Abstract
In the present paper, we propose a computationally efficient order test which first determines the process order and then the noise order. The process order is determined comparing the instrumental residuals derived from the input instrumental product moment matrix. The noise order is evaluated by the statistics yielded from the cross-covariances of the observed output and the composite noise which is a linear combination of the noise with the coefficient of the process parameter.
The noise covariances may be the useful information for determination of the noise order. Under the situation required for the process identification, however, the estimates of the noise covariances can not give the proper order because of the poor accuracy of them, even applying them to the order test. We, therefore, take advantage of the cross-covariance estimates of the composite noise and observed output since they have good accuracy for the purpose. We calculate the order test statistics from them by the recursive algorithm and determine the order.
