A technique of linear system identification using correlating filters

A technique for measuring the impulse response of linear processes while they are on line is described. Such an identification of process dynamics is necessary in process-adaptive control systems. A testing signal and correlating filter are employed after the manner of Turin. Such a procedure requires no multiplier, and the output of the filter is the impulse response as a continuous function of real time. To reduce accompanying output noise, the method of adding coherently the results of a number of tests made in succession is proposed. This idea is applied to the measurement of a member of an ensemble of slowly varying impulse responses. Optimum design of both the correlating filter and the necessary test signal is determined on the basis of minimum mean-square error of the resulting estimate. The optimization of the number of tests to be included in a measurement is described. The general results are applied to the case of a single, slowly time-varying process. In addition to optimum design, normalized curves showing the optimum number of tests for a particular mode of variation are included. A second application is made to the problem of measuring a member of an ensemble of fixed processes. The results of a digital computer simulation of this case are given.