Analytical expressions for position error in triangulation solution of point in space for several station configurations

Analytical expressions are derived to first order for the rms position error in the triangulation solution of a point object in space for several ideal observation-station configurations. These expressions provide insights into the nature of the dependence of the rms position error on certain of the experimental parameters involved. The station geometries examined are: (1) the configuration of two arbitrarily located stations; (2) the symmetrical circular configuration of two or more stations with equal elevation angles; and (3) the circular configuration of more than two stations with equal elevation angles, when one of the stations is permitted to drift around the circle from its position of symmetry. The expressions for the rms position error are expressed as functions of the rms line-of-sight errors, the total number of stations of interest, and the elevation angles.