Some Numerical Methods for Exponential Analysis with Connection to a General Identification Scheme for Linear Processes

摘要

A general identification scheme for linear processes is presented and related to some well-known exponential analysis methods such as Prony's method and the pencil-of-functions method. An elucidating explanation of the source of error (bias) for the general scheme is given. Some variations of the pencil-of-functions method are given an intense examination with some revealing numerical examples. A new exponential analysis method, called the adaptive method, is developed from the general scheme. Numerical examples of the adaptive method demonstrate its excellent performance in the presence at high levels of noise. Recommendations are made concerning the use of the adaptive method and directions for further work. (Author)