Research On Adaptive LMS And LMP Hybrid Algorithms

Adaptive filter is a very powerful filter, and is an important part of statistical signal processing. It can automatically adjust the parameters according to the needs of a particular norm, eventually filtering to achieve the best results. Adaptive filtering algorithms can be divided into two kinds of linear algorithms and nonlinear algorithms. The most typical representative of the former is the least mean square (LMS) algorithm, while the latter contains the algorithm is very rich, such as the least mean forth (LMF) algorithm, the least mean p-order (LMP) algorithm, and least mean mixed norm (LMMN) algorithm. The LMS algorithm for tracking performance is better to Gaussian noise, while the LMP algorithm for tracking performance is better to the long tail of the uniform distribution of noise conditions. Based on the previous work in the literature, we investigate the LMS and LMP hybrid algorithm, which is a combination of the LMS algorithm and the LMP algorithm, and its performances of steady-state excess mean square error (MSE) and tracking mean square error (TMSE) by theoretical analysis and simulations.This paper first introduces the basic principles of the adaptive filter, and focused on the structure of the adaptive filter and adaptive filtering algorithm and the LMS algorithm and the LMP algorithm combining the obtained hybrid algorithm of LMS and LMP. The hybrid algorithm combines the LMS algorithm and the LMP algorithm with their respective advantages, and have good performance in Gaussian noise environment and evenly distributed environment. Secondly, in the steady input conditions pushdown export the LMS and LMP hybrid algorithm of the steady-state mean square error expression, and gives step should satisfy the conditions. Mean square error in steady-state tracking of non-stationary input conditions pushdown export the hybrid algorithm of LMS and LMP expression, and reached its optimal step expression. Subsequently, in the Gaussian noise conditions, the maximum step size of LMS and LMP algorithm simulation in Gaussian noise, uniformly distributed noise conditions, LMS and LMP hybrid algorithm in a stable environment and non-stationary environment steady-state performance and tracking performance of the simulation. Finally, the LMS and LMP hybrid algorithm with the LMS algorithm and the LMP algorithm tracking performance comparison.