A preliminary algorithm for determining the order of a linear stochastic dynamic system

This paper presents a preliminary algorithm for determining the orders of a linear stochastic dynamic system solely from the observation of the system output. The scalar transfer function of the system contains both poles and zeros, however, no a priori information is available about the numbers and values of these poles and zeros. The driving input of this system is assumed to be white. Such a system is called a mixed type process, since it is a combination of the autoregressive (all-pole) and the moving-average (all zero) processes. The objective of this algorithm is thus to determine the number of poles (order of the autoregressive portion of the process) and the number of zeros (order of the moving-average portion of the process) of the mixed type process. The algorithm suggested in this paper is based on a two stage process: first take those output correlations which follow a repetitive pattern to determine the order of the autoregressive portion, then proceed to estimate the autoregressive parameters and lower the index of the correlation until the significant deviation from the repetitive pattern is observed, the order of the moving-average then can be determined.