This communication is devoted to the introduction and study of a new adaptive estimator of the fourth-order cumulant of a white, zero-mean stochastic process. We show that this estimator is asymptotically unbiased and normal. Moreover, we give an explicit form for the asymptotic variance. This allows us to show that the algorithm is robust with respect to the estimation of the second-order moment. This fact leads to the introduction of a simpler estimator of the cumulant which uses a single recursive equation.
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