Zero attracting recursive least square algorithms

Hong, Xia, Gao, Junbin and Chen, Sheng (2017) Zero attracting recursive least square algorithms. IEEE Transactions on Vehicular Technology, 66 (1), 213-221. (doi:10.1109/TVT.2016.2533664).

Record type: Article

Abstract

The $l_1$-norm sparsity constraint is a widely used technique for constructing sparse models. In this contribution, two zero-attracting recursive least squares algorithms, referred to as ZA-RLS-I and ZA-RLS-II, are derived by employing the $l_1$-norm of parameter vector constraint to facilitate the model sparsity. In order to achieve a closed-form solution, the $l_1$-norm of the parameter vector is approximated by an adaptively weighted $l_2$-norm, in which the weighting factors are set as the inversion of the associated $l_1$-norm of parameter estimates that are readily available in the adaptive learning environment. ZA-RLS-II is computationally more efficient than ZA-RLS-I by exploiting the known results from linear algebra as well as the sparsity of the system. The proposed algorithms are proven to converge, and adaptive sparse channel estimation is used to demonstrate the effectiveness of the proposed approach.

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