Fast and approximative estimation of continuous-time stochastic signals from discrete-time data

A fast and approximative method for estimating continuous-time stochastic disturbance signals, described as continuous-time autoregressive moving average processes, from discrete-time data is presented. First, it is shown how these processes can be regarded as continuous-time autoregressive processes and the relation between the two types of processes is derived. The relation is then used for mapping estimated autoregressive parameters from an instrumental variable approach onto autoregressive moving average parameters. The procedure provides a solution to the estimation problem that preserves the continuous-time parameterization.