The determination of the orders of process-and noise dynamics

• Authors: A. J. W. Van Den Boom;A. W. M. Van Den Enden
• Venue: Automatica (Journal of IFAC)
• Year: 1974

In most papers on parameter estimation schemes the order of the process under study is assumed to be known a priori. In many practical situations, however, this information is lacking. Consequently simple methods for the determination of the order are necessary. In this paper a description is given of five tests based on respectively: (1) the behaviour of the error function, (2) the whiteness of the residuals (correlation function), (3) the statistical independency of loss functions, (4) the behaviour of the determinant, and (5) the pole-zero cancellation effect. Some of these methods, the pole-zero cancellation, test of whiteness, and F-test are used as known, but the others are revised in such a way that a better discrimination of the order is obtained. The methods based on the behaviour of the error function and the behaviour of the determinant respectively are extended in such a way that the orders of both process- and noise dynamics are estimated separately. An extensive set of simulations of the Astrom-process is presented in order to elucidate the comparison of the different methods. It turns out that an acceptable determination of the order is possible even with a signal-to-noise ratio at the process output of - 15dB.