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Optimal linear filter design for systems with correlation in the measurement matrices and noises: recursive algorithm and applications

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  • J. Linares-Pérez
  • R. Caballero-Águila
  • I. García-Garrido

Abstract

This paper addresses the optimal least-squares linear estimation problem for a class of discrete-time stochastic systems with random parameter matrices and correlated additive noises. The system presents the following main features: (1) one-step correlated and cross-correlated random parameter matrices in the observation equation are assumed; (2) the process and measurement noises are one-step autocorrelated and two-step cross-correlated. Using an innovation approach and these correlation assumptions, a recursive algorithm with a simple computational procedure is derived for the optimal linear filter. As a significant application of the proposed results, the optimal recursive filtering problem in multi-sensor systems with missing measurements and random delays can be addressed. Numerical simulation examples are used to demonstrate the feasibility of the proposed filtering algorithm, which is also compared with other filters that have been proposed.

Suggested Citation

  • J. Linares-Pérez & R. Caballero-Águila & I. García-Garrido, 2014. "Optimal linear filter design for systems with correlation in the measurement matrices and noises: recursive algorithm and applications," International Journal of Systems Science, Taylor & Francis Journals, vol. 45(7), pages 1548-1562, July.
    • Handle: RePEc:taf:tsysxx:v:45:y:2014:i:7:p:1548-1562
    DOI: 10.1080/00207721.2014.909093
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    Cited by:

    1. Caballero-Águila, R. & García-Garrido, I. & Linares-Pérez, J., 2016. "Quadratic estimation problem in discrete-time stochastic systems with random parameter matrices," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 308-320.
    2. R. Caballero-Águila & A. Hermoso-Carazo & J. Linares-Pérez, 2017. "New distributed fusion filtering algorithm based on covariances over sensor networks with random packet dropouts," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(9), pages 1805-1817, July.

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