Abstract
In this paper, a new family of adaptive filtering algorithms is presented, which aims to combine the small misalignment resulting from the reuse of past weight vectors with the fast convergence arising from the proportionate adaptation and logarithmic cost functions. This family of algorithms is obtained as a solution to a deterministic constrained optimization problem, by using the Lagrange multipliers technique, which differs from the traditionally employed stochastic gradient technique. Two special cases are proposed, namely the improved mu-law proportionate least mean logarithmic square with reuse of coefficients (IMPLMLS-RC) algorithm and the improved mu-law proportionate least logarithmic absolute difference with reuse of coefficients (IMPLLAD-RC) algorithm. An energy conservation relationship is established, which can be employed to perform stochastic transient analyses of the proposed algorithms. Simulations in system identification and active noise control applications show the advantages of the IMPLMLS-RC and IMPLLAD-RC algorithms over the traditional LMS and LAD, and the recently proposed LMLS and LLAD, with respect to both steady-state performance and robustness against impulsive noise.
Published Version
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