23rd ITS World Congress, Melbourne, Australia, 10–14 October 2016
Paper number ITS- AP-SP0223
A machine learning approach to detect non-line-of-sight GNSS signals in Nav2Nav Monsak Socharoentum1*, Hassan A. Karimi2, and Yang Deng1 1. National Electronics and Computer Technology Center, 112 Thailand Science Park, Phahonyothin Road, Khlong Nueng, Khlong Luang, Pathum Thani 12120 Thailand; email:
[email protected] 2. Geoinformatics Laboratory, School of Information Sciences, University of Pittsburgh
Abstract— Vehicle positioning is a crucial requirement in car navigation systems. Despite tremendous advances in GNSS technology, multipath of non-line-of-sight (NLOS) GNSS signals still is a major drawback, especially in urban canyon areas. Mitigating the multipath problem has been addressed at the physical level (e.g., new antenna designs) and at the logical level (e.g., signal filtering). Improvement at the physical level requires extra hardware installation which may not be suitable for in-car navigation applications due to the compact size of navigation devices. The logical level is not practical in some cases. Take the signal filtering techniques as an example where due to the environment around a car (especially when travelling in urban canyons) sometimes only NLOS signals reach the receiver, thus, signal filtering cannot be performed. As an alternative approach to detect NLOS signals, this paper proposes a technique for a cooperative vehicle environment, called navigation-tonavigation (Nav2Nav), in which machine learning algorithms and pseudorange corrections work together to detect NLOS signals. To evaluate the approach, various machine learning algorithms were experimented through simulations and the results indicated better than 90% accuracy in detecting a satellite set with/without a NLOS signal from all satellites sets available.
Keywords— MULTIPATH, GNSS, AND NON-LINE-OF-SIGHT SIGNAL 1. Introduction Multipath and signal blockage, in some environments (such as urban areas), are the major shortcomings of GNSS-based navigation systems. In case the direct signal, due to the blockage, does not reach the GNSS receiver, identifying multipath without extra information (such as 3D city model) can be difficult. Mitigating multipath for GNSS-based navigation systems in such environments are of particular interest in this paper. The multipath problem has been addressed through various approaches, for example, at the physical level via hardware improvements (such as new antenna design), or at the logical level with signal filtering. However, for in-car navigation systems, hardware improvements can be impractical to implement. For example, installing an extra external antenna could be costly for the driver and inconvenient when driving. Even enhanced signal filtering (which does not require extra external hardware) may not be practical when direct signals cannot reach receivers. The multipath problem can also be addressed by using knowledge about nearby buildings, such as 3D city models, where satellites associated with multipath can be predicted through ray tracing analysis. However, 3D city models are not widely available yet
A machine learning approach to detect non-line-of-sight GNSS signals in Nav2Nav
for all areas. In addition, a 3D city model is not updated frequently and, compared to 2D maps, requires large data storage capacity and high-end computing resources. These limitations hinder their practical use in in-car GNSS-based navigation systems. As an alternative to the current approaches above, this paper offers a new approach, from a collaborative perspective, to the multipath problem. Through navigation-to-navigation (Nav2Nav) environment, the approach requires that the nearby cars share information that are typically available through in-car navigation systems such as Pseudo-Range Correction (PRC) and map matching. Nav2Nav relies on a peer-to-peer architecture where in-car navigation systems in nearby cars can communicate with each other to address specific problems such as crash avoidance (Karimi et al. 2010; Socharoentum and Karimi 2011). The peer-to-peer architecture in Nav2Nav assumes that: (1) peers are equipped with communication devices and can exchange information with one another and (2) computation is performed locally and independently of other peers. Expanding the idea of Nav2Nav, this paper assumes that the peers designated as “rovers” can broadcast a request for help, and the peers designated as “stations” can send back a message containing their PRCs calculated locally. Then, the “rovers” will analyze the PRCs and use the results to improve their positioning solutions. Furthermore, the Nav2Nav environment is dynamic as a peer could either assume the role of “station” or “rover” at any time depending on the environmental conditions. For example, at one time a peer in an open sky environment could be designated as “station” and another peer in an urban canyon as “rover”, but as “rover” moves to a better environment, its designation may change to “station”. The rest of the paper is organized as follows. Section 2 discusses related works. Section 3 describes PRC computation with respect to multipath. Section 4 describes methodology and simulation. Sections 5 and 6 discuss the validations and results. Section 7 provides discussion, and the conclusions are given in Section 8. 2. Related Works The related works in four areas, signal processing, hardware improvement, peer-to-peer cooperative positioning, and 3D city models, are discussed in this section. Signal processing has been applied for multipath mitigation in many studies; for example, see Ge et al. (2000), Veitsel et al. (1998), Bétaille et al. (2003), Townsend and Fenton (2004), and Lee et al. (2004). Ge et al. (2000) examined an adaptive filtering algorithm for decomposing NLOS signals from the C/A-code and P-code modulations. Veitsel et al. (1998) proposed a signal processing technique which they claimed to eliminate the multipath error completely if the difference in delays of direct and reflected signals are more than 30 meters. To improve Real-Time Kinematic (RTK) GNSS performance, Bétaille et al. (2003) developed methodologies to eliminate NLOS signals by sampling the received signals together with their possible NLOS signals before and immediately after code transitions. Townsend et al. (2004) introduced a new narrow correlator to be applied on a fixed differential GNSS (DGNSS) base station, where the multipath error effects in the DGPS position solution is reduced by 25-50% as compared to a standard narrow correlator receiver. Lee et al. (2004) applied channelwise test statistic (using standard 2 -distributions) on a sequence of successive-time double-differences of pseudorange and carrier phase measurements. The aforementioned works assume that both direct and NLOS (reflected) signals are able to reach the receiver, thus a signal processing technique can be applied to filter the NLOS signal. However, there are conditions where filtering is not practical; for example when only the NLOS signal reaches the receiver and the direct signal is blocked by an obstacle. Among hardware improvements, new antenna design (Counselman, 1999; Boccia et al., 2004; Kamarudin et al., 2004; and Tatarnikov et al., 2005), and laser scanner and inertial
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A machine learning approach to detect non-line-of-sight GNSS signals in Nav2Nav
navigation system (Soloviev and Graas 2008) were studied. However, installing an extra external or hardware antenna could be costly for the driver and inconvenient when driving. The solution proposed in this paper does not require installation of extra antenna or sensors. Peer-to-peer cooperative positioning enhances positioning performance among in-car GNSS-based navigation systems in a peer-to-peer architecture. Alam (2011) used Doppler shift of the carrier of Dedicated Short-Range Communications (DSRC) signals in cooperative positioning among neighbor cars, where up to 48% of GNSS positioning accuracy was improved. Yao et al. (2011) optimized VANET (Vehicular Ad hoc Network) and showed that packet loss rates could be decreased by half, and the positioning accuracy increased by 40%. By exploiting data from neighboring users (peers), a receiver may be able to significantly increase its time-to-first-fix (TTFF) performance using peers that provide GNSS quantities like Doppler frequency shift, carrier-to-noise ratio (C/N0), and secondary code delay (Garello et al. 2012). Different from current peer-to-peer cooperative positioning approaches, this paper utilizes different information (pseudorange and pseudorange corrections) and focuses on a different objective (multipath mitigation). Using 3D city models is another approach to predict multipath and improve vehicle localization. Studies such as Francois et al. (2011), Bourdeau et al. (2012), Groves et al. (2012), Obst et al. (2012a and 2012b), Wang et al. (2012), and Peyraud et al. (2013) use digital terrain data and building footprints to construct 3D city models for predicting satellites that are in line of sight. Although the approach seems to be reliable and straightforward, obtaining a 3D city model can be challenging; urban environments are very transient as new buildings are constructed at a fast pace and old buildings are torn down. The production rate of digital terrain data, considering current technologies, is unlikely to catch up with the rate of updates. For example, the latest global-scale digital terrain data is from Shuttle Radar Topography Mission (SRTM) project which was completed in 2000. High-precision digital terrain data using LIDAR is not available widely and regularly as it is costly. 3. Pseudorange Correction Model and Algorithm PRC refers to the correction value for pseudorange calculated for a satellite. In general, PRC varies with atmospheric conditions and the satellite orientation. Given two GNSS receivers observing a satellite in common and sharing the same atmospheric and local environment condition (i.e., they are close in proximity and both have no terrestrial obstruction), their PRCs should be relatively the same between the two receivers (Klobuchar, 1995 and Doherty et al., 1994). By deduction, if it turns out that the PRCs are significantly different between the two receivers and one of them is already known to be under open sky, it could be assumed that the other one is undergoing extra signal delay. Based on this observation, sharing PRCs between receivers could help indicate satellite signal delay due to local environment such as multipath provided that the following two criteria are met: (a) receivers share the same atmospheric condition and (b) one of the receivers is known to be under open sky and producing good positional accuracy. A. Multipath and PRC Model When two GNSS receivers are under the same atmospheric condition and in close proximity to each other, the observable satellites will be the only factor influencing PRC. For example, considering Figure 1, Station and Rover are observing two satellites in common (S1 and S2). PRA and PRB are the pseudoranges measured from S1 to Station and Rover. PRC and PRD are the pseudoranges measured from S2 to Station and Rover. For Station and Rover, PRCS1 (PRC value belonging to Satellite S1) will remain the same, and so does PRCS2 (PRCS1 does not need to be equal to PRCS2). An evidence to support the fact that GNSS receivers in
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A machine learning approach to detect non-line-of-sight GNSS signals in Nav2Nav
close proximity have similar atmospheric condition is that Station and Rover in a mid-latitude region could be apart up to 400 kilometers while the difference in ionospheric delay is less than 2 meters in magnitude 95% of the time (Klobuchar 1995). In case multipath interferes with Rover’s pseudorange measurement, PRC calculated by Rover will be imperfect and diverge from the counterpart calculated by Station. This behavior can be used to identify multipath.
Figure 1. Station and Rover receive same PRC from a satellite. Given the reported position of the ith satellite (xi, yi, zi) and the position of the GNSS receiver at the reference base station located at (xb, yb, zb), the computed geometric distance, Rib , from the reference base station to the satellite is: ) ( ) ( ) √( (1) th The reference station then makes a pseudorange measurement, , to the i satellite: (2) where are the pseudorange errors, c is the speed of light, and represents the reference base station clock offset from GNSS satellite time. The reference station differences the computed geometric range, with the pseudorange measurement to form the differential correction: (3) Similarly, if the rover identifies its estimate position through map matching, it will be able to form the differential correction, , to the ith satellite as follows: (4) And, in case the ith satellite signal is affected by the multipath problem, the equation will be: ( ) (5) In Equation (5), is the magnitude of the extended signal delay due to multipath of the th i satellite, and represents the rover clock offset from GNSS satellite time. From the correction in Equation (3), Equation (4) and Equation (5), the difference between and and are: ( ) (3) – (4): (6) ( ) (3) – (5): (7) Equation (6) is used when multipath does not exist, and Equation (7) is when multipath exists. (6) – (7): (8) Since can be observed and computed, Equation (8) indicates that if is known, it is possible to predict . This property is used to develop a modified PRC computation methodology in this paper.
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A machine learning approach to detect non-line-of-sight GNSS signals in Nav2Nav
B. A Modified PRC Computation Methodology This section introduces a modified PRC computation methodology which is fundamental for the solution proposed in this paper. The methodology is not only different from traditional DGNSS, but it also defines a new way for Rover to collect and utilize PRCs. The methodology has three phases, as is shown in Figure 2. Phase 1 (Step R1): Rover sends requests for help to all available Stations. Phase 2 (Step S1): after Stations receive the request message, they calculate Stations’ GNSS position (x1,y1,z1) and map match the position onto the road map in their navigation system (x2,y2,z1). Note that the third dimension (z1) remains the same since map matching only involves horizontal coordinates. In Step S2, the map matched position for PRC calculation is used. In traditional DGNSS, PRC is used to improve rover’s positioning accuracy, however, this paper uses PRC to detect multipath not to directly improve positioning accuracy. In Nav2Nav, a map matched position (a road map from NAVTEQ is used in the experiments) is considered as the best estimate of position.
Figure 2. Pseudorange correction computation methodology. In Step 3, after Station completes its PRC computation, the results are sent to Rover. Phase 3 (Step R2): Rover receives the PRCs from Stations and calculates their average. In Step R3, Rover computes its GNSS position (x3,y3,z3) and map matches the position (x4,y4,z3). Note that the third dimension (z3) remains the same since map matching only involves horizontal coordinates. In Step R4, Rover computes its PRCs using its map matched position (similar to the way it was performed by Station.) In Step R5, with a classifier, Rover classifies the satellite sets by calculating the difference between its PRCs with Station’s PRCs ( ). Note that the classifier in Step R5 is performed by using machine learning algorithms and has knowledge about by learning from previous observations.
4. Methodology and Simulation To validate the proposed solution, experiments were conducted in two (learning and evaluation) phases (described in Figure 4). The learning phase was to develop a prediction model using a machine learning algorithm, and the evaluation phase was to examine the performance of the prediction model. The scenarios of interest in the evaluation phase were related to number of stations, magnitudes of signal delay, locations of rover, and time of observation. For each phase, data was collected as follows. For the learning phase, one group of 20 stations, one rover, random values (between 5 and 80 meters) of signal delay, and 5
A machine learning approach to detect non-line-of-sight GNSS signals in Nav2Nav
operation time at 00:00, May-15-2011, were considered. For the evaluation phase, 5, 15, and 20 stations, random values (between 5 to 80 meters) of signal delay, four different rover locations (4, 6, 8, and 10 kilometers away from the average positions of the stations), and operation time at 13:00, Feb-16-2014, were considered. Figure 3 shows the location distributions of all the stations and rovers. Table 1 summarizes the five major scenarios considered for the two phases. First scenario is for developing a prediction model. Second scenario is to examine the performance of the prediction model when time of observation changes. Third scenario is to examine the performance of the prediction model when number of stations decreases and under certain magnitudes of signal delay. Fourth scenario is to examine the performance of the prediction model when location of rover changes. Fifth scenario is to examine the relationship between the performance of the prediction model and magnitudes of signal delay. Table 1. Five scenarios in two phases. Scenario 1 2 3 4 5
Numbers of Rover distance Magnitudes of signal stations (meters) delay(meters) 20 within cluster random 20 within cluster random 5, 15 10 5, 20, 35, 50, 65, 80 5 4, 6, 8, 10 Random 5 10 5, 10, 15, 20, 25, 30, 35
Time of observation 00:00; 2011-05-15 13:00; 2014-02-16 13:00; 2014-02-16 13:00; 2014-02-16 13:00; 2014-02-16
Figure 3. Location distributions of stations and rovers. The experiment in this work was set up to address two questions: Is there a machine learning algorithm suitable for the problem? Could the variables related to pseudorange measurement be used as predictors in the prediction model? Four machine learning algorithms were used: Logistic Regression, Support Vector Machine, Naïve Bayes, and Decision Tree.
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Figure 4. Methodology: learning and evaluation phases. To evaluate our model, computer simulation was used instead of real observations because of two reasons: (1) GNSS receivers do not provide pseudoranges to users (users only receive the final position which is based on pseudoranges), and (2) real multipath in an urban canyon environment is unlikely to be controlled and gathered for experimental purpose. A MATLAB-based GNSS simulation toolbox called Constellation Toolbox version 7.12 (Constell, 2012) was used to simulate the environment and multipath data. Through the toolbox, satellite masking was performed, pseudoranges were measured, and all relevant GNSS data were calculated. An area in Pittsburgh, PA, USA was selected for data simulation. A road map of the city of Pittsburgh was imported to an open source spatial database (PostGIS). All coordinates were converted into the GNSS coordinate reference system (WGS84), and this map was used for map matching. We predefined the locations of Stations and Rovers within an area of 14 km2 (5.4 mile2) in size. The GNSS simulation toolbox requires a GNSS almanac file as input. The almanac was converted into ephemeris, based on Ephemeris parameters from ICD-GPS-200 standard (Navstar, 1997), and then was used for positioning calculation. Using the almanac files (downloaded from U.S. Coast Guard Navigation Center, 2012) and the simulation toolbox, visible satellites were simulated. All Stations were able to observe the same set of satellites, whereas, for Rover, satellite masking was applied to vary the number of visible satellites to simulate urban canyons. To include the overhead computation time and the data transmission time between Stations and Rover, Rover’s observation time was intentionally delayed by 15 seconds. In practice the delay may not be this large, but we also wanted to examine whether or not PRC (with a large delay period) from the station were still useful. Thus, Rover computes its PRC using the observation based on the satellites’ orientations at 15 seconds delay. To account for all possible satellites configurations, two sets of satellites, 4 to 10 for the learning phase and 5 to 12 for the evaluation phase, resulting in 848 and 3,302 satellite sets, respectively, were selected. From each satellite set, another combinatorial selection was performed for multipath, such that, for a satellite set, a multipath may not happen at all, happen to some of the satellites, or happen to all the satellites in the set. After the two combinatorial selections, the total dataset contained 57,888 and 521,472 samples for the learning and evaluation phases, respectively. After removing samples with PDOP value >10, the data size for the learning phase decreased from 57,888 to 54,800 samples. Class 0 (no multipath) contained 715 samples, and Class 1 (multipath exists) contained 54,085 samples. The data size for the evaluation phase decreased from 521,472 to 518,528 samples. Class 0 7
A machine learning approach to detect non-line-of-sight GNSS signals in Nav2Nav
(no multipath) contained 3,224 samples, and Class 1 (multipath exists) contained 515,304 samples. Each sample contained Class label 0 (no multipath), 1 (multipath is added to one or more visible satellites) and seven predictor variables: PDOP, Maxdiff, Sumdiff, SDdiff, Maxtemp, Sumtemp, and NSAT. The first six predictors were chosen because they directly associate with satellite geometry where the pseudoranges is elongated due to the multipath problem. The last predictor (NSAT) is a complementary property of GNSS observations. Their definitions are: (1) Maxdiff: the maximum of absolute PRC differences*; (2) Sumdiff: the sum of all absolute PRC differences*; (3) SDdiff: the standard deviation of absolute PRC differences*; (4) Maxtemp: the maximum of all absolute PRC double differences**; (5) Sumtemp: the sum of all absolute PRC double differences**; (6) PDOP: the Position Dilution of Precision (the lower value indicates the higher probability to get better positional accuracy); (7) NSAT: the number of visible satellites of each observation. * PRC difference is the difference between the PRCs of Rover and the average PRCs of Stations ** PRC double difference is the difference between the PRCs of Rover and three times the standard deviation of the PRCs of Stations 5. Learning Phase: Training the Prediction Models In general, when a learning algorithm learns from a training dataset, it will try to determine a function that makes best prediction accuracy. Best prediction accuracy is quantified by the match rate against the training dataset where the function that returns maximum match rate between the prediction outcomes and the known class labels of the training dataset will be selected. Considering a training dataset with two classes yes and no, if the yes class is far larger than the no class (e.g., 99% of the data instances fall in the yes class) then the yes instances will overwhelm the training dataset and the learning algorithm will be biased by the yes instances. If the learning algorithm selects a prediction model that makes prediction correctly for most of the yes instances, the overall prediction accuracy will be very high, which can be implied that the no instances are ignored. As a consequence, the learning algorithm will be biased, as it tries to maximize the match rate. The bias can be detected by examining the true positive (TP) and true negative (TN). TP occurs when the outcome is correctly predicted as yes (or positive). TN occurs when the outcome is correctly predicted as no (or negative). For the training dataset in this paper, the yes class is Class 1 (multipath exists) and the no class is Class 0 (no multipath). For the learning phase, the ratio between Class 0 and Class 1 was 1:75, i.e., 98.7% of the instances fell in Class 1. The situation when a class overwhelms a dataset is called class imbalance problem. To address the class imbalance problem, the cost-sensitive learning (CSL) technique can be used (Witten et al., 2011). CSL works with a cost matrix containing the punishments weights for TP, TN, false positive (FP) and false negative (FN). FP occurs when the outcome is incorrectly predicted as yes and FN when the outcome is incorrectly predicted as no. Therefore, if less bias on the yes prediction is desired, the punishment weight for FP should be larger than the punishment weight for FN. Punishment weights for TP and TN are typically set to 0, as no punishment is necessary for making correct predictions. However, the optimal punishment weights are unknown and need to be identified. To determine optimum weights, a number of trials on punishment weights were conducted in
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form of ratios, i.e., 250, 200, 150, 100, 75, 50, 37, 25, and 10. The original trial ratios were 250, 200, 150, 100, 75, 50 and 10. The ratios 37 and 25 were added later as it was observed that the optimal ratio was located between 50 and 10. The numbers represent the ratio of the punishment weights of FP over the punishment weights of FN. Figure 5 depicts the behaviors of TP, TN, as well as AUC (Area Under the Curve; a closer value to 1 means better classification capability) with respect to the ratios when Logistic Regression was applied. The ideal value for TP, TN and AUC are 1. The behaviors show that TN increases while TP decreases as the ratio decreases. As shown in Figure 5, the trial with ratio around 37 provides optimal results; TP, TN, AUC, and overall accuracy of the trials are all high.
Figure 5. TP, TN, and AUC behaviors. CSL can be combined with almost any learning algorithms, including the four learning algorithms chosen in this work. The comparisons of different algorithms are shown in Table 2. CSL significantly improves TN for Logistic Regression, Support Vector Machine, and Decision Tree. Naïve Bayes is the only algorithm that has high TP and TN regardless of CSL. Table 2. Performance of learning algorithms (reflect scenario 1 in Table 1). Algorithms Logistic Regression Support Vector Machine
Learning Methods no CSL CSL* no CSL CSL*
no CSL CSL* no CSL Decision Tree CSL* Naïve Bayes
TP
TN
AUC
0.999 0.938 1.000 0.934
0.061 0.967 0.000 0.981
0.976 0.975 0.500 0.957
Overall Accuracy 0.9875 0.9383 0.9875 0.9345
0.917 0.894 0.998 0.984
0.949 0.969 0.239 0.657
0.965 0.963 0.883 0.821
0.9173 0.8951 0.9883 0.9798
*use cost ratio FP:FN = 37:1 6. Evaluation Phase Table 3 (reflecting scenario 2 in Table 1) shows the results for time at 13:00 (February 16, 2014), while the stations were shared with the learning phase. Generally, the results in Table 3 are similar to the results in Table 2, which indicate that time of observation change does not affect the prediction models. Table 3 also confirms that CSL does not influence
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Naïve Bayes as its TP and TN are both greater than 0.9 regardless of CSL. Since Naïve Bayes does not require extra processing (CSL), Naïve Bayes prediction model was chosen for all the rest of performance examinations. Table 3. Prediction performance of learning algorithms (reflect scenario 2 in Table 1). Algorithms Logistic Regression Support Vector Machine Naïve Bayes Decision Tree
Learning Methods no CSL with CSL no CSL with CSL no CSL with CSL no CSL with CSL
TP
TN
0.999 0.978 1.000 0.979
0.390 0.988 0.000 0.993
0.993 0.996 0.500 0.986
Overall accuracy 0.9949 0.9779 0.9938 0.9789
0.961 0.947 0.998 0.992
0.983 0.992 0.243 0.780
0.989 0.989 0.944 0.887
0.9615 0.9475 0.9930 0.9905
AUC
Table 4 shows a comparison of Naïve Bayes performance for the rover at different distances (4, 6, 8, and 10 kilometers) from the center of station cluster. The results show that Naïve Bayes provides TP, TN, AUC, and overall accuracy at a value > 0.9 for all the distances. This indicates that distance (up to 10 kilometers) of the rover does not affect the prediction performance. Table 5 shows the results for Naïve Bayes performance at different number of stations and magnitudes of signal delay. Considering each magnitude of signal delay, TP, TN, AUC, and overall accuracy have similar value for both 5 and 15 stations cases. Considering the prediction performance against magnitudes of signal delay, TP decreases dramatically while magnitude of signal delay is smaller than 35 meters. This indicates that the capability of the prediction model to identify a satellite set with a NLOS satellite decreases when the magnitude of signal delay is small. To find out the boundary of this capability, another experiment was conducted specifically for a range of small magnitudes of signal delay (5-35 meters), and the results are illustrated through the graphs in Figure 6. The graphs show that TP drops dramatically as magnitude of signal delay decreases from 35 to 5 meters, while TN is flat. AUC also drops but with a lower slope. This TP performance drop is reasonable because when magnitude of signal delay is small, differentiating between LOS and NLOS satellite based on pseudorange and PRC becomes difficult. Table 4. Naïve Bayes performance for different rover distances (reflect scenario 3 in Table 1). Rover A B C D
Distance (kilometers) 4 6 8 10
TP
TN
0.965 0.966 0.946 0.964
0.976 0.979 0.980 0.974
AUC 0.989 0.990 0.984 0.987
Overall accuracy 0.9650 0.9659 0.9463 0.9643
Table 5. Naïve Bayes performance for different number of stations and magnitudes of signal delay (reflect scenario 4 in Table 1) Signal delay Stations (meters) 5 5 15 5 20 15
TP 0.018 0.018 0.755 0.756
10
TN 0.974 0.973 0.974 0.973
AUC 0.695 0.703 0.944 0.944
Overall accuracy 0.241 0.244 0.7567 0.7573
A machine learning approach to detect non-line-of-sight GNSS signals in Nav2Nav
35 50 65 80
5 15 5 15 5 15 5 15
0.952 0.952 0.978 0.978 0.985 0.985 0.988 0.988
0.974 0.973 0.974 0.973 0.974 0.973 0.974 0.973
0.983 0.982 0.990 0.990 0.992 0.992 0.993 0.993
0.9524 0.9523 0.9777 0.9778 0.9846 0.9846 0.9879 0.9879
Figure 6. Naïve Bayes performance against magnitudes of signal delay (reflect scenario 5 in Table 1) 7. Discussion The results of the simulations show that a prediction model developed from the learning phase can be used in the evaluation phase which had different temporal and spatial scenarios than the learning phase. Table 3 shows that the prediction models have similar performance at different times (between 00:00 on May 15, 2011 and 13:00 on February 14, 2014). Table 4 shows that Naïve Bayes prediction model has similar performance for all the rovers located at 4, 6, 8, and 10 kilometers away from the station cluster. One reason for the flexibility in time and distance from stations is that Equation (8), which is used to develop the Modified PRC Computation Methodology in this paper, relies on magnitude of signal delay due to multipath which is independent of time and distance from stations. However, when the magnitude of signal delay decreases, the prediction performance also drops quickly (Figure 6) especially when the signal delay is between 20 and 5 meters. This range covers the error of pseudorange measurement 7.8 meters at a 95% confidence (DOD, 2008). Since the error of 7.8 meters is part of pseudorange measurement, the error is directly related to and in Equation (8) and could be the reason for the decrease of prediction performance. Despite intentional 15 seconds delay between Rover’s and Station’s observations, the average prediction correctness rate is still up to 90%. This indicates that the approach can be applied in a high latency connected vehicle network and that Station’s observations can be reused multiple times by multiple Rovers across a connected vehicle network.
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8. Conclusion and Future Research This paper presents an alternative approach for identifying a satellite set containing a NLOS satellite in a cooperative vehicle environment called Nav2Nav. The approach requires PRC exchange between Stations (cars in open sky environments) and Rovers (cars in multipath prone environments) and machine learning algorithms to train prediction models. Based on a number of simulated data sets, the prediction models are obtained and then used by Rover to distinguish the subset of visible satellites that are affected by signal delays due to multipath. For simulations, various different spatio-temporal scenarios with several different magnitudes of signal delays were considered. It was found that the prediction models can be used by Rover as part of its satellite selection process to mitigate NLOS satellites that are affected by multipath, and the averaged prediction correctness rate may be close to 90%. The results also indicate that a prediction model can be developed based on data from one location and time and used for a different location and time. As this work utilizes simulated data and is in a preliminary research stage, future research may be the refinements of the machine learning algorithms by using real satellite data and environment conditions. References 1. Alam, N., Tabatabaei Balaei, A., & Dempster, A. G. (2011). A DSRC Doppler-Based Cooperative Positioning Enhancement for Vehicular Networks with GPS Availability. Vehicular Technology, IEEE Transactions on, 60(9), 4462-4470. 2. Bétaille, D., Maenpa, J., Euler, H., and Cross, P. (2003). A New Approach to GPS Phase Multipath Mitigation. Proceedings of ION National Technical Meeting 2003, Anaheim, California, pp. 243-253. 3. Boccia, L., Amendola, G., & Di Massa, G. (2004). A Dual Frequency Microstrip Patch Antenna for High-Precision GPS Applications. Antennas and Wireless Propagation Letters, IEEE, 3(1), 157-160. 4. Bourdeau, A., Sahmoudi, M., & Tourneret, J. Y. (2012). Tight Integration of GNSS and a 3D City Model for Robust Positioning in Urban Canyons. Proceedings of ION GNSS 2012. 5. Constell, Inc. Constellation Toolbox [Online]. Available: http://www.constell.org/. Accessed 18 June 2012. 6. Counselman, C. C. (1999). Multipath-rejecting GPS Antennas. Proceedings of the IEEE, 87(1), 86-91. 7. Czepiel, S. A. (2002). Maximum Likelihood Estimation of Logistic Regression Models: Theory and Implementation. Available at http://czep.net/stat/mlelr.pdf. 8. Doherty, P. H., Raffi E., and Klobuchar, J. A. (1994). Statistics of Time Rate of Change of Ionospheric Range Delay. Proceedings of the Institute of Navigation ION GPS-94, Salt Lake City, UT. 9. Francois, P., David, B., & Florian, M. (2011, August). Non-Line-Of-Sight GNSS Signal Detection Using an On-Board 3D Model of Buildings. In ITS Telecommunications (ITST), 2011 11th International Conference on (pp. 280-286). IEEE. 10. Garello, R., Presti, L. L., Corazza, G. E., and Samson, J. (2012). Peer-to-Peer Cooperative Positioning; Part I: GNSS-Aided Acquisition. Inside GNSS [Online] March/April.
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