Approach to the Filter Derivation for Nonlinear, Discrete-Time Systems with Unknown, Time-Varying Parameters

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This paper is concerned with a problem of deriving an approximate filter for noisy nonlinear, discrete-time systems with unknown time-varying parameters.Firstly, a linearized filter is obtained by applying a Taylor series expansion to the nonlinearities of the system where the unknown parameters are assumed to be time-invariant.Secondly, this filter is tested whether or not the approximate innovation sequence is likely to have come from the calculated distribution for it. When the hypothesis test is rejected, the calculated covariance matrix for the approximate innovation sequence is modified so that the approximate innovation sequence lies on the boundary of the acceptable region.Numerical results of digital simulation for simple nonlinear systems indicate that the proposed filter gives better filtering performance than the filter presented by Tarn et. al.
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