Monte Carlo techniques for prediction and filtering of non-linear stochastic processes

Authors:
J. E. Handschin
Affiliations:
AG Brown, Boveri & Co., Research Department FoD CH-5401 Baden Switzerland
Venue:
Automatica (Journal of IFAC)
Year:
1970

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Abstract

This paper deals with the estimation of state variables for non-linear stochastic discrete-time processes. For the prediction problem, a direct evaluation of the Chapman-Kolmogorov equation may be prohibitive while the Monte Carlo approach offers an elegant alternative solution. The system is simulated and relevant data collected in order to estimate some parameters of the probability density function an arbitrary number of time steps ahead. The conjecture of inefficiency inherent in Monte Carlo work is invalidated with two variance reduction techniques. The non-linear filtering problem is discussed within the framework of the Bayesian approach. The problem of estimating the conditional mean of the posterior density function is formulated as a multidimensional integral. The control variate method presented shows that the Monte Carlo approach can successfully be adapted to estimate the approximation error of existing non-linear filtering equations and to improve their accuracy significantly.