Robust Regularized Recursive Least M-estimate Algorithm for Sparse System Identification

The l(0)-norm regularized recursive least square (l(0)-RLS) algorithm has excellent performance in sparse system identification scenarios. However, its convergence performance will be degraded when working in an environment with impulsive noise. To overcome the drawback, a robust regularized recursive least M-estimate (R3LM) algorithm is proposed in the letter. The algorithm employs a robust M-estimate cost function with a regularized convex term of the estimates of unknown system parameters. A normal equation is derived for minimizing the cost function. In order to solve the normal equation with lower computational complexity, the weight vector updating formula is obtained by the recursive method. Two convex functions are used to deduced two R3LM algorithms, called the l(1)-R3LM algorithm and the l(0)-R3LM algorithm. Computer simulations indicate that the proposed R3LM algorithm has the ability to work in the environment with impulsive noise and they have better convergence performance than the RLM algorithm.