Optimal recurrent logical-dynamical finite memory filter

Abstract

We consider the treatment problem of imprecise or incomplete observations of the state of a discrete Markovian stochastic object with a variable random structure. We aim to exactly estimate and forecast in one step this object’s variables of state and structure type. We propose to synthesize a simple finite dimensional switch filter which remembers only the last few measurements in its state vector. The dimension of this vector (the memory volume of the filter) can be chosen from the condition of the compromise between the achievable accuracy of the estimation and the complexity of the hardware implementation of the filter. We gain an impression of the optimal structural functions of the filter through the corresponding probability distributions and propose a numerical algorithm to compute them by the Monte-Carlo method.