Abstract:
The paper describes the method of inverse statistical linearization – the method of nonlinear filtering for state estimation in linear Gaussian differential systems with observation noise of unknown intensity. The proposed technique is based on finding a nonlinear perturbation of the innovation process while keeping the gain coefficient in the Kalman-Bucy filter. As a result, the nonlinear filter is defined by a system of differential equations of the same order as the state vector without using any additional equations for the error covariance matrix. The nonlinear filter is found in an analytical form for a one-dimensional motion model in which only the highest order derivative is affected by a white-noise stochastic disturbance, and only one output is available for observing the position with additive noise of unknown intensity. The recurrent nonlinear filtering scheme is examined to establish the unbiasedness of the estimates and to obtain the steady-state equation for their error variances and covariances. The theoretical results are confirmed on the basis of computer simulations carried out to compare the estimation accuracy of the optimal filter and the proposed nonlinear filtering scheme.
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