Continuous-Time AR Model Identification: Does Sampling Rate Really Matter?

We address the problem of identifying continuous-time auto regressive (CAR) models from sampled data. The exponential nature of CAR autocorrelation functions is taken into account by means of exponential B-splines modelling, allowing one to associate the available digital data with a CAR model. A maximum likelihood (ML) estimator is then derived for identifying the optimal parameters; it relies on an exact discretization of the sampled version of the continuous-time model. We provide both time- and frequency-domain interpretations of the proposed estimator, while introducing a weighting function that describes the CAR power spectrum by means of discrete Fourier transform values. We present experimental results demonstrating that the proposed exponential-based ML estimator outperforms currently available polynomial-based methods, while achieving Cramér-Rao lower bound values even for relatively low sampling rates.