Approximation Approach to Linear Filtering Problem with Correlated Noise
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.
[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.
[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.
@article{"International Journal of Electrical, Electronic and Communication Sciences:55364", author = "Hong Son Hoang and Remy Baraille", title = "Approximation Approach to Linear Filtering Problem with Correlated Noise", abstract = "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 = "Linear dynamical system, filtering, minimum meansquare filter, correlated noise", volume = "5", number = "11", pages = "1474-8", }
