[G05-P] Poster

[G05-P-07] MINIMUM MEAN SQUARE ERROR ADJUSTMENT, Part 2: The Empirical BLE and the reproBLE for multivariate positioning

Burkhard Schaffrin¹, ^○Peiliang Xu² (1.Ohio State University, Columbus, USA, 2.Kyoto University, Kyoto, Japan)

Abstract:
A little while ago, in 2000, Schaffrin showed how the weighted Least-Squares solution (LESS) within a model of direct observations (univariate case) may be improved by applying the minimum Mean Square Error (MSE) principle, either leading to the well established Empirical BLE (Best Linear Estimate) or the novel reproBLE. Here, an attempt will be made to generalize the concept to cover the multivariate case in form of a Gauss-Markov Model. First steps in this direction had been undertaken by Schaffrin in 2008 already, but with emphasis on the optimal choice for the Tykhonov-Phillips regularization parameter. Now, new aspects of any solutions of type reproBLE regarding questions of positioning will be the focus of this contribution.

Reference:
Schaffrin, B. (2000) Minimum mean squared error adjustment, Part I: The empirical BLE and the repro-BLE for direct observations. J Geod Soc Japan 46:21–30
Schaffrin, B. (2008) Minimum mean squared error (MSE) adjustment and the optimal Tykhonov–Phillips regularization parameter via reproducing best invariant quadratic uniformly unbiased estimates (repro-BIQUUE). 2008, 82(2): 113–121