A Stability Guaranteed Variational Bayesian Converted Measurement Kalman Filter for Radar Tracking With Unknown Noise Covariances

Abstract

Tracking with radar measurements is challenging due to the nonlinear relationship between the measurements and the target Cartesian state. Besides, the unknown noise covariances also trouble the design of the tracking filter. In this article, a variational Bayesian converted measurement Kalman filter (VBCMKF) is proposed to tackle the radar tracking problem with unknown process and measurement covariance matrixes. Aiming to gain better estimation accuracy, the idea of moving horizon estimation is adopted, namely, the states over a moving window of fixed length and the unknown process and measurement covariance matrixes are iteratively extracted from the collected measurements by exploiting variational Bayesian inference. During the iteration, the original measurement model is converted to an equivalent linear form in Cartesian coordinates by utilizing the measurement conversion technique, making the measurement update for the augmented state able to be conducted in an analytical style rather than by resorting to complex numerical approximations for high-dimension nonlinear Gaussian integral. Moreover, a stability guaranteed strategy is integrated into the filter to constrain the noise covariances within preset ranges through boundary overflow checks. It is proven that the obtained state estimation error is exponentially bounded in mean square. The effectiveness of the proposed VBCMKF is verified through simulations. The results demonstrate its outperformance in tracking accuracy and consistency.