Error analysis of hydrographic positioning and the application of least squares.

Abstract

Repeatable accuracy of hydrographic positioning was examined in terms of the two-dimensional normal distribution function which results in an elliptical error figure. The error ellipse was discussed, and two methods for conversion of elliptical errors to circular errors were given. These methods are "circle of equivalent probability" and "root mean square error" (d ) . Using the d error concept, repeatable accuracy of ranging, azimuthal, and hyperbolic systems was evaluated, and methods were developed to draw repeatability contours for those systems. A brief theoretical background was provided to explain the method of least squares and discuss its application to hydrographic survey positioning. For ranging, hyperbolic, azimuthal, sextant angle, and Global Positioning System the least squares observation equations were developed. Specific examples were constructed to demonstrate the capabilities of this data adjustment technique when applied to redundant position observations.