RECURSIVE NEURAL FILTERS

A recursive neurofilter comprising a recursive neural network (NN) is disclosed for processing an information process to estimate a signal process with respect to an estimation error criterion. The information process either consists of a measurement process, or if the signal and measurement processes are time-variant, consists of the measurement process as well as a time variance process, that describes the time-variant properties of the signal and measurement processes. The recursive neurofilter is synthesized from exemplary realizations of the signal and information processes. No assumptions such as Gaussian distribution, linear dynamics, additive noise, and Markov property are required. The synthesis is performed essentially through training recursive NNs. The training criterion is constructed to reflect the mentioned estimation error criterion with the exemplary realizations. If an estimation error statistics process of a primary recursive neurofilter is needed, an ancillary recursive neurofilter is used to produce an approximate of this estimation error statistics process. An ancillary recursive neurofilter inputs either said primary recursive neurofilter's input process or said primary recursive neurofilter's input and output processes.