Sparsity regularized recursive total least-squares

This paper introduces a new family of recursive total least-squares (RTLS) algorithms for identification of sparse systems with noisy input vector. We regularize the RTLS cost function by adding a sparsifying term and utilize subgradient analysis. We present ℓ1ℓ1 norm and approximate ℓ0ℓ0 norm regularized RTLS algorithms, and we elaborate on the selection of algorithm parameters. Simulation results show that the presented algorithms outperform the existing RLS and RTLS algorithms significantly in terms of mean square deviation (MSD). Furthermore, we demonstrate the virtues of our automatic selection for regularization parameter when ℓ1ℓ1 norm regularization is applied.