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There is a growing interest in adaptive filtering solutions whose learning processes are data selective, bringing about computational reduction and energy savings while improving estimation accuracy. The set-membership affine projection algorithms are a representative family of algorithms including data-selection mechanisms. The update process of these algorithms depends on the choice of a constraint...
We analyze two algorithms, viz. the affine projection algorithm for sparse system identification (APA-SSI) and the quasi APA-SSI (QAPA-SSI), regarding their stability and steady-state mean-squared error (MSE). These algorithms exploit the sparsity of the involved signals through an approximation of the l0 norm. Such approach yields faster convergence and reduced steady-state MSE, as compared to algorithms...
We propose two versions of affine projection (AP) algorithms tailored for sparse system identification (SSI). Contrary to most adaptive filtering algorithms devised for SSI, which are based on the l1 norm, the proposed algorithms rely on homotopic l0 norm minimization, which has proven to yield better results in some practical contexts. The first proposal is obtained by direct minimization of the...
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...
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