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Robust bayesian estimation for the linear model and robustifying the Kalman filter

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2 Author(s)
Masreliez, C. ; University of Washington, Seattle, Washington, USA ; Martin, R.

Starting with the vector observation model y = Hx + v , robust Bayesian estimates \hat{x} of the vector x are constructed for the following two distinct situations: 1) the state x is Gaussian and the observation error v is (heavy-tailed) non-Gaussian and 2) the state is heavy-tailed non-Gaussian and the observation error is Gaussian. Bounds with respect to broad symmetric non-Gaussian families are derived for the error covariance matrix of these estimates. These "one-step" robust estimates are then used to obtain robust estimates for the Kalman filter setup y_{k}= H_{k}x_{k}+ v_{k}, x_{k+1}=\Phi _{k}x_{k}+w_{k} . Monte Carlo results demonstrate the robustness of the proposed estimation procedure, which might be termed a robustified Kalman filter.

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Automatic Control, IEEE Transactions on  (Volume:22 ,  Issue: 3 )