Asymptotic Properties of Recursive Particle Maximum Likelihood Estimation

Using stochastic gradient search and the optimal filter derivative, it is possible to perform recursive (i.e., online) maximum likelihood estimation in a non-linear state-space model. As the optimal filter and its derivative are analytically intractable for such a model, they need to be approximated numerically. In [17], a recursive maximum likelihood algorithm based on a particle approximation to the optimal filter derivative has been proposed and studied through numerical simulations. Here, this algorithm and its asymptotic behavior are analyzed theoretically.

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