Kalman filter (KF) is an efficient approach for state estimation in integrated positioning systems of global navigation satellite systems and inertial navigation systems (GNSS/INS). Unfortunately, GNSS/INS integrated positioning systems are susceptible to state model perturbations and measurement outliers, which can severely degrade KF performance, especially in complex urban environments. To solve this problem, a robust adaptive filtering algorithm based on variational Bayesian (VBRAKF) is presented that can be employed in GNSS/INS tightly coupled positioning systems. In VBRAKF, the robust estimation approach is first introduced into the filter, followed by modeling the predicted covariance matrix using the inverse Wishart distribution, and finally the state is estimated using Variational Bayesian. The robustness is achieved by adjusting the noise by an equivalent weight matrix to reduce gross errors in observations, while the adaptiveness is realized by the variational Bayesian estimation method for the uncertain predicted noise covariance matrix. The positioning performance of the proposed algorithm in urban environments is verified through two sets of land vehicle experiments. The experimental results demonstrate that the 3D positioning accuracy of the VBRAKF algorithm is improved by 32.1% and 23.5% in experiment 1 and by 37.1% and 17.3% in experiment 2 when compared to KF and Robust Kalman Filter (RKF). The proposed VBRAKF algorithm has better positioning performance in all schemes, can simultaneously control the influence of measurement outliers and inaccurate noise statistics and improves the accuracy of filter estimation.
Kalman filter (KF) is an efficient approach for state estimation in integrated positioning systems of global navigation satellite systems and inertial navigation systems (GNSS/INS). Unfortunately, GNSS/INS integrated positioning systems are susceptible to state model perturbations and measurement outliers, which can severely degrade KF performance, especially in complex urban environments. To solve this problem, a robust adaptive filtering algorithm based on variational Bayesian (VBRAKF) is presented that can be employed in GNSS/INS tightly coupled positioning systems. In VBRAKF, the robust estimation approach is first introduced into the filter, followed by modeling the predicted covariance matrix using the inverse Wishart distribution, and finally the state is estimated using Variational Bayesian. The robustness is achieved by adjusting the noise by an equivalent weight matrix to reduce gross errors in observations, while the adaptiveness is realized by the variational Bayesian estimation method for the uncertain predicted noise covariance matrix. The positioning performance of the proposed algorithm in urban environments is verified through two sets of land vehicle experiments. The experimental results demonstrate that the 3D positioning accuracy of the VBRAKF algorithm is improved by 32.1% and 23.5% in experiment 1 and by 37.1% and 17.3% in experiment 2 when compared to KF and Robust Kalman Filter (RKF). The proposed VBRAKF algorithm has better positioning performance in all schemes, can simultaneously control the influence of measurement outliers and inaccurate noise statistics and improves the accuracy of filter estimation.