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A class of algorithms representing a robust variant of the proportionate normalised least-mean-square (PNLMS) algorithm is proposed. To achieve this, adaptive regularisation is introduced within the PNLMS update, with the analysis conducted for both individual and global regularisation factors. The update of the adaptive regularisation parameter is also made robust, to improve steady state performance and reduce computational complexity. The proposed algorithms are better suited not only for operation in nonstationary environments, but are also less sensitive to changes in the input dynamics and the choice of their parameters. Simulations in a sparse environment show the proposed class of algorithms offer enhanced performance and increased stability over the standard PNLMS.