Identification of continuous-time ARX models using sample cross-covariances

The problem of estimating the parameters of a continuous-time ARX (CARX) process from discrete-time data is studied. In the proposed solution, an expression for the cross-covariance function between the input and the output signal of the CARX process is derived. This expression is parameterized by the unknown and searched parameters. The parameters are estimated by fitting the theoretical expression for the cross-covariance function to sample cross-covariances.