Novel Sparse Algorithms based on Lyapunov Stability for Adaptive System Identification
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Adaptive filters are extensively used in the identification of an unknown system. Unlike several gradient-search based adaptive filtering techniques, the Lyapunov Theory-based Adaptive Filter offers improved convergence and stability. When the system is described by a sparse model, the performance of Lyapunov Adaptive (LA) filter is degraded since it fails to exploit the system sparsity. In this paper, the Zero-Attracting Lyapunov Adaptation algorithm (ZA-LA), the Reweighted Zero-Attracting Lyapunov Adaptation algorithm (RZA-LA) and an affine combination scheme of the LA and proposed ZA-LA filters are proposed. The ZA-LA algorithm is based on ℓ1-norm relaxation while the RZA-LA algorithm uses a log-sum penalty to accelerate convergence when identifying sparse systems. It is shown by simulations that the proposed algorithms can achieve better convergence than the existing LMS/LA filter for a sparse system, while the affine combination scheme is robust in identifying systems with variable sparsity.
KeywordsSparse system identification, Lyapunov adaptive filter (LA), ℓ1-norm, Zero-attracting LA, Reweighted ZA-LA, Affine combination, Convergence, Mean square deviation, Mean square error
Document typePeer reviewed
Document versionFinal PDF
SourceRadioengineering. 2018 vol. 27, č. 1, s. 270-280. ISSN 1210-2512
- 2018/1