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Modern parametric and nonparametric algorithms for discrete nonlinear filtering of random processes


M.A. Mironov, A.V. Bashaev, S.G. Andreev

We consider the parametric and nonparametric algorithms for discrete nonlinear filtering, obtained by the Markov theory of random processes estimation. Parametric nonlinear algorithm based on calculating the parameters of the approximating posterior probability density. We describe the parametric algorithms, obtained by Gaussian approximation without the use of expansions of nonlinear functions. There are discussed algorithms, founded on use for numerical calculation corresponding integrals Gauss-Hermite quadrature, the unscented transform and Monte Carlo method. Nonparametric nonlinear algorithms based on direct calculating the posterior probability density of the process being evaluated, followed by computation of optimal estimations in accordance with the selected optimization criterion. We present two types of nonparametric algorithms, obtained by the solution of the Stratonovich equation conventional numerical method, and Monte Carlo method. At building of nonparametric algorithms using Monte Carlo method (particle filters) is offered realize accumulation of the significant samples. Comparison of the characteristics of the nonparametric algorithms performed on the example of nonlinear models with scalar estimated and the observed processes.

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