The problem of identifying continuous-time systems is of fundamental interest in various areas, such as, astrophysics, economics, control and signal processing. Over the years there has been an extensive research going on in this field, which has resulted in numerous publications. The most obvious reason for working with continuous-time systems is that most physical systems are inherently continuous in time. Therefore, the parameters in the models often have a physical interpretation.
In this thesis some specific problems concerning identification of continuous-time autoregressive (CAR) processes are studied. The main approach is based on replacing the differentiation operator with some approximations and forming a discrete-time linear regression model. The continuous-time system parameters are then obtained by using the least squares method. It is, however, well known that this approach will result in biased estimates unless some modifications are introduced.
The first part of the thesis explores the possibility to extend some of the existing methods for identifying CAR-processes, using the approach described above, to the case of unevenly sampled data. Some computationally very efficient methods are presented.
In the second part of the thesis a simple method for computing the CRB for CAR-processes, given arbitrary sampling patterns, is introduced. Several simulation studies are considered with some interesting results.
In the third part of the thesis the problem of identifying CAR-processes, using limiting properties of sampled stochastic systems, is addressed. The presented method is intuitively clear and numerically sound, it is based on some new results regarding sampling of CAR-processes that are presented as well.
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