Based on the fractional lower order statistics theory,the deterministic averaging method and two lemmas introduced and proved,this paper gives an analysis of the convergence property of the DLMP algorithm theoretically.

Considering the effect of α-stable distributed noises for the classical second order statistics,combining fractional lower order statistics theory and chirp Z transformation(CZT),a novel multi-source time delay estimation method in impulsive noise environment is proposed.

According to the theory of the fractional lower order statistics and the characteristics of ship radiate noises,this paper proposed a new noise model of underwater acoustic signals,recalled general LMS metnod,analyzed performance degradation reason for non-gaussian noise model,and presented the fractional lower order lp-norm based approaches of adaptivef filter for underwater acoustic signals.

The fractional lower order cyclic statistics and its application in time delay estimation under impulsive noise conditions;

The fractional lower order statistics signal is one kind of random signal which contains the Gaussian signal and applies to much wide areas than the Gaussian signal.