DocumentCode :
797620
Title :
Nonlinear filters for linear models (a robust approach)
Author :
Liptser, R.Sh. ; Runggaldier, Wolfgang J.
Author_Institution :
Dept. of Electr. Eng. Syst., Tel Aviv Univ., Israel
Volume :
41
Issue :
4
fYear :
1995
fDate :
7/1/1995 12:00:00 AM
Firstpage :
1001
Lastpage :
1009
Abstract :
We consider the altering problem for linear models where the driving noises may be quite general, nonwhite and non-Gaussian, and where the observation noise may only be known to belong to a finite family of possible disturbances. Using diffusion approximation methods, we show that a certain nonlinear filter minimizes the asymptotic filter variance. This nonlinear filter is obtained by choosing at each moment, on the basis of the observations, one of a finite number of Kalman-type filters driven by a suitable nonlinear transformation of the “innovations”. As a byproduct we obtain also the asymptotic identification of the a priori unknown observation noise disturbance. By yielding an asymptotically efficient filter in face of an unknown observation noise, our approach may also be viewed as a robust approach to filtering for linear models
Keywords :
Kalman filters; approximation theory; filtering theory; noise; nonlinear filters; Kalman-type filters; asymptotic filter variance; asymptotic identification; asymptotically efficient filter; diffusion approximation methods; driving noises; innovations; linear models; non-Gaussian noise; nonlinear filters; nonlinear transformation; nonwhite noise; robust approach; robust filtering; unknown observation noise disturbance; Approximation methods; Discrete wavelet transforms; Filtering; Gaussian noise; Maximum likelihood detection; Noise robustness; Nonlinear filters; Yttrium;
fLanguage :
English
Journal_Title :
Information Theory, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9448
Type :
jour
DOI :
10.1109/18.391245
Filename :
391245
Link To Document :
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