Ronald Braff and Nathaniel Braverman

Peer Reviewed

Abstract: Constant-error isograms applicable to range-range navigation aids, in which the distances to two fixed stations are determined, are well known. The error (actually precision) of a two LOP fix, for such systems, may be expresed 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 "angle of cut" of the two lines of position, the standard deviation of the errors in measuring the distances to teh two stations, and the degree of correlation of these two measurement errors. Available error isograms are applicable to relatively short baseline systems and are based on a flat earth approximation. Proposed VLF systems would empl9y long baselines. When the baseline is several thougsand miles in length the flat earth approximation is no longer valid. The magnitude of the discrepancies which are caused by the plane earth approximation are shown to be appreciable. The equations for the constant-error contours are derived (based on a spherical earth) as a funtion of baseline length and the "angle of cut" of the two lines of position. Various error isograms were computed and plotted through the use of a digital computer. Several examples are presented. Area coverage is discussed as a function of baseline length, minimum and maximum reception distances, and the range of acceptable angles of cut between the two lines of position. The range of acceptalbe angles of cut is a function of the maximum acceptable drms error.
Published in: NAVIGATION: Journal of the Institute of Navigation, Volume 12, Number 1
Pages: 36 - 48
Cite this article: Braff, Ronald, Braverman, Nathaniel, "VLF RANGE-RANGE NAVIGATION ERROR CONTOURS", NAVIGATION: Journal of The Institute of Navigation, Vol. 12, No. 1, Spring 1965, pp. 36-48.
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