On Finding a Best Linear Approximation to System Dynamics from Short Duration Samples of Operating Data†

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Abstract
A method for the determination of a linear passive system, which most nearly approximates (in the sense that it yields a minimum mean square error) the dynamic behaviour of a given physical system, is described. The method is applicable to situations in which )a)the system investigated has N input variables defining M output variables ; (b)data is recorded at each of the input and output terminals during some finite time interval 0≤t≤1, which represents a short sample of a much longer past history. Unlike methods already developed, the techniques used here do not require any appeal to statistical properties such as stationarity or ergodicity of the data, neither is it necessary to attempt to find a realistic estimate of correlation or spectral density functions. It is suggested that the method described may help to decide whether,. in a given trial, the best approximation may be expected to be sensitive to changes in the sample of operating data fitted.

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