Parameter estimation of linear systems in the absence of process noise: (i) methods based on the least-squares principle.
Abstract:This Data Item presents a number of digital optimization techniques for the parameter estimation of linear systems. The methods presented are based on the least-squares principle and apply to system models in which process noise is assumed to be absent. The methods minimise a chosen Objective Function which is found from the square of the difference between the measured output of a chosen validation quantity and the model output of that same quantity found from the set of linear differential equations with constant coefficients known to characterise the true system behaviour. These constant coefficients contained within the system equations that are unknown, form the parameter set to be found. The techniques presented, broadly divide into those in which each of the system equations are used separately and provide a direct solution for the parameters and those in which the system equations are used as an interdependent set of differential equations providing an iterative solution for the parameters. Within these broad classes of techniques, the methods vary according to the validation quantity chosen from the available measured outputs of the system. A simple example is used to illustrate the application of each of the methods.
|Data Item ESDU 87039|