Adaptive Neural Filters with Fixed Weights

By the fundamental neural filtering theorem, a properly trained recursive neural filter with fixed weights that processes only the measurement process generates recursively the conditional expectation of the signal process with respect to the joint probability distributions of the signal and measurement processes and any uncertain environmental process involved. This means that said recursive neural filter with fixed weights has the ability to adapt to the uncertain environmental parameter. This ability is called accommodative ability. This paper shows that if the uncertain environmental process is observable (not necessarily constant) from the measurement process, then the estimate of the signal process generated by said recursive neural filter with fixed weights approaches the estimate of the signal process that would be generated as if the precise value of the uncertain environmental process were given and processed together with the measurement process by a minimal-variance filter.