Filtering for Nonlinear and Linear Markov Jump Systems

• Autor(a) principal: Costa, Oswaldo Luiz do Valle
• Data de Publicação: 2023
• Outros Autores: Oliveira, André Marcorin de
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Institucional da UNIFESP
• Texto Completo: https://ieeexplore.ieee.org/document/10273597; https://hdl.handle.net/11600/70880
• topic: Nonlinear systems; Discrete-time; Markovian jump systems; “prediction-correction” formula; Finite horizon; Riccati equations

In this paper we consider the finite horizon filtering problem of discrete-time Markov jump systems (MJS). In the first part we consider a MJS satisfying some general nonlinear conditions. It is obtained, for a fixed set of auxiliary constants, filter gains, based on a set of coupled Riccati like difference equations, that yield a minimum upper bound for the estimation error covariance matrix. When the nonlinear parameters are set to zero the MJS becomes a Markov jump linear system (MJLS) and, in the second part of the paper, it is shown that the obtained filter gains derived from a set of coupled Riccati like difference equations provide the optimal “prediction-correction” Markovian filter for the nominal MJLS (which reduces to the standard Kalman filter for the no jump case). The paper is concluded with some numerical examples © 2023 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.