Continuous-time AR process parameter estimation from discrete-time data

The problem of estimating continuous-time autoregressive process parameters from discrete-time data is considered. The basic approach used is based on replacing the derivatives in the model by discrete-time differences, forming a linear regression and using the least squares method. It is known, however, that all standard approximations of the highest order derivative give a biased least squares estimate even as the sampling interval tends to zero. Some of our previous approaches to overcome this problem are reviewed. Then two new methods are presented. One of them, termed bias compensation, can be easily implemented efficiently in an order recursive manner. Comparative simulation results are also presented.