Calibration of a Terrestrial Laser Scanner - Institute of Geodesy and ...

u140 C. Adjustment of SphereA =dfi,B =dfit(C6)The dimensions of the matrices and vectors aregiven by the number of observations n and byof unknowns u The redundancy r is obtained generally bythe numberr = n—(C 7)Thus, the following dimensions are obtained for the required matrices• P dim(n, =• A dim(n, =• B dim(r, =• w dim(r, =n)u)n)1)The implemented equations for the adjustment are well-known and can be found in various scientific pub¬lications and books, eg [Großmann, 1961], [Hopcke, 1980], [Leick, 2004], [Welsch et al, 2000]The weight matrix P is a diagonal matrix since the coordinates acquired by the laser scanner are indepen¬dent of each other This assumption is only conditionally valid since the Cartesian coordinates x, y, z arederived by the spherical coordinates h, v, s, which are independent of each otherHowever, the Cartesiancoordinates are correlated and the covanances have to be considered in a strict sense Nevertheless, forsimplification reasons, the assumption of uncorrelated coordinates is adhered to The weighttions is controlled by the weight matrix P In the case of blunders, the weightof observa¬can be reduced to eliminatethe influence of the blunder on the unknowns A blunder is detected by data snooping The normalizedresidual, which equals the distance of one point to the sphere surface, is a reliable criterion for eliminatingblundersThe aposteriori variance of the unit weight a\ estimates the variance of one single observation Here, it isthe variance of one single coordinate represented by x or y or z3D point