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

"5.3 Position-Fixing Using Total Station 105x (time)timeFigure 5.11: Polynomial interpolation and interpolation points.approximated by a regression line. The mathematical model for a regression line is described by [Bronsteinand Semendjajew, 1999]yi = a Xi + b (5.18)where a is the slope and b is the intercept of the ordinate. Considering a data set, the regressionline can becalculated by applying the Gauss-Markov-Model. Since the equation is linear in the unknowns, no initialvalues are required for a and 6:X\ 13/1x2 1ab=yi(5.19)•En 1_ .VnA regression line is also suitable for detecting blunders. Data snooping can be included in the adjustmentof the regression line since the median filter does not find consecutive blunders due to the window size.The criterion for blunders can either be normalized residuals or absolute distance offsets.The advantageof using an absolute distance error can be seen in a mathematical interpretation, which ease the search foroutliers. The adjustment of the regressionline is iterated until all blunders are disabled.5.3.4 Kaiman FilteringThe Kaiman filter has become very popular since its invention by [Kaiman, I960]. The Kaiman filter is arecursive filter and a favorite method for combining data acquired by sensors or instruments for achievingan optimal estimation of the state vector of a motion and its stochastic behaviour. Thus, the state vector andits covariance matrix become time-dependent and are a function of time. Therefore, optimal estimationmeans that within the estimation, the error variances are minimized and allavailable deterministic andstochastic information are included.