Hyperbolic SVD-based Kalman filtering for Chandrasekhar recursion

To appear in IET Control Theory & Applications
https://doi.org/10.1049/iet-cta.2018.5864

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 freshly proposed for implementing the
underlying classical KF Riccati recursion. In this paper, SVD-based filtering is derived for an alternative KF mechanization that is based on the so-called Chandrasekhar recursion and yields a family of fast KF implementations. The new methodology involves hyperbolic SVD (HSVD) factorization rather than usual SVD utilized 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.