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 JSIP  Vol.2 No.3 , August 2011
RLS Wiener Predictor with Uncertain Observations in Linear Discrete-Time Stochastic Systems
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)=Hx(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).
Cite this paper: nullS. Nakamori, R. Caballero-Águila, A. Hermoso-Carazo and J. Linares-Pérez, "RLS Wiener Predictor with Uncertain Observations in Linear Discrete-Time Stochastic Systems," Journal of Signal and Information Processing, Vol. 2 No. 3, 2011, pp. 152-158. doi: 10.4236/jsip.2011.23019.
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.

 
 
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