Optimal identification of regression-type processes under adaptively controlled observations

The paper presents a new approach for the design and analysis of adaptive systems for the optimal identification of physical processes and signals described by linear regression-type equations. Contrary to the traditional methods, a compound model of the observed process is proposed. This model describes an unobservable process that is subject to identification and the observing device (sensor) separately. The introduced adaptive model of the sensor with bounded linear range of its characteristic is more general and adequate than the commonly used ones. It is shown that optimal adaptive control of the sensor parameters and its fit to the statistics of the identified process significantly improve the accuracy of the parameter estimates and increase their convergence rate. Results of the theoretical part of the paper are illustrated by a simple analytic example and confirmed via simulation