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Approximation Approach to Linear Filtering Problem with Correlated Noise

Authors: Hong Son Hoang, Remy Baraille


The (sub)-optimal soolution of linear filtering problem with correlated noises is considered. The special recursive form of the class of filters and criteria for selecting the best estimator are the essential elements of the design method. The properties of the proposed filter are studied. In particular, for Markovian observation noise, the approximate filter becomes an optimal Gevers-Kailath filter subject to a special choice of the parameter in the class of given linear recursive filters.

Keywords: Filtering, Linear dynamical system, minimum meansquare filter, correlated noise

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[1] Albert A. (1972) Regression and Moore-Penrose Pseudoinverse. Academic Press, NY- London.
[2] Santamaria - G'omez A., Bouin M., Collilieux X. and Woppelmann G. (2011) Correlated errors in GPS position time series: Implications for velocity estimates. J. Geophys. Research, V. 116, B01405, doi:10.1029/2010JB007701.
[3] Bucy R.S. and Joseph D.P. (1968) Filtering for Stochastic Processes, with Applications to Guidance. Wiley, New York.
[4] Daley R. (1992) The effect of serially correlated observation and model error on atmospheric data assimilation. Monthly Weather Review, 120, pp. 165-177
[5] Damera-Venkata N. and Evans B.L. (2001) Design and Analysis of Vector Color Error Diffusion Halftoning Systems. IEEE Trans. Image Proc., V. 10, October , pp. 1552-1565.
[6] Gevers M. and Kailath T. (1973) An Innovations Approach to Least- Squares Estimation, Pt. VI: Discrete-Time Innovations Representations and Recursive Estimation, IEEE Trans. Automatic Control, 18(6), pp. 588-600, December.
[7] Golub G.H. and Van Loan C.F. (1996) Matrix Computations, Johns Hopkins Univ. Press, 1996.
[8] Hoang H.S., Nguyen T.L., Baraille R. and Talagrand O. (1997) Approximation approach for nonlinear filtering problem with time dependent noises: Part I: Conditionally optimal filter in the minimum mean square sense. J. "Kybernetika", Vol. 33, No 4, pp. 409-425.
[9] Hoang H.S., Baraille R., Talagrand O. and De Mey P. (2001) Approximate Bayesian Approach to Non-Gaussian Estimation in a Linear Model with Dependent State and Noise vectors. Applied Math. and Optim., 43, pp. 203-220.
[10] Maybeck P.S. (1979) Stochastic Models, Estimation, and Control. Vol. 1, Publisher: Academic Press.
[11] Morf M. and Kailath T. (1977) Recent results in least-squares estimation theory. In Annals of Economic and Social Measurement, V. 6, N. 3, pp. 19-32.
[12] Nguyen T.L. and Hoang H.S. (1982) On optimal filtering with correlated noises and singular correlation matrices. Automat. Remote Contr., 43(5), pp. 660-669.
[13] Popescu D.C.and Zeljkovic I. (1998). Kalman Filtering of Colored Noise for Speech Enhancement, Proc. IEEE ICASSP-98, V.2, pp. 997-1000, Seattle, USA, May.
[14] Wendel J. and Trommer G. F. (2004). An Efficient Method for Considering Time Correlated Noise in GPS/INS Integration. Proc. of the 2004 National Technical Meeting of The Institute of Navigation, San Diego, CA, January, pp. 903-911.