Parameter Estimation Using Least-Squares Polynomial Smoothing

This paper considers several aspects of parameter estimation using least-squares polynomial smoothing of noisy observations. These aspects are 1) the choice of estimation times, 2) the simultaneous or independent use of data, and 3) the use of a polynomial of improper degree to fit the observations. Mathematical expressions are presented for determining the significance of these aspects for any case of interest. Examples are included which show the importance of these aspects.