Technical Report 2001-006

Identification of Continuous-Time AR Processes by Using Limiting Properties of Sampled Systems

Erik K. Larsson and Torsten Söderström

March 2001

Consider the problem of estimating the parameters in a continuous-time autoregressive (CAR) model from discrete-time samples. In this paper a simple and computationally efficient method is introduced, and analyzed with respect to bias distribution. The approach is based on replacing the derivatives by delta approximations, forming a linear regression, and using the least squares method. It turns out that consistency can be assured by applying a particular prefilter to the data; a filter that is easy to compute and is only dependent on the order of the continuous-time system. As a side effect several general properties for discrete-time autoregressive moving average (ARMA) systems originating from sampled CAR-processes will also be presented. Finally, the introduced method is compared to other methods in some simulation studies.

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