Robust filtering for linear systems

Recursive robust filtering for a discrete, linear stochastic system with additive white noise disturbances is considered. The initial state and plant disturbances are assumed to be Gaussian and the partial covariance of each measurement over a finite region is assumed bounded from below. A soft limiter and patched-Gaussian density are shown to be the optimal min-max estimator and the least favorable measurement density, respectively. An approximate filter is proposed and an example is given.