Revisiting the basic issue of parameter estimation in system identification - a new approach for multi-value estimation

In this paper, we consider one of the basic estimation problem, that of identifying an unknown parameter in a given model from measurements of input/output data. The existing methods have been conceived for the estimation of the value taken by the parameter in a given functioning condition. However, there are situations where one has to provide an estimator equally valid for different values of the parameter associated with various functioning conditions (multi-value estimation problem). The application of the available techniques lead then to poor accuracy in estimation. In this paper we propose a novel approach, the two-stage approach, tailored to the multi-value estimation problem. We compare its performances with those achievable with other parameter estimation techniques such as prediction error and Kalman filter based methods. By means of a benchmark example, we spot out advantages and drawbacks of each method, by also discussing their domain of applicability. It turns that the two stage approach offers significant improvements.