Estimation of the Order of Linear Systems
Estimation de l'ordre de syst~mes lin6aires Sch~itzung der Ordnung linearer Systeme OtteHra nopmaxa YIHHe~HbIX CHCTeM C. M. WOODSIDE
.4 comparison of three procedures for estimating the order of a linear system, in preparation for statistical identification of its parameters, indicates that one is successful with up to 30 per cent white noise amplitude on input and output signals.
Summary--When modelling a single-input, single-output system by a difference equation a value for the model order must usually be assumed, and the system order is finally determined by comparing the goodness of fit of several orders of model Ill. This paper describes three ways to test for the order of the system without first fitting coefficients to models. They give intuitive rather than rigorous statistical tests. However once the order, or a range of orders, is determined, an iterative modelling procedure such as maximum likelihood can be applied and then stronger tests for the system order can be used. There is a saving of computer effort ff some system orders can be discarded before applying the iterative technique, which uses lengthy computations. Other uses for estimation of system order by itself might include medical diagnosis, where for instance the model for a healthy lung might be a different order than that for a diseased one.
Three procedures are developed on a largely intuitive basis, using an enhancement of a measured product-moment matrix. On a Monte Carlo example they function up to 30 per cent rms noise. The principal assumption is that noise is present as added noise of known correlation structure at input and output.
n, m) DR EDR MS EMS LR NOTATION vector of non-noisy input-output data noisy input-output data product-moment matrix for inputoutput data, 2n ร 2n enhanced version of Q(s, n) second enahancement of Q(s, n) or Q(z, n) determinant ratio enhanced determinant ratio mean squared residual enhanced mean squared residual likelihood ratio. *