The problem of identifying the dynamic characteristics of a process is an important one, and the various methods have been suggested and analyzed. This paper is concerned with the least squares estimates of the impulsive response of a linear process, and the validity of the method is considered.
Under the condition that the estimates are unbiased and also linear functions of the process output signals, the least squares estimates have minimum variance if the noise is white. If the noise is not white, the Markov estimates have minimum variance among all estimates, although it is not easy to obtain them because of the computational difficulties. It is true that the Markov estimates have minimum variance, but the examples in this paper show that the least squares estimates have almost the same variance as them in some situations. Two examples are given: one is the results of the experiments using an analog computer and the other is the comparison of variances of the both estimates of the process subjected to the special inputs.
The author admits that the conclusions in this paper follow from the results of the examples and will not be able to be accepted in all the cases, but he is sure that the method of process identification using the least squares estimates is a promising one.
In the remainder of this paper, an analysis of the error in the estimates is given to explain the results of the experiments on the analog computer. The theoretical analysis and the results of the experiments show clearly the fact that the error between the actual and the computed impulse or step response depends on the input and the noise characteristics.