently in the extended hand of an otherwise stationary user. The integer-valued state component nk is modeled as constant, since the phase ambiguities remain fixed so long as the receiver retains phase lock on each signal.
The filter ingests measurement vectors yk for k = 1, …, K, each populated with a single epoch of double-differenced carrier phase measurements for i = 1, 2, . . . , NSV–1. The filter’s measurement model relates yk to the real- and integer-valued state components through the following linearized GNSS carrier phase measurement model:
(3)
where rxk is a vector of double-differenced modeled ranges based on the filter’s real-valued state prior ,Hxk and Hn are the measurement sensitivity matrices for the real- and integer-valued state components, and vk is the double-differenced measurement noise vector, all at time k.
Phase Residuals. After processing data through the CDGNSS filter, the filter outputs, in addition to a time history of centimeter-accurate position estimates, a time history of phase residuals , which can be thought of as departures of each double-differenced phase measurement from phase alignment at the phase center of the antenna. These residuals can be modeled as
(4)
where rxk is now based on the filter’s real-valued state estimate at time k and represents the filter’s estimate of the integer ambiguities at time K.
Phase residuals have been produced for batches of data collected from four different grades of antennas, as described next. These residuals will be used to analyze the suitability of each antenna for CDGNSS positioning.
Antenna Performance Analysis
This section describes four antennas from which data were captured and processed using the test architecture and CDGNSS filter described previously. It also quantifies the characteristics that make low-quality smartphone-grade antennas poorly suited to CDGNSS.
Table 1 describes a range of antenna grades of decreasing quality, noting properties relevant to CDGNSS. The loss numbers in the far-right column represent the average loss in gain relative to a survey-grade antenna, where the average is taken over elevation angles above 15 degrees.
Table 1. Antenna properties.
Survey-grade antennas, whose properties are described in the first row of Table 1, have a uniform quasi-hemispherical gain pattern, right-hand circular polarization, a stable phase center, and a low axial ratio. These are all desirable properties for CDGNSS. Unfortunately, these properties inhere in the antennas’ large size; the laws of physics dictate that smaller antennas will typically be worse in each property.
The last row of Table 1 lists the properties for a smartphone-grade antenna. As shown subsequently, this antenna loses between 5 and 15 dB in sensitivity as compared to the survey-grade antenna. Such a loss makes it difficult to retain lock on GNSS signals. In addition, this antenna’s linear polarization leads to extremely poor multipath suppression.
Antenna Gain Analysis.Figure 2 quantifies one of the obvious drawbacks of a smartphone-grade antenna, namely, its low gain.
Figure 2, Drop in carrier-to noise ratio, from 2 hours of data and 9 tracked satellites. Antennas remained stationary.
The rightmost histogram, in green, shows that the decrease in carrier to noise ratio as compared to a survey-grade antenna is on average 11 dB, such that the smartphone-grade antenna only captures approximately 8 percent of the signal power as compared its survey-grade counterpart. For comparison, shown on the left, in blue, is a histogram of the decrease in carrier-to-noise ratio for the low-quality patch antenna. This antenna only suffers about a 0.6-dB drop in power on average relative to the survey-grade antenna. Each histogram was generated from 2 hours of data with nine tracked satellites ranging in elevation from 15 to 90 degrees. The antennas remained stationary. The variation in signal power around the means is due to the multipath-induced power variations in the signal as well as to the different gain patterns between each antenna and the survey-grade antenna.
Phase Residual Analysis. Shown in Figures 3, 4, and 5 are 2,000-second segments of double-differenced phase residual time histories for data collected from a survey-grade, a low-quality patch, and a smartphone-grade antenna, respectively.
Figure 3. Survey-grade antenna. Each trace represents a residual for a different satellite pair. Ensemble average standard deviation 3.4 millimeters.Figure 4. Low-quality patch antenna. Ensemble average deviation 5.5 mm.Figure 5. Smartphone-grade antenna.Ensemble average deviation 11.4 mm.
To produce these residuals, the antenna position was locked to its estimated value within the CDGNSS filter. The residuals represent departures of the carrier phase measurements from perfect alignment at the average phase center of the antenna. Each different colored trace corresponds to a different satellite pair. While the data segments were not captured at the same time of day, they were captured at the same location, and thus the multipath environment was similar.
The ensemble average residual standard deviations increase with decreasing antenna quality. The residuals for the survey-grade, low-quality patch, and smartphone-grade antennas have ensemble average standard deviations of 3.4, 5.5 and 11.4 millimeters, respectively. This increase is due to the lower gain and less effective multipath suppression of the lower quality antennas.
Figure 5 shows the presence of outlier residuals in the data collected from the smartphone-grade antenna. These outliers, one of which persists for over 1,000 seconds, are likely caused by either large and irregular azimuth- and elevation-dependent antenna phase center variations or a combination of poor antenna gain in the direction of the non-reference satellite coupled with ample gain in the direction of a multipath signal such that the multipath signal is received with more power than the direct-path signal. Obvious outliers such as these can be automatically excluded by the CDGNSS filter via an innovations test. However, the standard deviation of the remaining residuals still remains large compared to that of the other antennas; the ensemble average standard deviation decreases from 11.4 to 8.6 millimeters upon exclusion of the two large outliers.
For antennas with a large ensemble average standard deviation in their double-differenced phase errors, the time correlation in the phase errors becomes more important. This time correlation, which persists for 100–200 seconds, is a well-studied phenomenon caused by slowly varying carrier phase multipath. While correlation is present in the residuals of all antenna types, and manifests approximately the same decorrelation time, its effect is more of a problem for low-quality antennas because the phase errors are larger. Such correlation, coupled with a large deviation, ultimately leads to a longer time to ambiguity resolution, shown later.
Given a smartphone antenna’s extremely poor gain and multipath suppression as compared to even a low-quality stand-alone patch antenna, one might question the wisdom of attempting a CDGNSS solution using such an antenna. However, the next section reveals that it is indeed possible to achieve a centimeter-accurate positioning solution using a smartphone GNSS antenna despite its poor properties.
CDGNSS with Smartphone Antenna
Figure 6 shows the result of an attempt to compute a CDGNSS solution using data collected from the GNSS antenna of a smartphone. The cluster of red near the top of the phone represents 400 CDGNSS position estimates over a 5-minute interval, superimposed on the photo and properly scaled. This cluster is referenced to a marker immediately under the phone whose position was surveyed to approximately 1-centimeter accuracy using a high-quality patch antenna. The mean of the cluster’s horizontal coordinates is approximately 2 centimeters from the phone’s internal GNSS antenna. Figure 6 shows the absolute horizontal accuracy of a CDGNSS solution through the smartphone’s antenna is approximately 2 centimeters.
Figure 6 . Successful CDGNSS solution using data collected from smartphone antenna. The red cluster represents 400 CDGNSS solutions over 5 minutes, superimposed and properly scaled.
The data in Figure 6were collected with a large conductive backplane below the smartphone. However, the backplane is unnecessary. The opening photo shows the result of a CDGNSS positioning solution computed using data collected from the smartphone antenna while the device was held in the extended hand of the author. The cluster of red represents the computed 3-dimensional position of the phone over a 300-second interval, superimposed on the photo and properly scaled. The author’s hand moved slightly during the interval, as reflected in the figure.
The opening photo also shows the residuals corresponding to the handheld CDGNSS solution. This shows how the residuals look in practice for a scenario in which the phone is held by a user. The residuals look fairly clean, that is, they have a small variance and their mean is approximately zero. It is not uncommon for the residuals to look this good; however, cases do arise in which the residuals are considerably worse due to a combination of poor antenna gain in the direction of the non-reference satellite, coupled with ample gain in the direction of a multipath signal.
The possibility of CDGNSS-enabled centimeter positioning using a smartphone antenna has been previously conjectured, but — to our knowledge — Figure 6 and the opening photo represent the first published demonstrations that this is indeed possible. This significant result portends a vast expansion of centimeter-accurate positioning into the mass market. However, serious challenges must be overcome before mass-market CDGNSS can become practical. Some of these challenges will be studied in the next few sections.
Static Scenario. Figure 7 shows the empirical probability of successful ambiguity resolution for data collected from four antennas, one of each of the different grades discussed earlier. For each antenna, seven satellites were tracked at approximately the same location and time of day. Each trace was computed from 12 batches of double-differenced carrier phase data.
Each trace represents an empirically-derived success rate computed from 12 batches of phase data as follows:
For a given batch, at each epoch the filter outputs its best estimate of the integer ambiguities on the basis of the data ingested thus far.
The estimate from step 1 is compared against the true set of integer ambiguities which were acquired in advance by processing a much longer batch of data. If correct, a flag is set at that epoch to “1”; if incorrect, the flag is set to 0.
For each epoch, the flags produced in step 2 are averaged across all 12 batches to generate each trace.
Figure 7. Residuals for CDGNSS solution depicted in the opening photo.
As shown by the green trace in Figure 7, the smartphone-grade antenna required 400 seconds to achieve a 90% ambiguity resolution success rate; in other words, it manifested a 400-second TAR at 90%. This would surely exceed the patience of most smartphone users. Also shown are traces for the other three antenna grades. The higher-quality antennas yield shorter TARs for a given success rate, primarily due to their superior multipath suppression.
Note that the loss in received signal power due to the smartphone antenna’s poor gain turns out to be tolerable — the signals arriving from the smartphone-grade antenna can be tracked without cycle slipping. Therefore, the outstanding challenge preventing fast ambiguity resolution for data collected from smartphone-grade antennas is the severe time-correlated multipath errors in the double-differenced carrier phase data.
Decreasing TAR via More Signals. There are ways to mitigate the impact of multipath on the CDGNSS TAR, even the severe multipath experienced by low-quality antennas. It has been shown that the volume of the integer ambiguity search space, and thus TAR, decreases as a function of the number of double-differenced phase time histories available, which, for single-frequency CDGNSS, is one less than the number of satellites tracked. Consequently, an acceptable TAR can always be achieved with enough satellites tracked.
Figure 8 shows the reduction in TAR for an increasing number of satellites. Each trace was computed from 720 non-overlapping 2-minute batches of data taken from a survey-grade antenna over a 24-hour interval. A decreasing elevation mask angle was used to allow an increasing number of SVs to participate in the CDGNSS solution. For a given 2-minute batch of data, an elevation mask was first applied to all but the highest five satellites. Double-difference phase data from these satellites were then processed by the CDGNSS filter to compute an empirical probability of successful integer ambiguity resolution. Next, the elevation mask was reduced until one additional satellite was in view, and the process repeated to produce all traces shown.
Figure 8 makes clear that each additional double-differenced phase time history, although corrupted by its own multipath-induced phase errors, significantly decreases the overall TAR. Note that although Figure 8 was produced from data collected via a survey-grade antenna, a similar trend would apply for the smartphone-grade antenna. One implication of Figure 8 is that smartphone-based CDGNSS would benefit greatly from the additional double-differenced measurements that a multi-frequency GNSS receiver could provide. For example, at the time of writing there are 14 operational GPS satellites broadcasting unencrypted civil signals at the GPS L2 frequency (1227.6 MHz), and 7 broadcasting civil signals at the GPS L5 frequency (1176.45 MHz). With some modification of the smartphone GNSS antenna and chipset, these modernized GPS signals could be exploited to reduce TAR. However, the narrow profit margins on mass-market GNSS antennas and chipsets militate against multi-frequency architectures.
Figure 8. Probability of successful ambiguity resolution vs. time as a function of the number of satellite vehicles (SVs) tracked.
Decreasing TAR via Random Motion. There is a second way to reduce TAR under severe multipath conditions. Unlike TAR reduction via additional signals, the theory and practice of this second technique have not been previously treated in the literature. Moreover, the technique is well-suited for smartphones, which are typically hand-held and mobile. This simple technique consists of gently moving the smartphone in a quasi-random manner within a wavelength-scale volume. The key to this technique’s effectiveness is that, whereas multipath-induced phase measurement errors are typically time-correlated on the order of hundreds of seconds for a static receiving antenna, their spatial correlation is on the order of one wavelength, or approximately 19 centimeters at the GPS L1 frequency. As a result, random wavelength-scale antenna motion transforms the phase residuals from slowly-varying when the antenna is static, as shown in Figure 9, to quickly-varying when the antenna is dynamic, as shown in Figure 10.
Figure 9. Residuals for data captured from smartphone-grade antenna while static.Figure 10. Data from smartphone-grade antenna as it experienced wavelength-scale random motion, 2–5 cm/second.
Put another way, autocorrelation time of the phase residuals decreases from hundreds of seconds when the antenna is static, as shown in Figure 11, to less than a second when the antenna is moved even slowly (a few centimeters per second), as shown in Figure 12. More vigorous antenna motion would be possible if the phone’s inertial devices were used to aid the phase tracking loops.
Figure 11. Autocorrelation functions corresponding to the phase residuals in Figure 9.Figure 12. Autocorrelation functions corresponding to phase residuals in Figure 10.
The shorter phase error decorrelation time resulting from random antenna motion effectively increases the information content per unit time that each double-differenced phase measurement provides to the CDGNSS filter, thus decreasing the time to ambiguity resolution.
Figure 13 compares empirical success rates for three different antennas under static and dynamic scenarios. As expected, motion reduces the time-to-ambiguity resolution for the smartphone-grade and low-quality patch antenna. But, somewhat counterintuitively, motion increases the TAR for the survey-grade antenna. This discrepancy reflects a tradeoff within the CDGNSS filter. While it is true that the phase measurement errors decorrelate much faster when the antenna is moving — increasing the per-epoch information provided to the filter — it is also the case that the filter can no longer employ a hard motion constraint. For the high-quality antennas, the increased information per epoch due to faster phase error decorrelation is completely counteracted by a loss in information per epoch due to uncertainty (lack of constraint) in the motion model. Also, for the high-quality antennas, multipath in the reference antenna’s phase measurements is not insignificant compared to multipath in the mobile antenna, and this reference multipath exhibits the usual 100–200 second correlation time for a static antenna. On the other hand, phase error decorrelation via random antenna motion offers the lower-quality antennas a larger net information gain because their multipath-induced phase errors are so large. Consequently, for the smartphone-grade antenna, motion substantially reduces the 90 percent success TAR, which drops from 400 to 215 seconds.
Figure 13. Probability of successful ambiguity resolution versus time for three different antennas under static and dynamic scenarios.
Conclusions and Future Work
Centimeter-accurate positioning was demonstrated based on data sampled from a smartphone-quality GNSS antenna. An empirical analysis revealed that the extremely poor multipath suppression of these antennas is the primary impediment to fast resolution of the integer ambiguities that arise in the carrier phase differential processing used to obtain centimeter accuracy. It was shown that, for low-quality smartphone-grade GNSS antennas, wavelength-scale random antenna motion substantially reduces the ambiguity resolution time.
Future work will study the effectiveness of combining antenna motion with a motion trajectory estimate derived from non-GNSS smartphone sensors to further reduce the integer ambiguity resolution time. This technique, which is a type of synthetic aperture processing applied to the double-differenced GNSS phase measurements, effectively points antenna gain enhancements in the direction of the overhead GNSS satellites, thereby suppressing multipath arriving from other directions. Preliminary results show that this technique offers modest benefit beyond the unaided random motion technique discussed herein.
Acknowledgment
The material in this article was first presented at ION GNSS+ 2014 in the paper “Centimeter Positioning with a Smartphone-Quality GNSS Antenna.”
Kenneth M. Pesyna, Jr. is a Ph.D. candidate in the Department of Electrical and Computer Engineering at the University of Texas at Austin. He is a member of the University of Texas Radionavigation Laboratory and the Wireless Networking and Communications Group.
Robert W. Heath, Jr. is a Cullen Trust Endowed Professor in Electrical and Computer Engineering at UT-Austin, and director of the Wireless Networking and Communications Group. He received his Ph.D. in electrical engineeringfrom Stanford.
Todd E. Humphreys is an assistant professor in the department of Aerospace Engineeringand Engineering Mechanics at UT-Austin, and director of the UT Radionavigation Laboratory. He received a Ph.D. in aerospace engineering from Cornell University.
