On a nonlinear feedback filtering system

A nonlinear filtering scheme with noiseless feedback is presented, based on a consideration of the minimum-mean-squared error filtering of independent signal samples corrupted by additive noise. The explicit solution for the general case is very complex. However, if the signal-to-noise ratio is assumed to be large and the nonlinear estimating filter has zero memory, the problem may be simplified by reducing it to the zero-memory prefiltering problem combined with predictive feedback. The improvement over the linear case without feedback is shown to be the product of the improvements due to the zero-memory non-linearities and the feedback. An example is considered to illustrate the improvements in the error,