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Theory of Errors and Least Squares Adjustment

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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 …show more content…

The author wishes to acknowledge all the help and encouragement from his colleagues and students. Special thanks go to TeknL George Stoimenov for proof-reading the manuscript and Mr Hossein Nahavandchi for helping draw some of the …gures. Of particular bene…t have been my students in the classes MK-92, TL-93, TL-94 and TL-95, who have worked through the raw materials as the compendium evolved. To all of them, I express my sincere thanks !

Stockholm, August 1997.

Huaan Fan

Contents
1 Fundamentals of Theory of Errors 1.1 Standard Errors and Weights . . . . . . . . . . . . . . . 1.1.1 Standard Errors . . . . . . . . . . . . . . . . . . 1.1.2 Weights and Unit-Weight Standard Error . . . . 1.1.3 Variance-Covariance Matrix and Cofactor Matrix 1.2 Error Propagation . . . . . . . . . . . . . . . . . . . . . 1.2.1 Error Propagation in Linear Functions . . . . . . 1.2.2 Error Propagation in Non-Linear Functions . . . 1.2.3 Propagation of Weights . . . . . . . . . . . . . . 1.2.4 Propagation of Cofactor Matrices . . . . . . . . . 1.3 Error Ellipse and Error Ellipsoid . . . . . . . . . . . . . 1.3.1 Point Errors . . . . . . . . . . . . . . . . . . . . . 1.3.2 Error Curve and Error Ellipse . . . . . . . . . . . 1.3.3 Probability inside Error Ellipses . . . . . . . . . 1.3.4 Error Ellipsoid . . . . . . . . . . . . . . . . . . . 1.4 Statistical Analysis . . . . . . . . . . . . . . . . . . . . . 1.4.1 Probability

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