VLF MULTI-RANGE NAVIGATION-FIX ERROR CONTOURS.
NATIONAL AVIATION FACILITIES EXPERIMENTAL CENTER ATLANTIC CITY NJ RESEARCH DI V
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A study was made of the accuracy and coverage of long-distance navigation systems which employ very-low-frequencies in the range from ten to fourteen kilocycles per second and which are based upon the determination of the distances from the vehicle to two or three ground-based stations. The fix error actually precision, for such systems, may be expressed statistically in terms of the precise bivariate equi-probability error density ellipse or by the simpler, but conservatively approximate, drms circle. This error is a function of the angles of cut of the lines of position, the standard deviation of the errors in determination of the distances ranges to the stations, and the degree of correlation of these distance determinations. An analysis is made of the errors which occur in a range determination. Estimates, applicable when computing constant-error contours isograms, are given. Error isograms are available for the two-station case but are based on a flat earth approximation. Proposed VLF systems would employ long baselines where the flat earth approximation is shown to cause appreciable discrepancies. The equations for the constant-error contours are derived based on a spherical earth as a function of baseline length and orientation where three stations are used and the angles of cut of the lines of position. Various error isograms were computed and plotted through the use of a digital computer. A number of examples are presented. A method for determining the area covered acceptably by two stations is given and three-station coverage characteristics are discussed. Author