Fast ℓ1-recursive total least squares algorithm for sparse system identification

ℓ1-RTLS has been successfully applied to the identification of a sparse system whose input and output are contaminated by noise (the error-in-variables problem). This paper proposes a fast ℓ1-regularized recursive total least squares (fast ℓ1-RTLS) algorithm for sparse system identification. The proposed algorithm is based on the minimization of the ℓ1-regularized Rayleigh quotient by the line search method and the application of the fast gain vector (FGV). Simulation results show that the proposed algorithm requires less complexity than existing ℓ1-RTLS algorithms and that the estimation performance is also equivalent to existing ℓ1-RTLS algorithms in mean square deviation (MSD).