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Factored-form Kalman-like implementations under maximum correntropy criterion

SIGNAL PROCESSING 2019年 160卷 328-338页

作者： Kulikova, Maria V. Univ Lisbon Inst Super Tecn CEMAT Ctr Computat & Stochast Math Av Rovisco Pais 1 P-1049001 Lisbon Portugal

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. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Maximum correntropy filtering square-root algorithms Cholesky factorization Singular value decomposition

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Gradient-Based Parameter Estimation in Pairwise Linear Gaussian System

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2017年第3期62卷 1511-1517页

作者： Kulikova, M. V. Univ Lisbon Inst Super Tecn CEMAT P-1049001 Lisbon Portugal

This technical note addresses the gradient- based parameter estimation problem for pairwise linear Gaussian systems. The new adaptive filtering scheme is based on gradient-based optimization methods for estimating the uncertain system parameters and a robust square-root variant of the pairwise Kalman filter used for estimating the unknown states of the pairwise linear Gaussian systems. Hence, in the adaptive filtering techniques, the dynamic state and system parameters are estimated simultaneously. The method of the filter sensitivities computation required in gradient evaluation is derived in terms of square-root factors of covariance matrices.

关键词： Pairwise Kalman filter Pairwise linear Gaussian systems parameter estimation square-root algorithms

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A unified square-root approach for the score and Fisher information matrix computation in linear dynamic systems

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MATHEMATICS AND COMPUTERS IN SIMULATION 2016年 119卷 128-141页

作者： Kulikova, M. V. Tsyganova, J. V. Univ Lisbon Inst Super Tecn CEMAT P-1049001 Lisbon Portugal Ulyanovsk State Univ Ulyanovsk 432017 Russia

One of the most frequently encountered problems in practice is to combine a priori knowledge about a physical system with experimental data to provide on-line estimation of an unknown dynamic state and system parameters. The classical way for solving this problem is to use adaptive filtering techniques. The adaptive schemes for the maximum likelihood estimation based on gradient-based optimization methods are, in general, preferable. They require the likelihood function and its gradient evaluation (score), and might demand the Fisher information matrix (FIM) computation. All techniques for the score and the FIM calculation in linear dynamic systems yield the implementation of the Kalman filter (KF) and its derivatives (with respect to unknown system parameters), which is known to be numerically unstable. An alternative solution can be found among algorithms developed in the KF community for solving ill conditioned problems: the square-root algorithms, the UD-based factorization methods and the fast SR Chandrasekhar-Kailath-Morf-Sidhu techniques. Recently, these advanced KF implementations have been extended on the filter derivatives computation. However there is no systematic way of designing the robust "differentiated" methods. In this paper, we develop a unified square-root methodology of generating the computational techniques for the filter/smoother derivatives evaluation required in gradient-based adaptive schemes for the score and the FIM computation. (C) 2015 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

关键词： Kalman filtering Maximum likelihood estimation Gradient-based methods Fisher information matrix square-root algorithms

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square-root algorithms of RLS Wiener filter and fixed-point smoother in linear discrete stochastic systems

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APPLIED MATHEMATICS AND COMPUTATION 2008年第1期203卷 186-193页

作者： Nakamori, S. Kagoshima Univ Dept Technol Fac Educ Kagoshima 8900065 Japan

This paper addresses the QR decomposition and UD factorization based square-root algorithms of the recursive least-squares (RLS) Wiener fixed-point smoother and filter. In the RLS Wiener estimators, the Riccati-type difference equations for the auto-variance function of the filtering estimate are included. Hence, by the round-off errors, in the case of the small value of the observation noise variance, under a single precision computation, the auto-variance function becomes asymmetric and the estimators tend to be numerically instable. From this viewpoint, in the proposed square-root RLS Wiener estimators, in each stage updating the estimates, the auto-variance function of the filtering estimate is expressed in a symmetric positive semi-definite matrix and the stability of the RLS Wiener estimators is improved. In addition, in the square-root RLS Wiener estimation algorithms, the variance function of the state prediction error is expressed as a symmetric positive semi-definite matrix in terms of the UD factorization method. (c) 2008 Elsevier Inc. All rights reserved.

关键词： square-root algorithms discrete-time systems Wiener-Hopf equation covariance information

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