Robust Bayesian Filtering for Positioning using GPS & INS in Multipath Environments
Shun Taguchi and Takayoshi Yoshimura, Toyota Central R&D Labs., Inc., Japan
Location: Big Sur
This study presents a novel robust Bayesian filtering method that can distinguish outliers due to multipath. In order to improve advanced driver assistance systems and intelligent transportation systems, accurate vehicle positioning technologies have become increasingly important. The most widely used positioning system using global positioning systems (GPS) and inertial navigation systems (INS) can provide precision for several meters in the suburbs. However, in urban areas, GPS satellite signals are sometimes reflected on obstacles such as high-rise buildings. This phenomenon is called multipath, causing a large noise, which can degrade positioning accuracy by more than 10 m. In such an environment, it is necessary to distinguish GPS satellites affected by multipath. Multipath distinction is possible by using a threshold based on errors from assumed observations, but this method has low robustness; occasionally, the estimated position may deviate significantly. Thus, we propose a novel robust multipath discrimination method based on Bayesian filtering.
2. Proposed Method
The proposed method performs sequential estimation using multiple hypothesis tracking (MHT), which is a Bayesian filtering method. In the proposed method, the observation distribution of GPS satellite signals is assumed to be a mixture of Gaussian distribution representing normal values and Cauchy distribution representing abnormal values due to multipath. This approach is inspired by the robust Gaussian filtering method proposed in . Then, we generated two hypotheses on the normal values and abnormal values. This is MHT, which is a Bayesian filtering method that tracks the states of hypotheses.
In MHT, the number of hypotheses doubles every time a satellite is observed, making it necessary to prune or merge hypotheses to reduce computational costs. In general, hypothesis pruning is introduced in MHT, but in the case of the proposed method, many hypotheses often have almost same states. As a result, hypotheses of similar weights are generated in large quantities, and pruning does not function normally. This is because if normal data is treated as abnormal data, it often has little effect on states. Therefore, in this research we solve this problem by merging hypotheses via Gaussian mixture reduction (GMR) based on Kullback–Leibler divergence (KLD) .
We search for pair of hypotheses with the least change in KLD when they merge, from among the generated hypotheses, and then merge them. By repeating this process until the number of hypotheses becomes less than the threshold, hypotheses increase is prevented.
In conventional Bayesian filtering methods, such as the extended Kalman filter (EKF), it is assumed that all observation errors follow the Gaussian distribution. However, multipath error causes large errors that do not follow the Gaussian distribution. By contrast, in the proposed method, the outliers caused by multipath are modeled by Cauchy distribution, aside from the normal values which follow Gaussian distribution; therefore, the proposed method is more robust against outliers.
The proposed Bayesian filtering method is used for positioning vehicles by combining GPS and inertial navigation. Pseudo ranges and Doppler frequencies from each satellite are used as GPS observations, and vehicle speed and yaw-rate values are used as sensor information for inertial navigation. In order to apply the proposed method, GPS observations are sequentially filtered for each satellite. Since each hypothesis in MHT utilizes the EKF, and no abnormal values are assumed for the vehicle speed and yaw rate, filtering is performed as it is with EKF. We used the weighted average of the hypotheses for the output of the estimate.
3. Experimental Results
To evaluate the accuracy of the proposed method, we evaluated the precision in estimating position by GPS and INS using data traveled by GPS-equipped vehicles in Nagakute, Nagoya, and Shinjuku, Japan. Nagakute provides data on the suburbs, Shinjuku provides data on urban areas with many skyscrapers, and Nagoya is the intermediary. The positioning by tight coupling of GPS and INS using EKF and PRECISE proposed by Kojima et al. , which removes multipath by double optimization, was evaluated.
The mean absolute error (MAE) of the proposed method in Shinjuku is 8.8 m, which is more precise than that of the EKF, whose MAE is 17.8 m; the precision is as high as PRECISE, whose MAE is 9.2 m. The root-mean-square error (RMSE) of the proposed method in Shinjuku is 10.9 m, which is more precise than that of EKF and PRECISE, whose RMSEs are 20.6 m and 14.8 m, respectively. This is because in PRECISE, which is based on sliding window optimization, the estimated values occasionally have large deviations. Since the proposed method is a successive estimation method using Bayesian filtering, the smoothness of the trajectory is retained to some extent, and large estimation errors are unlikely to occur. This result shows that the proposed method is useful for eliminating multipath and improving the precision of GPS positioning.
In this research, we proposed a novel Bayesian filtering method which tracks vehicle positions based on GPS and INS while stochastically distinguishing abnormal values due to multipath. The proposed method realizes robust state estimation by GMR-MHT with mixture observation distribution of two distributions of normal data and abnormal data. By introducing this mixture observation distribution, the probability that data from the GPS satellite is normal or abnormal data can be calculated, and each hypothesis can be tracked by MHT. An increase in the number of hypotheses in MHT can be prevented using GMR. In the evaluation based on actual traveling data, we showed that the proposed method can be estimated with higher performance than the conventional Bayesian filtering method using EKF. Moreover, compared with PRECISE, which is an optimization-based positioning method to remove multipath, the proposed method is superior in that large outliers hardly come out.
The proposed Bayesian filtering method can be applied not only to multipath in GPS but also to any data as long as abnormal values occur in observations; it can be expected to perform robust state estimation for various data.
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