Fast learning set theoretic estimation

This paper addresses set theoretic estimation used for online learning in an adaptive filtering context. The advantages of set theoretic estimation over the traditional point estimation are shown, among which we highlight the capability of reducing the computational burden leading to energy saving. The set-membership affine projection (SM-AP) algorithm is the main framework because it generalizes many of the set theoretic algorithms, besides having a popular point estimation counterpart for benchmarking, viz. the affine projection (AP) algorithm. In addition, we discuss the effects of the design of the involved sets in convergence speed and steady-state MSE. Each iteration of the SM-AP algorithm exploits the intersection of constraint sets and, although any point in this set is acceptable, some of its parts should be avoided during the update. Moreover, we propose a new configuration for the error constraints, which leads to low steady-state MSE, high convergence speed, and low probability of update.