Online Sparse Volterra System Identification Using Projections onto Weighted l(1) Balls

In this paper, online sparse Volterra system identification is proposed. For that purpose, the conventional adaptive projection-based algorithm with weighted l(1) 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(N log(2) N) sorting-operation complexity. Furthermore, sparsity-aware least mean-squares and affine projection based algorithms are also tested.This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (grant no. 2012R1A1A2005378)