On The Use Of Second- And Higher-order Inverse Statistics

Inverse higher-order statistics of non-Gaussian, stationary random processes are introduced in this paper, as an extension of their 2nd- order counterparts, known as inverse correlations. Their use in system identification, and specifically in model order determination and parameter estimation problems, is investigated. Estimation procedures are proposed for obtaining sample estimates of inverse statistics and the corresponding (poly)spectra. The algorithms derived are illustrated by simulation examples, involving inverse 2nd- and 3rd-order statistics.