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Journal of Information

June 2015, Volume 1, 1, pp 23-35

RLS Fixed-Lag Smoother Using Covariance Information Based on Innovation Approach in Linear Continuous Stochastic Systems

Seiichi Nakamori

Seiichi Nakamori 1

  1. Faculty of Education, Department of Technology, Kagoshima University, Kohrimoto, Kagoshima, Japan 1

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Pages: 23-35

DOI: 10.18488/journal.104/2015.1.1/104.1.23.35

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Abstract:

This paper newly designs the RLS (recursive least-squares) fixed-lag smoother and filter, based on the innovation theory, in linear continuous-time stochastic systems. It is assumed that the signal is observed with additive white noise and the signal is uncorrelated with the observation noise. It is a characteristic that the estimators use the covariance information of the signal, in the form of the semi-degenerate kernel, and the observation noise. With respect to the RLS fixed-lag smoother, the algorithm for the estimation error variance function is developed to guarantee the stability of the fixed-lag smoother. The proposed estimators have the recursive property in calculating the fixed-lag smoothing and filtering estimates. Also, this paper proposes the Chandrasekhar-type RLS Wiener filter in linear wide-sense stationary stochastic system. Unlike the usual filter including the Riccati-type equations, the Chandrasekhar-type filter does not contain the Riccati-type differential equations and has an advantage of eliminating the possibility of the covariance matrix becoming nonnegative.
Contribution/ Originality

Keywords:

Linear continuous systems, Fixed-lag smoother, RLS estimation problem, Covariance information, Wiener-Hopf integral equation, Stochastic signal.

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Reference:

  1. S. Nakamori, A. Hermoso-Carazo, and J. Linares-Pérez, "Design of RLS fixed-lag smoother using covariance information in linear discrete stochastic systems," Applied Mathematical Modelling, vol. 34, pp. 1093-1106, 2010.
  2. S. Nakamori, A. Hermoso-Carazo, and J. Linarez-P'erez, "Design of fixed-lag smoother using covariance information based on innovations approach in linear discrete-time stochastic systems," Applied Mathematics and Computation, vol. 193, pp. 162-174, 2007.
  3. S. Nakamori, A. Hermoso-Carazo, and J. Linares-P'erez, "Design of RLS wiener fixed-lag smoother using covariance information in linear discrete stochastic systems," Applied Mathematical Modelling, vol. 32, pp. 1338–1349, 2008.
  4. S. Nakamori, "Design of recursive least-squares fixed-lag smoother using covariance information in linear continuous stochastic systems," Applied Mathematical Modelling, vol. 31, pp. 1609-1620, 2007.
  5. S. Nakamori, "RLS fixed-lag smoother using covariance information in linear continuous stochastic systems," Applied Mathematical Modelling, vol. 33, pp. 242-255, 2009.
  6. S. Nakamori, "Design of recursive wiener smoother given covariance information, IEICE trans. Fundamentals of electronics," Communication and Computer Sciences, vol. E79-A, pp. 864-872, 1996.
  7. T. Kailath, Lectures on Wiener and Kalman filtering, 2nd ed. Wien: Springer-Verlag, GMBH, 1981.
  8. J. S. Baras and D. G. Lainiotis, "Chandrasekhar algorithms for linear time varying distributed systems," Information Sciences, vol. 17, pp. 153-167, 1979.
  9. D. Simon, Optimal state estimation: Kalman, H infinity, and nonlinear approaches. Hoboken, NJ: Wiley-Interscience, 2006.

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