Sampling and data analysis properties of Prony's method applied to model identification†

The advantages and limitations of Prony's (1795) method as a scheme for model identification are explored. A description of the data requirements is followed by a presentation of a theory for bounds on the sample period for data collection. The validity of the existence of a sample period window is tested by Monte Carlo simulations. Many of the results presented in this paper are compared with those obtained with regression analysis techniques. Finally, using measured data, Prony's method is applied to the identification of a dynamic model for the movement of toxic material through an aquatic microcosm.