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access icon free Optimal filter for MJL system with delayed modes and observations

  • Author(s): Chunyan Han 1  and  Wei Wang 2
    • View affiliations
  • Source: Volume 12, Issue 1, 02 January 2018, p. 68 – 77
    DOI:  10.1049/iet-cta.2017.0692 , Print ISSN 1751-8644, Online ISSN 1751-8652
© The Institution of Engineering and Technology
Received 23/06/2017, Accepted 05/10/2017, Revised 15/09/2017, Published 10/10/2017

This study investigates the optimal filter for Markov jump linear (MJL) system with multiple delayed modes and observations, in which the data losses are introduced naturally and the Markov chains are assumed to be known up to the present time. To deal with the mode and observation delays, a reorganised observation sequence is defined. Moreover, the optimal filter problem is transformed into one of the delay-free system which is just with jumping parameters and multiplicative noises. An optimal MJL filter is presented based on the mean squared method, where the filter gains are determined by solving a set of generalised coupled Riccati difference equations based on a set of coupled Lyapunov equations. Alternatively, an optimal stationary MJL filter is developed, where the filter gains are derived by solving a set of generalised coupled algebraic Riccati equations based on coupled algebraic Lyapunov equations. It can be shown that the difference Riccati equations developed in the former filter converge to the stationary ones under appropriate conditions.

Inspec keywords: Markov processes; delay systems; difference equations; linear systems; Riccati equations; mean square error methods; stochastic systems; Lyapunov methods; filtering theory

Other keywords: optimal MJL filter; Markov jump linear system; CALE; jumping parameters; optimal stationary MJL filter; coupled Lyapunov equations; Markov chains; coupled algebraic Lyapunov equations; mean squared method; multiplicative noises; observation delays; delay-free system; filter gains; data losses; optimal filter problem; generalised coupled algebraic Riccati difference equations; multiple delayed modes

Subjects: Linear algebra (numerical analysis); Differential equations (numerical analysis); Interpolation and function approximation (numerical analysis); Markov processes; Signal processing theory; Interpolation and function approximation (numerical analysis); Filtering methods in signal processing; Differential equations (numerical analysis); Linear algebra (numerical analysis); Markov processes

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