Statistical testing of directions observations independence

Abstract

Independence of observations is often assumed when adjusting geodetic network. Unlike the\ud distance observations, no dependence of environmental conditions is known for horizontal\ud direction observations. In order to determine the dependence of horizontal direction observations,\ud we established test geodetic network of a station and four observation points. Measurements of\ud the highest possible accuracy were carried out using Leica TS30 total station along with precise\ud prisms GPH1P. Two series of hundred sets of angles were measured, with the first one in bad\ud observation conditions. Using different methods, i.e. variance–covariance matrices, x2 test and analyses of time series, the independence of measured directions, reduced directions and horizontal angles were tested. The results show that the independence of horizontal direction\ud observations is not obvious and certainly not in poor conditions. In this case, it would be appropriate for geodetic network adjustments to use variance–covariance matrix calculated from measurements instead of diagonal variance–covariance matrix