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Theory of Errors and Least Squares Adjustment

4763 words
20 pages

Theory of Errors and Least Squares Adjustment

Huaan Fan

ISBN 91-7170-200-8 Royal Institute of Technology (KTH) Division of Geodesy and Geoinformatics 100 44 Stockholm Sweden August 2010

Theory of Errors and Least Squares Adjustment

Huaan Fan, PhD Royal Institute of Technology (KTH) Division of Geodesy and Geoinformatics Teknikringen 72, 100 44 Stockholm, Sweden Phone: +46 8 7907340 Fax: +46 8 7907343 E-mail: hfan@kth.se URL: http://www.infra.kth.se/impgg

With 22 illustrations and 49 numerical examples

ISBN 91-7170-200-8 Copyright c 1997 by Huaan Fan All Rights Reserved Geodesy Report No. 2015 TRITA-GEOFOTO 1997:21 Printed by Universitetsservice AB, Drottning Kristinas väg 53 B, Stockholm October 1997, August 1998, August 1999, May
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. . . . . . . 1.4.4 Variance Analysis . . . . . . . . . . . . . . . . . 1.4.5 Regression Analysis . . . . . . . . . . . . . . . . 1.5 GUM-Terminology: Uncertainty in Measurement . . . . 1.6 Optimal Estimation . . . . . . . . . . . . . . . . . . . . 1.6.1 Least Squares Method . . . . . . . . . . . . . . . 1.6.2 Maximum Likelihood Method . . . . . . . . . . . 1.6.3 Minimum Error Variance Estimation . . . . . . . 1.7 Matrix Algebra and Numerical Methods . . . . . . . . . 1.7.1 Numerical Solutions of Linear Equation Systems 1.7.2 Special Identities in Matrix Algebra . . . . . . . 1.7.3 Trace of Square Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .