Estimação adaptativa de estados baseada na família de algoritmos LMS em Espaço de Estados (SSLMS)

Abstract

Through some estimation techniques, an unknown quantity of interest can be estimated, based on a set of measured data or possibly corrupted by measurement noise, being the quality of this estimate evaluated by its proximity to the true value. Filtering uses present and past observations to produce a current estimate of the unknown quantity. The structure in state space allows working with the dynamics of the system, as the algorithm LMS (Least-Mean Square) in state space SSLMS (State Space Least -Mean Square) that generates an estimated state vector, being a possible solution to the estimation problem. SSLMS outperform the tracking capability of the standard LMS, which is limited due to the assumption of linear regression model. By overcoming this constraint, SSLMS exhibits a marked improvement in tracking performance over the standard LMS and its known variants. Based on this principle, this work proposes a new variant of the adaptive filter of the LMS family in state space for estimating state variables. The proposed method, called ZA-LMS algorithm (Zero-Attracting LMS) is compared with other algorithms in the literature to evaluate performance in terms of convergence speed and tracking capacity.