The direct least mean p-norm (DLMP) algorithm is a robust algorithm for time delay estimation under both Guassian and fractional lower order α -stable noise conditions.Based on an important theorem of fractional lower order statistics

this paper gives an integrated mathematical analysis of the convergence property of the DLMP algorithm

including the convergence property of the cost function and the appropriate selection of the convergence parameter μ .In the case of

p

=2

it is presented that DLMP algorithm keeps consistent with DLMS algorithm

which is based on second order statistics

involving the cost function

the unbiasness of the estimate and the selection of the convergence parameter.Therefore

this paper proves in theory that DLMP algorithm is a generalization of DLMS algorithm in α -stable distribution noisy environments.