Abstract
This paper investigates the navigational performance of Global Positioning System (GPS) using the variational Bayesian (VB) based robust filter with interacting multiple model (IMM) adaptation as the navigation processor. The performance of the state estimation for GPS navigation processing using the family of Kalman filter (KF) may be degraded due to the fact that in practical situations the statistics of measurement noise might change. In the proposed algorithm, the adaptivity is achieved by estimating the time-varying noise covariance matrices based on VB learning using the probabilistic approach, where in each update step, both the system state and time-varying measurement noise were recognized as random variables to be estimated. The estimation is iterated recursively at each time to approximate the real joint posterior distribution of state using the VB learning. One of the two major classical adaptive Kalman filter (AKF) approaches that have been proposed for tuning the noise covariance matrices is the multiple model adaptive estimate (MMAE). The IMM algorithm uses two or more filters to process in parallel, where each filter corresponds to a different dynamic or measurement model. The robust Huber's M-estimation-based extended Kalman filter (HEKF) algorithm integrates both merits of the Huber M-estimation methodology and EKF. The robustness is enhanced by modifying the filter update based on Huber's M-estimation method in the filtering framework. The proposed algorithm, referred to as the interactive multi-model based variational Bayesian HEKF (IMM-VBHEKF), provides an effective way for effectively handling the errors with time-varying and outlying property of non-Gaussian interference errors, such as the multipath effect. Illustrative examples are given to demonstrate the navigation performance enhancement in terms of adaptivity and robustness at the expense of acceptable additional execution time.
Highlights
Non-Gaussian noise is often encountered in many practical environments and the estimation performance deteriorates dramatically
The results show that either the variational Bayesian (VB) or Huber’s algorithms can assist extended Kalman filter (EKF) to effectively deal with the outliers in the pesudorange observables individually and combination of the two algorithms can furtherly enhance the performance
Comparison of Global Positioning System (GPS) navigation accuracy for the EKF, variational Bayesian extended Kalman filter (VBEKF), Huber’s M-estimation-based extended Kalman filter (HEKF) and VBHEKF is shown in Fig. 4 where comparison of positioning accuracies without outlier and with outlier, respectively is provided
Summary
Non-Gaussian noise is often encountered in many practical environments and the estimation performance deteriorates dramatically. To solve the performance degradation problem with non-Gaussian errors or heavy-tailed non-Gaussian noises, some robust Kalman filters have been developed by using non-minimum MSE criterion as the optimality criterion. The technique that relies on Huber’s generalized maximum likelihood (ML) methodology exhibits robustness against deviations from the commonly assumed Gaussian probability density functions and can solve the non-Gaussian distribution problem efficiently and has been successfully employed for robust state estimation, inertial navigation system and visual tracking applications. The method utilizes the VB learning to approximate the noise strength for time-varying noise covariances, the Huber M-estimation methodology to enhance robustness especially for overcoming the problem of contamination distribution or outliers, and the IMM algorithm to furtherly tune the noise covariance matrices.
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