Identification of nonstationary parametric models using higher-order statistics

This thesis is concerned with parametric modelling techniques based on the higher order statistics (HOS) of output measurements from both stationary and nonstationary systems. Finite-dimensional parameter models, e.g. ARMA models, are extensively used in many areas of signal processing. There are advantages and drawbacks in the use of such models for the analysis of signals. Such estimators can give high resolution and can succinctly characterise a signal via few parameters. However, one has to select the structure of the model. Since the correlation carries no phase information, HOS have become increasingly popular in several areas of system identification and signal processing. HOS based algorithms are also robust to additive Gaussian noise.Initially this thesis considers the problem of estimating the parameters of a stationary ARMA system from noisy observations of its output in response to excitation by an unobservable independent, identically distributed sequence. Various algorithms are classified are compared in terms of complexities. Further, enhancements to existing algorithms are presented. The performance of the estimation algorithms is dependent upon accurate knowledge of the system order. Several algorithms for system order determination are considered and modified. Then the estimation of parameters of a time-varying linear model is considered. It is shown that a time-varying ARMA model of single-input single-output system is equivalent to a time-invariant ARMA model of multi-input multi-output system. The time varying parameters of the system are characterised via a set of basis functions. Novel methods for the parameter estimation task are developed based on the concepts of HOS. Throughout these studies, the robustness of the HOS based algorithms to additive Gaussian noise is demonstrated.Finally the application of these techniques to several nonstationary signals (a machine fault signal, a dispersive signal, a bat echolocation call, and a speech signal) is performed. The results are compared to conventional non-parametric (spectrogram and Wigner-Ville distribution) and parametric (moving window time-invariant model and basis function time-variant model) time-frequency representations. The application of time varying models to these signals demonstrates the utility of this approach.