Hyperbolic SVD‐based Kalman filtering for Chandrasekhar recursion
Maria Vyacheslavovna Kulikova · IET Control Theory and Applications · 2019
The problem of numerical instability of the classical Kalman filter (KF) still remains one of the most important topics in engineering literature. For improving its robustness with respect to roundoff errors, the singular value decomposition (SVD) methodology has been proposed for implementing the underlying classical KF Riccati recursion. In this study, SVD‐based filtering is derived for an alternative KF mechanisation that is based on the so‐called Chandrasekhar recursion and yields a family of fast KF implementations. The new methodology involves hyperbolic SVD (HSVD) factorisation rather than usual SVD utilised in the Riccati‐based filtering. The results of numerical study indicate that the HSVD‐based filtering strategy outperforms the conventional Chandrasekhar‐based KF while solving ill‐conditioned state estimation problem. Together with the existed Cholesky‐based algorithms, they are the preferred implementations when solving applications with high reliability requirements within the class of fast Chandrasekhar‐based KF implementations.