Block-Sparsity Log-Sum-Induced Adaptive Filter for Cluster Sparse System Identification

Abstract

In this work, an effective adaptive block-sparsity log-sum least mean square (BSLS-LMS) algorithm is proposed to improve the convergence performance of cluster sparse system identification. The main idea of the proposed scheme is to add a new block-sparsity induced term into the cost function of the LMS algorithm. We utilize the 1 norm of adaptive tap weights and log-sum as a mixed constraint, via optimizing the cost function through the gradient descent method, the proposed adaptive filtering method can iteratively move the identified signals towards the optimal solutions, and finally identify the unknown system accurately. The cluster-sparse system response, with block length and arbitrary average sparsity, is generated by a Markov-Gaussian (M-G) model. For the white Gaussian input data, the theoretical formulas of the steady-state mis-adjustment and convergence behaviors of the BSLS-LMS are derived in a general sparse system and a block sparse system, respectively. Numerical experiments demonstrate that the proposed adaptive BSLS-LMS algorithm achieves much better convergence behavior than conventional sparse signal recovery solutions. The experimental study also verifies the consistency between the simulation results and the theoretical analysis.

Adaptive PI Control Strategy for Optimal Microgrid Autonomous Operation

“…In addition, several techniques have been proposed in BS systems identification to minimize convergence time and improve algorithm resilience. For such applications, stochastic gradient descent techniques have been proposed [32].…”

Recovery Analysis of Log-Sum Minimization Under Mutual Coherence Condition

“…Throughout this paper, all the problems are discussed based on the assumption that the columns of Φ are standardized to have unit ℓ 2 norm. Since the optimization ( 1) is a NP-hard problem that has computational complexity growing exponentially with the signal dimension, many improved efficient methods have been proposed recently, such as, orthogonal matching pursuit (OMP) [4], the log-sum (q= 1, 2) minimization [5][6][7][8][9] min…”

“…Meanwhile, the work proposed insight on the advantages and drawbacks of ℓ 1 relaxation methods such as BPDN and the Dantzig selector, as opposed to greedy approaches such as OMP and thresholding. In [27] and [7], Shen and Fang respectively proved the existence of global minimum for the log-sum minimization without noise as q equal to 1 and 2. However, Shen considered the RIP condition, where the constant δ 3k > 0 is harsh and unsolvable.…”