Model-based discrete linear state estimator for nonlinearizable systems with state-dependent noise

A practical technique for deriving a discrete-time linear state estimator for estimating the states of a nonlinearizable stochastic system involving both state-dependent and external noises due to a linear noisy measurement system is presented. The existing technique for synthesizing a discrete-time linear state estimator is first to construct an equivalent reference linear model for the nonlinearizable system such that the equivalent model will provide the same stationary covariance response as the nonlinear system. From the linear continuous model, a discrete-time state estimator can be directly derived from the corresponding discrete-time model. The synthesis technique and filtering performance are illustrated and simulated by using linear, linearizable, and nonlinearizable systems with state-dependent noise.