Identification of a nonlinear system modeled by a sparse Volterra series

An algorithm based on recursive approximation and estimation is proposed for the identification of nonlinear systems which can be modeled by a sparse Volterra series. The algorithm detects the terms of the Volterra series on which the output depends and estimates the associated Volterra kernels using a least squares criterion. The performance of the algorithm is primarily dependent on the number of nonzero Volterra kernels and not on their distribution in the whole series. The input sequence can be either i.i.d. or correlated. The algorithm can also be directly applied to the delay estimation of a sparse finite impulse response (FIR) filter