A bayes‐closed approximation of recursive non‐linear estimation
Rudolf Kulhavý · International Journal of Adaptive Control and Signal Processing · 1990
Abstract To implement the Bayes estimation in a recursive manner means to cope with the need for storing a too large data statistic. We prove here that under certain assumptions, it is possible to construct a reduced description of posterior densities (a reduced statistic) which is closed with respect to the Bayes rule. Thus the optimal Bayes inference can be realized in terms of transitions between equivalence classes of densities matching the respective values of the description. Next we attempt to design a specific approximation of the recursive Bayes estimation by projecting the true posterior density orthogonally, along the appropriate equivalence class, onto a prespecified approximation family. We find that to ensure orthogonal projection globally, the approximation family must be of a mixture type and the description vector determined by the values of the Kullback‐Leibler distance between the ‘base’ densities of the mixture approximation family and the true density. A simple simulation example compares the Bayes‐closed approximation with some competitive methods.