A Statistical Analysis of Cross-Track Errors in a Navigation System Utilizing Intermittent Fixes

Abstract

A model is developed relating navigational instrument errors to the actual cross-track error of an aircraft. At a set of equispaced points, fixes on precisely known landmarks are obtained whose accuracy is assumed independent of the length of the flight. An optimum procedure is developed for utilizing these fixes to calibrate the compass on board the aircraft. Finally, the accuracy of arriving at a predetermined destination after the last checkpoint is evaluated. Because of the complexity of the problem, numerical calculations using the IBM 650 were used. Two interesting conclusions were reached: 1) for a fixed spacing between fixes the accuracy of arriving at the destination is improved as the length of the flight (and therefore the number of fixes taken) is increased, and 2) for a fixed length of flight, the accuracy of arriving at the destination is almost independent of the number of fixes.