Jianqing Cai

Systematical Analysis of the Transformation Between Gauss-Krueger-Coordinate/DHDN and UTM-Coordinate/ETRS89 in Baden-Württemberg with Different Estimation Methods

For the concrete “Introduction of ETRS89 into Baden-Wurttemberg” the transformation which transforms the existing two-dimensional Gauss-Krueger coordinates in German geodetic reference system (DHDN) into UTM coordinates in the ETRS89 datum with the models of the 7-parameter Helmert transformation and the 6-parameter affine transformation using the 131 collocated points (131 BWREF points in Baden-Wurttemberg) are tested and discussed. Because of the special characteristic of the main triangulation network in Baden-Wurttemberg (state-wide variable net scales, inhomogeneous point accuracies and network distortions in the decimetre level) an alternative transformation procedure based on the polynomial model is performed. Further more the Total Least-Squares method is also applied in estimating the parameters of the 6-parameter affine-transformation based on the 131 collocated points. The result is analysed and compared with these results of the conventional LS method. A systematic analysis of the transformation results is concluded.

The A-optimal regularization parameter in uniform Tykhonov-Phillips regularization — α-weighted BLE-

Numerical tests have documented that the estimate \(\hat \xi \) of type BLUUE of the parameter vector ξ within a linear Gauss-Markov model {Aξ=E{y}, Σ y = D{y}} is not robust against outliers in the stochastic observation vector y. It is for this reason that we give up the postulate of unbiasedness, but keeping the set-up of a linear estimation \(\hat \xi = Ly\) of homogeneous type. Grafarend and Schaffrin (1993) as well as Schaffrin (2000) have systematically derived the best linear estimators of type homBLE (Best homogeneously Linear Estimation), S-homBLE and α-homBLE of the fixed effects ξ, which turn out to enhance the best linear uniformly unbiased estimator of type BLUUE, but suffer from the effect being biased. Here the regularization parameter in uniform Tykhonov-Phillips regularization (α-weighted BLE) is determined by minimizing the trace of the Mean Square Error matrix MSE α,s {\(\hat \xi \)} (A-optimal design) in the general case. In lieu of a case study, both model and estimators are tested and analyzed with numerical results computed from simulated direct observations of a random tensor of type strain rate.

The Uniform Tykhonov-Phillips Regularization (α-weighted S-homBLE) and its Application in GPS Rapid Static Positioning

In high accuracy GPS positioning the conventional least-squares method is widely applied in processing of carrier phase observation. But it will not be always succeed in estimating of unknown parameters, in particular when the problem is ill-posed, for example, there is the weak multicollinear problem in the normal matrix with shorter period GPS phase observation. Here the newly developed method of determining the optimal regularization parameter α in uniform Tykhonov-Phillips regularization (α-weighted S-homBLE) by A-optimal design (minimizing the trace of the Mean Square Error matrix MSE) is reviewed. This new algorithm with A-optimal Regularization can be applied to overcome this kind problem in both GPS rapid static and real time kinematic positioning with single or dual frequency measurements, especially for the shorter period observation. In the case study, both the estimate methods are applied to process the two-epoch L1 data in single frequency GPS rapid static positioning. A detailed discuss about effects of the initial coordinate accuracy will also be presented. The results show that newly algorithm with optimal regularization can significantly improve the reliability the GPS ambiguity resolution in shorter observation period.