Abstract
Least squares is an important method for solving linear fitting problems and quadratic optimization problems. This paper explores the properties of the least squares methods and the multi-innovation least squares methods. It demonstrates lemmas and theorems about the least squares and multi-innovation least squares parameter estimation algorithms after reviewing and surveying some important contributions in the area of system identification, such as the auxiliary model identification idea, the multi-innovation identification theory, the hierarchical identification principle, the coupling identification concept and the filtering identification idea. The results of the least squares and multi-innovation least squares algorithms for linear regressive systems with white noises can be extended to other systems with colored noises.
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