RECURSIVE ESTIMATION OF 4TH-ORDER CUMULANTS WITH APPLICATION TO IDENTIFICATION

Nowadays, high order statistics (HOS) are used in many applications of signal processing. By HOS, we mean moments or cumulants of order high er than two in the time domain, and their multidimensional Fourier tra nsform called polyspectrum in the frequency domain. In real-time appli cations, it can be useful to recursively estimate the cumulants. By us ing the ergodicity assumption, we develop in this paper a recursive fo rmula for estimating the fourth-order cumulants of a real- or complex- valued, zero mean, stationary scalar stochastic process. The behaviour of this recursive estimator is illustrated in the cases of simulated stationary and non-stationary processes. We also present a least-squar es form of the C(Q,k) algorithm based on the use of this recursive for mula for identifying FIR models. The performance of this LS-C(Q,k) alg orithm is illustrated by some simulation results. (C) 1998 Published b y Elsevier Science B.V. All rights reserved.