Applied Research on Signal Processing Deducing by Method of Completing the Squares of Least Square Estimation
Eryan Zhang, Linlin Gao · Advances in engineering research/Advances in Engineering Research · 2015
The method of completing the squares is a method that is used to transform a math formula directionally in order to obtain a perfect square formula by making rational use of "splitting items" and "adding items".Least square estimation consists of the method of projection, the method of derivative and the method of completing the squares.By comparing and analyzing the three methods, the conclusion has been drawn that the method of completing the squares is the best, as it provides the necessary conditions in which the objective function can reduce to minimum.Such methods as solving Wiener filtering and system identification have been taken as examples to illustrate that not only optimal estimation but also the extreme value of the objective function can be obtained if the method of completing the squares is applied rationally into solving problems of least squares.