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Optimal Estimation in the Presence of Unknown Parameters

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2 Author(s)
Hilborn, C.G. ; Bell Telephone Laboratories, Inc., Winston-Salem, N.C. ; Lainiotis, D.G.

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.

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Systems Science and Cybernetics, IEEE Transactions on  (Volume:5 ,  Issue: 1 )