A Method of ARX Model Estimation of Errors-in-Variables Systems

This work proposes an estimation method of ARX (autoregressive with external input) models of errors-in-variables (EIV) systems. In ARX model estimation, the input noise variance needs to be estimated in order to obtain a consistent estimate. In this method, an error criterion is proposed and the input noise variance is obtained by minimizing the loss function. The global minimum can be obtained because the optimization procedure is a one-parameter optimization problem. Consistency of the proposed parameter estimation is proved. Simulations are used to illustrate its performance.