Die Bestimmung der 0rdnung der Prozess-und Rauschdynamik Oape eaeaae nopaaoic aaa a a apotteeca tay a A. J. W. VAN DEN BOOMt and A. W. M. VAN DEN ENDEN:~ The determination of the order is an essential part of the identification of unknown processes, and for several parameter estimation procedures the knowledge of the orders of both process and noise dynamics is necessary.
S'mm'T--In most papers on parameter estimation schemes the order of the process under study is assumed to he 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 hehaviour 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 .~str/im-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.