Comparison of least mean fourth and least mean square tracking

The paper provides new results concerning the tracking performance of the least mean fourth algorithm in comparison with that of the least mean square algorithm. The analysis is done in the context of tracking a Markov plant with a white Gaussian input. The comparison is done in terms of the minimum mean square deviation attained by each algorithm over the stability range of its step-size. Gaussian, uniform, and binary distributions of the plant noise are considered. Conditions that make one algorithm outperform the other are determined. Analytical results are supported by simulations.