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A Kushner-Stratonovich Monte Carlo filter applied to nonlinear dynamical system identification. (English) Zbl 1285.93101

Summary: A Monte Carlo filter, based on the idea of averaging over characteristics and fashioned after a particle-based time-discretized approximation of the Kushner-Stratonovich (KS) nonlinear filtering equation, is proposed. A key aspect of the new filter is the gain-like additive update, designed to approximate the innovation integral in the KS equation and implemented through an annealing-type iterative procedure, which is aimed at rendering the innovation (observation-prediction mismatch) for a given time-step to a zero-mean Brownian increment corresponding to the measurement noise. This may be contrasted with the weight-based multiplicative updates in most particle filters that are known to precipitate the numerical problem of weight collapse within a finite-ensemble setting. A study to estimate the a-priori error bounds in the proposed scheme is undertaken. The numerical evidence, presently gathered from the assessed performance of the proposed and a few other competing filters on a class of nonlinear dynamic system identification and target tracking problems, is suggestive of the remarkably improved convergence and accuracy of the new filter.

MSC:

93E12 Identification in stochastic control theory
93E11 Filtering in stochastic control theory
93E25 Computational methods in stochastic control (MSC2010)
93C10 Nonlinear systems in control theory
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