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.

I. Introduction

Kalman filter (KF) has become the most important estimation technique applied in multi-sensor fusion and integration such as GPS positioning, integrated navigation system and satellite attitude estimation [1]. It can be proven that the KF is optimal when two main assumptions hold, namely linear system and Gaussian distributed assumption [2], [3]. Unfortunately, linear system and Gaussian distributed assumption do not really exist in actual applications. If those assumptions do not hold, the KF cannot achieve the demanding filtering performance. Based on this point, some studies with extension of nonlinear system and non-Gaussian distributed assumption have been investigated [4], [5].