Adaptive sparse Volterra system identification with ℓ0‐norm penalty

This paper considers the adaptive identification of sparse Volterra systems. Based on the sparse nature of the Volterra model, a new cost function is proposed and a recursive method is derived for the estimation of Volterra kernel coefficients. Specifically, we exploit the system sparsity by incorporating an ℓ0‐normℓ0‐norm constraint in the standard recursive least squares (RLS) cost function and an approximation of ℓ0‐normℓ0‐norm is used to develop the recursive estimation method. Superior to the traditional RLS algorithm, our approach does not require a long data record to obtain a reliable estimation. Furthermore, compared to the existing methods, the proposed approach achieves comparable steady-state performance and lower computational complexity. The effectiveness of our method is illustrated by computer simulations.

► We investigate the identification of sparse Volterra systems.
► The system sparsity is exploited by penalizing the cost function with l0 norm.
► A low complexity adaptive algorithm is developed to estimate sparse kernels.