1. A system for augmenting a filter to track an observed system having an actual output signal y that is observable, the system comprising: a filter ( 20 ) comprising an observer or estimator for generating an estimated state signal {circumflex over (x)} representing the state of the observed system, the filter ( 20 ) connected to receive an output error signal ŷ that is a difference between an actual output signal y and an estimated output signal ŷ, the estimated output signal ŷ generated based on the estimated state signal {circumflex over (x)}, the filter further connected to receive an augmenting adaptive signal v ad , the filter configured to generate an improved estimated state signal {circumflex over (x)} based on the output error signal ŷ and the augmenting adaptive signal v ad ; and an adaptive unit ( 30 ) connected to receive the output error signal ŷ, the adaptive unit configured to generate a training error signal vector ê based on the output error signal ŷ, the adaptive unit having an adaptive element ( 34 ) including a neural network ( 36 ) with connection weights updated based on the training error signal vector ê, the neural network further connected to receive an input signal μ based on the actual output signal y, the adaptive unit generating the augmenting adaptive signal v ad based on the input signal μ and training error signal vector ê, the adaptive unit connected to provide the augmenting adaptive signal V ad to the filter for use in generating the estimated state signal {circumflex over (x)}.