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An adaptive approach is presented for optimal estimation of a sampled stochastic process with finite-state unknown parameters. It is shown that, for processes with an implicit generalized Markov property, the optimal (conditional mean) state estimates can be formed from 1) a set of optimal estimates based on known parameters, and 2) a set of "learning" statistics which are recursively updated. The formulation thus provides a separation technique which simplifies the optimal solution of this class of nonlinear estimation problems. Examples of the separation technique are given for prediction of a non-Gaussian Markov process with unknown parameters and for filtering the state of a Gauss-Markov process with unknown parameters. General results are given on the convergence of optimal estimation systems operating in the presence of unknown parameters. Conditions are given under which a Bayes optimal (conditional mean) adaptive estimation system will converge in performance to an optimal system which is "told" the value of unknown parameters.
Systems Science and Cybernetics, IEEE Transactions on (Volume:5 , Issue: 1 )
Date of Publication: Jan. 1969