Filtering for Nonlinear and Linear Markov Jump Systems

• 成果类型: Article
• 署名作者: Costa, Oswaldo L. V.; de Oliveira, Andre M.
• 署名单位: Universidade de Sao Paulo; Universidade Federal de Sao Paulo (UNIFESP)
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3322379
• 发表日期: 2024
• 页码: 3309-3316
• 关键词: Discrete-time; finite horizon; Markovian jump systems (MJS); Nonlinear systems; Riccati equations; prediction-correction formula

摘要

In this article, we consider the finite horizon filtering problem of discrete-time Markov jump systems (MJS). In the first part, we consider an 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 article, 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 article is concluded with some numerical examples.