Online Sparse Volterra System Identification Using Projections onto Weighted l₁ Balls

Abstract

In this paper, online sparse Volterra system identification is proposed. For that purpose, the conventional adaptive projection-based algorithm with weighted l₁ balls (APWL1) is revisited for nonlinear system identification, whereby the linear-in-parameters nature of Volterra systems is utilized. Compared with sparsity-aware recursive least squares (RLS) based algorithms, requiring higher computational complexity and showing faster convergence and lower steady-state error due to their long memory in time-invariant cases, the proposed approach yields better tracking capability in time-varying cases due to short-term data dependence in updating the weight. Also, when N is the number of sparse Volterra kernels and q is the number of input vectors involved to update the weight, the proposed algorithm requires O(qN) multiplication complexity and O(Nlog ₂N) sorting-operation complexity. Furthermore, sparsity-aware least mean-squares and affine projection based algorithms are also tested.