Adaptive nonlinear recursive state-space filters

Adaptive nonlinear filters previously reported often employ truncated Volterra series and have a finite impulse response (FIR). This paper introduces a nonlinear state-space structure for adaptive nonlinear filters. The adaptive filters are recursive and thus generally have an infinite impulse response (IIR). They are expected to be useful for many applications and are especially attractive for those with long memories where adaptive nonlinear FIR filters are too expensive to use. Efficient methods, which significantly reduce computation for gradients, have been developed to facilitate further their application in real-time signal processing. Numerical simulations have been performed to demonstrate the properties of the proposed algorithms