Abstract: 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.

Abstract: An adaptive neural system (ANS) disclosed herein comprises a processor and an adaptor. The processor includes mainly a neural network whose adjustable weights are divided into nonadaptively and adaptively adjustable weights. The nonadaptively adjustable weights are determined through minimizing or reducing a nonadaptive training criterion in an off-line nonadaptive training. Being constructed with a priori training data, the nonadaptive training criterion is a function of the nonadaptively adjustable weights and the diversity variables associated with typical values of the environmental parameter. During an operation of the adaptive neural system, only the adaptively adjustable weights are adjusted on-line to adapt to the unknown environmental parameter. This adaptive training is achieved by minimizing or reducing an adaptive training criterion.

Abstract: A method and apparatus is provided for processing a measurement process to estimate a signal process, even if the signal and/or measurement processes have large and/or expanding ranges. The method synthesizes training data comprising realizations of the signal and measurement processes into a primary filter for estimating the signal process and, if required, an ancillary filter for providing the primary filter's estimation error statistics. The primary and ancillary filters each comprise an artificial recurrent neural network (RNN) and at least one range extender or reducer. Their implementation results in the filtering apparatus. Many types of range extender and reducer are disclosed, which have different degrees of effectiveness and computational cost.