$$\ell _1$$ℓ1-regularized recursive total least squares based sparse system identification for the error-in-variables

In this paper an $$\ell _1$$ℓ1-regularized recursive total least squares (RTLS) algorithm is considered for the sparse system identification. Although recursive least squares (RLS) has been successfully applied in sparse system identification, the estimation performance in RLS based algorithms becomes worse, when both input and output are contaminated by noise (the error-in-variables problem). We proposed an algorithm to handle the error-in-variables problem. The proposed $$\ell _1$$ℓ1-RTLS algorithm is an RLS like iteration using the $$\ell _1$$ℓ1 regularization. The proposed algorithm not only gives excellent performance but also reduces the required complexity through the effective inversion matrix handling. Simulations demonstrate the superiority of the proposed $$\ell _1$$ℓ1-regularized RTLS for the sparse system identification setting.