Non-linear filters for linear models


We consider the filtering problem for linear models where the driving noises may be quite general, non-white 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.

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@inproceedings{Liptser1999NonlinearFF, title={Non-linear filters for linear models}, author={R. S. Liptser}, year={1999} }