Non-Convex Projection Adaptive Hammerstein Filtering

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, an algorithmic framework is developed based on recursive least-squares and Alternating Direction Method of Multipliers (ADMM). Under this framework, the solution to nonconvex constraint optimization problem can be obtained by implementing ridge regression and Euclidean projection. Simulation results in the context of system identification, nonlinear predication, and acoustic echo cancellation, reveal that the proposed algorithm has good convergence and stability, and can obtain more accurate identification and prediction results.