HIGH-ORDER FILTERS FOR ESTIMATION IN NON-GAUSSIAN NOISE

In this paper, high-order vector filter equations are developed for estimation in non-Gaussian noise. The difference between the filters developed here and the standard Kalman filter is that the filter equation contains nonlinear functions of the innovations process. These filters are general in that the initial estimation error, the measurement noise, and the process noise can all have non-Gaussian distributions. Two filter structures are developed. The first filter is designed for parameter estimation in systems for which the initial estimation error, the process noise, and/or the measurement noise have Gaussian and/or asymmetric non-Gaussian probability densities. The second filter is designed for estimation in Gaussian and/or symmetric non-Gaussian noise. Experimental evaluation of the high-order filters in non-Gaussian noise, formed from Gaussian sum distributions, shows that these filters perform significantly better than the standard Kalman filter, and close to the optimal Bayesian estimator.