@ARTICLE{Gajderowicz_Idzi_Comparison_2007,
author={Gajderowicz, Idzi},
volume={vol. 56},
number={No 2},
journal={Geodesy and Cartography},
pages={59-71},
howpublished={online},
year={2007},
publisher={Polska Akademia Nauk/ Komitet Geodezji Polskiej Akademii Nauk; Polish Academy of Sciences / Commitee on Geodesy Polish Academy of Sciences},
abstract={In the research it has been assumed that an observation corresponds to a measured height difference of a levelling section while a pseudo-observation corresponds to a sum of observations for consecutive levelling sections which make up a levelling line. Relations between observations and pseudo-observations are shown. It has also been assumed that observations are not correlated. The study compares Helmert - Pranis-Praniewicz. algorithm of parametric. multi-group (parallel) least squares adjustment of observations with the algorithm of rwo-stage least squares adjustment of levelling network. The two-stage adjustment consists of least squares adjustment of pseudo-observations and then the adjustment of observations, which is carried out separately for each levelling line. It was shown that normal equations concerning heights of nodal points, created on the basis of pseudo-observations, are identical to the reduced normal equations formed on the basis of observations in multi-group adjustment. So, adjusted heights of nodal points and their variance-covariance matrix are the same in the case of adjustment of observations and in the case of adjustment of pseudo-observations. Following a brief presentation of known algorithm of height computation for intermediate benchmarks of levelling lines there is shown the proof that the value of a square root of the a posteriori variance of unit weight 1110, known also as mean square error of a typical observation/pseudo-observation, is the same in the case of adjustment of observations and in the case of adjustment of pseudo-observations. The conclusion states that the results of two-stage adjustment and rigorous least squares adjustment of observations are identical.},
type={Article},
title={Comparison of algorithms of two-stage adjustment and multi-group adjustment of levelling network},
URL={http://journals.pan.pl/Content/121245/PDF-MASTER/3_GK_VOL_56_NO_2_2007_Gajderowicz_Porownanie.pdf},
keywords={Levelling network, Helmert - Pranis-Praniewicz algorithm, pseudo-observations, least squares adjustment},
}