Factored-form Kalman-like implementations under maximum correntropy criterion

Abstract

Abstract The maximum correntropy criterion (MCC) methodology is recognized to be a robust filtering strategy with respect to outliers and shown to outperform the classical Kalman filter (KF) for estimation accuracy in the presence of non-Gaussian noise. However, the numerical stability of the newly proposed MCC-KF estimators in finite precision arithmetic is seldom addressed. In this paper, a family of factored-form (square-root) algorithms is derived for the MCC-KF and its improved variant, respectively. The family traditionally consists of three factored-form implementations: (i) Cholesky factorization-based algorithms, (ii) modified Cholesky, i.e. UD-based methods, and (iii) the recently established SVD-based filtering. All these strategies are commonly recognized to enhance the numerical robustness of conventional filtering with respect to roundoff errors and, hence, they are the preferred implementations when solving applications with high reliability requirements. Previously, only Cholesky-based IMCC-KF algorithms have been designed. This paper enriches a factored-form family by introducing the UD- and SVD-based methods as well. A special attention is paid to array algorithms that are proved to be the most numerically stable and, additionally, suitable for parallel implementations. The theoretical properties are discussed and numerical comparison is presented for determining the most reliable implementations.