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Mathematical Considerations Pertaining to the Accuracy of Position Location and Navigation System - Part I

Report Number: NWRC-RM 34
Author: Burt, W. Allan
Author: Kaplan, David J.
Author: Keenly, Richard B.
Author: Reeves, John F.
Author: Shaffer, Francis B.
Corporate Author: Stanford Research Institute
Laboratory: Naval Warfare Research Center
Date of Publication: 1965-11
Pages: 122
Contract: Nonr-2332(00)
AD Number: AD0629609

The general case of the location of a point at the intersection of two lines-of-position involves different errors associated with each line. Also the general angle of intersection is other than 90 degrees. The distribution of error about such a point is an ellipse. A method of analysis has been developed to convert this general case to the more readily handled case of two different standard deviations along the major and minor axes of the error ellipse. Nomograms and graphs are given to facilitate computation of error probabilities. Curves are shown to indicate the geometrical magnification of error as the intersection angle departs from 90 degrees. In addition the development is shown of a total error ellipse resulting from the combination from several randomly oriented error ellipses representing error components. Numerical examples are given. Derivations of all formulas shown are given in the appendixes.

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