A Variational Bayesian-Based Unscented Kalman Filter With Both Adaptivity and Robustness

This paper proposes a modified unscented Kalman filter (UKF) with both adaptivity and robustness. In the proposed filter, the adaptivity is achieved by estimating the time-varying measurement noise covariance based on variational Bayesian (VB) approximation. The robustness is achieved by modifying the filter update based on Huber's M-estimation and Gaussian-Newton iterated method. In Gaussian assumptions, the proposed filter has a comparable filtering accuracy with the original UKF and better filtering consistency. When the measurement noise covariance is time-varying and there are outliers in the measurements, the proposed filter can outperform UKF and other adaptive or robust filters (such as VB-based UKF and Huber-based UKF) in terms of both filter accuracy and consistency. The efficacy of the proposed filter is demonstrated through the numerical simulation test and integrated navigation shipborne test.