International Journal of Information Technology and Computer Science(IJITCS)
ISSN: 2074-9007 (Print), ISSN: 2074-9015 (Online)
Published By: MECS Press
IJITCS Vol.6, No.1, Dec. 2013
New RLS Wiener Smoother for Colored Observation Noise in Linear Discrete-time Stochastic Systems
Full Text (PDF, 467KB), PP.13-24
In the estimation problems, rather than the white observation noise, there are cases where the observation noise is modeled by the colored noise process. In the observation equation, the observed value y(k) is given as a sum of the signal z(k)=Hx(k) and the colored observation noise v_c(k). In this paper, the observation equation is converted to the new observation equation for the white observation noise. In accordance with the observation equation for the white observation noise, this paper proposes new RLS Wiener estimation algorithms for the fixed-point smoothing and filtering estimates in linear discrete-time wide-sense stationary stochastic systems. The RLS Wiener estimators require the following information: (a) the system matrix for the state vector x(k); (b) the observation matrix H; (c) the variance of the state vector x(k); (d) the system matrix for the colored observation noise v_c(k); (e) the variance of the colored observation noise.
Cite This Paper
Seiichi Nakamori,"New RLS Wiener Smoother for Colored Observation Noise in Linear Discrete-time Stochastic Systems", International Journal of Information Technology and Computer Science(IJITCS), vol.6, no.1, pp.13-24, 2014. DOI: 10.5815/ijitcs.2014.01.02
Nakamori S. Recursive estimation technique of signal from output measurement data in linear discrete-time systems [J]. IEICE Trans. Fundamentals, 1995, E-78-A: 600-607.
Nakamori S. Chandrasekhar-type recursive Wiener estimation technique in linear discrete-time systems [J]. Applied Mathematics and Computation, 2007, 188: 1656-1665.
Nakamori S. Square-root algorithms of RLS Wiener filter and fixed-point smoother in linear discrete stochastic systems [J]. Applied Mathematics and Computation, 2008, 203(1): 186- 193.
Nakamori S. Design of RLS Wiener FIR filter using covariance information in linear discrete-time stochastic systems [J]. Digital Signal Processing, 2010, .20(5): 1310-1329.
Boll S. Suppression of acoustic noise in speech using spectral subtraction [J]. IEEE Trans. Acoustics, Speech and Signal Processing, 1979, ASSP-27(2): 113-120.
Xiong S. S., Zhou Z. Y. Neural filtering of colored noise based on Kalman filter structure [J]. IEEE Transactions on Instrumentation and Measurement, 2003, 52(3): 742-747.
Bryson A., Henrikson L. Estimation using sampled data containing sequentially correlated noise [J]. J. of Spacecraft and Rockets, 1968, 5(6): 662-665.
Simon D. Optimal state estimation: Kalman, H infinity, and nonlinear approaches [M]. John Wiley & Sons, New Jersey, NJ, 2006.
Must’iere F., Boli’c M., Bouchad M. Improved colored noise handling in Kalman filter-based speech enhancement algorithms [C]. In: Canadian Conference on Electrical Computer Engineering, 2008, CCECE 2008, 497-500.
Park S., Choi S. A constrained sequential EM algorithm for speech enhancement [J]. Neural Networks [J]. 2008, 21: 1401-1409.
Shuli Sun Reduced-order Wiener state estimators for descriptor system with multi-observation lags and MA colored observation noise [C]. In: Control Conference 2008, CCC 2008, 27th Chinese, 2008, 417-420.
Nakamori S. Estimation of signal and parameters using covariance information in linear continuous systems [J]. Mathematical and Computer modeling, 1992, 16(10): 3-15.
Mahmoudi A., Karimi M. Parameter estimation of autoregressive signals from observations corrupted with colored noise [J]. Signal Processing, 2010, 90(1): 157-164.
Sawada Y., Tanikawa A. An improved recursive algorithm of optimal filter for discrete-time linear systems subject to colored observation noise [J]. International J. of Innovative Computing, Information and Control, 2012, 8(3B): 2389-2397.
Nakamori S. Design of RLS Wiener smoother and filter for colored observation noise in linear discrete-time stochastic systems [J]. J. of Signal and Information Processing, 2012, 3(3): 316-329.
Nakamori S. RLS Wiener smoother for colored observation noise with relation to innovation theory in linear discrete-time stochastic systems [J]. I. J. Information Technique and Computer Science, 2013, 5(3): 1-12.
Kailath T. Lectures on Wiener and Kalman filtering [M]. CISM Monographs, No. 140, Springer-Verlag, New York, N Y, 1981.
Kailath T., Frost P. An innovations approach to least-squares estimation Part II: Linear smoothing in additive white noise [J]. IEEE Trans. Automatic Control, 1968, AC-13(6): 655-660.
Sage A. P., Melsa J. L. Estimation theory with applications to communications and control [M]. McGraw-Hill, New York, N Y, 1971.