Online Sparse Volterra System Identification Using Projections onto Weighted l1 Balls

Tae-Ho JUNG  Jung-Hee KIM  Joon-Hyuk CHANG  Sang Won NAM  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E96-A   No.10   pp.1980-1983
Publication Date: 2013/10/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E96.A.1980
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Sparsity-aware Signal Processing)
adaptive filtering,  sparse Volterra systems,  identification,  projections,  

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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.