Advanced square‐root cubature Kalman filters based on singular value decomposition and sequential processing

Abstract

Numerical accuracy of the cubature Kalman filter (CKF) is crucially degraded by the accumulated round-off errors. As a systematic solution to reduce the influence of round-off errors, the square-root filters are appealing. This study proposes a square-root CKF based on the singular value decomposition (SVD) approach to enhance the robustness against round-off errors. In addition, motivated by the impact of matrix inversion operation on the positive definiteness and symmetry of the error covariance matrix and numerical conditioning, the authors derive a sequential square-root CKF. The sequential CKF avoids matrix inversion operation involved in the original CKF and directly propagates square factor in each cycle step. The variation is a valid way to better preserve the positive definiteness and symmetry and numerical stability. To evaluate the proposed approaches, four numerical experiments are simulated. The results illustrate the numerical robustness and stability of the proposed approaches.