There are a number of challenges to localization of autonomous vehicles (AVs) and autonomous driving (AD) applications in northern latitudes. The primary challenge is the harsh winter weather, which limits the utility of imaging sensors — snow, fog, mist, and darkness adversely affect such sensors and extreme low temperature can affect sensor performance. Ice and snow on the roads magnifies slippage of wheels, reducing the accuracy of wheel-mounted sensors. 

From a GNSS perspective, GNSS and satellite-based augmentation system (SBAS) satellite visibility is limited and the more active ionosphere hampers high-accuracy GNSS positioning. GNSS interference monitoring networks in the Arctic region are also minimal meaning positioning systems are vulnerable in the absence of alternate solutions to improve robustness. 

In terms of infrastructure, the broadband cellular network connectivity — necessary to download assistance data for GNSS, map updates, and traffic information — has spatial gaps in uninhabited areas of the European Arctic, such as northern Norway, Finland and Sweden. Lack of high quality and detailed maps limits the usefulness of absolute LiDAR- and camera-based positioning methods. Also, transport infrastructure in sparsely populated areas is not regularly updated and hence limit the potential market opportunity. 

This article describes how a European Space Agency-supported research project called the Arctic-PNT Innovation Platform is investigating navigation accuracy and availability of signal and correction data using a specially equipped road segment in northern Finland and Norway.

The Aurora Borealis Intelligent Corridor

To address the many challenges described above, the Aurora Borealis Intelligent Corridor (“Aurora”) along the E8 highway was created to validate autonomous vehicle platforms under Arctic conditions. It consists of the Snowbox intelligent road inside Finland and the Borealis intelligent road inside Norway. Diverse infrastructure is deployed and otherwise available along these intelligent roads in order to provide precise absolute positioning capability to AVs. As part of this activity, a team of researchers from the Finnish Geospatial Research Institute (FGI) recorded relevant positioning data in March 2018 using an experimental autonomous vehicle called Martti developed by the RobotCar Crew of the VTT Technical Research Centre of Finland Ltd. Below presents the first results achieved from this campaign. 

As shown in Figure 1, the 10 km-long Snowbox test road section is located in Muonio in western (Finnish) Lapland, and the 35 km-long Norwegian Borealis test section is located between Skibotn and the Finnish border at Kilpisjärvi. Special instrumentation is installed along and underneath the Snowbox test road for sensing road conditions and the category of passing vehicles. Moreover, there are entities in the area providing high quality communication networks (e.g. LTE and pre-5G test-network) and precise positioning services for all major GNSS constellations. EGNOS is also available even though satellites are only visible below about 10° elevation. 

Figure 2 shows how reference stations from Finland, Sweden, and Norway were combined in the National Land Survey’s precise positioning service to offer a tailored correction service in the Aurora corridor area. 

Lastly, Snowbox provides high-definition map resources of the road and surroundings, and ultra-wideband beacons are available for GNSS-independent precise positioning. Data and services in Aurora Snowbox are freely available for potential users. Table 1 summarizes the available infrastructure at Snowbox and Borealis.

The Arctic-PNT Innovation Platform Project

The project Arctic Positioning Navigation and Timing Innovation Platform: Nordic Hub based on the Snowbox Infrastructure, (“Arctic-PNT”) is supported by the European Space Agency (ESA) to analyze the role of Aurora Snowbox as a key infrastructure with regards to precise absolute positioning and navigation needs for AVs in Arctic conditions. The project is broadly divided into two Tasks. Task 1 consists of understanding the state of the art in PNT for AVs, to study the capabilities of Snowbox through literature surveys and interviews with key stakeholders, and to prepare a test plan for the experimentation campaign at Snowbox. Task 2 consists of recording positioning data from the Snowbox test road during two consecutive winters. Analysis of the results will help potential users to exploit fully the capabilities of Snowbox towards precise absolute localization in their own AV platforms. The project has successfully accomplished Task 1 and this article presents the results of the first winter experimentation campaign at Aurora performed in 2018 as part of Task 2. 

Minimum Operational Requirements for Precise Absolute Positioning in AVs

Based on a literature survey it was observed that there is no single standard definition of minimum operational requirements for absolute positioning performance in autonomous driving, defined as Level 3 and above on the driving automation scale from SAE International. The European GNSS Agency (GSA) recently released a report on road user needs and requirements, which is based on studies conducted through the European GNSS’ User Consultation Platform. Table 2 shows a summary of the different category of user requirements for absolute positioning in AD, as defined in this report.

Autonomous driving requires horizontal accuracy of position estimates to be approximately 20 centimeters with 95% confidence and availability better than 99.9%. The objective of the first phase of data analysis in the Arctic-PNT project was to investigate whether this level of accuracy and availability performance is possible at Snowbox using GNSS, SBAS, and precise positioning using correction data from reference networks. Note that validation of the positioning performance using other techniques for localization as well as the integrity performance was out of scope of the experimentation campaign and therefore not included here.

Measurement Campaign

The measurement campaign was performed over three days between March 26-28, 2018 when there was still considerable snow cover along the Snowbox test road. Data was recorded at multiple times during each day, to ensure diverse conditions of weather, road surface, visibility, satellite geometry, ionosphere, and animal and vehicular traffic, etc. would be recorded. One day was reserved for data recording on the Borealis test route inside Norway. The reference trajectory was computed using a dedicated professional-grade GNSS receiver and a high-grade Inertial Measurement Unit (IMU). 

The VTT experimental autonomous car, Martti was used for the measurement campaign. It is a Volkswagen Touareg equipped with sensors, actuators, and control systems necessary for fully automated operations. The sensor set includes GNSS receivers, environment perception sensors (RADAR, LiDAR, and cameras), vehicle dynamics sensors, and a CAN-bus connection for data flow from the vehicle’s built-in sensors. In addition, the ITS-G5 and cellular LTE communication devices are available. The sensor data is readable via Ethernet inside the vehicle. Note that although the data from the diverse sensors was recorded, the vehicle was driven manually during the measurement campaign.

Both mass-market and professional-grade receivers were used in the experiments, and the same antenna input was provided to all the receivers (including the reference receiver). The mass-market receiver was not capable of processing the precise positioning correction data and therefore, it was used primarily for standard GNSS-only positioning. Also, the professional-grade receivers were capable of processing in real-time the DGNSS and RTK corrections but not the State Space Representation (SSR)-based PPP corrections. So, the DGNSS and RTK processing was performed in real-time, while PPP processing was performed post-mission using the in-house Matlab-based FGI-GSRx software navigation engine developed at FGI.

Positioning Results

Standard Positioning at Snowbox

Table 3 shows the results of standard positioning performance at Snowbox using GNSS and SBAS with 1 hertz update rate at different times of the day. Note that to save on space only those receiver configurations providing the best performance have been shown. In general it was observed that for the mass-market receiver, adding Galileo and EGNOS improved the GPS-only performance, especially in the afternoon (left green row). For the professional-grade receiver however, the benefits of EGNOS were evident in improving the height estimation during the afternoon (right green row). Overall, under dynamic (moving vehicle) conditions both category of receivers offered similar performance. 

Overall, using standard positioning, the best possible 95 Circular Error Probable (CEP) horizontal accuracy of about 60 centimeters in the early and late hours and 70 centimeters in the afternoon was obtained with better than 99.5% availability. A possible reason for this correlation between the performance and time of day may be the ionospheric delay, which is expected to be more pronounced during the afternoon as compared to early and late hours. 

Although these are promising results, they are not sufficient to satisfy the requirements of autonomous driving and are provided here to give an idea of the GNSS-only baseline performance for absolute positioning that can be expected at Snowbox.

Differential-GNSS and RTK at Snowbox

Table 4 shows the results of precise positioning performance using a professional-grade receiver at Snowbox at different times of the day. The receivers process GPS and GLONASS dual-frequency signals and are provided differential corrections in the form of DGNSS and RTK with a maximum baseline length of approximately 10 kilometers. This is possible due to the new FinnRef stations constructed in the vicinity of Snowbox to improve the local validity and density of the corrections. 

As can be observed, DGNSS improves the accuracy performance to approximately 25 centimeters with an availability of 100%. However, it is when we apply the RTK corrections that the horizontal accuracy improves to within the bounds set for autonomous driving (marked in green). The best possible 95 CEP horizontal accuracy obtained was 4 centimeters with an availability of 99.9%. (Note that this refers to availability of correction data. The position solution was available 100% of the test duration, out of which 0.1% of the time correction data for precise positioning was unavailable e.g. due to a gap in mobile internet connectivity. However, during this gap the receiver was still providing standard position estimates based on GNSS-only). 

Figure 3 plots the different precise positioning error estimates over a duration of 1 hour using a professional-grade receiver and Network-RTK corrections from FinnRef. Note that in all of these scenarios the vehicle averaged a speed of 80 km/hr.

Positioning Results Along the Aurora Borealis Intelligent Corridor 

Table 5 shows the positioning performance along the E8 highway, from Muonio to Skibotn (196 kilometers). This includes the 10 kilometers Snowbox intelligent road and the 35 kilometers Borealis intelligent road inside Norway. Here it can be observed that EGNOS provides benefit over GPS-only positioning accuracy (note that it was not possible to estimate the height accuracy over the total duration for the GPS-only case). Taking into account the very high latitudes (>69˚) and the mountainous terrain at Borealis, it has an adverse effect on the visibility of the EGNOS satellites, and consequently on the availability of EGNOS-enabled position solution. 

Table 5 also shows the results of precise positioning at Borealis using network-RTK corrections generated by the FinnRef and CPOS networks respectively. Note that the FinnRef corrections are computed based on the Finnish and nearby Swedish and Norwegian reference station data, while the CPOS corrections are computed exclusively from the Norwegian stations. The results show that the performance is comparable and satisfies the requirements for autonomous driving. 

The availability of the corrections data was found to be strongly influenced by the data link through the mobile internet. During the two test sessions, two separate subscriber identification module (SIM) cards from two different Finnish mobile service providers were used for mobile connectivity under international data-roaming conditions. It can be observed that when using the second SIM card, correction data availability is greatly improved as compared to the first. In the future, similar scenarios have to be investigated using a SIM card from a Norwegian mobile services provider. In fact, this result is significant as it shows one possible challenge in enabling continuous operation of fully autonomous vehicles across international borders. 

PPP Results

The PPP solution is calculated using the recorded single frequency GPS code and phase observables from professional grade receivers. Two receiver models from two manufacturers were used for logging the GPS data. As neither of these receivers support SSR corrections natively the PPP processing had to be conducted post-mission using the FGI-GSRx software navigation engine. Note that the PPP algorithm is currently based on float ambiguity estimation. The results (decimeter-level accuracy) achieved with this algorithm are in conformance with expected performance and background literature. Prior to PPP calculation, the observables are corrected using the State Space Representation (SSR) model and using the experimental SSR stream of the NLS precise positioning service. The SSR supplies corrections to orbit, clock, phase bias, code bias, and ionosphere errors. 

It was observed that single-frequency PPP with float ambiguity resolution provides sub-half-meter 3D positioning accuracy, which is improved compared to standard positioning, but not as good as differential positioning. Therefore, even though the best case 95% horizontal accuracy is 17 centimeters, the overall performance does not consistently (meaning over multiple trajectories) achieve the requirements for autonomous driving. 

The age of corrections does not critically affect the positioning accuracy at this level, since similar accuracy is achieved even when the corrections are several minutes old. Therefore the availability is resilient against network connectivity gaps to some extent, which is a significant advantage of PPP over RTK-based precise absolute positioning. Some test trajectories did not show an improvement over standard positioning; this result may indicate the experimental nature of both the SSR service and the positioning software at this stage.

Figure 4 shows the improved positioning accuracy performance of PPP-SSR (right) in comparison to GPS-only (left) using a professional-grade receiver and corrections from FinnRef at Snowbox (10 kilometers). Figure 5 shows a similar comparison of results obtained while driving over the E8 highway from Muonio to Skibotn (196 kilometers). In this case, even though PPP-SSR does provide improvement over standalone-GPS, the benefits are not as pronounced as those obtained in the Snowbox area. The best case 95% 3D accuracy was 26 centimeters. Note that in both figures the test trajectory was over 1 hour long.

Conclusions and Future Steps

This article describes the Aurora Snowbox and Borealis intelligent roads and the diverse infrastructure deployed along them for vehicle localization. Assuming a 95 CEP accuracy of 20 centimeters and availability of better than 99.9% as reasonable user requirements for autonomous driving, this paper illustrates FGI’s experimentation campaign at Aurora to validate if these requirements are achievable under Arctic conditions. It was shown that using precise point positioning and network-RTK corrections with a professional-grade receiver the accuracy and availability requirements can be satisfied under dynamic conditions. At the same time, gaps were identified especially in continuous availability of GNSS correction data through cellular data-link when crossing international borders or visibility of SBAS satellites. 

Acknowledgements

The Arctic-PNT project has been supported by the European Space Agency. The project acknowledges the assistance of the Finnish Transport Agency in providing access to Snowbox, of the Norwegian Public Roads Administration in providing access to Borealis, and of the Norwegian Kartverket in providing access to the CPOS corrections service. The experimentation campaign at Snowbox was conducted using the experimental autonomous vehicle Martti developed by the RobotCar Crew of the VTT Technical Centre of Finland Ltd.

Additional References

[1] Aurora Snowbox: https://www.liikennevirasto.fi/web/en/e8-aurora.

[2] Aurora Borealis: Norwegian Public Road Administration, ‘Intelligente Transportsystemer – ITS – E8 Troms’, map interface. Available at: http://vegvesen.maps.arcgis.com/apps/MapSeries/index.html?appid=aa75bc1fb9d741b3b0260dd241641e75.

[3] Arctic PNT project: https://arctic-pnt.org/.

[4] Martti experimental autonomous vehicle from VTT: vttresearch.com/ad

[5] Network-RTK: https://insidegnss.com/network-rtk-and-reference-station-configuration/

[6] “Report On Road User Needs And Requirements”: https://www.gsa.europa.eu/newsroom/news/gsa-road-report-highlights-user-pnt-requirements, European GNSS Agency

[7] SAE International’s definitions of terms related to autonomous driving: https://www.sae.org/standards/content/j3016_201806/

Authors

Sarang Thombre received his Doctoral degree from Tampere University of Technology in 2014. He works as a Research Manager and Research Group Leader at the Finnish Geospatial Research Institute. His research interests include positioning receiver implementation and performance validation, interference studies, and localization for autonomous vehicles.

Simo Marila received his M.Sc. degree in 2011 from Aalto University, Finland in the field of Geodesy. He is a Research Scientist at the Department of Geodesy and Geodynamics at FGI. He was involved in renewing the FinnRef network and his recent research is related to reliability and accuracy of GNSS positioning.

Martti Kirkko-Jaakkola received his Master’s and Doctoral degrees from TUT in 2008 and 2013, respectively. He works as a Research Manager at the FGI, National Land Survey of Finland. His research interests include precise satellite positioning and timing, MEMS inertial sensors, and indoor navigation.

Salomon Honkala

Michelle Koivisto is an assistant research scientist at FGI in the Department of Navigation and Positioning, where she has been working since 2017. Her research interests are GNSS receiver development, SBAS systems, Differential GNSS (DGNSS), GNSS modernization and autonomous navigation.

Hannu Koivula is the head of the Reference Systems research group at FGI. He has 20 years of research experience in high accuracy GNSS applications and GNSS networks. He has studied the accuracy of GNSS applications and lately specialized in metrological traceability of GNSS measurements.

Dr. M. Zahidul H. Bhuiyan is working as a Research Manager at the Department of Navigation and Positioning in the Finnish Geospatial Research Institute. His main research interests include various aspects of multi-GNSS receiver design, GNSS vulnerabilities, SBAS, differential GNSS, sensor fusion, etc.

Mark Petovello is a professor (on leave) at the University of Calgary. He has been actively involved in many aspects of positioning and navigation since 1997 and has led several research and development efforts involving Global Navigation Satellite Systems (GNSS), software receivers, inertial navigation systems (INS) and other multi-sensor systems. E-mail: mark.petovello@gmail.com

The post What are the challenges to localization in autonomous cars in the Arctic? appeared first on Inside GNSS - Global Navigation Satellite Systems Engineering, Policy, and Design.

Since a snapshot receiver can operate with such a short intervals of signal sampling, it is ideally suited for a wide variety of positioning applications where energy use is a significant limitation in adopting conventional GNSS chipset solutions. At the same time, the limited amount of data used requires several changes relative to a conventional GNSS receiver. This article describes the key differences and advantages of a snapshot approach to signal processing and position estimation compared to conventional GNSS techniques.

Snapshot vs. Traditional Receivers

Conceptually, a GNSS receiver can be divided into three logical blocks, as shown in Figure 1:

1. Signal Capture: Collects digital samples of the incoming GNSS Radio Frequency (RF) signals.

2. Signal Processing: Acquires satellites that are detectable and outputs measurements – code phase (pseudorange), Doppler frequency and, optionally, carrier phase.

3. Position Estimation: Computes a position using the code phase and Doppler frequency measurements.

One very unique feature of snapshot receivers is its flexibility to reconfigure and initiate these logical blocks on and off the device being located. For example, since Signal Processing and Position Estimation can be performed long after the signal has been captured, the snapshot receiver can be configured to further reduce power consumption on a battery-operated device by offloading these tasks onto another device such as a cloud-based server, if needed. That being said, with the short sampling time in the snapshot approach, Signal Processing and Position Estimation cannot be performed by conventional means. 

The standard steps in Signal Processing to search, acquire, and wait for tracking loops to converge are inapplicable in snapshot positioning. These steps must be replaced with an iterative approach to generate code phase and Doppler frequency measurements (the short sampling times mean that carrier phase data is not available). The Signal Processing block can be computationally complex so the sampling frequency and bit resolution of the digital samples must be carefully chosen for the trade-off between computation time (therefore power consumption) and, sensitivity and measurement quality.

The implications for the Position Estimation arise because there is not enough time to decode navigation data from the received signal. All GNSS receivers require the use of ephemeris information to compute satellite information and, by extension, the receiver position. For conventional receivers, the ephemeris can typically be obtained either directly by decoding the broadcast ephemeris or through alternative means via a communication network; this approach is commonly referred to as Assisted GNSS (AGNSS) technology. In contrast, a state of the art snapshot receiver does not attempt to download/decode the incoming satellite ephemeris information; instead, it takes advantage of utilizing extended ephemeris technology to enable the snapshot receiver to the predict ephemeris autonomously for up to 28 days between ephemeris updates. 

Even with the ephemeris obtained by means of broadcast, network assistance, prediction, or post-processing; conventional GNSS processing must still derive the transmit time from the satellite broadcast data. As a result, a pseudorange measurement cannot be obtained without reconstructing the transmit time or using a broader set of techniques also known as Coarse Time Positioning. 

Along with the requirement to obtain ephemerides from an alternative source, snapshot receivers cannot estimate receiver position from pseudoranges without an approximate initial time and position of the receiver.

In contrast to snapshot receivers of the past, a state of the art snapshot positioning process described below, has these initial time and receiver position requirements either eliminated or greatly relaxed. Some techniques for coarse time positioning require an a priori time within a few seconds and position within a few km. However, with more recent techniques, the initial position requirement can be relaxed to 75 km, and the initial time to 60 seconds. This wider requirement can be met using Doppler-based positioning so that, ultimately, there is no initial position requirement at all and the initial time requirement is 30 minutes, which can be easily achieved using a Real Time Clock (RTC) that is widely available in most low-cost consumer electronics. Further details are provided below.

Snapshot Position Estimation

As described above, the satellite signal transmit time cannot be decoded in snapshot GNSS receivers. In the example of a conventional GPS receiver, the integer component of transmit time in milliseconds can be derived from the Z-count time of week (TOW) and an integer count of elapsed C/A code epochs. The fractional component of transmit time is the measured code phase.

Then, the pseudorange (ρ) can be calculated as

Where c is the speed of light, t_r is the received time of the signal, and t_t is the transmit time with an integer millisecond component τ_t , and the code phase ρ as the fractional component. 

Because the integer component of transmit time (τ_t ) is unknown in a snapshot receiver because TOW cannot be extracted, the full pseudorange must be generated by other means. Broadly, for any coarse time positioning method, the pseudorange is calculated using an estimated range that comes from the initial approximation of receiver time and position, with careful handling of the receiver clock offset. 

In particular, using advanced techniques, the transmit time is reconstructed relative to the received time such that pseudorange can be calculated in the standard method of equation 1.

A common representation of pseudorange, ignoring noise and propagation errors, is

where r is the geometric range to the satellite, Δt_sv is the satellite clock correction, and b is the sub-millisecond receiver clock bias.

Combining equations 1 and 2, the integer component of the transmit time is solved as

representing the fact that the initial received time in a snapshot receiver may have an error of multiple seconds. This error in absolute time can be considered to be an integer number of milliseconds (ranging code periods) since the fractional component is absorbed by the receiver clock bias. Thus the error in approximated integer transmit time will be identical.

The geometric range r in equation 3 is approximated from the ephemeris and the initial estimates of position and received time. The satellite clock correction Δt_sv is known and the code phase p is measured. So all that remains to calculate an approximate integer transmit time is the clock bias b, which is unknown. 

An approximate clock bias can be determined by searching for a value that minimizes how far off  τ_t is from an integer value for all satellites. When the best clock bias is found, then all values of τ_t  can be rounded to integers. From these reconstructed transmit times, equation 4 can be used to calculate the pseudorange for each satellite. 

It should be noted that, although the error (ε_t) in the coarse initial received time (t_r) can be used in pseudorange construction without inducing pseudorange error, it will still induce an error in the satellite ephemeris calculation. In conventional GNSS processing, fine time is known well enough to be sufficient to be directly applied for position estimation. For any coarse time positioning method, the absolute time error must be an additional estimation state.

The Position Estimation in snapshot positioning can be implemented as an independent least-squares calculation or in a Kalman filter. The solution update interval is customizable for different use cases. In cases where position is only needed at infrequent intervals, accuracy requirements are usually less stringent and a least squares solution is sufficient even with the extra estimated absolute time error. With more frequent updates, a Kalman filter can be used to improve solution accuracy.

Conceptual Structure of a Snapshot Receiver

In a snapshot receiver, each Signal Capture is digitized and saved as a data file. The user has full control over how often and how many milliseconds of digital samples to capture. Signal processing is a key differentiator between the state of the art snapshot receiver and the conventional receiver. 

When compared with conventional GNSS receivers, there is a lot of flexibility when designing a snapshot receiver. A conventional receiver usually performs all the blocks of Signal Capture, Signal Processing, and Position Estimation in the hardware device, even if measurements are output for later post-processing. In contrast, a snapshot receiver can be designed to distribute these blocks to optimize energy consumption for their unique hardware platform and, indeed, use cases as described below.

As mentioned earlier, Signal Processing and Position Estimation can be performed long after the signal data has been captured. For use cases where maximizing battery life is more critical than real-time positioning, the snapshot receiver can be configured such that only the Signal Capture circuitry is implemented to temporarily store the digital samples. Signal processing will be postponed until such a time that the digital samples can be transmitted, without affecting the battery life of the device (e.g. during battery recharge), to a remote cloud server for Signal Processing and Position Estimation computations. This is illustrated in Figure 2.

For use cases where a position information is needed at the device, the snapshot receiver can be configured such that the Signal Capture, Signal Processing, Position Estimation blocks  are all implemented on a single circuitry, where the extended ephemeris is retrieved from a cloud server at time intervals that has the least impact on the battery life. Such a setup is illustrated in Figure 3.

Figure 4 shows a hybrid of the above two use cases, where the snapshot receiver is be configured to capture the digital sample data and then generates measurements prior to transmitting the pre-processed measurements to the remote cloud server for the final Position Estimation computation. In this approach, power consumed for transmitting measurement data is much smaller than for digital samples. Furthermore, the server can estimate a better position solution since it has access to precise orbits. 

In general, state of the art snapshot receiver offers system designers a lot of flexibilities to tailor make a low power and low cost GNSS solution that is most suitable for their hardware implementation and use cases. This is fundamentally different from the conventional GNSS chipset that most designers are accustomed to. 

In addition to the three configuration modes described above, to minimize energy further, designers can force the snapshot receiver to remain in a “deep sleep” state most of the time. The receiver will only wake up for a few milliseconds to periodically capture a user’s position, store the captured signal and then go back to a “deep sleep” state to conserve power. This essentially creates a GPS-on-demand operating mode.

Internet-connected smartphones have created an “always ON” world that has us conditioned to expect everything to be ON instantly. The penalty for using conventional GNSS receivers to satisfy our “instant everything” desire is the significant energy consumption. In contrast, snapshot receiver technology operates counter-intuitively by forcing the receiver to be always OFF to conserve this precious energy; it uses advanced signal processing techniques that require the receiver to be turned ON just for a few milliseconds. For low-power Wearables and IoT applications where position fixes are needed but energy consumption must be kept to a minimum, a snapshot receiver is ideal.

Additional Resources

For additional information about snapshot based receivers and positioning, please refer to the following resources

[1] “System, Method, and Computer Program for a Low Power and Low Cost GNSS Receiver”, United States Patent US 9,116,234 B2.

[2] Muthuraman, K., (2012) Coarse Time Positioning. Inside GNSS, March/April 2012

[3] van Diggelen, F., (2009) A-GPS: Assisted GPS, GNSS, and SBAS, Artech House, first edition

Authors

Keith Van Dierendonck is a Sr. GNSS Specialist at Baseband Technologies, Inc. in Calgary, Alberta, Canada. Keith has worked in GNSS system development ranging from high-precision to low-cost/low-power for more than 25 years.

Ossama Al-Fanek is a Sr. GNSS Engineer at Baseband Technologies, Inc. in Calgary, Alberta, Canada. Ossama received a PhD degree in Geomatics Engineering at the University of Calgary and has been working on low-power GNSS system development for the past 8 years.

Mark Petovello, co-author, is the editor of this column. 

The post What Is Snapshot Positioning and What Advantages Does It Offer? appeared first on Inside GNSS - Global Navigation Satellite Systems Engineering, Policy, and Design.

Dealing with NLOS-only signals is generally easier than dealing with multipath because the errors tend to be larger and are thus easier to detect with standard receiver autonomous integrity monitoring (RAIM) approaches. More recently, ray tracing has been used in combination with 3D building models (3BDM) to predict and correct NLOS-only signals for their path delay, thus making them behave more like LOS signals. 

In contrast, multipath — which we herein use exclusively to represent the contamination of the LOS signal, if it is present — is more difficult to deal with because the errors are smaller and harder to detect with RAIM. More importantly, even if the path delay of contaminating NLOS signal is known or can be computed, the relative carrier phase of the LOS and NLOS signal(s) can cause the resulting pseudorange measurement to appear too short, even though the NLOS signal is always, by definition, delayed relative to the LOS signal. Predicting the carrier phase(s) of the NLOS signal(s) relative to the LOS signal is generally not possible with sufficient accuracy due to the relatively short wavelength of GNSS signals involved (a 30 degree phase accuracy would require relative position accurate to better than 2 centimeters at L1).

However, most of the above problems arise from the fact that positioning algorithms typically assume their input to be measured pseudoranges. If we instead consider the input to be the receiver’s correlator outputs (which are used to compute the pseudorange), then entirely new options are possible. This article discusses one approach for combining correlator outputs with 3DBM data to derive position from only reflected signals. In essence, it demonstrates that when handled properly, reflected signal can actually be useful.

High-Level Concept

Before delving into some of the details of how NLOS signals can be used constructively, we first introduce some key concepts. 

First, let’s assume we have a candidate value of the user’s position. We will discuss how such a candidate value might be obtained later in the article, but for now we simply assume it is available.

Next, we use the candidate position along with a 3DBM and ray tracing techniques to compute/predict two important pieces of information: (i) the number of received signal paths (LOS and/or NLOS); and (ii) the path delay of each signal relative to the LOS signal, regardless of whether the LOS signal is actually present. Collectively, these values are referred to as the “predicted signal parameters”. Note that the algorithm does not require that the LOS signal be present — if it is, its path delay will be zero, by definition.

Not requiring the LOS to be present is one of the main advantages of our approach because, especially in urban areas, LOS signals are not always received. If the LOS signal is absent, then the path delay relative to the shortest received NLOS path can be computed as

Third, we perform a comparison between the predicted signal parameters and the received signal parameters. The latter are not known directly, but are completely contained in a GNSS receiver’s correlator outputs. If the predicted signal parameters agree with the correlator outputs, it suggests that the candidate position used to generate the predicted parameters was accurate. In contrast, if the agreement between the predicted and received signal parameters is poor, it suggests the candidate position was inaccurate.

This final point suggests that instead of a single candidate position, several candidate positions should be considered and the position whose predicted signal parameters best match the correlator outputs should be selected as the final position estimate. This is precisely how the algorithm works — we use a grid of candidate points as the input and select the “best” amongst these as the final position estimate (how we obtain a grid of points is discussed later).

Filling-In Some Details

Although a full mathematical description of the algorithm is beyond the scope of this article, some key details are described in this section to better explain what is happening. The Additional Reading section at the end of the article provides resources containing more of the mathematical details.

One of the more important aspects of the algorithm is the development of mathematical models of the correlator outputs that relate to the predicted signal parameters. Based on our empirical observations, we only considered one-, two- and three-path models for the correlator outputs, but additional paths could be included if necessary. For illustrative purposes, we only show the two-path model:

where  is the power of the correlator output; subscripts  denote the shortest, second-shortest, etc. signal paths; A is the signal amplitude; τ₁ is the code phase of the shortest path; бτ is the path delay as defined above; R(τ) is the auto-correlation function of the signal’s ranging code; and бϕ is the relative carrier phase. Although we model the correlator power, similar models could be derived for in-phase (I) and quadrature-phase (Q) signals.

The parameterization above intentionally includes the path delay which, as discussed above, can be obtained from ray tracing and a 3DBM. More specifically, it allows the predicted path delay values to be used as input to the signal model. 

This leads to the final step, which is the comparison of the predicted signal parameters to the received signal parameters. This is accomplished using a least-squares fit of the correlator outputs to the selected signal model. The state vector used for the two-path case is

The solution is computed using the predicted path delays as a priori information, meaning the least-squares estimator is primarily estimating all of the other (nuisance) parameters. The astute reader will notice the absence of an explicit clock term — this implicitly contained in the code phase for shortest received signal (τ₁).

As mentioned above, if the candidate position is accurate, the predicted path delays will also be accurate and the estimator should be able to reliably estimate the remaining signal parameters. The corresponding least-squares residuals should be small. In contrast, an inaccurate candidate position will lead to larger residuals. This works because of all of the parameters in the state vector, the one most sensitive to the input candidate position, is the path delay.

In light of all this, the root-sum-squares (RSS) of the residuals is the metric used to assess the goodness of fit of the predicted signal parameters to the correlator outputs (smaller is better). More specifically, the process described above is performed separately for each satellite and the RSS residuals across satellites is used as the final metric.

Over-parameterization of the signal model must be accounted for when computing the residuals for each satellite. This can happen when the predicted number of paths is larger than the number of paths actually received. In this case, the “extra” degrees of freedom in the model will artificially reduce the RSS of the residuals. When an over-parameterization is detected, the RSS residuals are set to be large to effectively de-weight the corresponding candidate position — this makes sense as the predicted signal parameters are effectively wrong, most likely because of an inaccurate candidate position.

Before showing results, it is worth noting the receiver’s correlator taps should span a sufficiently wide range of code phase values and use a sufficiently tight spacing so as to capture enough of the received signal’s “shape”. In our work, we used 61 correlator taps equally spaced across ±1 chips. 

Results

Data was collected in downtown Calgary, Canada on two separate days over a total of about 50 minutes. Figure 1 shows the trajectories of the two data sets in purple along with building outlines colored by building height. The tallest building exceeds 200 meters and there are parts of the trajectory where the sky visibility falls below 20%. This is therefore a relatively challenging environment for GNSS-based positioning. 

Data was collected using a front-end and processed using a software receiver to generate correlator outputs. For the results shown, the coherent integration time was 10 milliseconds and no non-coherent summation was performed. Such short coherent integration times would support snapshot based positioning, wherein a short period of data is recorded and used to compute a solution. In turn, this can offer tremendous power savings over “fully-tracking” receivers.

The correlator outputs and a 3DBM were then input into Matlab, where the algorithm described above was implemented. The computed positions were derived using the above algorithm only. In other words, only reflected signals were used, no LOS pseudoranges. This was done to directly assess the feasibility of using reflected signals for position determination. The computed positions were then compared against a GNSS/INS reference solution to assess performance.

To best analyze results, Figure 2 shows a box-and-whisker plot of the horizontal position errors binned according to sky visibility. The most striking result is that accuracy improves as sky visibility decreases. This happens because reduced sky visibility implies more NLOS signals, and since the algorithm only uses NLOS signals, it follows that results should improve in this case. Equally surprising is that for sky visibilities below 20%, the median error (denoted by red line) is only about 3 meters. Finally, the spread of the data in each bin indicates the results are repeatable between tests and at different locations along the trajectories.

As an extension of the above results, as sky visibility increases, the positioning error increases because there are fewer NLOS signals the algorithm can use. This behavior would change if LOS pseudoranges were used. 

Discussion

Although the results presented are promising, the algorithm does have its drawbacks. The most obvious drawback is the need to perform ray tracing, which is computationally intensive, especially for power- and/or resource-constrained platforms. Use of a graphics processing units (GPU) could improve processing throughput, as could offline processing, but each of these approaches pose challenges of their own.

The other drawback is initialization of the algorithm. Until now, we have assumed that a grid of candidate positions is available without consideration for how that may be obtained. Our research has demonstrated that the algorithm described above is robust to large uncertainty regions (with corresponding computational challenges) suggesting that a “standard” GNSS position could be used with a sufficiently conservative uncertainty region. However, further investigation would be necessary to verify this under a wide range of operational conditions.

Notwithstanding the above challenges, using NLOS signals to improve positioning performance has been demonstrated and it will be exciting to see how this emerging area of research and development evolves.

Additional Reading

More details on the algorithm described above is available here:

Kumar, R. and Petovello, M.G. (2017) “3D building model-assisted snapshot positioning algorithm”. GPS Solutions, 21(4), 1923–1935.

Kumar, R. (2017) “3D Building Model-Assisted Snapshot GNSS Positioning”. PhD Thesis, Department of Geomatics Engineering, University of Calgary, Calgary.

Authors

Rakesh Kumar received a PhD degree from the University of Calgary where he worked on improving GNSS-based navigation in urban canyons and integration of 3D city models with GNSS. Prior to this, he completed his bachelors and masters in electrical engineering from India and had more than 10 years of experience in the aerospace industry. Currently he works in systems engineering for the active safety and automated driving division of General Motors.

Mark Petovello, co-author, is the editor of this column.

The post Are Reflected Signals Always Undesirable? appeared first on Inside GNSS - Global Navigation Satellite Systems Engineering, Policy, and Design.

Many parts of critical infrastructures rely on uninterrupted access to GNSS positioning, navigation and timing services, but, at the same time, threats to denial of GNSS services are increasing. Radio frequency interference can be unintentionally emitted by commercial high power transmitters, ultra-wideband radar, television, VHF, mobile satellite services and personal electronic devices. Moreover, malicious intentional interference is produced by jammers, whose rapid diffusion is becoming a severe threat to GNSS.

To ensure GNSS is protected, there is now a need to respond at an international level to ensure that there is: i) a common standard for real-world GNSS threat monitoring and reporting, and ii) a global standard for assessing the performance of GNSS receivers and applications under threat. GNSS threat-reporting standards would allow for compilation of real-world threats into a database that could be analyzed to develop GNSS receiver test standards that ensure new applications are validated against the latest threats. Both standards are missing across all civil application domains and are considered a barrier to the wider adoption and success of GNSS in the higher value markets.

This article discusses the STRIKE3 project that was specifically developed to address the issues outlined above.

STRIKE3 Overview

The STRIKE3 (Standardizsation of GNSS Threat reporting and Receiver testing through International Knowledge Exchange, Experimentation and Exploitation) project is a European initiative that addresses the need to monitor, detect and characterize GNSS threats to support the increasing use of GNSS within safety, security, governmental and regulated applications. STRIKE3 has deployed an international network of GNSS interference monitoring sites that monitor interference on a global scale and capture real-world threats for analysis and to ultimately test GNSS receiver resilience.

Using thousands of threats collected from their network over a three-year period, STRIKE3 has developed a baseline set of threats that can be used to assess performance of different GNSS receivers under a range of typical real-world interference/jamming threats. The resulting specification consists of five different threats: wide swept frequency with fast repeat rate, narrow band signal at L1 carrier frequency, triangular and triangular wave swept frequency and tick swept frequency. For details of how these five threats were selected, refer to the Additional Reading section at the end of the article.

Finally, the STRIKE3 project has begun using its test specification to test receiver performance in the presence of various threats. Below is a discussion of how this is done as well as some results for a specific type of interference.

Collectively, the above activities aim to improve mitigation and resilience of future GNSS receivers against interference threats.

Receiver Testing

The main objectives of the testing component of the STRIKE3 project are: first, to validate the proposed testing standards to demonstrate they are clearly defined, useful, and practical; and second, to assess performance of a variety of receivers against real-world threats detected by the STRIKE3 monitoring network. Using real-world threats detected at the monitoring sites enables interested stakeholders (e.g., certification bodies, applic

ation developers, receiver manufacturers, etc.) to better assess the risk to GNSS performance during operations and to develop appropriate countermeasures.

The remainder of this article presents some illustrative examples for multi-GNSS mass-market and professional grade receiver testing against a single interference type that is very commonly detected at STRIKE3 monitoring sites, namely a triangular chirp swept frequency signal as depicted in Figure 1.

The test platform used is shown in Figure 2. The clean GNSS signal is generated from a multi-constellation, multi-frequency Spectracom GSG-6 hardware simulator, whereas the threat signature is generated using a Keysight Vector Signal Generator (VSG) N5172B through the replay of raw I/Q (In-phase/Quad-phase) sample data. Raw I/Q data captured in the field for a real-world event is used as input to the VSG which then re-creates the detected threat by continuously replaying the data in a loop.

Both the GNSS signal simulator and the VSG are controlled via software in order to automate the testing process. The automation script is used to control these devices remotely and to limit human intervention. The script also provides synchronization between the two instruments in order to ensure repeatability of the tests and the reliability of the results.

The clean GNSS signal and the interference signal are combined using an RF combiner, and the interferencecontaminated GNSS signal is fed to the Receiver Under Test (RUT), which produces its own output metrics. For the validation of

baseline performance under nominal signal conditions, the VSG does not generate any interference signal. In this case, the input signal to the RUT is only the clean GNSS signal produced by the GNSS constellation simulator.

A laptop is used to record and analyze the performance of the receiver against the different threat signals. The analysis is performed using a MATLAB-based script that processes the NMEA output messages from the RUT.

For each receiver category — namely mass-market and professional grade — three different test methodologies are performed:

• Baseline – a clean GNSS signal in the absence of interference is fed to the RUT to validate its performance under nominal conditions. The total duration of this test is 60 minutes.
• Time To Re-compute Position (TTRP) solution – this test is used to measure the time taken for the RUT to recover after a strong interference event. In this test, the interference is switched on 14 minutes after the simulated scenario starts and it is applied for 90 seconds. The interference power is fixed to a value such that the receiver immediately loses its position solution. In this test case scenario the interference power corresponds to a Jamming-to-Signal (J/S) ratio of ~90 dB. The time taken between switching off the interference source and the first position fix is recorded as the TTRP. The profile of this test

  

  methodology, whose total duration is 30 minutes, is illustrated in Figure 3.

• Sensitivity – this test scenario is conducted by varying the power of the interfering signal. The interference is turned on 10 minutes after the simulation starts and it follows a two-peak ramp power profile. The initial interference power is such that J/S is ~5 dB, and then the interference power is increased by
  5 dB every 45 seconds until reaching a J/S of 65 dB. After the first peak has been reached, the interference power is decreased in a reverse manner. The power profile is then repeated a second time. The profile of this test methodology is illustrated in Figure 4.

In order to assess the performance of the RUT in the presence of interference, different metrics were selected. The following outputs from the GNSS receiver are recorded and analyzed for all the test methodologies:

• Number of tracked satellites
• Position fix indicator (a Boolean to indicate if a 3D position fix is available or not)
• Number of satellites used in fix
• Carrier-to-Noise density (C/N0) ratio
• East-North-Up position error

Moreover, depending on the test methodology, additional parameters are evaluated. For example, in the case of the TTRP test method, the time tak

en for the RUT to re-obtain a position fix after a strong interference event is measured. For the sensitivity test method, the Jamming-to-Signal ratio at which the position solution is no longer available and the availability of the position solution during the interference event are computed. Furthermore, position accuracy statistics are computed for the interval in which the interference is present when the receiver offers a valid position fix.

Currently, only GPS L1 and Galileo E1 signals are used for testing and the RUT is configured to operate in static stand-alone mode.

Table 1 provides an overview of the simulated scenario settings, including the receiver location, the start time, the duration, the GNSS signal power and the interference power levels for the different test methodologies.

When performing the tests, an elevation mask of 5° is applied for the Position, Velocity and Time (PVT) computation. The RUT’s default C/N0 mask is used in all cases. The RUT settings are summarized in Table 2.

Results

This section presents the results of the standardized tests of a mass-market and a professional grade receiver against one of the most frequently detected interference types at STRIKE3 monitoring sites. The spectrum and the spectrogram of such interference signal are sho

wn in Figure 1.

The accuracy and availability of the receiver’s position solution during the interference interval is analyzed in the sensitivity tests. As the interference power increases, the receiver performance continues to degrade and at some point the RUT loses the position fix. The East-North-Up (ENU) deviations of the position solution for the mass-market (top) and the professional grade receiver (bottom) are shown in Figure 5.

Both receivers offer inaccurate position solutions in the beginning, especially in the vertical component. This is due to the cold start and the resulting unavailability of ionospheric parameters, and to the convergence of the navigation filter.

It can be seen that the mass-market RUT prioritizes the availability of the position solution over its accuracy. In particular, during the interference interval, there are only a few epochs at which the receiver does not yield a solution, but this high yield comes with degraded positioning accuracy.

On the other hand, the professional grade RUT prioritizes the accuracy over the availability. It does not offer the position solution as often during the interference interval, but when it does the position errors are minor.

In order to have a better understanding of the interference impact on the RUT, a comparison with respect to the baseline test case is also carried out. Figure 6 shows the drop in the average C/N0 of the satellites used in position fix with respect to the baseline for the entire duration of the test. As expected, in the presence of interference, the signal quality worsens as the interference signal’s power increases. Given the wideband nature of the interfering signal, GPS and

Galileo are affected similarly.

The difference between the mass-market and the professional grade receivers’ behavior is also visible here. While the former continues to use very low quality signals in order to provide a position solution, even if inaccurate, for as long as possible, the professional grade RUT stops computing the solution when the signal quality decreases by about 20 dB.

A summary of the results is given in Table 3. The maximum horizontal and vertical errors are computed for the interval in which the interference is present when the receiver offers a valid position fix. As already discussed, the position fix availability during the interference interval for the mass-market receiver is high at the expense of position accuracy. On the other hand, the professional grade RUT preserves the position accuracy at the expense of solution availability: the maximum horizontal and vertical errors in the test case are only slightly larger than in the baseline case.

The J/S at which the position solution is no longer available, J/SPVT_lost, is also determined. It can be observed from Table 3 that the mass market RUT has much higher sensitivity as compared to professional grade RUT, when manufacturer’s default receiver settings are used. Finally, it can be observed that TTRP values are much better for mass-market RUT than professional grade RUT.

Conclusion

Given the increasing dependence on GNSS technology and its vulnerability to intentional and unintentional interference, it is important to understand the magnitude and evolution of the GNSS threat scene. The STRIKE3 project is addressing this need through the development of monitoring and reporting standards, the deployment of a worldwide monitoring network to test the reporting standards and to provide a database of real-world events, the development of receiver testing standards against threats, and an intensive testing activity against the detected real-world interferences in order to test the resilience of different multi-GNSS receivers.

Additional Reading

For more details on the European H2020 project ‘STRIKE3’, please refer to: STRIKE3 (2016) Standardizsation of GNSS Threat reporting and Receiver testing through International Knowledge Exchange, Experimentation and Exploitation [STRIKE3]. http://www.gnss-strike3.eu/.

For more details on STRIKE3 proposed GNSS threat reporting standards, please refer to: Thombre, S., Bhuiyan, M. Z. H., Eliardsson, P., Gabrielsson, B., Pattinson, M., Dumville, M., Fryganiotis, D., Hill, S., Manikundalam, V., Pölöskey, M., Lee, S., Ruotsalainen, L., Söderholm, S., Kuusniemi, H. (2017) “GNSS Threat Monitoring and Reporting: Past, Present, and a Proposed Future”, The Journal of Navigation 71(3):513-529.

For more details on draft standards for receiver testing against threats, please refer to: Pattinson, M., Sanguk, L., Bhuiyan, M. Z. H., Thombre, S., Manikundalam, V., Hill, S. (2017) “Draft Standards for Receiver Testing against Threats”, available online via: http://www.gnss-strike3.eu/.

Authors

Nunzia Giorgia Ferrara is a Research Scientist in the Department of Navigation and Positioning at the Finnish Geospatial Research Institute and a PhD candidate at Tampere University of Technology where she was a Marie Curie Fellow from 2014 to 2016. Her research focuses on multi-GNSS receiver design and interference detection and mitigation.

Dr. M. Zahidul H. Bhuiyan is working as a Research Manager at the Department of Navigation and Positioning in the Finnish Geospatial Research Institute. He is also serving as the head of the Satellite and Radio Navigation research group of the institute. His main research interests include various aspects of multi-GNSS receiver design, GNSS vulnerabilities, SBAS, differential GNSS, etc.

Amin Hashemi is a Research Scientist with the Navigation and Positioning department of the Finnish Geospatial Research Institute. His current focus is on

localizing GNSS interference sources.

Dr. Sarang Thombre is a Research Manager and Deputy Leader of the Satellite and Radio Navigation research group at the Department of Navigation and Positioning of FGI. He earned his Ph.D. degree in April 2014 from Tampere University of Technology, Finland. His research interests include GNSS receiver design and implementation, autonomous vehicle PNT techniques, and RF interference to GNSS.

Dr. Michael Pattinson is a Principal Navigation Engineer at NSL and jointly leads the Safety and Integrity business unit. His main activities include advanced position techniques (high accuracy and high integrity), as well as GNSS performance monitoring and anomaly investigation to enhance GNSS robustness and reliability.

The post How can we ensure GNSS receivers are robust to real-world interference threats? appeared first on Inside GNSS - Global Navigation Satellite Systems Engineering, Policy, and Design.

It is important, therefore, to ensure satellite orbit calculations are as accurate as possible. As discussed in this article, Earth rotation plays a key role in this regard but surprisingly few references on orbit calculation actually mention its affect explicitly or how to compensate for it. Don’t fret, however, the correction is certainly applied or positioning accuracy would be much worse than is currently attained.

Reference Frames

Earth rotation is important because of the choice of reference system in which orbital calculations are performed. In particular, GNSS orbits — either from the broadcast orbital models or precise post-mission estimation — are parameterized in an
Earth-Centered Earth-Fixed (ECEF) coordinate frame such as the WGS84 reference frame used for GPS.

A common definition of an ECEF frame is one whose z-axis is the rotational axis of the Earth (pointing north), whose x-axis is in the equatorial plane and includes the median passing through Greenwich, and the y-axis completes the frame (typically in a right-handed sense). By definition,such a frame rotates with the Earth and is thus time-varying in inertial space with a period of 24 hours.

In the context of satellite position computations, this means that satellite locations can be computed at any given time, in an ECEF coordinate frame that is valid at that same time.

An easy way to visualize this point is to consider an ideal geostationary satellite whose position relative to the Earth does not change over time — orbital parameters or orbital files would always yield the same coordinates for the satellite.

Effect of Earth Rotation

So where does Earth rotation enter the picture? Well, precisely from the fact that the time at which a satellite transmits a signal, and the time a receiver receives that signal differs. Between the time of transmission (tt) and the time of reception (tr) — roughly 70 milliseconds (give or take few milliseconds) for medium-Earth orbiting (MEO) satellites — the Earth has rotated by ωe . (tr – tt), where ωe is the rotation rate of the Earth.

To illustrate the effect of this, we return to our idealized geostationary satellite. We further consider a user located directly below the satellite. Figure 1 shows this situation looking down on the north pole. To simplify later discussions, we consider this figure to apply at the time of signal transmission.

Since the orbital radius of a geostationary satellite is known (approximately 42,164 kilometers) and the radius of the Earth is known (approximately 6,371 kilometers) the separation of the user and satellite at any given instant is constant and can be easily computed.

Now consider Figure 2, which shows the same figure but also includes the location of the user and satellite at time of signal reception. Because of Earth rotation, the signal travels the path denoted by the blue line, which is obviously longer than the instantaneous separation of the satellite and user. This is the path in inertial space (ignoring the Earth’s orbit around the sun for simplicity).

The problem, however, is that because orbits are parameterized in an ECEF frame, the computed position of the satellite will still be directly above the user. This leads to a situation where the true signal path and the computed signal path differ. Unless accounted for, this difference will manifest as a ranging error in the receiver’s position engine, which computes the difference of the measured and predicted signal paths (i.e., ranges). The magnitude of the position error depends on the number and distribution of satellites, as well as user latitude. As an example, in Calgary, Canada, ignoring Earth rotation results in a shift in the estimated user position of about 20 meters, primarily in the east/west direction.

Before moving on, although we used the example of a geostationary satellite, the exact same effect applies to non-geostationary orbits as well. The main difference is that the satellite positions in Figures 1 and 2 would not necessarily be directly above the user, and the distance between the user and satellites, projected into the equatorial plane (which is shown in Figures 1 and 2), will vary with time as satellites move along their orbits. The good news is that regardless of the orbit, the method of compensation is the same.

Simple Solution

To remove the discrepancy between the measured and computed signal paths, we need to compute the ECEF position of the satellite at the time of transition in the ECEF frame at the time of signal reception. Fortunately, this is easily accomplished by realizing that the two coordinate frames are related by a rotation about the z-axis.

Mathematically, we can write

where is a position vector at the subscripted time (or frame), and R3 (ωe . (tr – tt)) is the rotation matrix about the z-axis by the angle subtended by the Earth rotated during signal propagation.

Applying the transformation in (1) yields the position of the yellow satellite in Figure 2, which allows for the proper computation of the (orange) user position.

The astute reader might be wondering how the propagation time is computed. This can be found by iterating to a solution: first, assume an initial distance between the user and satellite (e.g., 70 milliseconds); then compute the satellite position using this assumed distance (for Earth rotation compensation); use the approximate user position to re-compute the range to the satellite; and finally use this range to compute the satellite position.

The accuracy of the user position in the iteration is not typically a problem. The reason is because, even with a position error of 10 kilometers, the worstcase propagation time error would be 33.3 μs (i.e., 10 km / 3e8 m/s). Multiplying this by Earth rotation rate (~7.3e-5 rad/s) yields an angular error of about 2.4 nanoradians. Even over an orbital radius of 26,000 kilometers (assuming a MEO orbit), the orbital error is less than a decimeter. Then, of course, after the first epoch, the position error is typically several orders of magnitude smaller making the effect of user position error negligible.

Summary

This article has shown why Earth rotation needs to be accounted for when computing satellite coordinates for GNSS applications. The compensation is simple but crucial steps for obtaining the highest possible positioning accuracies.

The post How does Earth’s rotation affect GNSS orbit computations? appeared first on Inside GNSS - Global Navigation Satellite Systems Engineering, Policy, and Design.

Q: Do modern multi-frequency civil receivers eliminate the ionospheric effect?

Q: Do modern multi-frequency civil receivers eliminate the ionospheric effect?

A: It is common knowledge in the GNSS community that the ionosphere is dispersive in the L-band, meaning the refractive effects on the carrier phases are proportional to the wavelengths of the carriers, in turn causing differential variation in the measured codes and phases of the various navigation signals transmitted by the satellites. Use of multiple signals of distinct center frequency transmitted from the same GNSS satellite allows direct observation and removal of the great majority of the ionospheric delay, and gives the impression to users that the ionosphere may not be a problem for modernized receivers. While the general assumption of nearly perfect correlation between the effects measured on multiple independent signals is correct in normal conditions, it does not appear to hold in the presence of ionospheric scintillation.

High and Low Latitude Scintillation Effects
Scintillation refers to random fluctuations in the received wave field strength (“signal fading”), as well as phase and group delay caused by the irregular structure of the propagation medium. Ionospheric scintillations are random rapid variations in the intensity and phase of the received signals resulting from plasma density irregularities in the ionosphere.

Many of the important contributors to ionospheric scintillation are already known, such as the variation of scintillation activity with magnetic activity, geographic location, local time, season, and the 11-year solar cycle.

The most significant and frequent scintillation activity including both phase and amplitude variations is observed in low latitude regions within about 15° of the Earth’s magnetic equator, particularly in the hours after local sunset. In high latitude regions scintillation is frequent but generally less severe in terms of signal tracking disruptions than that in the equatorial regions. The high-latitude environment can be divided into two subregions, the polar caps (regions around the magnetic poles) and the auroral zones (approximately circular regions around the two geomagnetic poles located at about 67° north and south geographic latitudes, and about 3° to 6° wide). Of these, the polar cap experiences both amplitude as well as phase scintillation activity, while mainly phase scintillation is observed at high latitude auroral regions.

In mid-latitude regions scintillation is rarely observed, but during intense ionospheric storm conditions phenomena can extend into the mid-latitudes.

Figures 1 and 2 (see inset photo, above right, for all figures) show examples of ionospheric scintillation as observed on the detrended signal intensity (effectively power) and detrended carrier phase measurements at 69.5° latitude (Tromsø, Norway) and 21° latitude (Hanoi, Vietnam), respectively. In the particular event shown in Figure 2 the depth of fades reaches 43 decibels (dB) on L1CA which is severe by any metric, and is a substantial qualitative difference from the high-latitude phase scintillation events where only very weak fading activity is typically observed. It should be noted that ionospheric activity is more dependent on the geomagnetic latitude of the user than the geographic latitude. While it might be clear that Tromsø station is located in the auroral region, the Hanoi station has somewhat lower geomagnetic latitude than geographic latitude and is in fact located within the equatorial zone.

Since ionospheric scintillation is essentially a rapid variation in the apparent ionosphere it is easy to assume that the typical approaches applied for removing ionospheric influence will be effective during scintillation.

Ionosphere-Free Combination
The advantage of multi-frequency GNSS receivers in terms of handling the ionospheric error is that they can combine carrier phase measurements at different frequencies to cancel out the first order effect due to ionospheric refraction. The receiver does not typically measure the ionospheric delay directly, but is using the so-called ionosphere-free linear combination of the observables. Consider generalized versions of carrier phase measurements on two frequencies, i and j, expressed in meters:

Φ_Li = ρ + λ_iN_i − I_i     (1)
Φ_Lj = ρ + λ_jN_j − I_j

where ρ is the geometric range between the satellite and the receiver; λ_i and λ_j are the wavelengths, N_i and N_j are the integer ambiguity terms, I_i and I_j are the ionospheric propagation delay errors. For simplicity, the receiver noise and multipath errors are not included. The expression for an arbitrary linear combination of two carrier phase measurements can be written as follows: (For more on this topic, read the GNSS Solutions column from January/February 2009).

Φ_ij = αΦ_Li + βΦ_Lj     (2)

where α and β are constants. This allows one to model a linear combination of phases in the same way as the individual observables:

Φ_ij = ρ + λ_ijN_ij − I_ijη     (3)

In (3), λ_ij is the wavelength, N_ij is the integer ambiguity term, and I_ij is the ionospheric propagation delay error for the linear combination. In order to remove the ionospheric error (η = 0), but leave the geometric portion unchanged and the resulting ambiguity still an integer, the ionosphere-free combination has been proposed:

Φ_IFree = f_i²Φ_Li − f_j²Φ_Lj  ∕ f_i² − f_j²     (4)

where f_i and f_j are the carrier frequencies expressed in hertz. The phase scintillation is, however, caused by both refractive and diffractive effects. The diffractive effects cause rapid transitions in the phase which do not scale with the carrier wavelength resulting in a residual error in the ionosphere-free linear combination (4) of phase measurements.

While this correction term is for most purposes considered complete, there are factors that can cause apparent deviation between the two carriers including multipath, receiver noise, and un-modelled terms in (4). Corrections produced using (4) will have a residual error due to second and third order dispersion effects, which are conservatively bounded to 0–2 centimeters and 0–2 millimeters at zenith respectively, under an assumption of a 100 TECU (total electron content unit; 1 TECU ≈ 16 cm at GPS L1) background ionosphere. Since 100 TECU is a high value for zenith ionosphere the value of the higher order terms will often be well below 2 centimeters instantaneously, and will vary by only a small fraction of this amount over short time periods.

Although some recent findings have shown that magnitudes of 3 centimeters referenced to L1 are possible due to the higher order terms, it has also been shown that the variation rate is typically limited to the level of centimeters per hour.

During phase scintillation events it is possible that the multiple carriers of a given satellite will (when scaled for frequency as in Figure 3) track each other within the margins of error expected when accounting for thermal and oscillator phase noise on each channel. However, it is also possible that near total de-correlation of the phases will occur during phase scintillation accompanied by fading events as is depicted in Figure 4 where the detrended scaled carrier phase observables from L1, L2 and L5 transmitted by a block IIF GPS satellite visibly deviate from one another. Even the closely-spaced L2 and L5 carriers exhibit substantial decorrelation, equivalent at times to a full L1 carrier cycle of nearly 20 centimeters, well outside of the level which could be plausibly attributed to higher order terms ignored by (4).

On close inspection, the data shown in Figure 4 does not appear to contain any stepwise transitions of a magnitude commensurate with a full or half cycle slip on any of the carriers, meaning that this decorrelation is unlikely to be a signal tracking error. Unlike static group delay errors, it is not possible to measure and estimate this error contribution a priori. It is effectively an additional noise source present only during scintillation. Since it will influence the magnitude of the residual error in the case of multi/dual frequency processing it is interesting to analyze this phenomena and attempt to quantify its expected magnitude by considering the level of correlation between carriers during a cross section of scintillation events affecting modernized civil signals believed to be free of cycle slips.

To quantify the correlation level between the scintillation effects on GNSS frequencies, the phase correlation coefficient can be calculated for the observed scintillation events according to the following relationship:

ρ_δφ = ⟨δφ₁δφ₂⟩/(⟨δφ₁²δφ₂²⟩)^1/2, −1 < ρ_δφ < 1     (5)

where the terms δφ₁ and δφ₂ represent epoch to epoch changes in the detrended phases. Figures 5 and 6 show the results for the events observed at 69.5° latitude (Tromsø, Norway) and 21° latitude (Hanoi, Vietnam). In Figure 6 the level of correlation versus the intensity of the phase variation is plotted for L1CA vs. L2CM, and in contrast to the high latitude example shown in Figure 5, where increasing phase instability leads to an increasing level of phase correlation between the two carriers, for the Hanoi data the outcome is entirely different. Indeed, the phase correlation between the two carriers appears to be nearly non-existent on average, as the distribution of correlation measures is bifurcated with half the distribution tending towards higher positive correlation levels, while the other half of the sampled distribution tends towards anti-correlated results.

Ionosphere-free Residual
When scaled by their wavelengths, the carrier phase measurements on different GNSS frequencies appear to match closely when the scintillation effect is weak or moderate, but diverge from one another when the scintillation effect is strong regardless of whether the dominant scintillation effect is on the phase or amplitude of the signal. It is believed that these divergences occur when diffraction alters the phases by a factor that is not proportional to the wavelengths of their carriers leading to a residual in the ionosphere-free phase combination. An example of this phenomena is the so-called “canonical fade”, which may be the cause of the decorrelation events presented here. Figure 7 shows the average absolute L1/L2 ionosphere-free combination residual from Tromsø (69.5° N) observations, whereas results generated based on the data from Hanoi (21° N) are illustrated in Figures 8, 9 and 10.

Noting that the range of carrier phase standard deviation considered in Figures 8, 9 and 10 is smaller than that considered in the high latitude plot, it is clear that the level of ionosphere-free residual present in the Hanoi data increases much more rapidly with rising phase standard deviation than was the case with the high latitude observations.

While it is not unexpected that the L1/L5 combination residual is also substantial, as indicated in Figure 9, the more interesting observation is that the L2C and L5 signals also have considerable levels of decorrelation despite their relatively small 51 megahertz of spectral separation, compared to the nearly 350 megahertz of spectral separation between L1 and L2. In Figure 10, it is seen that for one of the tracked satellites during this event, the level of ionosphere-free residual in the L2CM/L5Q combination seems to exceed one meter even while the underlying data shows no signs of cycle slips.

Conclusion
To summarize, it has been demonstrated that ionospheric scintillation phenomena tend to cause an additional measurement residual in the nominal ionosphere-free combinations that greatly exceeds the expected value of the neglected higher order terms and may be a substantial or dominant nuisance term in some applications. While the residual is present with both phase and amplitude scintillation, and is more pronounced with strong scintillation to a point, the relationship appears stochastic and not deterministic.

It is tempting to assume that concerns about ionospheric effects during all but deep amplitude fades would disappear when users had switched from semi-codeless multi-frequency observables to the use of modernized civil signals due to their much higher tracking robustness. Instead, it seems that even with the modernized signals there is a measurable and occasionally meter level sense in which the ionosphere-free observables are not at all free of ionospheric influence.

Additional Resources

For additional information about ionospheric scintillation:
[1] Conker, R.S., M.B. El-Arini, C.J. Hegarty and T. Hsiao (2003) “Modelling the effects of ionospheric scintillation on GPS/Satellite-Based Augmentation System Availability”, Radio Science, vol.38, no.1.
[2] Carrano, C. S., K. M. Groves, W. J. McNeil, and P. H. Doherty (2013), Direct measurement of the residual in the ionosphere-free linear combination during scintillation, Proceedings of the 2013 Institute of Navigation ION NTM meeting, San Diego, CA, January 28-30, 2013.

For additional information on higher-order ionospheric effects:
[3] Hoque, M.M., and N. Jankowski (2007), “Higher order ionospheric effects in precise GNSS positioning,” Journal of Geodesy number 81, pp 259-268
[4] Liu, Z., Y. Li, J. Guo, and F. Li (2016) “Influence of higher-order ionospheric delay correction on GPS precise orbit determination and precise positioning,” Geodesy and Geodynamics, Volume 7, Issue 5, September 2016, pp 369-376

For information about canonical fades:
[5] Liu, Z., Y. Li, J. Guo, and F. Li (2016) “Influence of higher-order ionospheric delay correction on GPS precise orbit determination and precise positioning,” Geodesy and Geodynamics, Volume 7, Issue 5, September 2016, pp 369-376.

The post Do modern multi-frequency civil receivers eliminate the ionospheric effect? appeared first on Inside GNSS - Global Navigation Satellite Systems Engineering, Policy, and Design.