Adaptive Hammerstein Filtering via Recursive Non-Convex Projection

Hammerstein model with a static nonlinearity followed by a linear filter is commonly used in numerous applications. This paper focuses on adaptive filtering techniques for parameter identification of Hammerstein systems and output prediction of nonlinear systems. By formulating the underlying filtering problem as a recursive bilinear least-squares optimization with the non-convex feasible region constraint, we develop a recursive non-convex projected least-squares (RncPLS) algorithm based on alternating direction method of multipliers (ADMM). The RncPLS algorithm alternates between implementing ridge regression and projecting on the non-convex feasible set, which successively refines the system parameters. The convergence and accuracy properties of the proposed RncPLS algorithm are theoretically investigated. Moreover, extensive simulation results in the context of system identification, nonlinear predication, and acoustic echo cancellation, are also included to demonstrate the performance characteristics of the proposed algorithm.