Design of RLS Wiener Smoother and Filter for Colored Observation Noise in Linear Discrete-Time Stochastic Systems
Seiichi Nakamori
Kagoshima University.
DOI: 10.4236/jsip.2012.33041   PDF    HTML     3,698 Downloads   5,786 Views   Citations


Almost estimators are designed for the white observation noise. In the estimation problems, rather than the white observation noise, there might be actual cases where the observation noise is modeled by the colored noise process. This paper examines to design a new estimation technique of recursive least-squares (RLS) Wiener fixed-point smoother and filter for colored observation noise in linear discrete-time wide-sense stationary stochastic systems. The observation y(k) is given as the sum of the signal z(k)=Hx(k) and the colored observation noise vc(k). The RLS Wiener estimators explicitly require the following information: 1) the system matrix for the state vector x(k); 2) the observation matrix H; 3) the variance of the state vector x(k); 4) the system matrix for the colored observation noise vc(k); 5) the variance of the colored observation noise; 6) the input noise variance in the state equation for the colored observation noise.

Share and Cite:

S. Nakamori, "Design of RLS Wiener Smoother and Filter for Colored Observation Noise in Linear Discrete-Time Stochastic Systems," Journal of Signal and Information Processing, Vol. 3 No. 3, 2012, pp. 316-329. doi: 10.4236/jsip.2012.33041.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] S. Nakamori, “Recursive Estimation Technique of Signal from Output Measurement Data in Linear Discrete-Time Systems,” IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, Vol. E78-A, No. 5, 1995, pp. 600-607.
[2] S. Nakamori, “Chandrasekhar-Type Recursive Wiener Estimation Technique in Linear Discrete-Time Systems,” Applied Mathematics and Computation, Vol. 188, No. 2, 2007, pp. 1656-1665. doi:10.1016/j.amc.2006.11.021
[3] S. Nakamori, “Square-Root Algorithms of RLS Wiener Filter and Fixed-Point Smoother in Linear Discrete Stochastic Systems,” Applied Mathematics and Computation, Vol. 203, No. 1, 2008, pp. 186-193. doi:10.1016/j.amc.2008.04.026
[4] 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, No. 7, 2008, pp. 1338-1349. doi:10.1016/j.apm.2007.04.008
[5] S. Nakamori, “Design of RLS Wiener FIR Filter Using Covariance Information in Linear Discrete-Time Stochastic Systems,” Digital Signal Processing, Vol. 20, No. 5, 2010, pp. 1310-1329. doi:10.1016/j.dsp.2010.01.001
[6] S. Boll, “Suppression of Acoustic Noise in Speech Using Spectral Subtraction,” IEEE Transactions on Acoustics, Speech and Signal Processing, Vol. 27, No. 2, 1979, pp. 113-120. doi:10.1109/TASSP.1979.1163209
[7] S. S. Xiong and Z. Y. Zhou, “Neural Filtering of Colored Noise Based on Kalman Filter Structure,” IEEE Transactions on Instrumentation and Measurement, Vol. 52, No. 3, 2003, pp. 742-747. doi:10.1109/TIM.2003.814669
[8] D. Simon, “Optimal State Estimation: Kalman, H∞, and Nonlinear Approaches,” Wiley, New York, 2006. doi:10.1002/0470045345
[9] F. Must’iere, M. Boli’c and M. Bouchad, “Improved Colored Noise Handling in Kalman Filter-Based Speech Enhancement Algorithms,” Canadian Conference on Electrical Computer Engineering, Niagara Falls, 4-7 May 2008, pp. 497-500.
[10] S. Park and S. Choi, “A Constrained Sequential EM Algorithm for Speech Enhancement,” Neural Networks, Vol. 21, No. 9, 2008, pp. 1401-1409. doi:10.1016/j.neunet.2008.03.001
[11] S. Nakamori, “Estimation of Signal and Parameters Using Covariance Information in Linear Continuous Systems,” Mathematical and Computer Modeling, Vol. 16, No. 10, 1992, pp. 3-15. doi:10.1016/0895-7177(92)90056-Q
[12] A. Mahmoudi and M. Karimi, “Parameter Estimation of Autoregressive Signals from Observations Corrupted with Colored Noise,” Signal Processing, Vol. 90, No. 1, 2010, pp. 157-164. doi:10.1016/j.sigpro.2009.06.005
[13] A. P. Sage and J. L. Melsa, “Estimation Theory with Applications to Communications and Control,” McGraw-Hill, New York, 1971.

Copyright © 2024 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.