Applied Research on Signal Processing Deducing by Method of Completing the Squares of Least Square Estimation

DOI

10.2991/cmfe-15.2015.188How to use a DOI?

Keywords

least square method; method of completing the squares; Wiener filtering; system identification ;application

Abstract

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.

Copyright

© 2015, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Eryan Zhang
AU  - Linlin Gao
PY  - 2015/07
DA  - 2015/07
TI  - Applied Research on Signal Processing Deducing by Method of Completing the Squares of Least Square Estimation
BT  - Proceedings of the International Conference on Chemical, Material and Food Engineering
PB  - Atlantis Press
SP  - 801
EP  - 804
SN  - 2352-5401
UR  - https://doi.org/10.2991/cmfe-15.2015.188
DO  - 10.2991/cmfe-15.2015.188
ID  - Zhang2015/07
ER  -