Identification of Stochastic Continuous-time Systems : Algorithms, Irregular Sampling and Cramér-Rao Bounds

Abstract: The problem of identifying continuous-time systems is of fundamental interest in various areas, such as astrophysics, economics, control and signal processing. The most obvious reason for working with continuous-time models is that most physical systems are inherently continuous in time. Therefore, the parameters in the models often have a physical interpretation.The unifying theme of this thesis is identification of continuous-time stochastic systems using discrete-time data. Firstly, a thorough introduction to the topic is given. Basic concepts are described and previous results in the field are stated. A detailed description of various methods for identifying continuous-time systems is also provided. Secondly, some specific problems concerning identification of continuous-time autoregressive moving average (CARMA) processes, and continuous-time autoregressive (CAR) processes are studied.The effects of sampling a CARMA process are examined in detail. For example, more precise expressions than those available in the literature for how the zeros are transformed under sampling are derived. These results are then use in order to develop some simple schemes for estimating the parameters of CAR models. The more difficult problem of estimating the parameters of CARMA models is also treated. Irregular sampling is another major topic of this thesis. Some of the existing methods for identifying CAR processes are extended to handle the case of unevenly sampled data. The methods are computationally very efficient compared to standard methods for handling unevenly sampled data. Finally, the problem of computing the CRB for estimating the parameters of CAR and CARMA models, given arbitrary sampling patterns, is considered.