A Robust Stable Laplace Continuous Mixed Norm Adaptive Filter Algorithm

In this letter, a novel adaptive algorithm called Laplace continuous mixed norm (LCMN) is introduced, which utilizes a new continuous mixed p-norm (CMPN) technique. The CMPN algorithm incorporates an exponential weighting function, which is shown to improve the stability of the estimation process (i.e., CMPN shows less residual of error for a dc voltage estimation) compared with CMPN with uniform weighting function and other algorithms. The name "Laplace" is chosen for the LCMN algorithm due to the similarities it shares with the Laplace transform, which are utilized in the derivation of the algorithm. In addition, the mean convergence of LCMN is proven, and a sufficient condition for step-size value is determined to ensure mean convergence. Simulation results in impulsive noise environments also support the higher stability of LCMN compared with other algorithms (especially CMPN with uniform weight), albeit with a tradeoff of a slower convergence rate.