Estimation of continuous-time AR process parameters from discrete-time data

The problem of estimating continuous-time autoregressive process parameters from discrete-time data is considered The basic approach used here is base d on replacing the derivatives in the model by discrete-time differences, f orming a linear regression, and using the least squares method. Such a proc edure is simple to apply, computationally flexible and efficient, and map h ave good numerical properties. It is known, however, that all standard appr oximations of the highest order derivative. such as repeated use of the del ta operator, gives a biased feast squares estimate, even as the sampling in terval tends to zero, some of our previous approaches to overcome this prob lem are briefly reviewed. Then, two new methods, which avoid the shift in o ur previous results, are presented. One of them, which is termed bias compe nsation, is computationally very efficient. Finally, the relationship of th e above least squares approaches with an instrumental variable method is in vestigated. Comparative simulation results are also presented.