Fractional lower order moment based adaptive algorithms

We describe new fractional lower order moment (FLOM) based adaptive algorithms for non-Gaussian stable processes which are used to model signals of an impulsive nature. The least mean P-norm (LMP) algorithm has been shown to have better performance than the LMS algorithm for non-Gaussian stable processes. We propose two FLOM based adaptive algorithms which outperform the LMP algorithm for non-Gaussian stable processes: the median LMP algorithm and the normalized step size LMP (NSSLMP) algorithm. We also describe the generalized stochastic gradient (GSG) algorithm and the normalized GSG algorithm which are generalizations of LMS and normalized LMS algorithms. These FLOM algorithms are simulated and applied to an active noise control (ANC) problem. The results show great potential for FLOM algorithms under stable processes.