Partial States Estimation of Linear Stochastic Systems with Completely Unknown Disturbances

Abstract

The filtering problem for continuous-time linear stochastic systems with completely unknown disturbances is considered in this paper. Specifically the filter which estimates the maximum estimable subspace of the state from noisy observation is drived. The only assumption is that the system is left invertible. Hence the filter derived by Mehra is easily derived as a special case. The stability of the resulting filter is then investigated, and a condition for the filter to be stable is presented in terms of the invariant zeroes of the system. Furthermore a sufficient condition under which a given linear function of the state can be estimated is given. A design procedure of the filter to estimate a linear function of the state is also developed.