CHARACTERIZATION OF EXPONENTIAL DIVERGENCE OF THE KALMAN FILTER FOR TIME-VARYING SYSTEMS

Autor(es)

Costa, Eduardo F. ^[1] ; Astolfi, Alessandro ^{[2, 3]}

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Dept Matemat Aplicada & Estatist, BR-13560970 Sao Carlos, SP - Brazil

^[2] Univ Roma Tor Vergata, Dipartimento Informat Sistemi & Prod, I-00133 Rome - Italy

^[3] Univ London Imperial Coll Sci Technol & Med, Dept Elect & Elect Engn, London SW7 2AZ - England

• Tipo de documento: Artigo Científico
• Fonte: SIAM JOURNAL ON CONTROL AND OPTIMIZATION; v. 48, n. 5, p. 2917-2944, 2009.
• Citações Web of Science: 6

Resumo

This paper studies semistability of the recursive Kalman filter in the context of linear time-varying (LTV), possibly nondetectable systems with incorrect noise information. Semistability is a key property, as it ensures that the actual estimation error does not diverge exponentially. We explore structural properties of the filter to obtain a necessary and sufficient condition for the filter to be semistable. The condition does not involve limiting gains nor the solution of Riccati equations, as they can be difficult to obtain numerically and may not exist. We also compare semistability with the notions of stability and stability w.r.t. the initial error covariance, and we show that semistability in a sense makes no distinction between persistent and nonpersistent incorrect noise models, as opposed to stability. In the linear time invariant scenario we obtain algebraic, easy to test conditions for semistability and stability, which complement results available in the context of detectable systems. Illustrative examples are included. (AU)

• Processo FAPESP: 06/02004-0 - Estabilidade de observadores para sistemas dinâmicos
• Beneficiário: Eduardo Fontoura Costa
• Modalidade de apoio: Bolsas no Exterior - Novas Fronteiras
• Processo FAPESP: 06/04210-6 - Convergência do Filtro de Kalman para sistemas lineares com saltos markovianos com da variável de salto
• Beneficiário: Eduardo Fontoura Costa
• Modalidade de apoio: Auxílio à Pesquisa - Regular