On Saturday, December 10, at about 06:00 UTC, one of the two Galileo In-Orbit Validation (IOV) satellites launched on October 21 started transmitting navigation signals on the L1/E1 frequency using the E11 ranging code.
According to prediction visibilities based on NORAD/JSpOC tracking information, the transmitting satellite is PFM, the ProtoFlight Model (GSAT0101). The FM2 (Flight Model 2) satellite (GSAT0102) has not yet started transmitting navigation signals.
Stations of the COoperative Network for GIOVE Observation (CONGO) were among the first to track the satellite. Results have also been reported by Thales Avionics, JAVAD GNSS, Politecnico di Torino's NavSAS group, and Thales Alenia Space.
The following figure shows C/N0 values in dB-Hz of PFM 1-Hz data collected at the University of New Brunswick CONGO station on December 10. Time axis runs for 24 hours starting at 01:00 UTC. Receiver is a Javad Delta-G2T.
"An important point is that we tracked it with our units that are already in the market," said Javad Ashjaee, CEO. "This is not a lab tests. Our customers can track it too."
Here are the company's tracking results of PRN-11 for now, plots of pseudorange (in chips), doppler (in Hz), and SNR (relative number):
JAVAD GNSS expects to publish additional results soon.
Following the recent launch of two Galileo in-orbit validation satellites, Thales Avionics of Valence, France, has successfully acquired and tracked the new L1 Open Service signal transmitted by one of the space vehicles (PRN 11) on Monday, December 12, at 13:30 (GMT). Thales Avionics has developed a Galileo receiver capable of processing the Open Service, Commercial Service, and Safety of Life service of the Galileo constellation.
Figure 1 shows a screenshot of the receiver interface program highlighting the L1 signal energy (top right) and the pilot secondary code (bottom).
Figure 1: Real-time measurements.
The satellite Doppler and C/N0 values have been recorded and are provided below.
The raw navigation message has been decoded. It contains INAV type 0 and INAV dummy data as shown in the next figure. These messages enable Galileo system time transfer.
The signal modulation and characteristics show no discrepancy relative to the Galileo Open Service ICD released last year.
The fact that only L1 frequency is broadcast for the moment prevents providsion of further results based on dual-frequency measurements.
Thales has developed a coherent processing of the Galileo E5 AltBOC(15,10) signal compatible with hardware architecture designed for independent processing of both E5a and E5b. This processing is fully compatible with the mismatch between the two RF channels on E5a and E5b, thanks to real-time calibration based on satellite signals. This processing only requires software implementation, without additional recurrent costs. The technique is relevant for future receivers operating in the E5 band, in order to significantly enhance the accuracy, with respect to thermal noise and multi-path, and to improve the cycle slip probability.
Thales Avionics, involved for many years in GNSS receivers design and production, has developed a Galileo receiver capable of processing the Open Service, Commercial Service, and Safety of Life service of the Galileo constellation. This high-end receiver includes patented state of the art algorithms capable of processing up to four different frequencies.
By Saeed Daneshmand, Ali Jafarnia-Jahromi, Ali Broumandan, and Gérard Lachapelle
Most anti-spoofing techniques are computationally complicated or limited to a specific spoofing scenario. A new approach uses a two-antenna array to steer a null toward the direction of the spoofing signals, taking advantage of the spatial filtering and the periodicity of the authentic and spoofing signals. It requires neither antenna-array calibration nor a spoofing detection block, and can be employed as an inline anti-spoofing module at the input of conventional GPS receivers.
GNSS signals are highly vulnerable to in-band interference such as jamming and spoofing. Spoofing is an intentional interfering signal that aims to coerce GNSS receivers into generating false position/navigation solutions. A spoofing attack is, potentially, significantly more hazardous than jamming since the target receiver is not aware of this threat. In recent years, implementation of software receiver-based spoofers has become feasible due to rapid advances with software-defined radio (SDR) technology. Therefore, spoofing countermeasures have attracted significant interest in the GNSS community.
Most of the recently proposed anti-spoofing techniques focus on spoofing detection rather than on spoofing mitigation. Furthermore, most of these techniques are either restricted to specific spoofing scenarios or impose high computational complexity on receiver operation.
Due to the logistical limitations, spoofing transmitters often transmit several pseudorandom noise codes (PRNs) from the same antenna, while the authentic PRNs are transmitted from different satellites from different directions. This scenario is shown in Figure 1. In addition, to provide an effective spoofing attack, the individual spoofing PRNs should be as powerful as their authentic peers. Therefore, overall spatial energy of the spoofing signals, which is coming from one direction, is higher than other incident signals. Based on this common feature of the spoofing signals, we propose an effective null-steering approach to set up a countermeasure against spoofing attacks. This method employs a low-complexity processing technique to simultaneously de-spread the different incident signals and extract their spatial energy. Afterwards, a null is steered toward the direction where signals with the highest amount of energy impinge on the double-antenna array. One of the benefits of this method is that it does not require array calibration or the knowledge of the array configuration, which are the main limitations of antenna-array processing techniques.
Processing Method
The block diagram of the proposed method is shown in Figure 2. Without loss of generality, assume that s(t) is the received spoofing signal at the first antenna.
Figure 2. Operational block diagram of proposed technique.
The impinging signal at the second antenna can be modeled by , where θs and μ signify the spatial phase and gain difference between the two channels, respectively. As mentioned before, the spoofer transmits several PRNs from the same direction while the authentic signals are transmitted from different directions. Therefore, θs is the same for all the spoofing signals. However, the incident authentic signals impose different spatial phase differences. In other words, the dominant spatial energy is coming from the spoofing direction. Thus, by multiplying the conjugate of the first channel signals to that of the second channel and then applying a summation over N samples, θs can be estimated as (1)
where r1 and r2 are the complex baseband models of the received signals at the first and the second channels respectively, and Ts is the sampling duration. In (1), θs can be estimated considering the fact that the authentic terms are summed up non-constructively while the spoofing terms are combined constructively, and all other crosscorrelation and noise terms are significantly reduced after filtering. For estimating μ, the signal of each channel is multiplied by its conjugate in the next epoch to prevent noise amplification. It can easily be shown that μ can be estimated as (2)
where T is the pseudorandom code period. Having and a proper gain can be applied to the second channel in order to mitigate the spoofing signals by adding them destructively as (3)
Analyses and Simulation Results
We have carried out simulations for the case of 10 authentic and 10 spoofing GPS signals being transmitted at the same time. The authentic sources were randomly distributed over different azimuth and elevation angles, while all spoofing signals were transmitted from the same direction at azimuth and elevation of 45 degrees. A random code delay and Doppler frequency shift were assigned to each PRN. The average power of the authentic and the spoofing PRNs were –158.5 dBW and –156.5 dBW, respectively.
Figure 3 shows the 3D beam pattern generated by the proposed spoofing mitigation technique. The green lines show the authentic signals coming from different directions, and the red line represents the spoofing signals. As shown, the beam pattern’s null is steered toward the spoofing direction.
Figure 3. Null steering toward the spoofer signals.
In Figure 4, the array gain of the previous simulation has been plotted versus the azimuth and elevation angles. Note that the double-antenna anti-spoofing technique significantly attenuates the spoofer signals. This attenuation is about 11 dB in this case. Hence, after mitigation, the average injected spoofing power is reduced to –167.5 dBW for each PRN. As shown in Figure 4, the double-antenna process has an inherent array gain that can amplify the authentic signals. However, due to the presence of the cone of ambiguity in the two-antenna array beam pattern, the power of some authentic satellites that are located in the attenuation cone might be also reduced.
Figure 4. Array gain with respect to azimuth and elevation.
Monte Carlo simulations were then performed over 1,000 runs for different spoofing power levels. The transmitted direction, the code delay, and the Doppler frequency shift of the spoofing and authentic signals were changed during each run of the simulation. Figure 5 shows the average signal to interference-plus-noise ratio (SINR) of the authentic and the spoofing signals as a function of the average input spoofing power for both the single antenna and the proposed double antenna processes. A typical detection SINR threshold corresponding to PFA=10-3 also has been shown in this figure.
Figure 5. Authentic and spoofed SINR variations as a function of average spoofing power.
In the case of the single antenna receiver, the SINR of the authentic signals decreases as the input spoofing power increases. This is because of the receiver noise-floor increase due to the cross-correlation terms caused by the higher power spoofing signals. However, the average SINR of the spoofing signals increases as the power of the spoofing PRNs increase.
For example, when the average input spoofing power is –150 dBW, the authentic SINR for the single-antenna process is under the detection threshold, while the SINR of the spoofing signal is above this threshold. However, by considering the proposed beamforming method, as the spoofing power increases, the SINR of the authentic signal almost remains constant, while the spoofing SINR is always far below the detection threshold.
Hence, the proposed null-steering method not only attenuates the spoofing signals but also significantly reduces the spoofing cross-correlation terms that increase the receiver noise floor. Early real-data processing verifies the theoretical findings and shows that the proposed method indeed is applicable to real-world spoofing scenarios.
Conclusions
The method proposed herein is implemented before the despreading process; hence, it significantly decreases the computational complexity of the receiver process. Furthermore, the method does not require array calibration, which is the common burden with array-processing techniques.
These features make it suitable for real-time applications and, thus, it can be either employed as a pre-processing unit for conventional GPS receivers or easily integrated into next-generation GPS receivers. Considering the initial experimental results, the required antenna spacing for a proper anti-spoofing scenario is about a half carrier wavelength. Hence, the proposed anti-spoofing method can be integrated into handheld devices.
The proposed technique can also be easily extended to other GNSS signal structures. Further analyses and tests in different real-world scenarios are ongoing to further assess the effectiveness of the method.
Saeed Daneshmand is a Ph.D. student in the Position, Location, and Navigation (PLAN) group in the Department of Geomatics Engineering at the University of Calgary. His research focuses on GNSS interference and multipath mitigation using array processing.
Ali Jafarnia-Jahromi is a Ph.D. student in the PLAN group at the University of Calgary. His research focuses on GNSS spoofing detection and mitigation techniques.
Ali Broumandan received his Ph.D. degree from Department of Geomatics Engineering, University of Calgary, Canada. He is a senior research associate/post-doctoral fellow in the PLAN group at the University.
Gérard Lachapelle holds a Canada Research Chair in wireless location In the Department of Geomatics Engineering at the University of Calgary in Alberta, Canada, and is a member of GPS World’s Editorial Advisory Board.
Charting the Evolution of Signal-in-Space Performance by Data Mining 400,000,000 Navigation Messages
By Liang Heng, Grace Xingxin Gao, Todd Walter, and Per Enge
There are four important requirements of any navigation system: accuracy, availability, continuity, and integrity. In this month’s column we take a look at one particular aspect of GPS integrity: that of the signal in space and find out how trustworthy is the satellite ephemeris and clock information in the broadcast navigation message.
INNOVATION INSIGHTS by Richard Langley
BUT THE GREATEST OF THESE IS INTEGRITY. There are four important requirements of any navigation system: accuracy, availability, continuity, and integrity.
Perhaps the most obvious navigation system requirement, accuracy describes how well a measured value agrees with a reference value, typically the true value. In the case of GPS, we might talk about the accuracy of a range measurement. A receiver actually measures a pseudorange — a biased and noisy measure of the geometric range between the receiver and the satellite. After correcting for satellite ephemeris and satellite clock errors (the primary so-called signal-in-space errors), receiver clock errors, and atmospheric effects, we can get an estimate of the geometric range. How well we account for these errors or biases, will determine the accuracy of the corrected pseudorange measurement and ultimately, the accuracy of a derived position.
A navigation system’s availability refers to its ability to provide the required function and performance within the specified coverage area at the start of an intended operation. In many cases, system availability implies signal availability, which is expressed as the percentage of time that the system’s transmitted signals are accessible for use. In addition to transmitter capability, environmental factors such as signal attenuation or blockage or the presence of interfering signals might affect availability.
Ideally, any navigation system should be continuously available to users. But, because of scheduled maintenance or unpredictable outages, a particular system may be unavailable at a certain time. Continuity, accordingly, is the ability of a navigation system to function without interruption during an intended period of operation. More specifically, it indicates the probability that the system will maintain its specified performance level for the duration of an operation, presuming system availability at the beginning of that process.
The integrity of a navigation system refers to its trustworthiness. A system might be available at the start of an operation, and we might predict its continuity at an advertised accuracy during the operation.
But what if something unexpectedly goes wrong? If some system anomaly results in unacceptable navigation accuracy, the system should detect this and warn the user. Integrity characterizes a navigation system’s ability to provide this timely warning when it fails to meet its stated accuracy. If it does not, we have an integrity failure and the possibility of conveying hazardously misleading information. GPS has built into it various checks and balances to ensure a fairly high level of integrity. However, GPS integrity failures have occasionally occurred.
In this month’s column we take a look at one particular aspect of GPS integrity: that of the signal in space and find out how trustworthy is the satellite ephemeris and clock information in the broadcast navigation message.
The Navstar Global Positioning System is so far the most widely used space-based positioning, navigation, and timing system. GPS works on the principle of trilateration, in which the measured distances from a user receiver to at least four GPS satellites in view, as well as the position and clock data for these satellites, are the prerequisites for the user receiver to fix its exact position. For most GPS Standard Positioning Service (SPS) users, real-time satellite positions and clocks are derived from ephemeris parameters and clock correction terms in navigation messages broadcast by GPS satellites. The GPS Control Segment routinely generates navigation message data on the basis of a prediction model and the measurements at more than a dozen monitor stations. The differences between the broadcast ephemerides/clocks and the truth account for signal-in-space (SIS) errors. SIS errors are usually undetectable and uncorrectable for stand-alone SPS users, and hence directly affect the positioning accuracy and integrity. Nominally, SPS users can assume that each broadcast navigation message is reliable and the user range error (URE) derived from a healthy SIS is at the meter level or even sub-meter level. In practice, unfortunately, SIS anomalies have happened occasionally and UREs of tens of meters or even more have been observed, which can result in an SPS receiver outputting a hazardously misleading position solution. Receiver autonomous integrity monitoring (RAIM) or advanced RAIM is a promising tool to protect stand-alone users from such hazards; however, most RAIM algorithms assume at most one satellite fault at a time. Knowledge about the SIS anomalies in history is very important not only for assessing the GPS SIS integrity performance but also for validating the fundamental assumption of RAIM.
A typical method for calculating SIS UREs is to compare the broadcast ephemerides/clocks with the precise, post-processed ones. Although this method is very effective in assessing the GPS SIS accuracy performance, few attempts have been made to use it to assess the GPS SIS integrity performance because broadcast ephemeris/clock data obtained from a global tracking network sometimes contain errors caused by receivers or data conversion processes and these errors usually result in false SIS anomalies. In this article, we introduce a systematic methodology to cope with this problem and screen out all the potential SIS anomalies in the past decade from when Selective Availability (SA) was turned off.
GPS SIS Integrity
The integrity of a navigation system refers — just as it does to a person — to its honesty, veracity, and trustworthiness. In the case of GPS, this includes the integrity of the ephemeris and clock data in the broadcast navigation messages. We refer to this as signal-in-space integrity.
GPS SIS URE. As indicated by the name, GPS SIS URE is the pseudorange modeling inaccuracy due to operations of the GPS ground control and the space vehicles. Specifically, SIS URE includes satellite ephemeris and clock errors, satellite antenna performance variations, and signal imperfections, but not ionospheric or tropospheric delay, multipath, or any errors due to user receivers. SIS URE is dominated by ephemeris and clock errors because antenna variations and signal imperfections are at a level of millimeters or centimeters.
In broadcast navigation messages, there is a parameter called user range accuracy (URA) that is intended to be a conservative representation of the standard deviation (1-sigma) of the URE at the worst-case location on the Earth. For example, a URA index value of 0 means that the 1-sigma URE is expected to be less than 2.4 meters, and a URA index value of 1 means that the 1-sigma URE is expected to be greater than 2.4 meters but less than 3.4 meters, and so on. In the past several years, most GPS satellites have a URA index value of 0. A nominal URA value, in meters, can be computed as X = 2(1+N/2), where N is the index value, for index values of 6 or less. For 6 < N < 15, X = 2(N-2).
GPS SPS SIS Integrity. In the SPS Performance Standard (PS), as well as the latest version of the Interface Specification (IS-GPS-200E), the GPS SPS SIS URE integrity standard assures that for any healthy SIS, there is an up-to-10−5 probability over any hour of the URE exceeding the not-to-exceed (NTE) tolerance without a timely alert during normal operation. The NTE tolerance is currently defined to be 4.42 times the upper bound (UB) on the URA value broadcast by the satellite. Before September 2008, the NTE tolerance was defined differently, as the maximum of 30 meters and 4.42 times URA UB. The reason for the “magic” number 4.42 here is the Gaussian assumption of the URE, although this assumption may be questionable. (4.42 sigma corresponds to a probability level of 99.999 percent (1 – 10–5)).
In this article, a GPS SPS SIS anomaly is defined as a threat of an SIS integrity failure; that is, a condition during which an SPS SIS marked healthy results in a URE exceeding the NTE tolerance. Because the definition of the NTE tolerance is different before and after September 2008, we consider both of the two NTE tolerances for the sake of completeness and consistency.
Methodology
The SIS anomalies are screened out by comparing broadcast ephemerides/clocks with precise ones. As shown in Figure 1, the whole process consists of three steps: data collecting, data cleansing, and anomaly screening.
Figure 1. Framework of the whole process. XYZB values refer to the coordinates of satellite position and satellite clock bias.
In the first step, the navigation message data files are downloaded from the International GNSS Service (IGS). In addition, two different kinds of precise ephemeris/clock data are downloaded from IGS and the National Geospatial-Intelligence Agency (NGA), respectively. The details about these data sources will be discussed in the next section.
Since each GPS satellite can be observed by many IGS stations at any instant, each navigation message is recorded redundantly. In the second step, a data-cleansing algorithm exploits the redundancy to remove the errors caused on the ground. This step distinguishes our work from that of most other researchers because the false anomalies due to corrupted data can be mostly precluded.
The last step is computing worst-case SIS UREs as well as determining potential SIS anomalies. The validated navigation messages prepared in the second step are used to propagate broadcast orbits/clocks at 15-minute intervals that coincide with the precise ones. A potential SIS anomaly is claimed when the navigation message is healthy and in its fit interval with the worst-case SIS URE exceeding the SIS URE NTE tolerance.
Data Sources
We obtained broadcast navigation message data and precise ephemeris and clock data from publicly available sources.
Broadcast Navigation Message Data. Broadcast GPS navigation message data files are available at IGS Internet sites. All the data are archived in Receiver Independent Exchange (RINEX) navigation file format, which includes not only the ephemeris/clock parameters broadcast by the satellites but also some information produced by the ground receivers, such as the pseudorandom noise (PRN) signal number and the transmission time of message (TTOM).
The IGS tracking network is made up of more than 300 volunteer stations all over the world (a map is shown in Table 1) ensuring seamless, redundant data logging. Since broadcast navigation messages are usually updated every two hours, no single station can record all navigation messages. For the ease of users, two IGS archive sites, the Crustal Dynamics Data Information System (CDDIS) and the Scripps Orbit and Permanent Array Center (SOPAC), provide two kinds of ready-to-use daily global combined broadcast navigation message data files, brdcddd0.yyn and autoddd0.yyn, respectively, where ddd is the day of year yy. Unfortunately, these files sometimes contain errors that can cause false anomalies.
Table 1. Comparison of IGS and NGA precise ephemeris/clock data.
Therefore, we devised and implemented a data-cleansing algorithm to generate the daily global combined navigation messages, which are as close as possible to the navigation messages that the satellites actually broadcast, from all available navigation message data files of all IGS stations. The data-cleansing algorithm is based on majority vote, and hence all values in our data are cross validated. Accordingly, we name our daily global combined navigation messages “validated navigation messages,” as shown in Figure 1.
Precise Ephemeris and Clock Data. Precise GPS ephemerides/clocks are generated by some organizations such as IGS and NGA that routinely post-process observation data. Precise ephemerides/clocks are regarded as “truth” because of their centimeter-level accuracy.
Table 1 shows a side-by-side comparison between IGS and NGA precise ephemeris/clock data, in which the green- and red-colored text implies pros and cons, respectively. For NGA data, the only con is that the data have been publicly available only since January 4, 2004. As a result, for the broadcast ephemerides/clocks before this date, IGS precise ephemerides/clocks are the only references. Nevertheless, care must be taken when using IGS precise ephemerides/clocks due to the following three issues.
The first issue with the IGS precise ephemerides/clocks is the relatively high rate of bad/absent data, as shown in the third row of Table 1. For a GPS constellation of 27 healthy satellites, 1.5 percent bad/absent data means no precise ephemerides or clocks for approximately 10 satellite-hours per day. This issue can result in undetected anomalies (false negatives).
The second issue is that, as shown in the fourth row of Table 1, IGS switched to IGS Time for its precise ephemeris/clock data on 22 February, 2004. The IGS clock is not synchronized to GPS Time, and the differences between the two time references may be as large as 3 meters. Fortunately, the time offsets can be extracted from the IGS clock data files. Moreover, a similar problem is that IGS precise ephemerides use a frame aligned to the International Terrestrial Reference Frame (ITRF) whereas broadcast GPS ephemerides are based on the World Geodetic System 1984 (WGS 84). The differences between ITRF and the versions of WGS 84 used since 1994 are on the order of a few centimeters, and hence a transformation is not considered necessary for the purpose of our work.
The last, but not the least important, issue with the IGS precise ephemerides is that the data are provided only for the center of mass (CoM) of the satellite. Since the broadcast ephemerides are based on the satellite antenna phase center (APC), the CoM data must be converted to the APC before being used. Both IGS and NGA provide antenna corrections for every GPS satellite. Although the IGS and the NGA CoM data highly agree with each other, the IGS satellite antenna corrections are quite different from the NGA’s, and the differences in z-offsets can be as large as 1.6 meters for some GPS satellites. The reason for these differences is mainly due to the different methods in producing the antenna corrections: the IGS antenna corrections are based on the statistics from more than 10 years of IGS data, whereas the NGA’s are probably from the calibration measurements on the ground. In order to know whose satellite antenna corrections are better, the broadcast orbits for all GPS satellites in 2009 were computed and compared with three different precise ephemerides: IGS CoM + IGS antenna corrections, IGS CoM + NGA antenna corrections, and NGA APC. Generally, the radial ephemeris error is expected to have a zero mean. However, the combination “IGS CoM + IGS antenna corrections” results in radial ephemeris errors with a non-zero mean for more than half of the GPS satellites. Therefore, the NGA antenna corrections were selected to convert the IGS CoM data to the APC.
Data Cleansing
Figure 2 shows a scenario of data cleansing. Owing to accidental bad receiver data and various hardware/software bugs, a small proportion of the navigation data files from the IGS stations have defects such as losses, duplications, inconsistencies, discrepancies, and errors. Therefore, more than just removing duplications, the generation of validated navigation messages is actually composed of two complicated steps.
Figure 2. A scenario of data cleansing: In the figure, the GPS satellite PRN32 started to transmit a new navigation message at 14:00. Receiver 1 had not observed the satellite until 14:36, and hence the TTOM in its record was 14:36. Additionally, Receiver 1 made a one-bit error in ∆n (4.22267589140 × 10-9 11823 × 2−43 π). Receiver 2 perhaps had some problems in its software: the IODC was unreported and both the toc and ∆n were written weirdly. Receiver n used an incorrect ranging code, PRN01, to despread and decode the signal of PRN32; fortunately, all the parameters except TTOM were perfectly recorded. Moreover, the three receivers interpreted URA (SV accuracy) differently. A computer equipped with our data cleansing algorithms is used to process all the data from the receivers. The receiver-caused errors are removed and the original navigation message is recovered.
First step. Suppose that we want to generate the validated navigation messages for day n. In the first step, we apply the following operations sequentially to each RINEX navigation data file from day n − 1 to day n + 1:
1) Parse the RINEX navigation file;
2) Recover least significant bit (LSB);
3) Classify URA values;
4) Remove the navigation messages not on day n;
5) Remove duplications;
6) Add all remaining navigation messages into the set O.
The reason why the data files from day n − 1 to day n + 1 are considered is that a few navigation messages around 00:00 can be included in some data files on day n − 1, and a few navigation messages around 23:59 can be included in some data files on day n + 1. The LSB recovery is used here to cope with the discrepant representations of floating-point numbers in RINEX navigation files. The URA classifier is employed to recognize and unify various representations of URA in the files. The duplication removal is applied because some stations write the same navigation messages repeatedly in one data file, which is unfavorable to the vote in the second step.
Second Step. At the end of the first step, we have a set O that includes all the navigation messages on day n. The set O still has duplications because a broadcast navigation message can be reported by many IGS stations. However, as shown in Figure 2, duplications of a broadcast navigation message may come with different errors and are not necessarily identical. Several other examples of such problems can be found in our journal paper listed in Further Reading. Fortunately, most orbital and clock parameters are seldom reported incorrectly, and even when errors happen, few stations agree on the same incorrect value. In our work, these parameters are referred to as robust parameters. On the contrary, some parameters, such as TTOM, PRN, URA and issue of data clock (IODC), are more likely to be erroneous and when errors happen, several stations may make the same mistake. These parameters are referred to as fragile parameters. The cause of the fragility is either the physical nature (for example, TTOM, PRN) or the carelessness in hardware/software implementations (for example, URA, IODC).
Majority vote is applied to all fragile parameters (except TTOM, which is determined by another algorithm described in our journal paper) under the principle that the majority is usually correct. Meanwhile, the robust parameters are utilized to identify the equivalence of two navigation messages — two navigation messages are deemed identical if and only if they agree on all the robust parameters, although their fragile parameters could be different. Therefore, the goal of duplication removal and majority vote is a set P, in which any navigation message must have at least one robust parameter different from any other and has all fragile parameters confirmed by the largest number of stations that report this navigation message.
After the operations above, we have a set P in which there are no duplicated navigation messages in terms of robust parameters and all fragile parameters are as correct as possible. A few navigation messages in P still have errors in their robust parameters. These unwanted navigation messages feature a small number of reporting stations. Finally, the navigation messages confirmed by only a few stations being discarded and the survivors are the validated broadcast navigation messages, stored in files sugldddm.yyn. For further details of our algorithms, see our journal paper.
Anomaly Screening
The validated broadcast navigation messages prepared using the algorithm described in the previous section were employed to propagate broadcast satellite orbits and clocks. For each 15-miniute epoch, t, that coincides with precise ephemerides/clocks, the latest transmitted broadcast ephemeris/clock is chosen to calculate the worst-case SIS URE – the maximum SIS URE that a user on Earth can experience.
Finally, a potential GPS SIS anomaly is claimed when all of the following conditions are fulfilled.
The worst-case SIS URE exceeds the NTE tolerance;
The broadcast navigation message is healthy; that is,
The RINEX field SV health is 0, and
The URA UB ≤ 48 meters;
The broadcast navigation message is in its fit interval; that is, ∆t = t − TTOM ≤ 4 hours;
The precise ephemeris/clock is available and healthy.
Results
A total of 397,044,414 GPS navigation messages collected by an average of 410 IGS stations from June 1, 2000 (one month after turning off SA), to August 31, 2010, have been screened. The NGA APC precise ephemerides/clocks and the IGS CoM precise ephemerides/clocks with the NGA antenna corrections were employed as the truth references. Both old and new NTE tolerances were used for determining anomalies.
Before interpreting the results, it should be noted that there are some limitations due to the data sources and the anomaly-determination criteria. First, false anomalies may be claimed because there may be some errors in the precise ephemerides/clocks or the validated navigation messages. Second, some short-lived anomalies may not show up if they happen to fall into the 15-minute gaps of the precise ephemerides/clocks. Third, some true anomalies may not be detected if the precise ephemerides/clocks are temporarily missing. The third limitation is especially significant for the results before January 3, 2004, because only the IGS precise ephemerides/clocks are available, which feature a high rate of bad/absent data. (For example, the clock anomaly of Space Vehicle Number (SVN) 23/PRN23 that occurred on January 1, 2004 is missed by our process because the IGS precise clocks for PRN23 on that day were absent.) Last but not least, users might not experience some anomalies because a satellite was not trackable at that time, or the users were notified via a Notice Advisory to Navstar Users (NANU). (A satellite may indicate that it is unhealthy through the use of non-standard code or data. The authors’ future work will include using observation data to verify the potential anomalies found in the results presented here.) Therefore, all the SIS anomalies claimed in this article are considered to be potential and under further investigation.
Potential SIS Anomalies. A total of 1,256 potential SIS anomalies were screened out under SPS PS 2008 (or 374 potential SIS anomalies under SPS PS 2001). Figure 3 shows all these anomalies in a Year-SVN plot. It can be seen that during the first year after SA was turned off, SIS anomalies occurred frequently for the whole constellation.
Figure 3. Potential SIS anomalies from June 1, 2000, to August 31, 2010. The horizontal lines depict the periods when the satellites were active (not necessarily healthy). The color of the lines indicates the satellites’ block type, as explained by the top left legend.
Moreover, 2004 is apparently a watershed: before 2004, anomalies occurred for all GPS satellites (except two satellites launched in 2003, SVN45/PRN21 and SVN56/PRN16) whereas after 2004, anomalies occurred much less frequently and more than 10 satellites have never been anomalous. Figure 4 further confirms the improving GPS SIS integrity performance in the past decade, no matter which SPS PS is considered.
Figure 4. Number of potential SIS anomalies per year. The SIS performance was improved during the past decade. There were 0 anomalies in 2009 according to SPS PS 2001 and this number is represented by 0.1 in the figure.
Therefore, it is possible to list all potential SIS anomalies from January 4, 2004, to August 31, 2010, in a compact table: Table 2. Most anomalies in the table have been confirmed by NANUs and other literature. The table reveals an important and exciting piece of information: never have two or more SIS anomalies occurred simultaneously since 2004. Accordingly, in the sense of historical GPS SIS integrity performance, it is valid for RAIM to assume at most one satellite fault at a time.
Table 2. List of potential anomalies from January 4, 2004, to August 31, 2010.
Validated Navigation Messages. For the purpose of comparison and verification, the IGS daily global combined broadcast navigation message data files brdcddd0.yyn and autoddd0.yyn were used to propagate broadcast satellite orbits and clocks as well. The NGA APC precise ephemerides/clocks were employed for the truth references. The SPS PS 2008 NTE tolerance was used for determining anomalies. The other criteria for anomaly screening that are the same as in the previous section were still applied.
All the potential SIS anomalies for 2006–2009 were found based on the three kinds of daily combined broadcast navigation messages. Table 3 shows a comparison of the total hours of the anomalies per year. It can be seen that brdcddd0.yyn and autoddd0.yyn result in approximately 11 times more false anomalies than true ones. Moreover, all potential anomalies derived from sugldddm.yyn are confirmed by brdcddd0.yyn and autoddd0.yyn, which indicates that our sugldddm.yyn does not introduce any more false anomalies than brdcddd0.yyn and autoddd0.yyn.
Table 3. Total hours of anomalies per year computed from three different kinds of daily global combined broadcast navigation messages.
Conclusion
In this article, the GPS SIS integrity performance in the past decade was assessed by comparing the broadcast ephemerides/clocks with the precise ones. Thirty potential anomalies were found. The fundamental assumption of RAIM is valid based on a review of the GPS SIS integrity performance in the past seven years.
Acknowledgments
The authors gratefully acknowledge the support of the Federal Aviation Administration. This article contains the personal comments and beliefs of the authors, and does not necessarily represent the opinion of any other person or organization.
The authors would like to thank Mr. Tom McHugh, William J. Hughes FAA Technical Center, for his valuable input to the data-cleansing algorithm. This article is based on the paper “GPS Signal-in-Space Integrity Performance Evolution in the Last Decade: Data Mining 400,000,000 Navigation Messages from a Global Network of 400 Receivers” to appear in the Institute of Electrical and Electronics Engineers (IEEE) Transactions on Aerospace and Electronic Systems..
Liang Heng is a Ph.D. candidate under the guidance of Professor Per Enge in the Department of Electrical Engineering at Stanford University.
Grace Xingxin Gao is a research associate in the GPS Research Laboratory of Stanford University.
Todd Walter is a senior research engineer in the Department of Aeronautics and Astronautics at Stanford University.
Per Enge is a professor of Aeronautics and Astronautics at Stanford University, where he is the Kleiner-Perkins, Mayfield, Sequoia Capital Professor in the School of Engineering. He directs the GPS Research Laboratory, which develops satellite navigation systems based on GPS.
FURTHER READING
• Authors’ Research Papers
“GPS Signal-in-Space Integrity Performance Evolution in the Last Decade: Data Mining 400,000,000 Navigation Messages from a Global Network of 400 Receivers” by L. Heng, G.X. Gao, T. Walter, and P. Enge in Transactions on Aerospace and Electronic Systems, the Institute of Electrical and Electronics Engineers, accepted for publication.
“GPS Signal-in-Space Anomalies in the Last Decade: Data Mining of 400,000,000 GPS Navigation messages” by L. Heng, G.X. Gao, T. Walter, and P. Enge in Proceedings of ION GNSS 2010, the 23rd International Technical Meeting of The Satellite Division of the Institute of Navigation, Portland, Oregon, September 21–24, 2010, pp. 3115–3122.
“GPS Ephemeris Error Screening and Results for 2006–2009” by L. Heng, G.X. Gao, T. Walter, and P. Enge in Proceedings of ION ITM 2010, the 2010 International Technical Meeting of the Institute of Navigation, San Diego, California, January 24–26, 2010, pp. 1014–1022.
• Earlier Work on Assessing GPS Broadcast Ephemerides and Clocks
“GPS Orbit and Clock Error Distributions” by C. Cohenour and F. van Graas in Navigation, Vol. 58, No. 1, Spring 2011, pp. 17–28.
“Statistical Characterization of GPS Signal-in-Space Errors” by L. Heng, G.X. Gao, T. Walter, and P. Enge in Proceedings of ION ITM 2011, the 2011 International Technical Meeting of the Institute of Navigation, San Diego, California, January 24–26, 2011, pp. 312–319.
“Broadcast vs. Precise GPS Ephemerides: A Historical Perspective” by D.L.M. Warren and J.F. Raquet in GPS Solutions, Vol. 7, No. 3, 2003, pp. 151–156, doi: 10.1007/s10291-003-0065-3.
“Accuracy and Consistency of Broadcast GPS Ephemeris Data” by D.C. Jefferson and Y.E. Bar-Sever in Proceedings of ION GPS-2000, the 13th International Technical Meeting of the Satellite Division of The Institute of Navigation, Salt Lake City, Utah, September 19–22, 2000, pp. 391–395.
“The GPS Broadcast Orbits: An Accuracy Analysis” by R.B. Langley, H. Jannasch, B. Peeters, and S. Bisnath, presented in Session B2.1-PSD1, New Trends in Space Geodesy at the 33rd COSPAR Scientific Assembly, Warsaw, July 16–23, 2000.
• Signal-in-Space Anomalies
“GNSS: The Present Imperfect” by D. Last in Inside GNSS, Vol. 5, No. 3, May 2010, pp. 60–64.
“Investigation of Upload Anomalies Affecting IIR Satellites in October 2007” by K. Kovach, J. Berg, and V. Lin in Proceedings of ION GNSS 2008, the 21st International Technical Meeting of the Satellite Division of The Institute of Navigation, Savannah, Georgia, September 16–19, 2008, pp. 1679–1687.
“GPS Receiver Responses to Satellite Anomalies” by J.W. Lavrakas and D. Knezha in Proceedings of the 1999 National Technical Meeting of The Institute of Navigation, San Diego, California, January 25–27, 1999, pp. 621–626.
• GPS Integrity and Receiver Autonomous Integrity Monitoring
“Prototyping Advanced RAIM for Vertical Guidance” by J. Blanch, M.J. Choi, T. Walter, P. Enge, and K. Suzuki in Proceedings of ION GNSS 2010, the 23rd International Technical Meeting of the Satellite Division of The Institute of Navigation, Portland, Oregon, September 21–24, 2010, pp. 285–291.
“The Integrity of GPS” by R.B. Langley in GPS World, Vol. 10, No. 3, March 1999, pp. 60–63.
• International GNSS Service Ephemerides and Clocks
“On the Precision and Accuracy of IGS Orbits” by J. Griffiths and J.R. Ray in Journal of Geodesy, Vol. 83, 2009, pp. 277–287, doi: 10.1007/s00190-008-0237-6.
• National Geospatial-Intelligence Agency Ephemerides and Clocks
“NGA’s Role in GPS” by B. Wiley, D. Craig, D. Manning, J. Novak, R. Taylor, and L. Weingarth in Proceedings of ION GNSS 2006, the 19th International Technical Meeting of the Satellite Division of The Institute of Navigation, Fort Worth, Texas, September 26–29, 2006, pp. 2111–2119.
“Generation of a Consistent Absolute Phase-center Correction Model for GPS Receiver and Satellite Antennas” by R. Schmid, P. Steigenberger, G. Gendt, M. Ge, and M. Rothacher in Journal of Geodesy, Vol. 81, No. 12, 2007, pp. 781–798, doi: 10.1007/s00190-007-0148-y.
By Pratibha B. Anantharamu, Daniele Borio, and Gérard Lachapelle
Spatial and temporal information of signals received from multiple antennas can be applied to mitigate the impact of new GPS and Galileo signals’ binary-offset sub-carrier, reducing multipath and interference effects.
New modernized GNSS such as GPS, Galileo, GLONASS, and Compass broadcast signals with enhanced correlation properties as compared to the first generation GPS signals. These new signals are characterized by different modulations that provide improved time resolution, resulting in more precise range measurements, along with the advantage of being more resilient to multipath and RF interference. One of these modulations is the binary-offset-carrier (BOC) modulation transmitted by Galileo and modernized GPS.
Despite the benefits of BOC modulation schemes, difficulties in tracking BOC signals can arise. The autocorrelation function (ACF) of BOC signals is multi-peaked, potentially leading to false peak-lock and ambiguous tracking. Intense research activities have produced different BOC tracking schemes that address the issue of multi-peaked BOC signal tracking. Additionally, new tracking schemes including space-time processing can be adopted to further improve the performance of existing algorithms.
Space-time equalization is a technique that utilizes spatial and temporal information of signals received from multiple antennas to compensate for the effects of multipath fading and co-channel interference. In the context of BOC signals, these kinds of techniques can be applied to mitigate the impact of the sub-carrier, which is responsible for a multi-peaked ACF, reducing multipath and interference effects. In temporal processing, traditional equalizers in time-domain are useful to compensate for signal distortions. But equalization becomes more challenging in the case of BOC signals, where the effect of both sub-carrier and multipath must be accounted for. On the other hand, by using spatial processing, it should be possible to extract the desired signal component from a set of received signals by electronically varying the antenna array directivity (beamforming).
The combination of an antenna array and a temporal equalizer results in better system performance. Hence the main objective of this research is to apply space-time processing techniques to BOC modulated signals received by an antenna array. The main intent is to enhance the signal quality, avoid ambiguous tracking and improve tracking performance under weak signal environments or in the presence of harsh multipath components.
The focus of previous antenna-array processing using GNSS signals was on enhancing GNSS signal quality and mitigating interference and/or multipath related issues. Unambiguous tracking was not considered. Here, we develop a space-time algorithm to mitigate ambiguous tracking of BOC signals along with improved signal quality. The main objective is to obtain an equalization technique that can operate on BOC signals to provide unambiguous BPSK-like correlation function capable of altering the antenna array beam pattern to improve the signal to interference plus noise ratio.
Space-time adaptive processing structure proposed for BOC signal tracking; the temporal filter provides signal with unambiguous ACF whereas the spatial filter provides enhanced performance with respect to multipath, interference, and noise.
Initially, temporal equalization based on the minimum mean square error (MMSE) technique is considered to obtain unambiguous ACF on individual antenna outputs. Spatial processing is then applied on the correlator outputs based on a modified minimum variance distortionless response (MVDR) approach. As part of spatial processing, online calibration of the real antenna array is performed which also provides signal and noise information for the computation of the beamforming weights. Finally, the signal resulting from temporal and spatial equalization is fed to a common code and carrier tracking loop for further processing.
The effectiveness of the proposed technique is demonstrated by simulating different antenna array structures for BOC signals. Intermediate-frequency (IF) simulations have been performed and linear/planar array structures along with different signal to interference plus noise ratios have been considered. A modified version of The University of Calgary software receiver, GSNRx, has been used to simultaneously process multi-antenna data. Further tests have been performed using real data collected from Galileo test satellites, GIOVE-A and GIOVE-B, using an array structure comprising of two to four antennas. A 4-channel front-end designed in the PLAN group, and a National Instruments (NI) signal vector analyzer equipped with three PXI-5661 front-ends (NI 2006) have been used to collect data synchronously from several antennas. The data collected from the antennas were progressively attenuated for the analysis of the proposed algorithm in weak signal environments.
From the performed tests and analysis, it is observed that the proposed methodology provides unambiguous ACF. Spatial processing is able to efficiently estimate the calibration parameters and steer the antenna array beam towards the direction of arrival of the desired signal. Thus, the proposed methodology can be used for efficient space-time processing of new BOC modulated GNSS signals.
Signal and Systems Model
The complex baseband GNSS signal vector received at the input of an antenna array can be modeled as (1)
where
• M is the number of antenna elements;
• L is the number of satellites;
• C is a M × M calibration matrix capturing the effects of antenna gain/phase mismatch and mutual coupling;
• si = is the complex M × 1 steering vector relative to the signal from the ith satellite. si captures the phase offsets between signals from different antennas;
• is the noise plus interference vector observed by the M antennas.
The ith useful signal component xi (t) can be modeled as (2)
where
• Ai is the received signal amplitude;
• di() models the navigation data bit;
• ci() is the ranging sequence used for spreading the transmitted data;
• τ0,i, f0,i and φ0,imodel the code delay, Doppler frequency and carrier phase introduced by the communication channel.
The index i is used to denote quantities relative to the ith satellite. The ranging code ci() is made up of several components including a primary spreading sequence, a secondary code and a sub-carrier.
For a BPSK modulated signal, the sub-carrier is a rectangular window of duration Tc. In the case of BOC modulated signals, the sub-carrier is generated as the sign of a sinusoidal carrier. The presence of this sub-carrier produces a multi-peaked autocorrelation function making the acquisition/tracking processes ambiguous.
In order to extract signal parameters such as code delay and Doppler frequency of the ith useful signal xi(t), the incoming signal is correlated with a locally generated replica of the incoming code and carrier. This process is referred to as correlation where the carrier of the incoming signal is at first wiped off using a local complex carrier replica. The spreading code is also wiped off using a ranging code generator. The signal obtained after carrier and code removal is integrated and dumped over T seconds to provide correlator outputs. The correlator output for the hth satellite and mth antenna can be modeled as: (3)
where vm,kare the coefficients of the calibration matrix, C and R(Δτh) is the multi-peaked ACF. τh, fD,h and φh are the code delay, Doppler frequency and carrier phase estimated by the receiver and Δτh, ΔfD,h and Δφh are the residual delay, frequency, and phase errors. is the residual noise term obtained from the processing of η(t). Eq. (3) is the basic signal model that will be used for the development of a space-time technique suitable for unambiguous BOC tracking.
When BOC signals are considered, algorithms should be developed to reduce the impact of that include receiver noise, interference and multipath components, along with the mitigation of ambiguities in R(Δτh). Space-time processing techniques have the potential to fulfill those requirements.
Space-Time Processing
A simplified representation of a typical space-time processing structure is provided in Figure 1. Each antenna element is followed by K taps with δ denoting the time delay between successive taps forming the temporal filter. The combination of several antennas forms the spatial filter. wmk are the space-time weights with 0 ≤ k ≤ K and 0 ≤ m ≤ M. k is the temporal index and m is the antenna index.
Figure 1. Block diagram of space-time processing.
The array output after applying the space-time filter can be expressed as (4)
where (wmk)* denotes complex conjugate. The spatial-only filter can be realized by setting K=1 and a temporal only filter is obtained when M=1. The weights are updated depending on the signal/channel characteristics subject to user-defined constraints using different adaptive techniques. This kind of processing is often referred to as Space-Time Adaptive Processing (STAP). The success of STAP techniques has been well demonstrated in radar, airborne and mobile communication systems. This has led to the application of STAP techniques in the field of GNSS signal processing. Several STAP techniques have been developed for improving the performance of GNSS signal processing. These techniques exploit the advantages of STAP to minimize the effect of multipath and interference along with improving the overall signal quality.
Space-time processing algorithms can be broadly classified into two categories: decoupled and joint space-time processing. The joint space-time approach exploits both spatial and temporal characteristics of the incoming signal in a single space-time filter while the decoupled approach involves several temporal equalizers and a spatial beamformer that are realized in two separate stages (Figure 2).
Figure 2. Representation of two different space-time processing techniques
When considering the decoupled approach for GNSS signals, temporal filters can be applied on the data from the different antennas whereas the spatial filter can be applied at two different stages, namely pre-correlation or post-correlation. In the pre-correlation stage, spatial weights are applied on the incoming signal after carrier wipe-off while in the post-correlation stage, spatial weights are applied after the Integrate & Dump (I&D) block on the correlator outputs. In pre-correlation processing, the update rate of the weight vector is in the order of MHz (same as the sampling frequency) whereas the post-correlation processing has the advantage of lower update rates in the order of kHz (I&D frequency). In the pre-correlation case, the interference and noise components prevail significantly in the spatial correlation matrix and would result in efficient interference mitigation and noise reduction. But the information on direct and reflected signals are unavailable since the GNSS signals are well below the noise level. This information can be extracted using post-correlation processing.
In the context of new GNSS signals, efforts to utilize multi-antenna array to enhance signal quality along with interference and multipath mitigation have been documented using both joint and decoupled approaches where the problem of ambiguous signal tracking was not considered.
In our research, we considered the decoupled space-time processing structure. Temporal processing is applied at each antenna output and spatial processing is applied at the post-correlation stage. Temporal processing based on MMSE equalization and spatial processing based on the adaptive MVDR beamformer are considered.
Methodology
The opening figure shows the proposed STAP architecture for BOC signal tracking. In this approach, the incoming BOC signals are at first processed using a temporal equalizer that produces a signal with a BPSK-like spectrum. The filtered spectra from several antennas are then combined using a spatial beamformer that produces maximum gain at the desired signal direction of arrival. The beamformed signal is then fed to the code and carrier lock loops for further processing. The transfer function of the temporal filter is obtained by minimizing the error: (5)
where H(f) is the transfer function of the temporal filter that minimizes the MSE, εMMSES, between the desired spectrum, GD(f), and filtered spectrum, Gx(f)H(f). The spectrum of the incoming BOC signal is denoted by Gx(f). λ is a weighting factor determining the impact of noise with respect to that of an ambiguous correlation function. N0 is the noise power spectral density and C the carrier power. The desired spectrum is considered to be a BPSK spectrum. Since this type of processing minimizes the MSE, it is denoted MMSE Shaping (MMSES).
Figure 3 shows a sample plot of the ACF obtained after applying MMSES on live Galileo BOCs(1,1) signals collected from the GIOVE-B satellite. The input C/N0 was equal to 40 dB-Hz and the ACF was averaged over 1 second of data. It can be observed
that the multi-peaked ACF was successfully modified by MMSES to produce a BPSK-like ACF without secondary peaks. Also narrow ACF were obtained by modifying the filter design for improved multipath mitigation. Thus using temporal processing, the antenna array data are devoid of ambiguity due to the presence of the sub-carrier.
After temporal equalization, the spatial weights are computed and updated based on the following information:
The signal and noise covariance matrix obtained from the correlator outputs;
Calibration parameters estimated to minimize the effect of mutual coupling and antenna gain/phase mismatch;
Satellite data decoded from the ephemeris/almanac containing information on the GNSS signal DoA.
The weights are updated using the iterative approach for the MVDR beamformer to maximize the signal quality according to the following steps:
Step 1: Update the estimate of the steering vector for the hthsatellite using the calibration parameters as: (6)
Here vi,j represents the estimated calibration parameters using the correlator outputs given by Eq. (3) and shm is the element of the steering vector computed using the satellite ephemeris/almanac data.
Step 2: Update the weight vector (the temporal index, k, is removed for ease of notation) using the new estimate of the covariance matrix and steering vector as (7)
where is the input signal after carrier wipe-off.
Repeat Steps 1 and 2 until the weights converge. Finally compute the correlator output to drive the code and carrier tracking loop according to Equation (4).
The C/N0 gain obtained after performing calibration and beamforming on a two-antenna linear array and four-antenna planar array data collected using the four channel front-end is provided in Figure 4 and Figure 5. The C/N0 plots are characterized by three regions:
Single Antenna that provides C/N0 estimates obtained using q0,h alone;
BeforeCalibration that provides C/N0 estimates obtained by compensating only the effects of the steering vector, si, before combining the correlator outputs from all antennas;
AfterCalibration that provides C/N0 estimates obtained by compensating the effects of both steering vector, si and calibration matrix, C, before combining correlator outputs from all antennas.
After calibration, beamforming provides approximately a C/N0 gain equal to the theoretical one on most of the satellites whereas before calibration, the gain is minimal and, in some cases, negative with respect to the single antenna case. These results support the effectiveness of the adopted calibration algorithm and the proposed methodology that enables efficient beamforming.
Figure 4. C/N0 estimates obtained after performing calibration and beamforming on linear array data.Figure 5. C/N0 estimates obtained after performing calibration and beamforming on the planar array data.
Results and Analysis
IF simulated BOCs(1,1) signals for a 4-element planar array with array spacing equal to half the wavelength of the incoming signal has been considered to analyze the proposed algorithm. The input signal was characterized by a C/N0 equal to 42 dB-Hz at an angle of arrival of 20° elevation and 315° azimuth angle.
A sample plot of the antenna array pattern using the spatial beamformer is shown in Figure 6. In the upper part of Figure 6, the ideal case in the absence of interference was considered. The algorithm is able to place a maximum of the array factor in correspondence of the signal DoA.
Figure 6. Antenna array pattern for a 4-element planar array computed using a MVDR beamformer in the presence of two interference sources.
In the bottom part, results in the presence of interference are shown. Two interference signals were introduced at 60 and 45 degree elevation angles. It can be clearly observed that, in the presence of interference, the MVDR beamformer successfully adapted the array beam pattern to place nulls in the interference DoA.
In order to further test the tracking capabilities of the full system, semi-analytic simulations were performed for the analysis of digital tracking loops. The simulation scheme is shown in Figure 7 and consists of M antenna elements. Each antenna input for the hth satellite is defined by a code delay (τm,h) and a carrier phase value (φm,h) for DLL and PLL analysis. φm,h captures the effect of mutual coupling, antenna phase mismatch and phase effects due to different antenna hardware paths. To analyze the post-correlation processing structure, each antenna input is processed independently to obtain the error signal, Δτm,h / Δφm,h as where are the current delay/phase estimates.
Figure 7. Semi-analytic simulation model for a multi-antenna system comprising M antennas with a spatial beamformer.
Each error signal is then used to obtain the signal components that are added along with the independent noise components, . The combined signal and noise components from all antenna elements are fed to the spatial beamformer to produce a single output according to the algorithm described in the Methodology section. Finally, the beamformer output is passed through the loop discriminator, filter and NCO to provide a new estimate . The Error to Signal mapping block and the noise generation process accounts for the impact of temporal filtering.
Figure 8 shows sample tracking jitter plots for a PLL with a single, dual and three-antenna array system obtained using the structure described above.
Figure 8. Phase-tracking jitter obtained for single, dual and three-antenna linear array as a function of the input C/N0 for a Costas discriminator (20 milliseconds coherent integration and 5-Hz bandwidth).
The number of simulation runs considered was 50000 with a coherent integration time of 20 ms and a PLL bandwidth equal to 5 Hz. As expected the tracking jitter improves when the number of antenna elements is increased along with improved tracking sensitivity. As expected, the C/N0 values at which loss of lock occurs for a three antenna system is reduced with respect to the single antenna system, showing its superiority.
Real data analysis. Figure 9 shows the experimental setup considered for analysis of the proposed combined space-time algorithm. Two antennas spaced 8.48 centimeters apart were used to form a 2-element linear antenna array structure. The NI front-end was employed for the data collection process to synchronously collect data from the two-antenna system.
Data on both channels were progressively attenuated by 1 dB every 10 seconds to simulate a weak signal environment until an attenuation of 20 dB was reached. When this level of attenuation was reached, the data were attenuated by 1 dB every 20 seconds to allow for longer processing under weak signal conditions. In this way, data on both antennas were attenuated simultaneously. Data from Antenna 1 were passed through a splitter, as shown in Figure 9, before being attenuated in order to collect signals used to produce reference code delay and carrier Doppler frequencies.
Figure 9. Experimental setup with signals collected using two antennas spaced 8.48 centimeters apart.
BOCs(1,1) signals collected using Figure 9 were tracked using the temporal and spatial processing technique described in the opening figure. The C/N0 results obtained using single and two antennas are provided in Figure 10. In the single antenna case, only temporal processing was used. In this case, the loop was able to track signals for an approximate C/N0 of 19 dB-Hz. Using the space-time processing, the dual antenna system was able to track for nearly 40 seconds longer than the single antenna case, thus providing around 2 dB improvement in tracking sensitivity.
Figure 10. C/N0 estimates obtained using a single antenna, temporal only processing and a dual-antenna array system using space-time processing.
Conclusions
A combined space-time technique for the processing of new GNSS signals including a temporal filter at the output of each antenna, a calibration algorithm and a spatial beamformer has been developed. The proposed methodology has been tested with simulations and real data. It was observed that the proposed methodology was able to provide unambiguous tracking after applying the temporal filter and enhance the signal quality after applying a spatial beamformer. The effectiveness of the proposed algorithm to provide maximum signal gain in the presence of several interference sources was shown using simulated data. C/N0 analysis for real data collected using a dual antenna array showed the effectiveness of combined space-time processing in attenuated signal environments providing a 2 dB improvement in tracking sensitivity.
Pratibha B. Anantharamu received her doctoral degree from Department of Geomatics Engineering, University of Calgary, Canada. She is a senior systems engineer at Accord Software & Systems Pvt. Ltd., India.
Daniele Borio received a doctoral degree in electrical engineering from Politecnico di Torino. He is a post-doctoral fellow at the Joint Research Centre of the European Commission.
Gérard Lachapelle holds a Canada Research Chair in Wireless Location in the Department of Geomatics Engineering, University of Calgary, where he heads the Position, Location, and Navigation (PLAN) Group.
By Jenna R. Tong, Robert J. Watson, and Cathryn N. Mitchell, University of Bath
Using signal-to-noise measurements from a single commercial-grade L1 GPS receiver, it is possible to detect interference or jamming that is above the thermal noise floor and below a power that causes loss of position.
Interference, intentional or unintentional, is an acknowledged vulnerability of GPS systems. Many of the potential sources of interference are unintentional: interference can caused by harmonics of out-of-band signals, electronic noise, or malfunctioning equipment. The effect, however, is the same independent of intent.
The presence of high-power interference which causes continual denial of service is fairly easy to detect, but lower power interference may still degrade performance, for example by causing loss of lock on some satellites, thus increasing position dilution of precision, although the receiver continues to output a position. Short periods of denial of service caused by intermittent high-power interference may not be immediately detected depending on the timing and ability of the system in use to deal with temporary loss of signal.
Therefore, to fully characterize an antenna environment requires a 24/7 system, whether the purpose is to determine whether a location is suitable prior to installation, to identify whether problems at an existing site are due to interference, or to provide warnings of the presence of interference on a continuous basis. In particular, information on timing — for example finding a time of day or day of the week when interference is regularly seen — may assist in determining the source of the interference.
This research forms part of the GNSS Availability Accuracy Reliability anD Integrity Assessment for timing and Navigation (GAARDIAN) project, which provides a mesh of sensors to monitor the integrity, reliability, continuity, and accuracy of the locally received GPS (or other GNSS) and eLoran signals continuously and to detect anomalous conditions such as local interference, differentiating between possible sources of errors such as interference, multipath, satellite errors, or space weather.
Here we look at using the signal-to-noise ratio (SNR) values from a single-frequency GPS receiver to detect interference. There are two stages to the algorithm: determining the local environment of the antenna in terms of multipath and interference, and identifying and recording potential interference events.
Since this method uses values output from a GPS receiver, characterizing the response to interference of the receiver used in the probe is necessary, to indicate what level interference can be detected with the system, as well as ensuring that false positives are not produced, and the effects of interference can be separated from those of multipath and scintillation, which can also cause decreases in SNR.
We used a commercial, single-frequency receiver, recording this data from NMEA messags for analysis:
SNR, in dB, reported as an integer
elevation, in degrees, reported as an integer
azimuth, in degrees, reported as an integer
carrier lock time, in seconds.
Algorithm. To determine the presence of interference, the normal state of the receiver must first be calculated. Initially it is assumed the receiver is fixed with an unchanging multipath environment. SNR and elevation values from all satellites are accumulated for several hours. To reduce influence of the unknown multipath environment, values from satellites below 10 degrees elevation and from those where the carrier lock time is less than four minutes are removed from the data set.
A polynomial fit between elevation and SNR is then calculated from the remaining data. A second- or third-degree polynomial generally fits the high-elevation data with deviations from the profile at low elevations being primarily due to multipath where interference is not present.
The standard deviation of SNR at each elevation is then calculated. The combination of the polynomial and these values of standard deviation characterize the normal environment of the receiver, for the case where interference is not present in the data gathered (Figure 1).
Figure 1. Raw SNR data against elevation, for all satellites in view over a period of 12 hours (blue), and a polynomial fitting to the same data (green).
To confirm that the threshold values returned by the first stage of the algorithm are valid, a value is calculated for the elevation where the SNR value drops below the polynomial curve by the greatest amount.
If interference is not present, this is normally found at the point where multipath begins to influence the incoming signal and can be considered as a rough multipath cutoff, used to remove signals that may be influenced by multipath from later stages of the analysis.
Assuming a well-sited antenna, a value greater than 25 degrees for this value indicates the possible presence of interference in the data used to calculate the polynomial. In cases where this value is high, the data in question would be rejected, and optionally a user may be warned that there may be pre-existing interference. If the antenna-receiver combination has been previously calibrated in a known good environment, it would be also possible to identify interference based on the difference in polynomial and standard deviation values between that environment and the location being tested.
Figure 2 shows the value of this multipath cutoff (in degrees) for a set of data where interference was known to be present initially, against the start time for the data used to calculate the polynomial and multipath cutoff values, by number of hours from the start of the file.
Once the mask is developed, a threshold value can be set to be n standard deviations below the polynomial, and events are detected by the combination of:
At least four satellites with elevations above the multipath cutoff which are below the threshold value or which were above the multipath cutoff previous to losing lock.
This status is continuous for more than a set time t.
Requiring multiple satellites limits the effects of other influences on SNR such as multipath; requiring an extended time period removes very short-term fluctuations.
The number of false positives and the power of interference required to cause an alarm then depends primarily on the value of the threshold factor n, and on the time period t, which here we kept at a constant of 30 seconds.
Testing
To avoid radiating interference, we constructed an RF network to facilitate injection of jamming signals into the GPS signal path. The GPS signal from a roof-mounted choke-ring antenna was passed through an amplifier and attenuator chain to provide 0 dB forward gain, but around 40 dB reverse isolation. An additional stepped attenuator (0–40 dB in 1 dB steps) was also included. The buffered signal from the antenna was then combined with the output of a vector signal generator used to provide the jamming signal.
The combined signal was then fed into the GPS receiver via a DC-block to remove the antenna bias voltage. The signal generator is capable of producing a wide variety of jamming including matched spectrum wideband noise, CW, and pulsed signals. The adjustment of both the signal generator output power and the signal attenuator a
llow the replication of a variety of signal-to-noise and jammer-to-noise scenarios.
With the receiver locked onto a stable position, CW signals at L1 frequency were introduced into the receiver at levels from –125 dBm to –90 dBm in steps of 5 dBm, with at least 15 minutes of buffer time for the receiver to recover between each step (Table 1). Data was logged at 1 Hz throughout. We collected 20 hours of data, to calculate threshold values from data with no known interference.
Table 1.
Results
Twelve hours of data from a period where no known interference was present was used to form the SNR mask, and events longer than 30 seconds were looked for using various values of n for the threshold across all 20 hours of data. A false alarm was considered to be any event where interference was detected while the signal generator was off. Table 2 summarizes the response for different threshold levels.
Table 2.
In this test, CW interference of –100 dBm was required before the number of satellites with carrier lock dropped below four even for a single epoch, and –90 dBm was required to cause a sustained loss of lock, but jamming of –105 dBm was still detectable by this system with no false positives returned.
Decreasing the threshold began to produce false positives without detecting the smaller interference signals. This is not surprising as the thermal noise floor, assuming 2 MHz bandwidth, is about –110 dBm.
In the raw data from the detected events, a sharp dip in SNR is often seen at the beginning of an event, followed by recovery as the receiver compensates. In this particular case, where the aim is to detect the interference, this could lead to interference going undetected if the initial sharp dip was underneath the time threshold (30 seconds) and the recovery took the SNR of some of the satellites above the SNR threshold (Figure 3).
Figure 3. Value of polynomial mask (blue) and actual SNR (red) as recorded for four satellites during the period around the injection of the -100 dBm CW signal, showing initial dip and partial recovery.
Conclusion
Using only SNR values from a low-cost L1 GPS receiver, it is possible to detect CW interference which is above the thermal noise floor and below a power that causes loss of position. Different types of interference are expected to produce a different response, and unintentional interference is likely to be broadband or not directly centered on L1. The antenna used may also have a strong effect. These factors have not been examined here, although in practice the algorithm has run in multiple locations with different antennas, both direct and via splitters.
Regardless of the precise type of interference, the system would be expected to detect any interfering signal which impacts the SNR of the receiver, and to do so even if the signal strength was below a level which caused denial of service in that area.
The results are specific to the receiver used and its response to interference, although the algorithm would be capable of using data from any receiver that provided SNR values. Ideally the system used for measurement would have little or no built-in interference rejection.
Although this data was collected and then examined after the fact for signs of interference, the system works in precisely the same way in real time. Further trials will test the algorithm’s performance in real time and with different jamming scenarios, and compare results from multiple receivers in a single location and the performance of the algorithm with different antennas.
Acknowledgments
This work was funded by the Engineering and Physical Sciences Research Council and the Technology Strategy Board.
Jenna R. Tong is a postdoctoral researcher in electronic and electrical engineering at the University of Bath. Her Ph.D. in electron tomography is from the University of Cambridge.
Robert J. Watson received a Ph.D. degree in electronic engineering from the University of Essex, and is senior lecturer in electronic and electrical engineering at the University of Bath.
Cathryn N. Mitchell is a professor of engineering at the University of Bath and the Director of Invert Centre for Imaging Science. She received a Ph.D. from the University of Wales Aberystwyth.
By Thomas A. Stansell, Kenneth W. Hudnut, and Richard G. Keegan
The new GPS L1C signal will be broadcast by the Block III satellites, with first launches as early as 2014. L1C innovations significantly enhance PNT performance as well as interoperability with other GNSS signals. The authors describe the benefits of its new features and how best to make use of each one.
A highly evolved racehorse of a signal with outstanding technical performance, L1C was designed to significantly improve autonomous navigation, and to be interoperable with L1 signals from other GNSS providers. Its structure evolved from the earliest GPS signals: it shares with the C/A signal the L1 center frequency of 1575.42 MHz, coherence between the carrier frequency, the code clock rates, and the data rate, and the provision of a navigation data message.
L1C inherited significant improvements from subsequent developments, specifically WAAS, L5, and L2C. WAAS was the first GPS-related signal to use forward error correction (FEC) for its data. L5 was the first open signal design to use longer spreading codes (10,230 chips), to have separate data and data-less (pilot carrier) signal components, to employ an improved navigation message structure (CNAV), and to employ overlay codes to achieve a longer equivalent code length, improve correlation performance, and eliminate the need for bit synchronization. The L2C signal adopted most of these improvements but, instead of an overlay, substituted a much longer pilot carrier spreading code, not only to optimize correlation performance but also to decrease the number of time ambiguities after tracking the spreading codes.
The L1C signal design is amazing, not only because of its highly evolved and outstanding technical performance but also because a committee designed this racehorse of a signal rather than it becoming a camel. Table 1 lists key members of the L1C technical committee in alphabetical order. The list has two groups, technical contributors and government chairpersons. When each new signal aspect is introduced, the key contributor or contributors from this list will be identified.
Table 1. Key L1C contributors.
L1C is intended to be interoperable with L1 signals from other GNSS providers. To identify its signal type, we note that Galileo officials have identified three types of services, “open”, “commercial”, and “publicly regulated”. An open service is freely available to all users. A commercial service is limited to users who pay a fee to access the signal, which otherwise is denied by encryption. A publicly regulated service (PRS) also is encrypted but intended only for public safety applications. GPS is adopting the open service definition but will continue to distinguish encrypted signals as “military” because there are no encrypted commercial GPS services. L1C will be a new GPS open service signal, joining L1 C/A, L2C, and L5.
Although the term “civil signal” often is used, there can be confusion about its meaning. Within the U.S. government it is common to use the word “civil” to mean civil government agencies, e.g., the Department of Transportation (DOT). However, it’s clear the GPS C/A, L2C, L5, and L1C signals are “open” and intended for use by anyone. Therefore, we will use the term “civilian” or “open” in order not to imply that any of these signals is restricted in its use.
L1C Signal Development
The L1C signal structure has evolved from the earliest GPS signals first launched in 1978. It shares with the C/A signal the L1 center frequency of 1575.42 MHz, coherence between the carrier frequency, the code clock rates, and the data rate, and the provision of a navigation data message. Significant improvements have been inherited from subsequent developments, specifically WAAS, L5, and L2C. For GPS or GPS-related signals, WAAS was the first to use forward error correction (FEC) for its data. L5 was the first open signal design to use longer spreading codes (10,230 chips), to have separate data and data-less (pilot carrier) signal components, to employ an improved navigation message structure (CNAV), and to employ overlay codes to achieve a longer equivalent code length, improve correlation performance, and eliminate the need for bit synchronization. The L2C signal adopted most of these improvements but, instead of an overlay, substituted a much longer pilot carrier spreading code, not only to optimize correlation performance but also to decrease the number of time ambiguities after tracking the spreading codes, i.e., extend the duration of GPS time ambiguity from 1 ms after tracking the C/A code and 20 ms after tracking the L5Q code to 1.5 sec for L2C.
Before giving details of the L1C signal in which we identify the primary contributor(s) for each innovation, it’s appropriate to recognize the special contributions of two members of the L1C technical team.
The first is Dr. Charles R. (Charlie) Cahn. Cahn has been a major contributor to GPS since before GPS was conceived. In particular, he was a key contributor to the Air Force 621B program which anticipated GPS. (He, Dr. James J. (Jim) Spilker, Dr. Robert Gold, and Mr. Burt Glazer deserve most of the credit for developing the original GPS C/A and P code signal structures, other than the NAV message.) Cahn discussed the merits of having a separate data-less or pilot channel in a 621B report [1], with Stansell he again recommended this for GPS in a 1975 Spartan Study Report, and finally the idea was adopted by the RTCA for L5 in accordance with recommendations from Cahn, Stansell, and Keegan. Also, Cahn was the first to recommend an overlay code on the L5 data signal to eliminate the need for the always problematic bit synchronization process. In a step toward L1C, Cahn was a primary contributor to the L2C design. In particular, he designed the code generators, including the 1.5 sec pilot code, and the chip by chip multiplexing technique which permitted two signal components in one bi-phase signal. In addition to consulting for The Aerospace Corporation and several commercial GPS companies, Cahn recently invented a more effective method to combine multiple signals on one carrier, called Phase-Optimized Constant-Envelope Transmission (POCET) modulation [2]. It is expected to be used on later versions of GPS III satellites to improve transmitter efficiency.
The second special recognition is for Dr. John Betz. Betz has played a very significant role for more than a decade in helping define the military M-code, in working with international partners to define and negotiate compatibility and interoperability signal parameters, in helping negotiate a significant part of the 2004 EU/US agreement, and in evaluating and supporting a wide variety of GPS programs and initiatives. Betz was a vital contributor to the overall L1C design through interaction with other team members, development of ways to compare alternatives, suggesting use of new signal processing concepts, and bringing experts from MITRE who performed significant analyses and developed key signal components.
Table 2 lists, in order of the authors’ judgment of value to user communities, the most important new characteristics of the L1C signal. The list also shows the primary contributor(s) for each characteristic.
Table 2. L1C Innovations in order of judged value.
Improvements made to the previously modernized civilian GPS signals, L5 and L2C, were a starting point for the L1C design. These included: having a pilot carrier; longer spreading codes (10,230 chips minimum); overlay or long pilot codes to eliminate the need for bit synchronization, to improve correlation properties, and to decrease the number of time ambiguities aft
er locking to the spreading codes; use of FEC to improve data demodulation performance and provide bit synchronization; and the flexible and higher precision CNAV message. The following paragraphs describe the additional improvements incorporated in L1C.
A key issue was whether additional signals could be added to the L1 carrier without negatively impacting legacy signals. Several combining methods were considered, and it was determined that, with the right combining technique, L1C could be added without detriment. Use of POCET, subsequently invented by Cahn, will further enhance this capability.
An “industry standard” rate ½ constraint length 7 convolutional coding method had been adopted for forward error correction (FEC) on WAAS, L2C, and L5 signals. However, the team agreed it was appropriate to consider other possibilities. Betz arranged for Ma to address the team on at least two occasions, providing a good tutorial on other advanced FEC methods which would allow message demodulation at even lower signal-to-noise ratios.
While the FEC options were being considered, another breakthrough occurred. Since at least 1999 Stansell had encouraged development of a way to take better advantage of GPS message redundancy. Rising to this challenge, Kovach proposed a modification of the CNAV message structure that he and Art Dorsey (Lockheed-Martin) had developed for L5 and L2C. The modified message, called CNAV-2, is equally flexible, equally precise, but more efficient, allows faster time to first fix (TTFF), and permits message demodulation at signals as weak as the carrier can be tracked. This final attribute requires FEC encoding of entire message blocks (sub-frames) rather than having the continuous process used for L2C and L5. As a result, when signal levels are very weak, bit symbols from two or more messages can be combined to improve the energy available per symbol, i.e., the L1C data demodulation threshold can be improved by combining symbols from two or more messages.
As a result of the message format improvements and performance evaluations by Shane, the team settled on the Low Density Parity Check (LDPC) FEC block encoding technique. This technique is as effective as turbo codes but without intellectual property constraints. Software developed by Shane was used by Sklar and Wang to define the specific L1C implementation, with performance simulation help from Kasemsri and Zapanta.
The most important new attribute of L1C resulted from a proposal by Betz to take advantage of the improved FEC and message redundancy attributes of L1C by having two separate data messages. Half the total signal power would be in the pilot carrier and the other half would be split evenly between two messages, one with full precision and the second with less precision but which could be acquired more quickly for faster TTFF. Stansell appreciated the opportunity for less power in the message but recommended that instead of having a second message the saved power should be added to the pilot carrier, for a 75/25 split between pilot and data power. The reasoning was that code and carrier measurements on the pilot are vital to navigation whereas messages are redundant, slowly changing, and are becoming available from other sources, such as the Internet and from cell phone networks. The issue was settled by an international survey of manufacturers, universities, and government organizations. The final L1C signal design, with the 75/25 power split, was selected by these experts from a group of five signal options.
Another L1C message innovation came about through a collaboration between Kovach and Cahn. The idea was to have a separate message sub-frame with very powerful encoding to identify GPS time of week to within a two hour interval. The sub-frame is called Time of Interval (TOI), and Cahn recommended a 52 symbol (26 bit) BCH code to provide the 9 bits of TOI information. Although orbit parameters may be available from a number of sources, precise and unambiguous time is vital for navigation, and TOI serves this and other purposes. With this level of encoding, TOI can be obtained from just one message at very low signal levels. Furthermore, the identical TOI is broadcast from every GPS satellite at the beginning of every 18 second L1C message. Therefore, it is possible to combine symbols from two or more GPS signals to demodulate TOI even under very adverse signal conditions. After locking to the pilot code and its overlay, one TOI establishes time of week within ±1 hour for all GPS signals.
TOI is particularly effective because of a recommendation by Cahn to overlay the pilot spreading code with another code which frames the entire data message. The L1C overlay code is 18 seconds long (the message length) and is unique to each GPS satellite. Because of this, the TOI defines which of the 400 possible 18 second intervals within a 2 hour time span begins at the next message frame, which also is the beginning of the next overlay code. If receiver time is known or can be determined to within an hour, TOI and the GPS spreading codes establish time for all GPS satellites.
Although it would have been adequate to adopt spreading codes from the L5 signal design, Betz introduced Rushanan to the L1C technical team and recommended that he study alternate code structures with improved characteristics. After an extensive study, Rushanan recommended a set of length-10223 Weil-codes extended with a fixed 7-bit pad to provide the primary L1C spreading codes. These codes have improved performance characteristics, as detailed in [3], [4], and [5]. In addition, the team asked Rushanan to define the 1800 chip pilot overlay codes, also described in [3], [4], and [5]. Stansell specifically requested that Rushanan optimize the ability to synchronize to the overlay code with as little observation time as possible. As a result, within one or two seconds after a signal is acquired, its 18-second time frame is established. After the first satellite is acquired, the maximum time difference for signals from other satellites is less than ±10 ms for receivers near the earth, so only two possible states of the overlay code must be examined to resolve the 18 second message phase for any other satellite. If the GPS almanac, an estimated position, and even a rough time estimate are available, as usually is the case, message time phase can be resolved even faster for subsequent signal acquisitions.
The L1C waveform originally was to have been a pure BOC(1,1) (a 1.023 MHz square wave modulated by a 1.023 MHz spreading code). Negotiations between the U.S. and the European Union (EU) at that time resulted in an agreement [6] that both GPS and Galileo would use a baseline BOC(1,1) signal. However, the EU reserved the right to further optimize their signal within certain bounds. Some of the optimization proposals were known as CBCS and CBCS. However, in further EU/US discussions it was decided that L1C and the Galileo E1 open service signal should have identically the same spectrum. This was a significant challenge because of different baseline signal structures and existing designs. The breakthrough came when Betz proposed what is called MBOC. The MBOC waveform has 10/11th of its power in BOC(1,1) and 1/11th in BOC(6,1). However, L1C and E1 OS achieve this result in very different ways. The Galileo technique is called CBOC, as described in a number of papers. [8], [9], and [10]. The GPS technique is called TMBOC and is defined by IS-GPS-800A [11] as well as by [3], [4], [5], and [8]. Whereas Galileo has a 50/50 power split between pilot and data and includes the BOC(6,1) component in each, GPS includes the BOC(6,1) waveform only in the pilot component by modulating four of every 33 spreading code chips with a 6 MHz square wave and 31 chips with a 1 MHz square wave. With 75% of the power in the pilot, the result is 3/4 x 4/33 or 1/11, as required. It is likely the BOC(6,1) signal component will be ignored by consumer grade GNSS receivers where a narrow RF bandwidth is preferred. Fortunately that is a loss of only 12% (0.56 dB) of the L1C pilot power. However, for commercial and professional grade receivers, the extra waveform transitions (wider Gabor bandwidth) can be used to improve code tracking signal-to-noise ratio, and with certain advanced techniques it should be possible to improve multipath mitigation. This final point depends on careful control or calibration of the transmitted code timing and symmetry.
Finally, Dafesh recommended that the team consider data symbol interleaving. The team accepted this suggestion, and Sklar and Wang designed the interleaver. Because of the powerful FEC, by scattering data symbols throughout sub-frames 2 and 3, it is possible to recover an entire message even if portions are blocked by, for example, walking or driving past trees or other obstructions.
All team members deserve credit for sharing, challenging, and improving concepts. Particular examples are the strong aviation navigation background provided by Hegarty and the in depth design experience for a wide range of receiver types and civilian applications provided by Keegan. In addition, Yi had the primary responsibility for documenting L1C in IS-GPS-800.
It also is important to recognize the contributions of the many professionals who responded to the worldwide survey of manufacturers, universities, and government experts. Stansell conducted each of the survey presentations, some in person and others over the Internet. One or more of the Government Chairpersons also participated, usually Hudnut or Lenahan. There were responses from organizations in 10 countries: Japan (34), the USA (26), Russia (7), the United Kingdom (5), Canada (4), Australia (1), Finland (1), Germany (1), Switzerland (1), and Taiwan (1). This is not a complete picture because a number of the responses were from individual experts while others were a consensus response from a larger group. Five signal design options were presented, and the preferred design received 62 percent of the 81 responses. As a result, the L1C signal has a 75/25 split between pilot and data power and the data rate is 50 bits per second.
L1C Signal Description
The official L1C signal description is given by IS-GPS-800; the most recent version A was released on June 8, 2010. Figures 1 and 2 show the L1C power spectral density with, respectively, a logarithmic (dBW/Hz) scale and a linear (Watts per Hz) scale. Figure 3 is the same as Figure 1 but also includes the C/A and M Code signals; it assumes both signals are transmitted with the same total power.
Figure 1.Figure 2.Figure 3.
These plots illustrate three important aspects of the L1C spectrum. First, L1C is designed to have only a small impact on reception of the legacy C/A signal. This is important for the compatibility of signals with respect to each other. A good way to evaluate the impact of one signal on another is called the Spectral Separation Coefficient (SSC), which quantifies the amount of interfering power from one signal to another, under the assumption that each signal is transmitted with the same power but with different spreading codes.
The SSC between a C/A signal and the L1C signal is –68.3 dB/Hz. The spectral separation illustrated in Figures 1, 2, and 3 assures that L1C signals will have very little impact on acquiring and tracking the legacy C/A signals. Therefore, L1C is judged to be compatible with the C/A signal.
Figure 3 also illustrates that L1C and the M Code signals have very little impact on each other. The SSC between L1C and M Code is –82.8 dB/Hz. This is important because M-Code power may be substantially higher than the civilian signals, so a larger negative SSC is important to maintaining compatibility.
The third aspect of the L1C spectrum is the additional signal power at ±6.138 MHz. This component of signal power differentiates a binary offset carrier BOC(1,1) waveform from the L1C multiplexed BOC or MBOC waveform. Exactly 1/11th of the L1C signal power is a BOC(6,1) component, whereas 9/11th of the power is a BOC(1,1) component.
75 Percent in the Pilot Carrier. Figure 4, which shows the required post-correlator C/N0 required to phase track either the L1C or C/A signals as a function of tracking loop bandwidth, illustrates the main advantages of having 75 percent of the L1C signal power in the pilot component. The carrier-tracking threshold for equivalent signal power using a Costas loop is 6 dB worse than tracking with a phase-locked loop (PLL). A Costas loop is needed for the C/A signal because it is modulated by data, whereas a PLL can be used for the dataless L1C pilot signal. This 6 dB advantage more than compensates for having only 75 percent (-1.25 dB) of the L1C power in the pilot. The vertical displacement between the two curves illustrates the 4.75 dB L1C tracking threshold advantage.
Figure 4. Required post Correlator C/N0 versus tracking loop bandwidth.
The horizontal displacement of the curves shows another L1C advantage. For a given C/N0 threshold, the L1C loop bandwidth can be increased by a factor of three. In turn, this allows tracking with G forces 32, or nine times higher. For third-order loops capable of tracking acceleration, this allows tracking with 27 times higher jerk. Such differences are likely to be more important than tracking threshold for high-dynamic applications such as machine control.
Although Figure 4 assumes the L1C and L1 C/A signals have the same total power, the minimum received L1C signal power specified in IS-GPS-800A is –157 dBW, and the equivalent for C/A in IS-GPS-200E is –158.5 dBW. In other words, the intent is for L1C to be transmitted with 1.5 dB more power than C/A. Therefore, the figure is conservative by 1.5 dB in evaluating the L1C advantages over C/A. Thus, the actual threshold advantage is 4.75 + 1.5 = 6.25 dB.
For narrowband or other receivers not punctual correlating the BOC(6,1) signal component, the pilot carrier is 29/33 or 0.56 dB weaker, so the net advantage is 4.75 – 0.56 + 1.5 = 5.69 dB.
LDPC Block Encoding
Low-density parity check (LDPC) encoding provides three key advantages. First, to demodulate the critical part of the L1C message with a bit error rate (BER) of 10-5 requires an Eb/N0 (ratio of energy per bit to the noise power in a 1-Hz bandwidth) of 2.2 dB versus 96 dB for the C/A signal. When taking into account that only 25 percent of L1C signal power is in the data component, the required total power of the L1C signal can be 1.4 dB less than the C/A signal for an equivalent BER. As a result, this performance allows the pilot component of L1C to have 75 percent of the total L1C power.
Second, LDPC gives near-optimum performance with no intellectual property constraints. Third is the ability to block-encode Subframes 2 and 3 of the L1C message, described next.
CNAV-2 Message. Figure 5 compares the L5 and L2C CNAV message structure to the L1C CNAV-2 structure. CNAV was a major step forward compared to the original NAV message in terms of flexibility, precision, time to first fix (TTFF), and integrity. Instead of the fixed 30-second structure of the NAV message, CNAV consists of multiple six-second messages that are differentiated by a message-type number. The sequence of broadcast message types is defined by the GPS control segment, which greatly improves flexibility. The round-off error in the NAV message can affect pseudorange calculations
by up to 40 centimeters, whereas the equivalent CNAV error contributes about 3 centimeters. Orbit and clock precision is substantially improved. Because a minimum of three message types are needed for the necessary orbit and clock parameters, as little as 18 seconds is needed to gather the necessary information after locking to a signal. On the other hand, if four message types are being sent sequentially, and the receiver locks just after the beginning of a message, it can take 30 seconds to gather the necessary data. TTFF typically is improved. Importantly, each CNAV message includes a 24-bit cyclic redundancy check (CRC) word that makes it practically impossible to have bit errors in a message that passes the CRC check.
Figure 5. CNAV and CNAV-2 message structures.
CNAV-2 improvements to the CNAV structure all but guarantee an 18-second TTFF after signal acquisition. Message efficiency is improved by eliminating the need to identify each six-second message, to have complete time-of-week (TOW) information in each six-second message, and to have three rather than two 24-bit CRC words every 18 seconds. Even more important, GPS time is defined modulo 18 seconds upon acquisition of only one signal, and it is defined modulo two hours by decoding only one 26-bit, 0.52-second time-of-interval (TOI) word at the beginning of each message. In addition, TOI is so well encoded (52 symbols for nine data bits) that it can be demodulated in very weak signal conditions, which can be further enhanced by combining the identical TOI symbols transmitted by every satellite at the beginning of every 18-second message.
Figure 6 illustrates the ability to combine message symbols from several sequential Subframe 2 data blocks so vital clock and ephemeris data can be demodulated at the weakest signal level the receiver can track. This feature is made possible because the symbols in subframe 2 will not change for at least 15 minutes (50 repeats) and typically no more often than one to two hours (200 to 400 repeats). This provides up to 8.4 dB of message demodulation improvement. The figure also shows other L1C improvements: 4.8 dB of carrier track threshold extension, and a TTFF of 18 seconds after successfully demodulating subframe 2 from the minimum number satellites for a position fix.
Subframe 3 of the L1C message contains less time-critical information such as almanac, ionospheric correction terms, and so on. This subframe also is LDPC block-encoded so it is quite robust, although it does not offer the ability to combine symbols from sequential messages.
Figure 6. L1C and C/A performance comparison.
Pilot Overlay Code
Figure 5 shows that the pilot overlay code consists of 1,800 chips that frame the 18-second message. In comparison with the L5 20-millisecond (ms) pilot overlay code, it not only is 900 times longer but also is unique to each satellite. This improves cross-correlation performance in general and particularly when two satellites have the same pseudorange.
The long L1C overlay code can be acquired reliably after only one or two seconds of signal lock. Its length does not cause a relevant delay in TTFF, but it provides many advantages. First, synchronizing to the overlay code on one satellite defines GPS time for all satellites modulo 18 seconds (in comparison to 1 ms with the C/A code). Even with infrequent use, the receiver’s RTC, which typically is better than 5 parts per million (ppm), should have sufficient accuracy — better than ± 9 seconds — to completely resolve GPS time with one signal acquisition. In 24 hours with a clock frequency error of 5 ppm the time drift would be less than ½ second.
Even if the RTC is in error by several times 18 seconds, resolving accurate time can be done quickly by computing position fixes with multiple time hypotheses spaced 18 seconds apart. Pseudorange changes at rates up to ±1,440 kilometers per 18 seconds. Because some satellites are approaching, others are moving away, and all of them are changing range at different speeds (different Doppler frequencies), determining which position fix is correct out of several 18-second GPS time hypotheses will be straightforward since only one will be reasonable. (Care must be taken to avoid any extremely rare instances where two results may seem reasonable.)
The worst clock error with aided GPS (A-GPS) is ±2 seconds, which is adequate to completely resolve GPS time after acquiring only one L1C signal. This capability can aid acquisition of and navigation with other signals, such as C/A or signals from other GNSS providers. The 18-second overlay code will provide benefits as soon as even a few L1C signals are available.
The L1C overlay code, in conjunction with the repeating symbols of message subframe 2, also enables data demodulation to begin at any point within an 18-second message. It is not necessary to wait for the message frame to begin. The receiver can begin collecting data symbols at any time, and 18 seconds later it will have assembled all the subframe 2 clock and ephemeris information and can begin to navigate. An exception occurs when the satellite message is updated, between once every 15 minutes to once every two hours. This capability significantly improves TTFF whenever satellite messages are needed for navigation, for example, when they aren’t still valid from a previous collection or aren’t provided by an A-GPS service.
Spreading and Overlay Code Designs
The L1C MBOC waveform (time-multiplexed BOC, or TMBOC), shown in Figure 7, enabled GPS and Galileo to have open-service L1 signals with an identical spectrum, although implemented quite differently. L1C places all the BOC(6,1) chips in the pilot carrier. This is because the BOC(6,1) component is intended to improve code-tracking performance by increasing code loop signal-to-noise ratio (SNR) and by allowing advanced multipath-mitigation techniques to have the advantage of more code transitions. Because these measurements are made almost exclusively on the three times (4.8 dB) more powerful pilot signal, there is no reason to lose the code tracking benefit by having BOC(6,1) chips in the data signal component. In addition, narrowband receivers such as those predominantly used for consumer applications cannot process BOC(6,1) chips, so it would be undesirable to deny full message signal power to such receivers.
Figure 7. The GPS MBOC (TMBOC) modulation.
For receivers tracking only the BOC(1,1) component of L1C MBOC, there are on average 43.5 code transitions per 33 chips. For those tracking both components, there are on average 89.5 code transitions per 33 chips. This provides up to 3.1 dB of improvement in code loop SNR for wideband receivers code tracking with both types of chips. (The amount of improvement depends on receiver RF bandwidth.)
Classic multipath-mitigation techniques such as the double-delta don’t work well with the BOC(6,1) waveform, but recent advances promise improvement by using the extra transitions in the MBOC signal. Some developers worry that the full benefit may not be achieved unless code symmetry and time alignment of the two components is better than the signal specification permits. If the satellites cannot provide the needed signal symmetry and alignment, such problems likely can be overcome by ground calibration of these characteristics, either directly by each receiver or indirectly by an observing network.
Symbol Interleaving. Symbol interleaving means that before a message is transmitted, the satellite scatters the 10-ms message data symbols from subframes 2 and 3 throughout these subframes in
a fixed and known pattern. After a receiver has demodulated (or otherwise measured) the symbols belonging in a subframe, they are reassembled into the proper order before the LDPC block decoding is performed. In other words, the scattering done in the satellite is undone by the receiver. The objective is to provide a measure of protection against certain types of signal fading. For example, if a sequence of symbols from the satellite is lost because the receiver passes behind an object such as a tree, only half the symbols in this part of the message would be affected if the adjacent symbols in the original message are received either before or after the signal blockage. Thus, with reasonable signal levels and the benefit of powerful LDPC block encoding, the entire message could be reconstructed.
Performance Metrics and Comparison
A main objective for the L1C signal structure was to significantly improve the autonomous navigation capability for GPS users. Key weaknesses in the current C/A signal include the thresholds for bit synchronization, message synchronization, and data-bit demodulation. To achieve navigation at very low signal levels, users of the L1 C/A signal had to employ external sources for time synchronization, data acquisition, and, to extend the tracking loop threshold, external data-bit aiding to enable phase-locked tracking rather than Costas tracking of the C/A signal. The new signal structure addresses all of these shortcomings and provides a robust autonomous navigation system that requires no external aiding for most commercial applications.
Message Frame Synchronization and Time of Transmission. For autonomous navigation, frame synchronization has two important roles. The first is to set GPS time, modulo frame duration, which is required to establish the unambiguous time of transmission. Frame synchronization, or knowledge of frame start, also enables assembly of the received bits into the appropriate data words. In both L1 C/A and L5, frame synchronization is accomplished by recognizing a synch word within a data subframe, which requires accurate demodulation of data bits. For L1C, frame synchronization is inherent in the signal structure and does not require demodulation of data bits. This is very important for two reasons. The first is to establish GPS time of transmission very quickly, especially when the satellite message is not needed, for example, if it was acquired previously or obtained by other means. The second is when satellite ephemeris data is necessary, but the signals are very weak. The L1C message structure facilitates this capability.
Overlay Code on Pilot Carrier. One frame of data consists of 1,800 symbols modulated onto the data carrier which, at 100 symbols per second, is 18 seconds long. However, synchronized to this 18-second data frame is a pseudorandom code modulated on the dataless pilot carrier. This 100 chips per second overlay code is a linear-shift-register code that is truncated to be 1,800 chips long. The overlay codes were chosen to have very low minor auto-correlation and cross-correlation peaks so a very short segment of the code can be used to establish its underlying code phase.
If a 100-chip segment of the received code is correlated over a replica of the entire code, the proper correlation peak would be easily distinguished, thus establishing the GPS time epoch at the start of the code. Since this code epoch and the start of the data frame are synchronized, the start of the entire data frame is established, modulo 18 seconds. The start of the data frame by definition establishes the GPS time of transmission, also modulo 18 seconds. This is accomplished without decoding a single data bit by using the power advantage of the pilot carrier.
However, using the message to resolve the 18-second time ambiguity often is not needed. For example, the receiver’s real time clock (RTC) is likely to be accurate to within ±9 seconds. Alternately, almost any source of external aiding can provide time to within ±2 seconds. In either case, if the receiver already has a valid satellite ephemeris, navigation can begin after receiving a little over 1 second of the stronger pilot carrier signal. Ephemeris data can be available in a number of ways, including prior reception from the satellite, from a separate communications channel, or from one of several predicted ephemeris sources.
Message Frame – Data Format. A message frame consists of 1,800 symbols that comprise two distinct data types. The first data type, in subframe 1, is the Time of the Frame (TOI or Time of Interval) modulo two hours. The second data type is further separated into two blocks, subframe 2 containing data that is fixed for a period of time and subframe 3 containing data that can change from frame to frame.
Time of Interval Subframe. The TOI is a count of the number of 18-second message intervals in each 2 hour time period. Two hours is the maximum duration of any ephemeris message before being replaced by the satellite. (Fifteen minutes is the minimum.) There are 400 18-second intervals in 2 hours, so it requires 9 bits to represent the 400 intervals. These nine bits are block-encoded into 52 symbols using a BCH(51,8) code, where the 8 data bits are the least significant bits of the TOI. The most significant bit (MSB) of the TOI is then mod-2 added to the BCH codeword and also appended to the resulting codeword as its MSB, resulting in a 52-symbol codeword. This coding provides a BER of 10-5 for an Eb/N0 of –1.9 dB per coded symbol or a C/N0 of +18.2 dB-Hz at the correlator output for the data channel. Since the data channel contains only 25 percent of the total L1C power, the C/N0 of the composite signal would be +24.2 dB Hz. Symbol demodulation is performed using the pilot carrier tracked by a PLL as the phase reference. Since the pilot carrier contains 75 percent of the total power, its C/N0 would be +23 dB-Hz. With a (single-sided) loop-noise bandwidth of 10 Hz, the loop SNR for the carrier channel PLL would be +10 dB.
Note that a 10-5 BER is not required for successful demodulation of TOI. Therefore, weaker signals can be used successfully if the PLL loop bandwidth can be smaller in such weak signal conditions.
The most straightforward method to decode the TOI is brute force maximum likelihood estimation. All possible code words for the 400 possible data words can be pre-computed. Each then can be compared (correlated) with the received code word. The data word that corresponds to the code word with the highest correlation would be the result of the decoding process.
Finally, since all satellites simultaneously transmit the same TOI, the received code word from several satellites can be combined to increase the effective Eb/N0. The target BER of 10-5 thus can be achieved at an even a lower C/N0 than the single satellite value. In this case, the decoding process described above can be performed on a composite code word derived from two or more satellite signals, weighted appropriately for the signal strength from each one.
As an example, consider a receiver with access to an external source of the ephemerides. By combining the TOI code word from five satellites, the average C/N0 required per satellite would only be 17.2 dB-Hz, so time could be established to ±1 hour in slightly over 1 second.
Because of the 18-second overlay code, decoding TOI is not required for receivers with an internal clock good to ±9 seconds or with external time aiding, the worst of which today is within ±2 seconds.
Data Subframes. The remaining data bits are separated into two additional subframes. (TOI is in the first subframe.) The second subframe contains data that does not change for at least 15 minutes, and typically for an hour or two. This subframe provides the satellite ephemeris and the interval time-of-week (ITOW) count, which identifies the start time of the two-hour interval since the beginning of the GPS week, which, in turn, frames the TOI count of 18-second intervals within each two-hour frame. The third subframe contains data that normally changes from frame to frame, such as the satellite constellation almanac.
The block of data containing the satellite ephemeris (subframe-2) consists of 576 clock and ephemeris bits along with a 24-bit CRC, for a total of 600 bits. These are encoded with a rate-½ LDPC Block code into 1,200 symbols. The block of data containing variable data (subframe-3) consists of 250 data bits along with a 24-bit CRC, for a total of 274 bits. These are also encoded with a rate-½ LDPC Block code into 548 symbols. The 1,748 symbols of the two data subframes are combined and interleaved using a simple 38 x 46 row-column block interleaver. These interleaved symbols plus the 53 TOI symbols make up the entire 1,800-symbol (900-bit) message frame.
Since both the LDPC codes and the interleaver operate on independent blocks of data, the resulting symbols for subframe-2 are identical and in the same location in each message frame for between 15 minutes and two hours. Since the data decoding uses the pilot carrier as the phase reference, the subframe-2 symbols can be coherently combined over many 18-second message frames before decoding to improve BER performance.
One reasonable subframe-2 strategy would be to check the CRC after LDPC-decoding the first received message to determine if there are any remaining bit errors. If errors are detected, do the same with the second message. If errors exist in the second message, coherently combine the symbols from the two messages, properly weighted, LDPC-decode the combination, and check the resulting CRC for errors. If necessary, this process can be used on as many messages as needed to obtain a perfect result.
Framing the data messages with the pilot overlay code and the repeating characteristic of subframe 2 permits data collection over any arbitrary 18-second interval. It doesn’t matter where data collection begins. The overlay code tells the receiver which symbol is which, and the repeating subframe-2 message can be compiled from any place in the previous message to the same place in the following message. The powerful CRC assures that a good message is perfect. When the ephemeris is needed from a satellite, rather than from an alternate source, these characteristics allow TTFF to be slightly over 18 seconds, with assurance the information is correct.
Since LDPC FEC has been adopted by the current state-of-the-art wireless standards such as 802.11n and 802.16e, employing it in the latest GPS signal structure should be simple for the receiver designer. In fact, synthesizable cores are available for WiMax LDPC decoders from several sources, and LDPC decoders are as commonplace in wireless signal basebands as Viterbi decoders for the convolutional codes of L2C, L5, and SBAS have become in GPS basebands.
For subframe-2 data, the Eb/N0 required to achieve a BER of 10-5 is approximately 2.2 dB. For subframe-3 data, the Eb/N0 required for this same performance is approximately 2.7dB.
Signal Structure
The L1C signal is a composite of two signals that are phase/frequency coherent with synchronized spreading codes and symbol timing. The pilot signal has 75 percent of the total power, is a carrier-only signal, and is spread by a 10-ms long code plus an 18-second overlay code. The data signal has 25 percent of the total power, is spread by a 10-ms long code, and is data modulated with 10-ms symbols.
Spreading Codes. The spreading code for both L1C signals are 10,230 chip codes with a chip rate of 1.023 MHz, producing a 10-ms long code. This corresponds to one symbol for the data carrier and one chip of the overlay code for the pilot carrier. These codes are not linear shift register sequences like all other codes employed by GPS, but are pseudo-random sequences derived from Weil sequences of length 10223. This sequence is extended by a 7-bit sequence 0110100, which is the same for all satellites, to the required length of 10230. The location within the particular Weil sequence where the extension sequence is inserted is called the insertion index. A pair of Weil indices and a corresponding pair of insertions points then determines the pair of codes for each satellite.
Synchronization to one of these Weil-based codes can be accomplished with a standard time-domain correlator, but the number of potential hypotheses has increased by a factor of ten compared to the C/A signal. However, this is no different than time-domain correlation for an L5 code, which also are 10,230 chips long. Synchronization also can be accomplished using FFT-based frequency-domain correlation, however it does require an FFT of length 65,536 (for a standard radix-2 implementation) since the FFT must span 2 full code periods at a minimum of 2 samples per code chip (40,920).
To compare L1C frequency domain correlation with L1 C/A, a frequency search window and integration time must be hypothesized. A simple example would be a 10-ms coherent integration time and ±250 Hz frequency uncertainty. Table 3 compares the number of complex operations required for L1 C/A vs. L1C.
Table 3. Comparison of FFT-based correlation for L1C versus L1 C/A. (Click to enlarge.)
For cases where large search window uncertainties exist, and frequency domain correlation provides a computational benefit, an alternate approach to L1C synchronization would be to first obtain L1 C/A synchronization using an FFT-based search, providing frequency and 10 timing hypotheses (perhaps more with potential cross-correlations for L1 C/A). These L1C hypotheses could be tested by simple time-domain correlation that would benefit from the much better cross-correlation properties of the L1C codes.
For cases where time uncertainty is not large, a time domain search of the L1C code would be no more difficult than the equivalent for L1 C/A. For cases where the time uncertainty is small but the frequency uncertainty is large, time-domain partial-period correlations could be combined in an FFT structure that would span a large frequency uncertainty with a single time hypothesis. For example, the 10,230 chips could be separated into 62 segments, each 165 chips long. The 62 segments could then be combined using a zero filled 64-pt FFT to produce 64 full correlations spanning ±3 kHz.
MBOC Waveform. The L1C spreading code is further modulated with a code clock synchronized 1.023 MHz square wave creating the BOC(1,1) signal that forms the majority of the L1C code symbols. This produces a code that appears as a 1 MHz square wave, synchronized to the Weil-based code edge, whose polarity indicates the state of the Weil-based code chip. This BOC(1,1) sequence modulates all of the data channel chips and 29 of every 33 pilot channel chips. The other 4 out of 33 Pilot channel chips are modulated by a BOC(6,1) code symbol in which a 6 MHz square wave is used instead of the 1 MHz square wave for the BOC(1,1) chips. (Recall that ‘1’ signifies 1.023 MHz and ‘6’ signifies 6.138 MHz.) For receiver designers who choose not to punctual correlate the BOC(6,1) component of the pilot carrier, the pilot carrier power will be reduced by ~0.6 dB.
The BOC(6,1) signal component provides an opportunity for better performance of advanced multipath mitigation techniques. The presence of multipath interference not only impacts the code-tracking process of a GPS receiver but also distorts the waveform seen by the phase-tracking process of the receiver. The distortion of the phase of the received signal is most problematic when the reflector creating the multipath signal is very close to the receiving antenna, because the path length of such a multipath signal changes very slowly. Since the path length changes very slowly, it appears as an almost constant bias error in the phase measurements. The only way to observe this distortion, and hence measure its impact on the phase measurements, is to observe the phase of the carrier very close to the code transitions. The estimate of this distortion obviously is better the more frequently it can be observed. This is particularly important because the distortion is not constant but slowly changes. The MBOC signal combination provides
just over twice the number of transitions at which to observe the phase distortion than the BOC(1,1) signal alone, which is important for higher fidelity measurements during short intervals when the slowly changing distortion is highly correlated .
L1C Status
Companies already are designing L1C into their new chipsets, even though the first satellite to carry the signal is not expected before 2014. When will L1C be available from enough satellites to be meaningful? Figure 8 is a guesstimate of how modernized GPS signals will become available over the next decade. The projections assume either two or three successful satellite launches per year, and many observers think two per year may be realistic. Because GPS only launches on need to sustain the constellation, the actual launch rate depends on the lifetime of the satellites now in orbit. The first launch of a GPS III may be delayed until all IIF satellites have been launched, or the first GPS III, if available, may be launched before the last IIF to test the new design in space as soon as possible.
Some L1C signal and message characteristics will significantly benefit users of C/A and other GNSS signals by, for example, quickly resolving time for all GNSS signals. Therefore, L1C will provide meaningful benefit as soon as even one signal can be tracked from any location on earth. That might be possible with as few as six GPS III satellites in orbit, depending on where in the constellation they are deployed.
Figure 8. Guesstimate of modernized GPS signal availability.
Tom Stansell heads Stansell Consulting, after eight years with the Johns Hopkins Applied Physics Laboratory, 25 years with Magnavox (staff VP), and five years with Leica Geosystems (VP), pioneering Transit and GPS navigation and survey products. He led technical development of the GPS L2C signal and coordinated the GPS L1C project (2004–2006). He is a member of the Editorial Advisory Board of GPS World.
Ken Hudnut applies new technologies such as GPS to earthquake research as a geophysicist for the U. S. Geological Survey in Pasadena, California. He served as project manager for the GPS L1C signal design project from 2003. He received his Ph.D. from Columbia University.
Rich Keegan has 36 years of experience in radio navigation including Transit, Timation, Omega, Loran C, as well as GPS for the past 28 years. He has been the principal of a consultancy in digital communications and navigation since 2000. He was a member of the L2C and L1C modernization committees.
GNSS RECEIVER TESTING SHOULD NEVER BE LEFT TO CHANCE. Or should it? There are two common approaches to testing GNSS receivers: synthetic and realistic. In synthetic testing, a signal simulator is programmed with specific satellite orbits, receiver positions, and signal propagation conditions such as atmospheric effects, signal blockage, and multipath. A disadvantage of such testing is that the models used to generate the synthetic signals are not always consistent with the behavior of receivers processing real GNSS signals. Realistic testing, on the other hand, endeavors to assess receiver performance directly using the signals actually transmitted by satellites. The signals may be recorded digitally and played back to receivers any number of times. While no modeling is used, the testing is specific to the particular observing scenario under which the data was recorded including the satellite geometry, atmospheric conditions, multipath behavior, and so on. To fully examine the performance of a receiver using data collected under a wide variety of scenarios would likely be prohibitive. So, neither testing approach is ideal. Is there a practical alternative? The roulette tables in Monte Carlo suggest an answer.
Both of the commonly used testing procedures lack a certain characteristic that would better assess receiver performance: randomness. What is needed is an approach that would easily provide a random selection of realistic observing conditions. Scientists and engineers often use repeated random samples when studying systems with a large number of inputs especially when those inputs have a high degree of uncertainty or variability. And mathematicians use such methods to obtain solutions when it is impossible or difficult to calculate an exact result as in the integration of some complicated functions. The approach is called the Monte Carlo method after the principality’s famous casino. Although the method had been used earlier, its name was introduced by physicists studying random neutron diffusion in fissile material at the Los Alamos National Laboratory during the Second World War.
In this month’s article, we look at an approach to GNSS receiver testing that uses realistic randomization of signal amplitudes based on histograms of carrier-to-noise-density ratios observed in real-world environments. It can be applied to any simulator scenario, independent of scenario details (position, date, time, motion trajectory, and so on), making it possible to control relevant parameters such as the number of satellites in view and the resulting dilution of precision independent of signal-strength distribution. The method is amenable to standardization and could help the industry to improve the testing methodology for positioning devices — to one that is more meaningfully related to real-world performance and user experience.
Virtually all GNSS receiver testing can be classified into one of two broad categories: synthetic or realistic. The former typically involves simulator-based trials, using a pre-defined collection of satellite orbits, receiver positions, and signal propagation models (ionosphere, multipath, and so on). Examples of this type of testing include the 3rd Generation Partnership Project (3GPP) mobile phone performance specifications for assisted GPS, as well as the “apples-to-apples” methodology described in an earlier GPS World article (see Further Reading).
The primary advantage of synthetic testing is that it is tightly controllable and completely repeatable; where a high degree of statistical confidence is required, the same scenario can be run many times until sufficient data has been collected. Also, this type of testing is inherently self-contained, and thus amenable to testing facilities with modest equipment and resources.
Synthetic approaches have significant limitations, however, particularly when it comes to predicting receiver performance in challenging real-world environments. Experience shows that tests in which signal levels are fixed at predetermined levels are not always predictive of actual receiver behavior. For example, a receiver’s coherent integration time could in principle be tuned to optimize acquisition at those levels, resulting in a device that passes the required tests but whose performance may degrade in other cases. More generally, it is useful to observe that the real world is full of randomness, whereas apart from intentional variations in receiver initialization, the primary source of randomness in most synthetic tests is simply thermal noise.
By comparison, most realistic testing approaches are designed to measure real-world performance directly. Examples include conventional drive testing and so-called “RF playback” systems, both of which have also been described in recent literature (see Further Reading). Here, no modeling or approximation is involved; the receiver or recording instrument is physically operated within the signal environment of interest, and its performance in that environment is observed directly. The accuracy and fidelity of such tests come with a price, however. All measurements of this type are inherently literal: the results of a given test are inseparably linked to the specific multipath profile, satellite geometry, atmospheric conditions, and antenna profile under which the raw data was gathered. In this respect, the direct approach resembles the synthetic methods outlined above — little randomness exists within the test setup to fully explore a given receiver’s performance space.
Designing a practical alternative to the existing GNSS tests, particularly one intended to be easy to standardize, represents a challenging balancing act. If a proposed test is too simple, it can be easily standardized, but it may fall well short of capturing the complexities of real-world signals. On the other hand, a test laden with many special corner cases, or one that requires users to deploy significant additional data storage or non-standard hardware, may yield realistic results for a wide variety of signal conditions, but it may also be impractically difficult to standardize.
With those constraints in mind, this article attempts to bridge the gap between the two approaches described above. It describes a novel method for generating synthetic scenarios in which the distribution of signal levels closely approximates that observed in real-world data sets, but with an element of randomness that can be leveraged to significantly expand testing coverage through Monte Carlo methods. Also, the test setup requires only modest data storage and is easily implemented on existing, widely deployed hardware, making it attractive as a potential candidate for standardization.
The approach consists of several steps. First, signal data is gathered in an environment of interest and used to generate a histogram of carrier-to-noise-density (C/N0) ratios as reported by a reference receiver, paying particular attention to satellite masking to ensure that the probability of signal blockage is calculated accurately. The histogram is then combined with a randomized timing model to create a synthetic scenario for a conventional GNSS simulator, whose output is fed into the receiver(s) under test (RUTs). The performance of the RUTs in response to live and simulated signals is compared in order to validate the fidelity and usefulness of the histogram-based simulation. This hybrid approach combines the benefits of synthetic testing (repeatability, full control, and compactness) with those of live testing (realistic, non-static distribution of signal levels), while avoiding many of the drawbacks of each.
Histograms
The method explored in this article relies on cumulative histograms of C/N0 values reported by a receiver in a homogeneous signal environment. This representation is compact and easy to implement with existing simulator-based test setups, and provides information that can be particularly useful in tuning acquisition algorithms.
Motivation and Theoretical Considerations. To motivate the proposed approach, consider an example histogram constructed from real-world data, gathered in an environment (urban canyon) where A-GPS would typically be required. This is shown in FIGURE 1, together with a representative histogram of a standard “coarse-time assistance” test case (as described in the 3GPP Technical Standard 34.171, Section 5.2.1) for comparison. (Note that the x-axis is actually discontinuous toward the left side of each plot: the “B” column designates blocked signals, and thus corresponds to C/N0 = –∞.)
From the standpoint of signal distributions, it is evident that existing test standards may not always model the real world very accurately.
FIGURE 1a. Example histogram of a real-world urban canyon, the San Francisco financial district;.Figure 1b. Example histograms of 3GPP TS 34.171 “coarse-time assistance” test case).
The histogram is useful in other ways as well. Since the data set is normalized (the sum of all bin heights is 1.0), it represents a proper probability mass function (PMF) of signal levels for the environment in question. As such, several potentially useful parameters can be extracted directly from the plot: the probability of a given signal being blocked (simply the height of the leftmost bin); upper and lower limits of observed signal levels (the heights of the leftmost and rightmost non-zero bins, respectively, excluding the “blocked” bin); and the center of mass, defined here as
(1)
where y[n] is the height of the nth bin (dimensionless), x[n] is the corresponding C/N0 value (in dB-Hz), and x[“B”] = –∞ by definition.
Finally, representing environmental data as a PMF enables one additional theoretical calculation. The design of the 3GPP “coarse-time assistance” test case illustrated above assumes that a receiver will be able to acquire the one relatively strong signal (the so-called “lead space vehicle (SV)” at -142 dBm) using only the assistance provided, and will subsequently use information derivable from the acquired signal (such as the approximate local clock offset) to find the rest of the satellites and compute a fix. Suppose that for a given receiver, the threshold for acquisition of such a lead signal given coarse assistance is Pi (expressed in dB-Hz). Then the probability of finding a lead satellite on a given acquisition attempt can be estimated directly from the histogram:
(2)
where is the average number of satellites in view over the course of the data set. A similar combinatorial calculation can be made for the conditional probability of finding at least three “follower” satellites (that is, those whose signals are above the receiver’s threshold for acquisition when a lead satellite is already available).
The product of these two values represents the approximate probability that a receiver will be able to get a fix in a given signal environment, expressed solely as a function of the receiver’s design parameters and the histogram itself. When combined with empirical data on acquisition yield from a large number of start attempts in an environment of interest, this calculation provides a useful way of checking whether a particular histogram properly captures the essential features of that environment. This validation may prove especially useful during future standardization efforts.
Application to Acquisition Tuning. In addition to the calculations based on the parameters discussed above, histograms also provide useful information for designing acquisition algorithms, as follows.
Conventionally, the acquisition problem for GNSS is framed as a search over a three-dimensional space: SV pseudorandom noise code, Doppler frequency offset, and code phase. But in weak signal environments, a fourth parameter, dwell time – the predetection integration period, plays a significant role in determining acquisition performance. Regardless of how a given receiver’s acquisition algorithm is designed, dwell time (or, equivalently, search depth) and the associated signal detection threshold represent a compromise between acquisition speed and performance (specifically, the probabilities of false lock and missed detection on a given search). To this end, any acquisition routine designed to adjust its default search depth as a function of extant environmental conditions may be optimized by making use of the a priori signal level PMF provided by the corresponding histogram(s).
Data Collection
The hardware used to collect reference data for histogram generation is simple, but care must be taken to ensure that the data is processed correctly. The basic setup is shown in FIGURE 2.
Figure 2. Data collection setup with a reference receiver generating NMEA 0183 sentences or in-phase and quadrature (I/Q) raw data and one or more test receivers performing multiple time-to-first-fix (TTFF) measurements.
It is important to note that the individual components in the data-collection setup are deliberately drawn here as generic receivers, to emphasize that the procedure itself is fundamentally generic. Indeed, as noted below, future efforts toward standardizing this testing methodology will require that it generate sensible results for a wide variety of RUTs, ideally from different manufacturers. Thus, the intention is that multiple receivers should eventually be used for the time-to-first-fix (TTFF) measurements at bottom right in the figure. For simplicity, however, a single test receiver is considered in this article.
Procedure. The experiment begins with a test walk or drive through an environment of interest. Since an open sky environment is unlikely to present a significant challenge to almost any modern receiver, a moderately difficult urban canyon route through the narrow alleyways of Stockholm’s Gamla Stan (Old Town) was chosen for the initial results presented in this article. The route, approximately 5 kilometers long, is shown in FIGURE 3 (top). For the TTFF trials gathered along this route, assisted starts with coarse-time aiding (±2 seconds) were used to generate a large number of start attempts during the walk, ensuring reasonable statistical significance in the results (115 attempts in approximately 60 minutes, including randomized idle intervals between successive starts).
Once the data collection is complete, the reference data set is processed with a current almanac and an assumed elevation angle mask (typically 5 degrees) to produce an individual histogram for each satellite in view, along with a cumulative histogram for the entire set, as shown in Figure 3 (bottom). The masking calculation is particularly important in properly classifying which non-reported C/N0 values should be ignored because the satellite in question is below the elevation angle mask at that location and time, and which should be counted as blocked signals.
Figure 3a. Data collection, Gamla Stan (Old Town), Stockholm (route and street view).Figure 4. Fluctuation timing models (top: “Multi SV” variant; bottom: “Indiv SV” variant).
In addition to proper accounting for satellite masking, the raw source data should also be manually trimmed to ensure that all data points used to build the histogram are taken homogeneously from the environment in question. Thus the file used to generate the histogram in Figure 3 was truncated to exclude the section of “open sky” conditions between the start of the file and the southeast corner of the test area, and similarly between the exit from the test area and the end of the file.
Finally, the resulting histogram is combined with a randomized timing model to create a simulator scenario, which is used to re-test the same RUTs shown in Figure 2.
Reference Receiver Considerations. The accuracy of the data collection described above is fundamentally limited by the performance of the reference receiver in several ways.
First, the default output format for GNSS data in many receivers is that of the National Marine Electronics Association (NMEA) 0183 standard (the histograms presented in this article were derived from NMEA data). This is imperfect in that the NMEA standard non-proprietary GSV sentence requires C/N0 values to be quantized to the nearest whole dB-Hz, which introduces small rounding errors to the bin heights in the histograms. (In this study, this effect was addressed by applying a uniformly distributed ±0.5 dB-Hz dither to all values in the corresponding simulated scenario, as discussed below.) If finer-grained histogram plots are required, an alternative data format must be used instead.
Second, many receivers produce data outputs at 1 Hz, limiting the ability to model temporal variations in C/N0 to frequencies less than 0.5 Hz, owing to simple Nyquist considerations. While the raw data for this study was obtained at walking speeds (1 to 2 meters per second), and thus unlikely to significantly misrepresent rapid C/N0 fading, studies done at higher speeds (such as test drives) may require a reference receiver capable of producing C/N0 measurements at a higher rate.
A third limitation is the sensitivity of the reference receiver. Ideally, the reference device would be able to track all signals present during data gathering regardless of signal strength, and would instantaneously reacquire any blocked signals as soon as they became visible again. Such a receiver would fully explore the space of all available signals present in the test environment. Unfortunately, no receiver is infinitely sensitive, so a conventional commercial-grade high sensitivity receiver was used in this context. Thus the resulting histogram is, at best, a reasonable but imperfect approximation of the true signal environment.
Finally, a potentially significant error source may be introduced if the net effects of the reference receiver’s noise figure plus implementation loss (NF+IL) are not properly accounted for in preparing the histograms. (If an active antenna is used, the NF of the antenna’s low-noise amplifier essentially determines the first term.) The effect of incorrectly modeling these losses is that the entire histogram, with the exception of the “blocked” column, is shifted sideways by a constant offset.
The correction applied to the histogram to account for this effect must be verified prior to further acquisition testing. This can be done by generating a simulator scenario from the histogram of interest, as described below, and recording a sufficiently long continuous data set using this scenario and the reference receiver. A corresponding histogram is then built from the reference receiver’s output, as before, and compared to the histogram of the original source data. The amplitude of the “blocked” column and the center of mass are two simple metrics to check; a more general way of comparing histograms is the two-sided Kolmogorov-Smirnov test (see “Results”).
Timing Models
The histograms described in the preceding section specify the amplitude distribution of satellite signals in a given environment, but they contain no information about the temporal characteristics of those signals. This section briefly describes the timing models used in the current study, as well as alternatives that may merit further investigation.
In real-world conditions, the temporal characteristics of a given satellite signal depend on many factors, including the physical features of the test environment, multipath fading, and the velocity of the user during data collection. Various timing models can be used to simulate those temporal characteristics in laboratory scenarios.
Perhaps the simplest model is one in which signal levels are changed at fixed intervals. This is trivial to implement on the simulator side, but it is clearly unlikely to resemble the real-world conditions mentioned above. A second alternative would be to generate timing intervals based on the Allan (or two-sample) variance of individual C/N0 readings observed during data collection as a measure of the stability of the readings. While this is more physically realistic than an arbitrarily chosen interval as described above, it is still a fixed interval. These observations suggest that a timing model including some measure of randomness may represent a more realistic approach.
One statistical function commonly used for real-world modeling of discrete events (radioactive decay, customers arriving at a restaurant, and so on) is the Poisson arrival process. This process is completely described with a single non-negative parameter, λ, which characterizes the rate at which random events occur. Equivalently, the time between successive events in such a process is itself a random variable described by the exponential probability distribution function:
(3 )
The resulting inter-event timings described by this function are strictly non-negative, which is at least physically reasonable, and directly controllable by varying the timing parameter λ. For simplicity, then, the Poisson/exponential timing model was chosen as an initial attempt at temporal modeling, and used to generate the results presented in this article.
Two variants of the Poisson/exponential timing model are considered. In the first, defined herein as the “Multi SV” case, a single thread determines the timing of fluctuation events, and the power levels of one or more satellites are adjusted at each event. In the second variant, defined as the “Indiv SV” case, each simulator channel receives its own individual timing thread, and all fluctuation events are interleaved in constructing the timing file for the simulator. These two variants are shown schematically in FIGURE 4.
Once a target histogram is available, it is necessary to generate random signal amplitudes for use with a simulator scenario. This is done by means of a technique known as the probability integral transform (PIT). This approach uses the c
umulative distribution function (or, in the discrete case considered here, a modified formulation based on the cumulative mass function) of a probability distribution to transform a sequence of uniformly distributed random numbers into a sequence whose distribution matches the target function.
Finally, the random signal levels generated by the PIT process are assigned to individual simulator channels according to a set of timed events as described in the preceding section, completing the randomized scenario to be used for testing.
Results
Given a simulator scenario constructed as described above, the RUTs originally included in the data collection campaign are again used to conduct acquisition tests, this time driven from the simulator.
To validate that a particular fluctuating scenario properly represents the live data, it is necessary to quantify two things: how well a generated histogram matches the source data, and how well a receiver’s acquisition performance under simulated signals matches its behavior in the field. At first these may appear to be two qualitatively different problems, but a mathematical tool known as the two-sided Kolmogorov-Smirnov (K-S) test can be used for both tasks.
Validation of Experimental Setup. As a first step toward validating that the C/N0 profile of the simulated signals matches that of the reference data, TABLE 1 gives the values of the two-sided K-S test statistic, D (a measure of the greatest discrepancy between a sample and the reference distribution), for histograms generated with the reference receiver for the two timing-thread models described above and several values of the Poisson/exponential parameter, λ. The reference cumulative mass function (CMF) for each test was derived from the histogram generated for the raw (empirically collected) data set.
These results illustrate good agreement (D < 0.05) between the overall signal distribution profile in the empirical data set and that in each of the six simulated fluctuating scenarios.
As a further check, TABLE 2 shows the same K-S statistic for the histogram generated from the “Multi SV” timing model as a function of several NF+IL values. As before, the reference CMF comes from the raw (empirically collected) data set, and the same reference receiver was used to generate data from the simulator scenario. Evidently, an NF+IL value of 4 dB gives good agreement between empirical and simulated data sets.
Validation of Receiver Performance. Finally, TTFF tests with the simulated scenarios described above are conducted with the same receiver(s) used in the original data gathering session. Here, the K-S test is used to compare the live and simulated TTFF results rather than signal distributions. An example result, illustrating cumulative distribution functions of TTFF, is shown in FIGURE 5 for the live data set collected during the original data gathering session, alongside three results from the “Multi SV” fluctuating model, generated with NF+IL = 4 dB and several different values of the Poisson/exponential timing parameter, λ. While agreement with live data is not exact for any of the simulated scenarios, the λ-1 = 3.0 seconds case appears to correspond reasonably well (D < 0.10).
FIGURE 5 Time-to-first-fix cumulative distribution functions from live and simulated data (“Multi SV” variant with NF+IL = 4 dB).
Conclusions and Future Work
This article has introduced a novel approach to testing GNSS receivers based on histograms of C/N0 values observed in real-world environments.
Much additional work remains. For the proposed method to be amenable to standardization, it is obviously necessary to gather data from many additional environments. Indeed, it appears likely that no one histogram will encapsulate all environments of a particular type (such as urban canyons), so significant additional experimentation and data collection will be required here. Also, as mentioned at the beginning of the article, the proposed method will need to be tested with multiple receivers to verify that a particular result is not unique to any specific brand or architecture. Finally, higher rate C/N0 source data may also be necessary to capture the rapid fades that may be encountered in dynamic scenarios, such as drive tests, and the fluctuation timing models will need to be revisited once such data becomes available.
Acknowledgments
The author gratefully acknowledges the assistance of Jakob Almqvist, David Karlsson, James Tidd, and Christer Weinigel in conducting the experiments described in this article. Thanks also to Ronald Walken for valuable insights on the accurate treatment of the source environment in calculating target histograms. This article is based on the paper “Fluctuation: A Novel Approach to GNSS Receiver Testing” presented at ION GNSS 2010.
Alexander Mitelman is the GNSS research manager at Cambridge Silicon Radio, headquartered in Cambridge, U.K. He earned his S.B. degree from the Massachusetts Institute of Technology and M.S. and Ph.D. degrees from Stanford University, all in electrical engineering. His research interests include signal-quality monitoring and the development of algorithms and testing methodologies for GNSS.
Universal Mobile Telecommunications System (UMTS); Terminal conformance specification; Assisted Global Positioning System (A-GPS); Frequency Division Duplex (FDD), 3GPP Technical Specification 34.171, Release 7, Version 7.0.1, July 2007, published by the European Telecommunications Standards Institute, Sophia Antipolis, France. Available online at http://www.3gpp.org/.
“Proper GPS/GNSS Receiver Testing” by E. Vinande, B. Weinstein, and D. Akos in Proceedings of ION GNSS 2009, the 22nd International Technical Meeting of the Satellite Division of The Institute of Navigation, Savannah, Georgia, September 22–25, 2009, pp. 2251–2258.
“Advanced GPS Hybrid Simulator Architecture” by A. Brown and N. Gerein in Proceedings of The Institute of Navigation 57th Annual Meeting/CIGTF 20th Guidance Test Symposium, Albuquerque, New Mexico, June 11–13, 2001, pp. 564–571.
• Receiver Noise
“Measuring GNSS Signal Strength: What is the Difference Between SNR and C/N0?” by A. Joseph in Inside GNSS, Vol. 5, No. 8, November/December 2010, pp. 20–25.
Global Positioning System: Theory and Applications, Vol. I, edited by B.W. Parkinson and J.J. Spliker Jr., published by the American Institute of Aeronautics and Astronautics, Inc., Washington, D.C., 1996.
• Test Statistics
“The Probability Integral Transform and Related Results” by J. Agnus in SIAMReview (a publication of the Society for Industrial and Applied Mathematics), Vol. 36, No. 4, December 1994, pp. 652–654, doi:10.1137/1036146
• NMEA 0183 NMEA 0183, The Standard for Interfacing Marine Electronic Devices, Ver. 4.00, published by the National Marine Electronics Association, Severna Park, Maryland, November 2008.
u-blox and Rohde & Schwarz (R&S), a supplier of test and measurement equipment, have successfully concluded a simulation of the European Galileo satellite positioning system. The test, carried out with the R&S SMBV100A vector signal generator and its GNSS simulation options, verified the u-blox proof-of-concept and the compatibility of u-blox receiver technology with the Galileo transmission protocol.
The cooperation with R&S is also being extended to the Russian GLONASS satellite system, which is targeted to be fully operational with 24 satellites in 2012.
“Our close cooperation with R&S has proven to be a valuable and strategic asset, allowing us to develop advanced satellite receiver technology well before the actual satellites are available” said Clemens Bürgi, vice president of software development at u-blox.
“u-blox, with its depth of expertise in GNSS technologies, has helped us to validate our satellite simulator technology,” said Andreas Pauly, head of R&D Signal Generators Baseband at Rohde & Schwarz. “Now we have developed cutting-edge test equipment that simulates the protocol and physical layer.”
Although the sun can become disturbed at any time, solar activity is correlated with the approximately 11-year cycle of spots on the sun’s surface. We are just coming out of a minimum in the solar cycle and headed for the next maximum, predicted to occur around the middle of 2013. How significantly will GNSS users be affected? In this month’s column, two ionosphere experts tell us what might be in store.
INNOVATION INSIGHTS by Richard Langley
“HERE COMES THE SUN / here comes the sun / And I say / it’s all right.”
Is it? Of course, George Harrison was referring to the welcome return of the sun after a long dreary English winter. But can GNSS users sing the same refrain?
The signals from global navigation satellites must transit the ionosphere on their way to receivers on or near the Earth’s surface. The passage exacts a toll in the form of an added delay of the pseudorandom-noise-code signals and an advance of the phase of the signals’ carriers, due to the presence of the ionosphere’s free electrons. These perturbations must be ameliorated in some way to achieve high accuracy in GNSS positioning, navigation, and timing applications.
Where do the ionosphere’s electrons come from? For the most part, they are valence electrons, stripped from upper atmosphere atoms and molecules by the extreme ultraviolet light continuously emitted by the sun. On the Earth’s night-side, the electrons and the ionized atoms and molecules tend to recombine. This ionization and recombination process, along with the interactions of the particles with the Earth’s magnetic field, governs the density of the electrons at a particular location and time. The ionosphere is also affected by the solar wind, and its associated magnetic field, but the cocoon established by the Earth’s magnetic field (the magnetosphere) tends to deflect the solar wind so that it usually has little influence on the ionosphere.
Normally, the sun is quiescent: its electromagnetic and particle radiation is fairly constant, and its effects on the ionosphere benign. The delay in GNSS code observations and the advance in phase observations can be readily estimated and removed from the observations using a variety of models and methods. However, the sun can become disturbed, giving rise to occasional violent outbursts with large increases in electromagnetic and particle radiation. These outbursts can radically change the distribution of the electrons in the ionosphere, reducing the effectives of some amelioration methods. The electron density variability can become so rapid that a GNSS receiver can lose lock on satellite signals. And an increase in the sun’s radio emissions can become so large as to drown out GNSS signals on the sunlight side of the Earth.
Although the sun can become disturbed at any time, solar activity is correlated with the approximately 11-year cycle of spots on the sun’s surface. We are just coming out of a minimum in the solar cycle and headed for the next maximum, predicted to occur around the middle of 2013. How significantly will GNSS users be affected? In this month’s column, two ionosphere experts tell us what might be in store.
GNSS satellite signals are affected by the space environment and the Earth’s atmosphere as they travel from satellites at an altitude of about 20,000 kilometers above the surface of the Earth to receivers located at, or close to, the surface.
In the upper part of the Earth’s atmosphere, the ionosphere, which is located from about 80 to 1,000 kilometers above the surface of the Earth, satellite signals are affected by the free electrons stripped from atoms and molecules by ionization. The signals are refracted by this plasma, which changes their speed of travel. The effect is mainly a function of the number of free electrons present, the electron density.
In the lower parts of Earth’s atmosphere, in the troposphere and the stratosphere — where the atoms and molecules are electrically neutral — the satellite signals experience additional refraction. Here the effect is a function of pressure, temperature, and humidity. The effect of the troposphere and stratosphere is often just referred to as the “tropospheric effect” in GNSS positioning as it is in the troposphere where most of the neutral atmosphere refraction occurs.
The ionospheric and tropospheric effects on satellite signals must be accounted for in the GNSS positioning process in order to obtain reliable and accurate position solutions. In this article, we look at the ionospheric effect on satellite signals. Although the variation in signal speed is the largest direct ionospheric effect on the GNSS satellite signals, scintillation is another important effect. Scintillation occurs when irregularities in the electron density of the ionosphere cause rapid changes in the phase and amplitude of the transmitted signals. These changes might cause a GNSS receiver to lose lock on a satellite signal. This means in practice that satellite signals are lost, or signal tracking can be rather difficult, during scintillation events. However, we restrict our article to the subject of the propagation speed of the signals and do not consider scintillation further.
In the following, we review characteristics of the ionospheric effect on GNSS satellite signals as well as the predictions of increased ionospheric activity for the coming years and the consequences for GNSS users.
Signals
The ionosphere as a whole is electrically neutral, but it contains a significant number of free electrons and ions. The negatively charged free electrons affect the electromagnetic satellite signals in various ways. Most important is the signal delay affecting code (pseudorange) measurements, also called the “ionospheric delay” (and the associated advance of carrier-phase measurements), which is caused by a change in the refractive index along the signal path. The refractive index changes continuously as a function of the composition of the transmission media all the way from the satellites to the GNSS receivers.
For the majority of the signal path — that is, from the satellite at an altitude of about 20,000 kilometers down to approximately 1,000 kilometers above the surface of the Earth — the change in the refractive index is usually sufficiently small to ignore when the GNSS satellite signals are used for positioning at the surface of the Earth (although, at times, the region above the ionosphere — the plasmasphere — can affect GNSS signals). We therefore use the approximation that the first part of the signal path is in a vacuum where the propagation of GNSS satellite signals is not affected.
Then, when the signals enter the ionosphere, we must consider the signal delay, and even though the density of electrons is largest at an altitude around 300 kilometers, we must consider the total number of electrons experienced by a satellite signal all the way through the ionosphere.
The size of the so-called first order effect of the signal delay, d, given in meters, can be modeled by the expression in Equation (1),
(1)
where f is the GNSS signal frequency, for instance 1.57542 x 109 Hz for the GPS L1 frequency. The constant 40.3 is derived from the values of the electron charge, the electron mass, and the permittivity of free space. Finally, TEC is an abbreviation for total electron content and this value is given by integrating the number of free electrons along the signal path in a cross section of one square meter.
It turns out that the “delay” affecting carrier-phase measurements has exactly the same magnitude as the signal delay but is negative. In other words, the phase is advanced.
In practice, for single-frequency receivers, it is not possible to obtain the actual number of electrons along the signal path for every satellite signal, and we therefore need other models to predict or estimate the electron density or the signal delay.
A large number of models and methods for estimating the ionospheric signal delay have been developed. A comparison of some of them is given in a paper by Allain and Mitchell (see Further Reading). The most widely used model is probably the Klobuchar model, named after John Klobuchar, its developer. Coefficients for the Klobuchar model are determined by the GPS control segment and distributed with the GPS navigation message to GPS receivers where the coefficients are inserted into the model equation and used by receivers for estimation of the signal delay caused by the ionosphere.
Dispersion. The ionosphere is dispersive for radio waves, which means that the GNSS ionospheric signal delay is a function of the frequency of the signal. If pseudorange measurements from more than one frequency are available, for instance from dual-frequency GPS receivers, this can be used for enhanced modeling of the ionospheric effect by using combinations of the measurements made on both frequencies.
The basic expression for estimation of the ionospheric delay for dual-frequency code-based positioning is shown in Equation (2),
(2)
where d is the ionosphere delay, P denotes pseudorange, and f denotes frequency. The subscript notation L1 and L2 refers to the GPS L1 and L2 frequencies, respectively.
For high-accuracy carrier-phase-based positioning, an ionosphere-free combination of carrier-phase observations of the L1 and L2 frequencies is often used to reduce the effect of the ionospheric phase advance in the positioning process.
Estimating the ionosphere delay with Equation (2) for code observations or utilizing the ionosphere-free combination of the phase observations compensates for the first order ionospheric effect. This is the major part of the effect, but higher order effects are present, and the size of the residual higher order effects is increased (up to some centimeters) when the ionospheric activity is increasing.
For high-accuracy applications, the difference in the time of transmission and reception of the satellite signals of the various frequencies also must be considered as the signals on various frequencies are not transmitted from the satellites (nor received at a GNSS receiver) at exactly the same time epochs. These differences are normally referred to as the satellite and receiver differential code biases.
It is important also to note in this context that the noise level on the pseudorange corrected for the ionosphere and on the ionosphere-free carrier-phase observation is increased compared to using the pure single-frequency observations for positioning, but nevertheless these first-order approaches are used successfully in most software and receiver firmware for dual-frequency positioning.
Further developments of ionosphere-free combinations will evolve in the future as the new GPS L5 frequency and the new Galileo and GLONASS frequencies become fully available for multi-frequency ionosphere-free combinations. These more advanced combinations have the potential to further reduce the residual effect of the ionospheric delay in the positioning process.
Summing up, the GNSS signal delay caused by the ionosphere is a function of the electron density of the ionosphere. But what is driving the variation in electron density, and how do we know if it is changing?
Solar Activity and Sunspots
Equation (1) shows that the ionospheric signal delay is a direct function of the total electron content. The number of free electrons in the ionosphere is not constant; it varies significantly with time and space. The number of free electrons is driven by the ionization and recombination processes of the ionosphere, and these processes are in turn driven mainly by extreme ultraviolet radiation from the sun. Radiation from other cosmic sources also has an influence but it is minor compared to the effect of the solar radiation. There are also significant short-term (minutes to hours) changes caused by wave activity from the neutral atmosphere. The ionosphere itself is embedded in the neutral atmosphere — at these altitudes this is known as the thermosphere. The thermosphere is in constant movement due to waves and tides that are generated in situ or ascending from the underlying atmosphere. This thermosphere activity affects the ionosphere and causes some of the short-term variability in the electron density. However, the term “ionospheric activity” generally refers to the variability in electron density as driven by solar activity.
The fact that ionospheric activity is mainly driven by solar activity implies that the temporal variation of the electron content of the ionosphere follows a daily cycle, with the largest TEC values in the early afternoon local time, when the effect of the solar radiation has reached a maximum. Consequently, we see the lowest activity late at night just before sunrise.
There is also a geographic variability in the electron content with the highest electron density in the equatorial region and the lowest density in the high latitude regions. The latter, however, is affected by a larger variability, correlated with auroral activity.
The geographic variation of TEC is illustrated with a global ionosphere map from the Center for Orbit Determination in Europe (CODE) shown in Figure 1. Global ionosphere maps are generated at CODE on a daily basis, and the maps are available on the CODE website (see Further Reading).
Figure 1. Global ionosphere map for November 22, 2010, at 14:00 UTC. (Map generated by CODE, University of Bern.)
The TEC is provided in TEC units (TECU), where one TECU equals 1016 electrons per meter squared.
The sun also emits a constant flow of charged particles called the solar wind. The particles, mostly electrons and protons with energies between about 10 and 100 kilo-electron-volts, travel at an average speed of about 450 kilometers per second, but varying from 200 to 900 kilometers per second depending on solar activity. Although the Earth’s magnetosphere deflects most of the solar wind, the interplanetary magnetic field, which is associated with the solar wind, can cause disturbances in the geomagnetic field. When this happens, particles of the solar wind enter the geomagnetic field and cause increased ionization in the ionosphere. The solar wind therefore also has a large influence on the variability of ionospheric activity. Also, sudden eruptions of the sun such as solar flares and coronal mass ejections (CMEs) cause increased ionization and thereby a larger ionospheric variability.
Figure 2 shows a CME blast and subsequent impact at the Earth.
Figure 2. Coronal mass ejection (CME) and subsequent impact at the Earth. The left part of the illustration is composed of an image from NASA’s Solar Dynamics Observatory spacecraft superimposed on an image from the Solar and Heliospheric Observatory spacecraft jointly operated by NASA and the European Space Agency. The CME cloud arrives at the Earth about two to four days later and is shown being mostly deflected around the Earth’s magnetosphere. The blue paths emanating from the Earth’s poles represent some of its magnetic field lines. (Image: NASA/Goddard Space Flight Center.)
Solar activity and the quantity of emissions from the sun are highly correlated with the number of sunspots on its surface. A sunspot looks like a dark spot because the temperature in a sunspot is lower than that in its surroundings. The generation of sunspots is not well understood, but it is related to anomalies in the solar magnetic field. What is well known, however, is the history of the number of sunspots, because these have been observed since the early 1600s.
The number of sunspots generally follows a cycle of about 11 years. During the last few years (2007–2009), we have experienced a time period with a low number of sunspots. In fact, there were many days in a row without any sunspots visible (see Figure 3). During the next three to four years, the number of sunspots is expected to increase, and this will be followed by a decrease until we reach a new period of low solar activity in 2019–2020.
Figure 3. Images of the sun taken by the Solar and Heliospheric Observatory spacecraft. On the left is an image taken on March 27, 2001, at the peak of the last sunspot cycle. The daily sunspot count was 241. On the right is an image taken on December 15, 2008, near the minimum of the last sunspot cycle, showing no sunspots. (Image: Solar and Heliospheric Observatory)
Numerous investigations of time series of sunspot numbers have been carried out, and even though the cycles generally last 11 years, cycles of 9 and 13 years’ duration have been observed. Also, the cycles vary with respect to the maximum number of sunspots observed during a cycle, and various “cycles of cycles” appear to be present with respect to the strength of the sunspot cycles. For instance, a cycle with a period of about 420 years has been identified in the historic listings of sunspot numbers combined with other observations contributing to the knowledge of solar activity. A very low number of sunspots was observed for a number of years between 1645 and 1715 when the sun was especially calm. This period is often referred to as the Maunder Minimum after the solar astronomer Edward W. Maunder. If the theory of the 420-year cycle is correct, then we will see a period with lower solar activity and fewer sunspot numbers by the end of this century.
But let’s turn our attention to the previous and current sunspot cycles referred to as cycles number 23 and 24 (The 1755–1766 cycle is traditionally numbered “1.”). A new cycle begins with the first observed high-latitude, reversed-polarity sunspot. Reversed polarity means a sunspot with opposite magnetic polarity compared to sunspots from the previous solar cycle. Sunspots from the new and previous cycles initially coexist. Eventually, only the new-cycle sunspots are present. Cycle 24 began on January 4, 2008, when the first reversed-polarity sunspot appeared.
Analyses of observations of solar activity show that the density of the solar wind increases with increasing sunspot number. Also, with a large sunspot number, solar flares and CMEs happen more frequently. Ionospheric storm activity is more common when the sunspot number is high, and this activity increases the variability in ionospheric delays. This all adds up to an increased number of free electrons in the ionosphere and a larger variability, which provides a larger and more variable signal delay for all types of GNSS-based positioning, navigation, and timing during periods with high sunspot numbers.
We know that the sunspot number is expected to increase during the next three to four years. What can be expected and what can we do to minimize the effects of the increased ionospheric activity on positioning, navigation, and timing applications?
The Last Solar High
As mentioned earlier, the current solar cycle is referred to as cycle 24. During the last solar cycle, cycle 23, the GNSS community was alert and aware of what could happen, and therefore many events were observed and analyzed. Among the most well-known events is a sequence of storms during October and November 2003, commonly referred to as the Halloween Storms. The most extreme was the storm on October 30, 2003, which resulted from a CME on October 29 at 20:49 UTC, which subsequently impacted Earth’s magnetic field at 16:20 UTC on October 30 and produced a great geomagnetic storm, which lasted for many hours.
Effects on GPS positioning of this storm have been documented by the GNSS research group of the Royal Observatory of Belgium, where kinematic analyses of data from 36 GNSS stations in Europe showed position errors of more than 10 centimeters in the horizontal and up to 26 centimeters in the vertical between 21:00 and 22:00 UTC on October 30. The position errors were largest for locations in northern Europe including Sweden and Norway. The data analysis was carried out using high-quality carrier-phase data, and the processing was based on using an ionosphere-free linear combination of observations from the L1 and L2 frequencies, whereby the first-order effect of the ionosphere is removed from the results. The position errors are thus caused by mainly higher order ionospheric effects.
For navigation-grade GPS positioning, a U.S. National Atmospheric and Oceanic Administration technical memorandum (see Further Reading) reported that the Wide Area Augmentation System (WAAS) vertical error limit of 50 meters was exceeded for a period of about 11 hours on October 30, 2003. This means that, in practice, WAAS was not available for precision aircraft approaches during that time. The European Geostationary Navigation Overlay Service (EGNOS) was not transmitting during the storm, but simulations carried out later by ESA showed that the boundary regions of the EGNOS coverage area would have been especially affected by a reduction in service availability of about 20–60 percent during that day. The simulations also showed, however, that in the center of the EGNOS coverage area (in the vicinity of northern Italy), the effect would have been much smaller with a reduction in service availability of only 5–6 percent over the day.
Such large storms are also often accompanied by displays of aurora (aurora borealis and aurora australis) at lower latitudes than normal. Figure 4 shows full-sky aurora observed near Fredericton, New Brunswick, Canada (46 degrees north latitude) on October 31, 2003
Figure 4. Photo of red and green auroras observed near Fredericton, New Brunswick, Canada (46 degrees north latitude) early on October 31, 2003. (Courtesy of Richard and Marg Langley.)
During a storm event on November 20, 2003, auroral activity was visible at mid-latitudes over most of North America as far south as Florida and in southern Europe including Italy and Greece.
Eruptions of the sun, often occurring in connection with high sunspot numbers, can have other effects besides the influence on GNSS-based positioning, navigation, and timing. Power-grid blackouts are known to have happened because of geomagnetic storms in connection with the sunspot peaks of both cycles 22 and 23 in 1989 and in 2003, respectively. For instance, the southern part of Sweden experienced a power blackout for several hours during the evening of October 30, 2003.
Also, orbiting satellites can experience problems with the increased radiation and solar wind density. Solar panels are, for instance,
susceptible to increased aging. And many types of satellite communication can be affected by increased ionospheric activity, not only GNSS satellite signals. Signals used for satellite phones, satellite TV, and so on can be affected.
Another phenomenon that can affect GNSS positioning is solar radio storms (also referred to as solar radio bursts) caused by events on the sun, often a solar flare, which creates radio waves that are emitted from the solar atmosphere and can propagate to the Earth where they cause an increased noise level in radio signals. Solar radio storms can cover a wide range of frequencies, including the frequencies used for GNSS. One such storm occurring on December 6, 2006, did affect GNSS positioning. With an increased noise level on the satellite signals, GNSS performance is reduced. If the noise level becomes too large, as a consequence of, for instance, a solar radio storm, GNSS receivers will lose lock on the GNSS signals, whereby positioning performance is further reduced or positioning might even be impossible. Solar radio storms are expected to happen more frequently during the peak of a solar cycle, but the event in December 2006 happened during a period with low solar activity, highlighting the fact that GNSS performance can be affected at any time, even when the sunspot number is low.
Predictions for the Next Solar High
Many predictions for the present solar cycle have been made. Because of the very long period with low solar activity during 2007–2009, some predictions expected a sudden outburst of activity and a very large cycle maximum, while other predictions foretold another increase in solar activity might not occur for many years.
However, with a general increase in the number of sunspots during 2010, it looks like we are now well into solar cycle number 24. Things can still change, but the current predictions say the maximum of the current solar cycle will be lower than the maximum of the last cycle encountered in 2001.
Predictions of sunspot numbers are based on history, logged information on sunspot numbers, and on observations of related geomagnetic activity.
The latest prediction for the current cycle as generated by NASA is shown in Figure 5.
Figure 5. Sunspot cycle 23 and predictions for cycle 24 from NASA’s Marshall Space Flight Center. (Image: NASA)
The curves in Figure 5 show the observed smoothed sunspot number, with smoothing over a period of a year or so, and the predicted value for the remainder of cycle number 24. The dotted lines indicate the observed or expected range of the monthly-averaged sunspot numbers. The plot is updated every month as new data is obtained.
The current prediction for cycle 24 gives a smoothed sunspot number maximum of about 59 in June/July of 2013. This peak is much lower than that of the previous cycle. We are currently two years into cycle 24 and the predicted size continues to fall. According to forecasters, predicting the behavior of a sunspot cycle is fairly reliable once the cycle is well under way (about three years after the minimum in sunspot number occurs). Prior to that time, the predictions are less reliable but nonetheless equally as important.
Even though the maximum of the current solar cycle is expected to be lower than the last peak, it is important for GNSS users to be aware of the effects to be expected during the coming years.
Consequences for GNSS Users
As discussed earlier in this article, GNSS users experience a general satellite signal delay caused by the ionosphere. This signal delay is always present but varies in size. The delay is generally well modeled by most receivers and software to an extent that makes GNSS useable for all of the purposes we know today.
During enhanced ionospheric activity, GNSS users can experience residual ionospheric effects, which can cause reduced positioning, navigation, and timing performance. In such cases, dual-frequency receivers might improve the situation because of the enhanced possibilities for handling the ionospheric effect with dual-frequency data.
During enhanced ionospheric or geomagnetic storm activity caused by sudden eruptions of the sun, increased ionospheric variability will occur. Apart from causing an increased ionospheric signal delay, and thereby increased residual effects in the positioning process, this will also cause increased scintillation effects. These might cause GNSS receivers to lose lock on some or all GNSS satellite signals, reducing performance of the GNSS receiver. In the few very worst cases, GNSS-based positioning, navigation, and timing might not be possible at all for a short interval of time during very high ionospheric activity.
These worst-case scenarios are more prone to happen close to the peak of a solar cycle, which we will meet next during 2013–2014.
However, it is worth noting that for the next peak of the solar cycle, we are much better prepared for the consequences than during the last cycle. GNSS software and receiver technology has been improved to better resist the challenges of increased ionospheric activity during this solar cycle. The improvements are based on experiences gained during the last solar cycles and are to the benefit of many GNSS users. For example, users of wide area augmentation systems such as WAAS and EGNOS have correction and integrity information available, which can be a great help in identifying time epochs when positioning and navigation solutions might not be trustable because of increased ionospheric activity. The integrity information is transmitted from geostationary satellites, and during time periods with extremely high ionospheric activity, the signals with integrity information might be disrupted. This should, however, be detected by the GNSS receiver, so warning messages will be displayed for navigators.
High-accuracy real-time kinematic (RTK) positioning is today often carried out with RTK correction data from a service provider generated using a network of reference stations. Here, indications of increased ionospheric activity can be detected by the software operated by the service provider, and warnings can be distributed to the RTK users.
Warning systems have been improved, and a number of sites on the Internet provide information on current and predicted ionospheric activity (see Further Reading).
Also, in the future, GNSS users will be able to benefit from the increased number of GNSS frequencies available. These frequencies open up opportunities for new and improved methods for correction of the ionospheric delay to the benefit of users who will experience more stable and reliable GNSS performance.
Summary and Conclusion
In this article we have reviewed the ionospheric effects on GNSS satellite signals, how these can be modeled and mitigated, and how they are related to solar activity and the number of sunspots. We have also described how sudden eruptions of the sun can cause increased ionospheric activity and how these events are often correlated with a high sunspot number. Some examples of consequences for GNSS users during the last solar high have been provided, and we have evaluated the predictions for the next solar high and possible consequences for GNSS users.
We are heading towards a period of increased solar activity. GNSS users must expect more disturbances compared to what we have seen for the last four to five years. The peak of the current solar cycle is expected to be lower than the last peak, and therefore consequences for GNSS users should also be less significant. Most of the time GNSS will work very well. But we will likely see a few days with major effects, and since the number of GNSS users is increasing, the overall consequences might also be more severe, not because the ionospheric activity is worse, but simply because more people will be affected.
ANNA B.O. JENSEN is the owner of AJ Geomatics in Copenhagen and a part-time associate professor of the National Space Institute at the Technical University of Denmark (DTU Space). She has a Ph.D. from the University of Copenhagen with co-supervision from the University of Calgary, and has worked in research and development within GNSS and geodesy for more than 15 years. Her current research interests include ionospheric modeling, high accuracy positioning, and navigation in the Arctic.
CATHRYN MITCHELL is a professor in the Department of Electronic and Electrical Engineering at the University of Bath in the United Kingdom and heads the INVERT Centre, which studies inverse problems and tomography over a range of scientific fields, including navigation, space science, and medical imaging. She has a Ph.D. from the University of Wales in Aberystwyth. Mitchell has a particular interest in the use of GNSS measurements to characterize and map the ionosphere.
FURTHER READING
• Introduction to the Ionosphere and Its Effects on GNSS
“The Perfect Solar Storm” by D.N. Baker and J.L. Green in Sky & Telescope, Vol. 121, No. 2, February 2011, pp. 28–34.
Severe Space Weather Events–Understanding Societal and Economic Impacts: A Workshop Report by the National Research Council Committee on the Societal and Economic Impacts of Severe Space Weather Events, published by National Academies Press, Washington, D.C., 2008; available on line: http://www.nap.edu/openbook.php?record_id=12507.
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A comprehensive methodology combines spectral-separation and code-tracking spectral-sensitivity coefficients to analyze interference among GPS, Galileo, and Compass. The authors propose determining the minimum acceptable degradation of effective carrier-to-noise-density ratio, considering all receiver processing phases, and conclude that each GNSS can provide a sound basis for compatibility with other GNSSs with respect to the special receiver configuration.
Power spectral densities of GPS, Galileo, and Compass signals in the L1 band.
As GNSSs and user communities rapidly expand, there is increasing interest in new signals for military and civilian uses. Meanwhile, multiple constellations broadcasting more signals in the same frequency bands will cause interference effects among the GNSSs. Since the moment Galileo was planned, interoperability and compatibility have been hot topics. More recently, China has launched six satellites for Compass, which the nation plans to turn into a full-fledged GNSS within a few years. Since Compass uses similar signal structures and shares frequencies close to other GNSSs, the radio frequency (RF) compatibility among GPS, Galileo, and Compass has become a matter of great concern for both system providers and user communities.
Some methodologies for GNSS RF compatibility analyses have been developed to assess intrasystem (from the same system) and intersystem (from other systems) interference. These methodologies present an extension of the effective carrier power to noise density theory introduced by John Betz to assess the effects of interfering signals in a GNSS receiver. These methodologies are appropriate for assessing the impact of interfering signals on the processing phases of the receiver prompt correlator channel (signal acquisition, carrier-tracking loop, and data demodulation), but they are not appropriate for the effects on code-tracking loop (DLL) phase. They do not take into account signal processing losses in the digital receiver due to bandlimiting, sampling, and quantizing. Therefore, the interference calculations would be underestimated compared to the real scenarios if these factors are not taken into account properly. Based on the traditional methodologies of RF compatibility assessment, we present here a comprehensive methodology combining the spectral separation coefficient (SSC) and code tracking spectral sensitivity coefficient (CT_SSC), including detailed derivations and equations.
RF compatibility is defined to mean the “assurance that one system will not cause interference that unacceptably degrades the stand-alone service that the other system provides.” The thresholds of acceptability must be set up during the RF compatibility assessment. There is no common standard for the required acceptability threshold in RF compatibility assessment. For determination of the required acceptability thresholds for RF compatibility assessment, the important characteristics of various GNSS signals are first analyzed, including the navigation-frame error rate, probability of bit error, and the mean time to cycle slip. Performance requirements of these characteristics are related to the minimum acceptable carrier power to effective noise power spectral density at the GNSS receiver input. Based on the performance requirements of these characteristics, the methods for assessing the required acceptability thresholds that a GNSS receiver needs to correctly process a given GNSS signal are presented.
Finally, as signal spectrum overlaps at L1 band among the GPS, Galileo, and Compass systems have received a lot of attention, interference will be computed mainly on the L1 band where GPS, Galileo, and Compass signals share the same band. All satellite signals, including GPS C/A, L1C, P(Y), and M-code; Galileo E1, PRS, and E1OS; and Compass B1C and B1A, will be taken into account in the simulation and analysis.
Methodology
To provide a general quantity to reflect the effect of interference on characteristics at the input of a generic receiver, a traditional quantity called effective carrier-power-to-noise-density (C/N0), is noted as (C/N0)eff_SSC. This can be interpreted as the carrier-power-to-noise-density ratio caused by an equivalent white noise that would yield the same correlation output variance obtained in presence of an interference signal. When intrasystem and intersystem interference coexist, (C/N0)eff_SSC can be expressed as
Ĝs(f) is the normalized power spectral density of the desired signal defined over a two-sided transmit bandwith ßT, C is the received power of the useful signal. N0 is the power spectral density of the thermal noise. In this article, we assume N0 to be –204 dBW/Hz for a high-end user receiver. Ĝi,j(f) is the normalized spectral density of the j-th interfering signal on the i-th satellite defined over a two-sided transmit bandwith ßT, Ci,jthe received power of the j-th interfering signal on the i-th satellite, ßr the receiver front-end bandwidth, M the visible number of satellites, and Kithe number of signals transmitted by satellite i.Iext is the sum of the maximum effective white noise power spectral density of the pulsed and continuous external interference.
It is clear that the impact of the interference on (C/N0)eff_SSC is directly related to the SSC of an interfering signal from the j-th interfering signal on the i-th satellite to a desired signal s, the SSC is defined as
From the above equations it is clear that the SSC parameter is appropriate for assessing the impact of interfering signals on the receiver prompt correlator channel processing phases (acquisition, carrier phase tracking, and data demodulation), but not appropriate to evaluate the effects on the DLL phase. Therefore, a similar parameter to assess the impact of interfering signals on the code tracking loop phase, called code tracking spectral sensitivity coefficient (CT_SSC) can be obtained. The CT_SSC is defined as
where Δ is the two-sided early-to-late spacing of the receiver correlator.
To provide a metric of similarity to reflect the effect of interfering signals on the code tracking loop phase, a quantity called CT_SSC effective carrier power to noise density (C/N0), denoted (C/N0)eff_CT_SSC, can be derived. When intrasystem and intersystem interference coexist, this quantity can be expressed as
where IGNSS_CT_SSC is the aggregate equivalent noise power density of the combination of intrasystem and intersystem interference.
Equivalent Noise Power Density. When more than two systems operate together, the aggregate equivalent noise power density IGNSS ( IGNSS_SSC or IGNSS_CT_SSC ) is the sum of two components
IIntra is the equivalent noise power density of interfering signals from satellites belonging to the same system as the desired signal, and IInter is the aggregate equivalent noise power density of interfering signals from satellites belonging to the other systems.
In fact, recalling the SSC and CT_SSC definitions, hereafter, denoted or as , the equivalent noise power density (IIntra or IInter) can be simplified as
where Ci,j is the user received power of the j-th signal belonging to the i-th satellite, as determined by the link budget.
For the aggregate equivalent noise power density calculation, the constellation configuration, satellite and user receiver antenna gain patterns, and the space loss are included in the link budget. User receiver location must be taken into account when measuring the interference effects.
Degradation of Effective C/N0. A general way to calculate (C/N0)eff, (C/N0)eff_SSC , or (C/N0)eff_CT_SSC introduced by interfering signals from satellites belonging to the same system or other systems is based on equation (1) or (4). In addition to the calculation of (C/N0)eff , calculating degradation of effective C/N0 is more interesting when more than two systems are operating together. The degradation of effective C/N0 in the case of the intrasystem interference in dB can be derived as
Similarly, the degradation of effective C/N0 in the case of the intersystem interference is
Bandlimiting, Sampling, and Quantization. Traditionally, the effect of sampling and quantization on the assessment of GNSS RF compatibility has been ignored. Previous research shows that GNSS digital receivers suffer signal-to-noise-plus interference ration (SNIR) losses due to bandlimiting, sampling, and quantization (BSQ). Earlier studies also indicate a 1.96 dB receiver SNR loss for a 1-bit uniform quantizer. Therefore, the specific model for assessing the combination of intrasystem and intersystem interference and BSQ on correlator output SNIR needs to be employed in GNSS RF compatibility assessment.
Influences of Spreading Code and Navigation Data. In many cases, the line spectrum of a short-code signal is often approximated by a continuous power spectral density (PSD) without fine structure. This approximation is valid for signals corresponding to long spreading codes, but is not appropriate for short-code signals, for example, C/A-code interfering with other C/A-code signals. As one can imagine, when we compute the SSC, the real PSDs for all satellite signals must be generated. It will take a significant amount of computer time and disk storage. This fact may constitute a real obstacle in the frame of RF compatibility studies. Here, the criterion for the influences of spreading code and navigation data is presented and an application example is demonstrated. For the GPS C/A code signal, a binary phase shift keying (BPSK) pulse shape is used with a chip rate fc = 1.023 megachips per seconds (Mcps). The spreading codes are Gold codes with code length N = 1023. A data rate fd = 50 Hz is applied. As shown in Figure 1, the PSD of the navigation data (Gd(f) = 1/fd sin c2 (f/fd) ) replace each of the periodic code spectral lines. The period of code spectral lines is T = 1/LTC. The mainlobe width of the navigation data is Bd =2fd.
Figure 1. Fine structure of the PSD of GPS C/A code signal (fd = 50 Hz ,without logarithm operation).
For enough larger data rates or long spreading codes, the different navigation data PSDs will overlap with each other. The criterion can be written as:
Finally,
When criterion L ≥ fc/fd is satisfied, navigation signals within the bandwidth are close to each other and overlap in frequency domain. The spreading code can be treated as a long spreading code, or the line spectrum can be approximated by a continuous PSD.
C/N0 Acceptability Thresholds
Receiver Processing Phase. The determination of the required acceptability thresholds consider all the receiver processing phases, including the acquisition, carrier tracking and data demodulation phases.The signal detection problem is set up as a hypothesis test, testing the hypothesis H1 that the signal is present verus the hypothesis H0 that the signal is not present. In our calculation, the detection probability pd and the false alarm probability pf are chosen to be 0.95 and 10–4, respectively. The total dwell time of 100 ms is selected in the calculation.
A cycle slip is a sudden jump in the carrier phase observable by an integer number of cycles. It results in data-bit inversions and degrades performance of carrier-aided navigation solutions and carrier-aided code tracking loops. To calculate the minimum acceptable signal C/N0 for a cycle-slip-free tracking, the PLL and Costas loop for different signals will be considered. A PLL of third order with a loop filter bandwidth of 10 Hz and the probability of a cycle slip of 10–5 are considered. We can find the minimum acceptable signal C/N0 related to the carrier tracking process. For the scope of this article, the vibration induced oscillator phase noise, the Allan deviation oscillator phase noise, and the dynamic stress error are neglected.
In terms of the decoding of the navigation message, the most important user parameters are the probability of bit error and the probability of the frame error. The probability of frame error depends upon the organization of the message frame and various additional codes. The probability of the frame error is chosen to be 10–3. For the GPS L1C signal using low-density parity check codes, there is no analytical method for the bit error rate or its upper bound. Due to Subframe 3 data is worst case, the results are obtained via simulation. In this article, the energy per bit to noise power density ratio of 2.2 dB and 6 dB reduction due to the pilot signal are taken into account, and the loss factor of the reference carrier phase error is also neglected.
Minimum Acceptable Degradation C/N0. The methods for accessing the minimum acceptable required signal C/N0 that a GNSS receiver needs to correct
ly process a desired signal are provided above. Therefore, the global minimum acceptable required signal carrier to noise density ratio (C/N0)global_min for each signal and receiver configuration can be obtained by taking the maximum of minima. In addition to the minimum acceptable required signal C/N0, obtaining the minimum acceptable degradation of effective C/N0 is more interesting in the GNSS RF compatibility coordination. For intrasystem interference, when only noise exists, the minimum acceptable degradation of effective C/N0 in the case of the intrasystem interference can be defined as
Similarly, the minimum acceptable degradation of effective C/N0 in the case of the intersystem interference can be expressed as
Table 1 summarizes the calculation methods for the minimum acceptable required of degradation of effective C/N0.
Simulation and Analysis
Table 2 summarizes the space constellation parameters of GPS, Galileo, and Compass.
For GPS, a 27-satellite constellation is taken in the interference simulation. Galileo will consist of 30 satellites in three orbit planes, with 27 operational spacecraft and three in-orbit spares (1 per plane). Here we take the 27 satellites for the Galileo constellation. Compass will consist of 27 MEO satellites, 5 GEO, and 3 IGSO satellites. As Galileo and Compass are under construction, ideal constellation parameters are taken from Table 2.
Signals Parameters. The PSDs of the GPS, Galileo and Compass signals in the L1 band are shown in the opening graphic. As can be seen, a lot of attention must be paid to signal spectrum overlaps among these systems. Thus, we will concentrate only on the interference in the L1 band in this article. All the L1 signals including GPS C/A, L1C, P(Y), and M-code; Galileo E1 PRS and E1OS; and Compass B1C and B1A will be taken into account in the simulation and analysis.
Table 3 summarizes GPS, Galileo and Compass signal characteristics to be transmitted in the L1 band.
Simulation Parameters. In this article, all interference simulation results refer to the worst scenarios. The worst scenarios are assumed to be those with minimum emission power for desired signal, maximum emission power for all interfering signals, and maximum (C/N0)eff degradation of interference over all time steps. Table 4 summarizes the simulation parameters considered here.
SSC and CT_SSC. As shown in expression (1) or (4), (C/N0)effis directly related to SSC or CT_SSC of the desired and interfering signals. Figure 2 and Figure 3 show both SSC and CT_SSC for the different interfering signals and for a GPS L1 C/A-code and GPS L1C signal as the desired signal, respectively. The figures obviously show that CT_SSC is significantly different from the SSC. The results also show that CT_SSC depends on the early-late spacing and its maximal values appear at different early-late spacing.
FIGURE 2. SSC and CT_SSC for GPS C/A-code as desired signal.FIGURE 3. SSC and CT_SSC for GPS L1C as desired signal.
The CT_SSC for different civil signals in the L1 band is calculated using expression (3). The power spectral densities are normalized to the transmitter filter bandwidth and integrated in the bandwidth of the user receiver. As we saw in expression (3), when calculating the CT_SSC, it is necessary to consider all possible values of early-late spacing. In order to determine the maximum equivalent noise power density (IIntra or IInter), the maximum CT_SSC will be calculated within the typical early-late spacing ranges (0.1–1 chip space).
Results and Analysis
In this article we only show the results of the worse scenarios where GPS, Galileo, and Compass share the same band. The four worst scenarios include:
◾ Scenario 1: GPS L1 C/A-code ← Galileo and Compass (GPS C/A-code signal is interfered with by Galileo and Compass)
◾ Scenario 2: GPS L1C ← Galileo and Compass (GPS L1C signal is interfered with by Galileo and Compass)
◾ Scenario 3: Galileo E1 OS ← GPS and Compass (Galileo E1 OS signal is interfered with by GPS and Compass)
◾ Scenario 4: Compass B1C ← GPS and Galileo (Compass B1C signal is interfered with by GPS and Galileo)
Scenario 1. The maximum C/N0 degradation of GPS C/A-code signal due to Galileo and Compass intersystem interference is depicted in Figure 4 and Figure 5.
Scenario 2. Figure 6 and Figure 7 also show the maximum C/N0 degradation of GPS L1C signal due to Galileo and Compass intersystem interference.
Scenario 3. The maximum C/N0 degradation of Galileo E1OS signal due to GPS and Compass intersystem interference is depicted in Figure 8 and Figure 9.
Scenario 4. For scenario 4, Figure 10 and Figure 11 show the maximum C/N0 degradation of Compass B1C signal due to GPS and Galileo intersystem interference.
From the results from these simulations, it is clear that the effects of interfering signals on code tracking performance may be underestimated in previous RF compatibility methodologies. The effective carrier power to noise density degradations based on SSC and CT_SSC are summarized in Table 5. All the results are expressed in dB-Hz.
C/N0 Acceptability Thresholds. All the minimum acceptable signal C/N0 for each GPS, Galileo, and Compass civil signal are simulated and the results are listed in Table 6. The global minimum acceptable signal C/N0 is summarized in Table 7. All the results are expressed in dB-Hz.
Effective C/N0 Degradation Thresholds. All the minimum effective C/N0 for each GPS, Galileo and Compass civil signal due to intrasystem interference are simulated, and the results are listed in Table 8. Note that the high-end receiver configuration and external interference are considered in the simulations. According to the method summarized in Table 1, the effective C/N0 degradation acceptability thresholds can be obtained. The results are listed in Table 9.
As can be seen from these results, each individual system can provide a sound basis for compatibility with other GNSSs with respect to the special receiver configuration used in the simulations. However, a common standard for a given pair of signal and receiver must be selected for all GNSS providers and com
munities.
Conclusions
At a minimum, all GNSS signals and services must be compatible. The increasing number of new GNSS signals produces the need to assess RF compatibility carefully. In this article, a comprehensive methodology combing the spectral separation coefficient (SSC) and code tracking spectral sensitivity coefficient (CT_SSC) for GNSS RF compatibility assessment were presented. This methodology can provide more realistic and exact interference calculation than the calculation using the traditional methodologies. The method for the determination of the required acceptability thresholds considering all receiver processing phases was proposed. Moreover, the criterion for the influences of spreading code and navigation data was also introduced.
Real simulations accounting for the interference effects were carried out at every time and place on the earth for L1 band where GPS, Galileo, and Compass share the same band. It was shown that the introduction of the new systems leads to intersystem interference on the already existing systems. Simulation results also show that the effects of intersystem interference are significantly different by using the different methodologies. Each system can provide a sound basis for compatibility with other GNSSs with respect to the special receiver configuration in the simulations.
At the end, we must point out that the intersystem interference results shown in this article mainly refer to worst scenario simulations. Though the values are higher than so-called normal values, it is feasible for GNSS interference assessment. Moreover, the common standard for a given signal and receiver pair must be selected for and coordinated among all GNSS providers and communities.
This article is based on the ION-GNSS 2010 paper, “Comprehensive Methodology for GNSS Radio Frequency Compatibility Assessment.”
WEI LIU is a Ph.D. candidate in navigation guidance and control at Shanghai Jiao Tong University, Shanghai, China. XINGQUN ZHAN is a professor of navigation guidance and control at the same university. LI LIU and MANCANG NIU are Ph.D. candidates in navigation guidance and control at the university.
