Relationship Between the Ellipse Combination Method and the Perpendicular Method for Fixing

摘要

Given the proper interpretation the perpendicular method may be thought of as a version of ellipse combination. A number of observations about this relationship will be made in this memo. The sections of this memo correspond to different major points or point of views. To summarize these are: 1. Geometric interpretation of lines of bearings as ellipses. 2. Interpretation of EEPs (Error Ellipse Probable) as a geometric combination of lines of bearing in the ellipse format. 3. Algebraic version of the correspondence between the perpendicular method and ellipse combination. 4. Weighted perpendicular versus perpendicular. 5. Ellipse combination sample size implications with relation to the F statistic. 6. The statistical test for acceptance of ellipse combination applied to combination of lines of bearing.