A causal optimal filter of the second order

We provide a non-linear optimal physically realizable filter which guarantees a smaller associated error than those of the known linear optimal filters proposed by H.W. Bode and C.E. Shannon (see Proc. IRE, vol.38, p.417-25, 1950) and M.V. Ruzhansky and V.N. Fomin (see Bulletin of St. Petersburg University, Mathematics, vol.28, p.50-5, 1995). The technique presented has potential applications to numerous areas in signal processing including, for example, filtering, blind channel equalization, feature selection and classification in pattern recognition, target detection, etc. The technique is based on the best approximation of a stochastic signal by a specific non-linear operator acting on the noisy observed data.