Abstract
We consider a discrete linear dynamical system with known Gaussian system disturbances and known non-Gaussian observation noises. We propose an approximation filter which is optimal in the sense that the trace of the estimation error-covariance matrix is minimum for the optimal score function belonging to a preassigned class of score functions. Then, a recursive system of equations is derived for a scalar dynamical system which gives a lower and an upper bound of the filter's performance. In order to illustrate the properties of the proposed filter, a scalar system is considered. Results of simulation are presented for two cases; a) mixture Gaussian observation noise, and b) Cauchy observation noise. The lower and upper bounds of the filter's performance are also included for the case b.
