DERIVATION OF FORMULAS FOR ROOT-MEAN-SQUARE ERRORS IN LOCATION, ORIENTATION, AND SHAPE IN TRIANGULATION SOLUTION OF AN ELONGATED OBJECT IN SPACE

摘要

Formulas are derived for the root-mean-square (rms) displacement, slope, and curvature errors in an azimuth-elevation image trace of an elongated object in space, as functions of the number and spacing of the input data points and the rms elevation error in the individual input data points from a single observation station. Also, formulas are derived for the total rms displacement, slope, and curvature error vectors in the triangulation solution of an elongated object in space due to the rms displacement, slope, and curvature errors, respectively, in the azimuth-elevation image traces from different observation stations.nThe total rms displacement, slope, and curvature error vectors provide useful measure numbers for determining the relative merits of two or more different triangulation procedures applicable to elongated objects in space. They also provide useful measure numbers for determining the effect of various experimental parameters - such as the number and relative location of the observation stations, the spacing of the input data points along the azimuth-elevation image traces, etc. - on the triangulation solution of an elongated object in space.