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Title: MA parameter estimation using higher-order cumulant statistics
Author: Stogioglou, Achilleas G.
Awarding Body: University of Edinburgh
Current Institution: University of Edinburgh
Date of Award: 1996
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The ability of higher-order statistics to preserve phase information makes them particularly useful in the study of non-Gaussian stationary linear processes. This thesis presents some new results in the estimation of the parameters of MA models, from the cumulants of the output processes. New general relationships between the output cumulants and the system parameters are presented. These relationships are used to develop new system identification methods which use only third-order or only fourth-order cumulants. Both least squares and recursive versions of the system identification algorithms are presented. The identifiability of the algorithms is formally proved and asymptotic performance expressions are derived. The issues of MA model order selection and ARMA parameter estimation are also discussed. In many applications the primary objective is the estimation of the inverse filter coefficients. New general relationships are presented which involve the output cumulants and the inverse filter coefficients. Based on these relationships, a unified description of existing deconvolution methods is presented and new deconvolution methods based on fourth-order cumulants or on a combination of second- and fourth-order cumulants are developed. Finally, this thesis investigates properties that characterise sets of numbers as being the cumulants of some MA model. This problem is easier to analyse if the numbers are organised in a matrix form and the properties are expressed using matrix theoretical notions such as the rank of a matrix and the features of linear structured matrices. Because of estimation errors sets of sample cumulants are not real cumulants of some MA model. Based on the characteristic properties of sets of cumulants, this thesis presents an iterative composite property mapping algorithm which maps the sample cumulants to a set of enhanced cumulants. If convergence is achieved the enhanced cumulants are true cumulants of some MA model. If convergence has not been achieved, the enhanced cumulants are "nearer" to a set of true MA cumulants than the original set of sample cumulants was. It is shown that when the enhanced cumulants are used for parameter estimation, they can improve the performance of parameter estimation algorithms.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available