An Overview of Important Practical Aspects of Continuous-Time ARMA System Identification

Abstract

The problem of estimating the parameters in continuous-time autoregressive moving average (ARMA) processes from discrete-time data is considered. Both direct and indirect methods are studied, and similarities and differences are discussed. A general discussion of the inherent difficulties of the problem is given together with a comprehensive study on how the choice of the sampling interval influences the estimation result. A special focus is given to how the Cramér-Rao lower bound depends on the sampling interval.

Closed-loop Parametric Identification for Continuous-time Linear Systems via New Algebraic Techniques

“…It is a delicate matter to compare our theoretical techniques and results with today's parametric identification of linear continuous-time systems (see, e.g., [13,15,18,19,26,33] and the references therein), which is perhaps less developed than its discrete-time counterpart, but nevertheless makes also generally a heavy utilization of statistical methods 16 . Let us stress that all those approaches seem to rest on standpoints and therefore on mathematical tools which are rather far from ours.…”

Resolution-invariant separable ARMA modeling of images

“…Continuous-domain ARMA parameters associated (through sampling) to a given set of discrete-domain ARMA parameters are not guaranteed to exist. This stems from the fact that the sampled process introduces an ARMA for which the zeros and poles are coupled in a non-trivial manner [6]. For example, an ARMA(1,0) model with a pole at z = −0.5 has no continuous-domain ARMA(1,0) counterpart.…”

“…Continuous-domain ARMA estimators from sampled data have been suggested in the past for the one-dimensional case [6,7], requiring relatively high sampling rate values in order to avoid aliasing effects. An alternative estimator, however, was recently suggested in [8].…”

On the Unique Identification of Continuous-Time Autoregressive Models From Sampled Data

“…Taking an indirect approach (cf. [22]), the algorithm of [27] fits available sample data of a continuous-time AR(2) process with a discrete-domain ARMA(2,1) model and inverse-transforms the discretedomain parameters to their continuous-domain AR(2) counterparts. The continuous-domain zero is determined by solving a set of linear equations that stem from the partial fraction decomposition of the continuous-domain power spectrum; the imaginary parts of the poles are restricted to .…”