
January/February 2018
How Effective Are Signal Quality Monitoring Techniquesfor GNSS Multipath Detections?Equations 1, 2, 3, 4, 5 & 8 An analytical discussion on the sensitivity and effectiveness of signal quality monitoring (SQM) techniques for multipath detection and mitigation is presented in this article. This includes narrow and high resolution tracking strategies under BPSK(1) and BOC(1,1) modulations as the base signaling schemes used for GPS and Galileo. A field data analysis is carried out for static and dynamic scenarios to examine SQM performance in actual multipath environments.
Share via: Slashdot Technorati Twitter Facebook Multipath is a major phenomenon that degrades the integrity of GNSSbased navigation services. Under multipath, a receiver DelayLock Loop (DLL) does not correctly estimate the actual peak of the correlation curve, resulting in ranging errors. To overcome this effect, mitigation techniques have been developed, a detailed discussion of which is found in Bhuiyan and Lohan (Additional Resources). As a general observation, some of these mitigating techniques attempt to minimize the effect by modifying the receiver hardware or tracking structure and others try to jointly estimate the multipath parameters. Among these wellinvestigated mitigation techniques, the selection of least distorted measurements is receiving attention in the context of GNSS multiconstellations in which case the number of available signals is large enough to deweight or exclude faulty ones without significant degradation in solution geometry. In this context, SQM techniques have been developed to detect multipath distortions by incorporating monitoring correlators at the tracking level. The general approach is based on the linear or nonlinear combination of different earlylate monitoring correlators to define symmetric and asymmetric test statistics and detect multipath distortions in the tracking correlation peaks. The correlator output samples are evaluated and integrity warning is set when the SQM metrics deviate from nominal values. While different SQM metrics have been defined and extensively applied for GNSS multipath detection, little investigation has been conducted to provide insight on how theoretically sensitive and effective these metrics are under different scenarios. It has been shown that multipath affects SQM statistics (e.g., mean and variance) by distorting the correlation peak, but there is no analytical discussion about how sensitive such an approach is for detection. Some works show that SQMbased monitoring techniques can be used for multipath reduction by excluding or deweighting affected measurements, but their effectiveness is an issue requiring more investigations under different tracking and signaling strategies. This article evaluates the performance of SQM techniques under a broad range of multipath scenarios. In the sequel, after modelling the received GNSS signals in the tracking output, monitoring correlators are defined based on their relative code delays from the reference tracking correlators. A DoubleDelta SQM metric is defined as a basic test statistic to detect distortions. SQM metric variation profiles are then proposed as a function of multipath relative delay and power. It is shown that such profiles, along with conventional multipath error envelopes, provide an appropriate framework to jointly analyze the sensitivity and effectiveness of the SQM approach under different multipath scenarios. SQM variation profiles are extracted and discussed for the Binary Phaseshift Keying (BPSK(1)) and Binary Offset Carrier (BOC(1,1)) signaling schemes. Two different tracking discriminators, namely Narrow Correlator (NC) (See Van Dierendonck et alia, Additional Resources) and High Resolution Correlator (HRC) (McGraw and Braasch, Additional Resources), are considered. These tracking strategies are commonly used in many receivers to mitigate multipath. Field data analysis is carried out to validate the analytical discussion and examine SQM detection performance under real static and kinematic multipath scenarios.
Signal Model Equation (1) (see inset photo, above right, for all equations) where I is the PRN index, L is the number of satellites, C_{I} is the power of the received signal from the I^{th} satellite, b_{I} is the binary navigation data and c_{I} is the spreading code used to modulate the navigation data; τ_{I}, f_{d,I} and ϕ_{I} are code delay, Doppler frequency and carrier phase introduced by the communication channel; f_{IF} is the IF and f_{s} = 1/T_{s} is sampling frequency. η_{fe} (nT_{s}) is front end complex zero mean Gaussian noise. For each PRN, a reference tracking correlator multiplies the received signal by a corresponding replica and the samples are integrated over a coherent integration time period. The output of the I^{th} channel at time kN_{s}T_{s} (k^{th} coherent integration epoch) is given by
Equation (2) where N_{s} is the number of samples in the coherent integration period. Using a sum of geometric series, Equation (2) becomes
Equation (3) where the effect of bit transition is neglected due to an assumed bit synchronization process; the index I is omitted for simplicity. Δτ_{0} = τ − ̂τ, Δf = f_{d} − f̂_{0} and Δφ_{0} = φ − ̂φ are code, frequency and phase offsets between the received and the replica signal generated by the reference tracking correlator. NT_{s} is the coherent integration time, also noted by T_{I} • η consists of inphase and quadraturephase Gaussian noise and R_{τ}(Δτ_{0}) is the correlation function which is related to the choice of the GNSS signaling scheme. When the received signal is stabilized in PLL mode, it is assumed that there are no tracking code and phase offsets and thus the inphase output of the i^{th} early or late correlator is defined in the codedelay domain as
Equation (4) where T_{c} is the chip duration and u_{i}T_{c} denotes the spacing of the i^{th} early (for u_{i} < 0) or late (for u_{i} > 0) correlator from the reference prompt correlator. η^{I}_{ui} is the corresponding inphase noise described above. Since the tracking loops are locked and the received signal is tracked in PLL mode, the inphase component is considered. If the receiver operates in a noncoherent mode, both inphase and quadraturephase components should be taken into account.
SQM Metric Definition
Equation (5) where the tracking and monitoring earlylate correlator spacings are chosen as 0.2 and 1 chips. I_{0} is the inphase output of the prompt correlator. At each synchronized correlation epoch, the constituent components of the defined SQM metric have the same binary data with either a positive or negative sign (i.e., +1 or 1) in the corresponding numerator and denominator. Therefore, the navigation data has no effect on the SQM metric outputs. Under nominal conditions, in low multipath open sky environments and the absence of other GNSS signal degradation errors, the output of the SQM metric is a random process whose statistical properties are determined based on the location of the constituent correlators and receiver noise. The methodology of the SQM statistical analysis can be found in Pirsiavash et alia in Additional Resources, where numerical results have been presented for the mean and variance of the defined SQM metric.
Performance Analysis and SQM Variation Profiles
D_{NC} = (I_{d}_{trk I}_{2}−I_{+d}_{trk I}_{2}) (6) where a coherent tracking procedure is assumed and thus the inphase tracking outputs are used. d_{trk} is set to 0.2 chips to build up the tracking discriminator functions and extract the corresponding tracking range error envelopes. These envelopes are shown in Figure 1 (righthand vertical axis in red) for 3 and 6 dB SignaltoMultipath Ratio (SMR) values and BPSK(1) and BOC(1,1) signaling schemes. To extract these envelopes, a single reflection is considered and the relative delay of the reflected signal with respect to LineOfSight (LOS) signal is swept through a range of values to assess DLL code misalignment and resulting tracking range errors for inphase and outofphase multipath components. Figure 1a also determines the approximate range of short, medium and long delay multipath considered here for 1 megahertz chipping rate. Reflected signal delays less than 0.1 chips (about 30 meters for the GPS L1 C/A case) are considered as shortdelay multipath; a range of 0.1 to 0.75 chips is considered for mediumdelay multipath and longdelay multipath covers reflected signal delays longer than 0.75 chips. Figure 1 shows that for shortdelay multipath the error envelopes are almost the same for all tracking strategies and signaling schemes. For path delays longer than approximately 0.5 chips, when NC is used as the tracking strategy, the corresponding tracking range error for the BOC(1,1) modulation is less than (about one third of) that of the BPSK(1) signal. This is because of the difference in the shape of the correlation functions for BPSK(1) and BOC(1,1) signaling schemes. For the HRC technique, the maximum tracking range error is the same for both signals under the effect of shortdelay multipath. While the BPSK(1) ranging error is reduced to zero under mediumdelay multipath, the tracking range error of the BOC(1,1) is significantly lower than that of the BPSK(1) signal for a longdelay multipath scenario. To extract the SQM variation profiles shown in Figure 1 (lefthand vertical axis in blue), a similar methodology was used. A single reflection is considered and then the relative delay of the reflected signal is swept through a range of values to evaluate SQM metric outputs for inphase and outofphase multipath components. It is observed that the SQM variation envelopes take their maximum absolute values around 0.5 chips where the late monitoring correlator is overlapped by the peak of the reflected correlation curve. When the multipath correlation curve passes the late monitoring correlator, the SQM variation envelopes decrease until the multipath correlation curve no longer overlaps with tracking and monitoring correlators for multipath signal delays greater than 1.5 chips. For the BOC(1,1) signaling scheme, due to the different shape of the BOC(1,1) correlation function, the reduction in variation envelopes shows a different behavior between 0.5 and 1 chips. In all cases, a lower SMR and consequently higher level of multipath relative power result in higher SQM variations as expected. For a CarriertoNoisedensity ratio (C/N_{0}) value of 45 dBHz (decibelhertz), detection thresholds have been set to three times the corresponding nominal Standard Deviation (SD) to satisfy a false alarm probability of 0.0027. The SQM profiles are now being used to evaluate the theoretical sensitivity and effectiveness of the SQM metric in multipath detection. SQM “sensitivity” and “effectiveness” are first defined as the critical keywords for the subsequent discussion.
SQM Sensitivity and Effectiveness for Multipath Detection Effectiveness is based on the multipath error magnitude. An approach is considered effective when the threshold excess of the SQM outputs coincides with a significant range error on the corresponding measurements. Effectiveness is important since ideally SQM based measurement weighting should be based on it and not on sensitivity. Based on the aforementioned definitions and considering the SQM profiles shown in Figure 1, the following conclusions can be made regarding the sensitivity and effectiveness of the SQM metric under different multipath scenarios.
The SQM variation envelopes show the maximum level of SQM sensitivity under specific multipath delay and power. In practice, due to satellite motion and other effects, there are always phase variations between LOS and multipath signals causing SQM outputs to fluctuate between inphase and outof phase envelopes. This will drop the practical sensitivity of the SQM metric for multipath detection. The same argument applies to multipath range error envelopes and consequently SQM effectiveness.
Field Data Analysis
Static test scenario Figure 3 shows CodeMinusCarrier phase (CMC) and C/N_{0} measurements for selected PRNs. C/N_{0} values are computed using the NarrowbandWideband Power Ratio (NWPR) method (See Parkinson and Spilker, Additional Resources). CMC measurements are extracted to characterize code multipath errors (See Braasch, Additional Resources) where carrier phase measurements are subtracted from the corresponding pseudorange measurements. In addition to code and carrier noise and multipath errors, the subsequent outcome includes carrier phase ambiguities and twice the ionospheric errors (due to ionospheric code delay and phase advance). The effects of ambiguity and ionosphere are approximated and removed through polynomial curve fitting. Neglecting residual effects of carrier phase noise and multipath errors, the resulting values are a valid measure of code multipath and noise. PRN 23 can be considered to be in a multipathfree measurement while PRN 22 is heavily affected as shown by corresponding CMC values. Figure 4 shows monitoring results for the DoubleDelta SQM metric calibrated and normalized using its nominal SD. In this normalization, the C/N_{0} values are smoothed by a moving average with length of 60 seconds. Detection thresholds are fixed to ±3 for the normalized metric. The M of N detection strategy is used by taking windows of N samples and comparing them to the predefined threshold. If M or more samples exceed the threshold, then the detection output will be 1 and otherwise 0. This procedure is repeated for each step of the sliding search window. With this detection strategy, the overall probability of false alarm in N trials is given by Kaplan and Hegarty (see Additional Resources) Equation (8) P_{fa} is the false alarm probability in each trial equals to 0.27% under the assumption of normal distribution for the SQM metric and ±3SD as the detection threshold. Figure 4 shows monitoring results for PRN 23 and 22 when N = 500 (samples or 10 seconds) and M = 12, 15 and 20 are chosen to satisfy the overall probability of false alarm around and 2 °— 10^{8}, 1.6 °— 10^{11} and 1.8 °— 10^{14}, respectively. As shown in Figure 4a, the output of the designed detection algorithm for PRN 23 is zero for almost all epochs identifying this PRN as clean. In the case of PRN 22 (shown in Figure 4b), while medium effect of multipath (according to its CMC measurements) remains almost undetected, code measurements with errors above 5 meters are clearly detected.
Kinematic test scenario Figure 6 and Figure 7 show PRN7 monitoring results. According to CMC measurements, multipath during the data collection is generally low and errors do not exceed 5 meters except for some epochs between 20 seconds and 60 seconds. The corresponding SQM results were then extracted for each 20 milliseconds of the coherent integration time. The metric was calibrated and normalized using its nominal standard deviation. In this normalization, the C/N_{0} values were smoothed using a moving average window. Compared to the static scenario, the length of the smoothing window was reduced to 4 seconds due to the dynamic characteristic of the data and consequently faster multipath variations as a function of time. The detection thresholds were fixed to ±3 times the normalized SD. The length of the sliding search window (N) was 2 seconds and M = 5, 6 and 7 were chosen to detect multipath with overall false alarm probabilities 8.7 × 10^{6}, 3.7 × 10^{7}, 1.3 × 10^{8}, respectively. The sensitivity of the SQM metric is limited to epochs whose multipath error is in the order of 5 meters or more. For M ≥ 9, The SQM detection output is zero for all epochs and multipath errors remain undetected. A second kinematic data set was collected in the urban canyon shown in Figure 8a. The building on the right has smooth surfaces considered as strong reflective sources. The GPS L1 data was collected with the same setup but mounted on a vehicle driving at a velocity of 1 m/s in the west direction through the canyon. Figure 9 and Figure 10 show the PRN 21 monitoring results during the different segments of the trajectory. Similar results were observed for other PRNs. The data collection was started in a fairly open sky environment whose first 5 seconds is shown in the figures. The vehicle then passed through the canyon for 100 seconds and ended in a fairly open sky environment (the last 35 seconds). Corresponding multipath was observed in the CMC measurements shown in Figure 9 where segments with relatively strong multipath are marked in red while medium and low multipath segments are marked in yellow and green. Figure 10 shows the SQM and detection results for PRN 21 with the same settings as mentioned previously. This time M = 7, 9 and 11 were chosen over a 2 second sliding search window (N). With this assumption, the overall false alarm probabilities are approximated by 1.3 × 10^{8}, 1.2 × 10^{11}, 1 × 10^{14}, respectively. In Figure 10, the detection output for the regions with low multipath (green region shown in Figure 9) is zero, indicating clean range measurements for PRN 21. It is also shown that the medium effect of multipath (multipath is below 3 meters according to CMC measurements) is buried under the SQM metric noise and remains almost undetected. However, for those epochs strongly affected by multipath (when multipath error is in the order of 5 meters or more), the SQM metric is mostly sensitive and the metric outputs show multipath occurrence.
Summary and Conclusions
Additional Resources ManufacturersThe mass market receiver antenna used in the referenced static and kinematic data collection is a NovAtel GPS703GGG antenna made by NovAtel, Calgary, Canada. The RF sampling frontends used in the static and kinematic scenarios are respectively from National Instrument (NI), headquartered in Austin, Texas, and Fraunhofer, headquartered in Munich, Germany.Author Profiles
Ali Pirsiavash
Ali Broumandan
Gérard Lachapelle
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