Following a saturation point of advances in spectral estimation, the last decade has witnessed a resurgence in research and applications of higher-order statistics (HOS) to address the following 'non' topics in signals and systems: non-Gaussianity, non-minimum phase, noncausality, non-linearity , non-additivity and non-stationarity . HOS is a rather generic term often used to encompass moments, cumulants and polyspectra of order greater than two, thereby generalizing the traditional second-order statistical information offered by correlations and spectra. They have found application in: time delay and Doppler estimation for sonar and radar, reconstruction of astronomical objects from photon-limited frames in astronomy, imaging through turbulence, seismic deconvolution and blind channel equalization, separation of signal mixtures received by sensor arrays, detection and classification of non-Gaussian signals in Gaussian noise, retrieval of coupled harmonics, nonlinear ocean wave interactions, analysis of chaotic systems and biosignal processing.
The roots of HOS go back to Kolmogorov and the pioneering work of Eastern European (Leonov, Shiryaev, Sinai) and North American statisticians in the 1960s (Rosenblatt, Tukey, Brillinger).'s2 Scattered contributions appeared in the optical and physical sciences, but signalprocessing and systems communities picked up HOS interest in the 1980s. Since then there have been three biannual international five special issues devoted to this subject"-" and a number of tutorial treatments"-" (see also Reference 18 for a comprehensive bibliography).
The present special issue is concerned with recent advances in HOS-based detection, input-output system identification of linear and nonlinear systems, blind identification and time series modelling, identification of closed loop systems and implementation issues. The emphasis is on adaptive algorithms-a direction largely ignored by existing collections despite its importance for on-line application of HOS-based approaches to real life problems. In the following we motivate each contribution, highlight its main points and attempt to discuss open problems for future research in each sub-area.