Improved simple set‐membership affine projection algorithm for sparse system modelling: Analysis and implementation

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Abstract
Recently, the improved simple set‐membership affine projection (IS‐SM‐AP) algorithm has been proposed in order to exploit sparsity in system models. Although its update equation resembles that of the set‐membership affine projection (SM‐AP) algorithm, the IS‐SM‐AP algorithm has two fundamental advantages over the SM‐AP algorithm: (i) it can exploit sparsity in system models and (ii) its computational complexity is lower. Up to now, the properties of this algorithm have been addressed only through numerical simulations, and no analytical study has been presented. To fill this gap, in this study, the authors analyse the steady‐state mean squared error of the IS‐SM‐AP algorithm using the energy conservation method. Furthermore, some important implementation issues are addressed, and a time‐varying parameter for the discard function is proposed. Finally, the authors present numerical results corroborating the theoretical analysis and the effectiveness of the proposed time‐varying parameter.

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