Neural Network Approach to Optimal Filtering

摘要

This report describes the results of a study investigating a new approach to theproblem of optimal filtering. The approach involves synthesizing realizations of a signal process and a measurement process into a filter for estimating the signal process. The filter is made out of an artificial recurrent neural network (RNN). The synthesis is performed through training RNNs. The weights/parameters of an RNN are determined by minimizing a training criterion. After adequate training, the result is a recursive filter optimal for its given RNN architecture where the lagged feedbacks carry the optimal conditional statistics. If an appropriate RNN paradigm and estimation error criterion are selected, the filter of such a paradigm is proven to approximate an optimal filter in performance to any desired degree of accuracy, provided the RNN that constitutes the filter is of a sufficient size. Range extenders and reducers are introduced to minimize the required RNN size, especially when the signal and/or measurement processes keep increasing in magnitude. Some schemes for adapting to unknown filtering environments are presented. These schemes yield maximum likelihood estimates of the unknown parameters and minimum variance estimates of the signals.