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Quadratic estimation problem in discrete-time stochastic systems with random parameter matrices

Author

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

Abstract

This paper addresses the least-squares quadratic filtering problem in discrete-time stochastic systems with random parameter matrices in both the state and measurement equations. Defining a suitable augmented system, this problem is reduced to the least-squares linear filtering problem of the augmented state based on the augmented observations. Under the assumption that the moments, up to the fourth-order one, of the original state and measurement vectors are known, a recursive algorithm for the optimal linear filter of the augmented state is designed, from which the optimal quadratic filter of the original state is obtained. As a particular case, the proposed results are applied to multi-sensor systems with state-dependent multiplicative noise and fading measurements and, finally, a numerical simulation example illustrates the performance of the proposed quadratic filter in comparison with the linear one and also with other filters in the existing literature.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:273:y:2016:i:c:p:308-320
    DOI: 10.1016/j.amc.2015.10.005
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    References listed on IDEAS

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    1. 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.
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