GPS Satellite Surveying, 4th Edition

Appendix AGeneral Background

This appendix provides mathematical and statistical material that is handy to have available in a classroom situation to support key derivations or conclusions given in the main chapters. The appendix begins with a listing of expressions from spherical trigonometry. The rotation matrices are given along with brief definitions of positive and negative rotations. The sections on eigenvalues, matrix partitioning, Cholesky decomposition, partial minimization, rank one update, linearization, and statistics contain primary reference material for the least-squares Chapters 2 and 3. The subsection on the distribution of simple functions of random variables primarily supports these chapters also.

A.1 Spherical Trigonometry

The sides of a spherical triangle are defined by great circles. A great circle is an intersection of the sphere with a plane that passes through the center of the sphere. It follows from geometric consideration of the special properties of the sphere that great circles are normal sections and geodesic lines. Figure A.1.1 shows a spherical triangle with corners , sides , and angles . Notice that the sequence of the elements in the respective triplets ...