Updating Optimal Coefficients and Selected Observations Affine Projection is an effective way to reduce the computational and power consumption of this algorithm in the application of adaptive filters. On the other hand, the calculation of this algorithm can be reduced by using subbands and applying the concept of filtering the Set-Membership in each subband. Considering these concepts, the fir...

In this paper, we develop a numerically efficient scheme for setmembership prediction and filtering for discrete-time nonlinear systems, that takes into explicit account the effects of nonlinearities via local second-order information. The filtering scheme is based on a classical prediction/update recursion that requires at each step the solution of a convex semidefinite optimization problem. T...

This paper deals with conditional central estimators in a set membership setting. The role and importance of these algorithms in identification and filtering is illustrated by showing that problems like worst-case optimal identification and state filtering, in contexts where disturbances are described through norm bounds, are reducible to the computation of conditional central algorithms. The c...

This paper shows that optimal set-membership filtering (SMF) is identical to minimax ( ) filtering, if optimal SMF corresponds to the smallest error bound specification that leads to a non-empty feasible solution. An adaptive minimax filtering algorithm that uses optimal quadratic approximations to the minimax cost function is proposed for adaptive implementation of optimal SMF. The proposed al...

This paper deals with adaptive solutions to the socalled set-membership filtering (SMF) problem. The SMF methodology involves designing filters by imposing a deterministic constraint on the output error sequence. A set-membership decision feedback equalizer (SM-DFE) for equalization of a communications channel is derived, and connections with the minimum mean square error (MMSE) DFE are establi...

In this paper, we address the robustness, in the sense of l2-stability, of the set-membership normalized least-meansquare (SM-NLMS) and the set-membership affine projection (SM-AP) algorithms. For the SM-NLMS algorithm, we demonstrate that it is robust regardless of the choice of its parameters and that the SM-NLMS enhances the parameter estimation in most of the iterations in which an update o...

We introduce a new linearly constrained minimum variance (LCMV) beamformer that combines the set-membership (SM) technique with the conjugate gradient (CG) method, and develop a low-complexity adaptive filtering algorithm for beamforming. The proposed algorithm utilizes a CG-based vector and a variable forgetting factor to perform the dataselective updates that are controlled by a time-varying ...

This paper addresses the set-membership filtering problem for a class of discrete time-varying systems with sensor saturation in the presence of unknown-but-bounded process and measurement noises. A sufficient condition for the existence of set-membership filter is derived. A convex optimisationmethod is proposed to determine a state estimation ellipsoid that is a set of states compatiblewith s...