Accommodative neural filters

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 a recursive neural filter with fixed weights has the ability to adapt to the uncertain environmental parameter. The neural filter with this ability is called an accommodative neural filter. In this paper, we show that if the uncertain environmental process is observable from the measurement process, the accommodative neural filter outputs virtually the estimate of the signal process that would be generated by a non-adaptive minimal-variance filter as if the precise value of the uncertain environmental process were given. Numerical results comparing the accommodative neural filter and the existing non-adaptive filters each designed for a precise value of the environmental process confirm our theorem and show the advantages of the accommodative neural filter in both accuracy and efficiency.