Robust adaptive estimator based on a novel objective function—Using the L1-norm and L0-norm

To fully take advantage of LMS, LMAT, and SELMS, a novel adaptive estimator using the L1-norm and L0-norm of the estimated error is proposed in this paper. Then based on minimizing the mean-square deviation at the current time, the optimal step-size, parameters $\delta$ and $\theta$ of the proposed adaptive estimator are obtained. Besides, the stability and computational complexity of the mean estimation error is analyzed theoretically. Experimental results (both simulation and real mechanical system datasets) show that the proposed adaptive estimator is more robust to input signals and a variety of measurement noises (Gaussian and non-Gaussian noises). In addition, it is superior to LMS, LMAT, SELMS, the convex combination of LMS and LMAT algorithm, the convex combination of LMS and SELMS algorithm, and the convex combination of SELMS and LMAT algorithm. The theoretical analysis is consistent with the Monte-Carlo results. Both of them show that the adaptive estimator has an excellent performance in the estimation of unknown linear systems under various measurement noises.