A Consideration on Sub-Optimal Weighting in Parameter Estimation

This paper deals with a parameter estimation method which yields the more suitable estimate of the parameter using noisy data or measured values. The estimation method is one that uses a kind of a weighted mean, and weighting at taking a weighted mean is interested in particularly. That is to say, as the grade of 'more suitable' depends upon the weighting, we can obtain the more suitable estimate by choosing the weighting coefficients suitablly. When the function which yields the estimate using finite measured values, i.e., the estimator is a particular form, sub-optimal weighting in the practical sense is discussed. Here, the concept of 'optimal' implies that the variance of the final estimate is minimum. And the particular form is one that both the denominator and the numerator of the estimator are first order formulas or second order formulas of finite measured values. And two theorems in relation to this problem are proposed and proved. Moreover, for an exsample of application of these theorems, a parameter estimation method is dealt with, which estimates the parameters of the pulse transfer function of a control system using the sampled measured values of the impulse response of that system.