On the equivalence of Kalman filtering and least-squares estimation

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• 作者：E. Mysen
• 关键词：Kalman filter ; Least ; squares method ; Normal equations ; Power law noise
• 刊名：Journal of Geodesy
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：91
• 期：1
• 页码：41-52
• 全文大小：
• 刊物类别：Earth and Environmental Science
• 刊物主题：Geophysics/Geodesy; Earth Sciences, general;
• 出版者：Springer Berlin Heidelberg
• ISSN：1432-1394
• 卷排序：91

文摘

The Kalman filter is derived directly from the least-squares estimator, and generalized to accommodate stochastic processes with time variable memory. To complete the link between least-squares estimation and Kalman filtering of first-order Markov processes, a recursive algorithm is presented for the computation of the off-diagonal elements of the a posteriori least-squares error covariance. As a result of the algebraic equivalence of the two estimators, both approaches can fully benefit from the advantages implied by their individual perspectives. In particular, it is shown how Kalman filter solutions can be integrated into the normal equation formalism that is used for intra- and inter-technique combination of space geodetic data.