RLS Wiener Predictor with Uncertain Observations in Linear Discrete-Time Stochastic Systems

Seiichi Nakamori, Raquel Caballero-Águila, Aurora Hermoso-Carazo, Josefa Linares-Pérez

.

DOI: 10.4236/jsip.2011.23019                

Abstract

This paper proposes recursive least-squares (RLS) l-step ahead predictor and filtering algorithms with uncertain observations in linear discrete-time stochastic systems. The observation equation is given by y(k)=y(k)z(k)+v(k), z(k)=H_x(k), where {y(k)} is a binary switching sequence with conditional probability. The estimators require the information of the system state-transition matrix Ф, the observation matrix H, the variance K(k,k) of the state vector x(k), the variance R(k) of the observation noise, the probability p(k)=p{y(k)=1} that the signal exists in the uncertain observation equation and the (2,2) element [p(k|j)]_2,2 of the conditional probability of y(k), given y(j).

Keywords

Estimation Theory, Synthesis of Stochastic Systems, RLS Wiener Predictor, Uncertain Observations, Markov Probability

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	H. L. Van Trees, “Detection, Estimation and Modulation Theory (Part I),” Wiley, New York, 1968.
[2]	N. Nahi, “Optimal Recursive Estimation with Uncertain Observation,” IEEE Transactions on Information Theory, Vol. IT-15, No. 4, 1969, pp. 457-462. doi:10.1109/TIT.1969.1054329
[3]	N. Hadidi and S. Schwartz, “Linear Recursive State Estimators under Uncertain Observations,” IEEE Transactions on Automatic Control, Vol. AC-24, No. 6, 1979, pp. 944-948. doi:10.1109/TAC.1979.1102171
[4]	S. Nakamori, “Estimation Technique Using Covariance Information in Linear Discrete-Time Systems,” Signal Processing, Vol. 58, No. 3, 1997, pp. 309-317. doi:10.1016/S0165-1684(97)00032-7
[5]	S. Nakamori, R. Caballero-águila, A. Hermoso-Carazo and J. Linares-Pérez, “Linear Recursive Discrete-Time Estimators Using Covariance Information under Uncertain Observations,” Signal Processing, Vol. 83, No. 7, 2003, pp. 1553-1559. doi:10.1016/S0165-1684(03)00056-2
[6]	S. Nakamori, R. Caballero-águila, A. Hermoso-Carazo and J. Linares-Pérez, “Fixed-Point Smoothing with Non- Independent Uncertainty Using Covariance Information,” International Journal of Systems Science, Vol. 34, No. 7, 2003, pp. 439-452. doi:10.1080/00207720310001636390
[7]	A. P. Sage and J. L. Melsa, “Estimation Theory with Applications to Communications and Control,” McGraw-Hill, New York, 1971.
[8]	S. Haykin, “Adaptive Filter Theory,” Prentice-Hall, New Jersey, 2003.