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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
Publication Date: 2013/10/01
Online ISSN: 1745-1337
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.