Application of multiple regression analysis to identification of time-varying linear dynamic systems

A technique for determining the dynamic response characteristics of time-varying linear systems is presented. A model composed of a parallel connection of filters whose impulse responses are orthogonalized exponential functions is used. The input to the system is fed to each of the filters. The coefficients of linear regression of the system output on each of the filter outputs are determined. Time-varying characteristics are measured by determining successively the coefficients from short samples of the input and output signals of the system. Many of the statistical properties of regression coefficients are known and can be used to estimate the length of sample of input and output signals required to determine the coefficients with given variance. The measurement technique has been implemented on a high speed digital computer. Results obtained by applying the technique to measurement of a variety of digitally simulated filters and to measurement of human pilot control characteristics are presented.