Suboptimal robust asymptotic observer for stochastic continuous time nonlinear system: numerical procedure and convergence analysis

In this paper we show that for stationary stochastic nonlinear systems (satisfying a Globally Lipschitz Condition) the high-gain observer with a constant gain matrix may guarantee an upper bound for the averaged quadratic error of state estimation. The nonlinearities are assumed to be a priory known. The main contribution of this paper consists in the designing of a numerical procedure for the optimal gain matrix minimizing this upper bound. The convergence analysis of this procedure is presented as well as an example illustrating its finite steps workability: it is shown that within a neighborhood of the optimal matrix gain the others provide less estimation performance.