Abstract
A possibly globally convergent approximation to the optimal continuous time non linear filter for n pole parameters and n states only is found by computing the first, second, and third order moment equations. Closure of the moment equations results from approximating fourth order moments by the Gaussian formula involving second order moments. Five necessary conditions for stability are given. The unique convergence point of the algorithm is shown to be the true pole parameter value in the scalar case. The new algorithm is asymptotically equivalent to the non-stationary version of the recursive prediction error method. The error incurred by the Gaussian approximation is shown to be small in several examples of the discrete time optimal nonlinear filter.
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