Satellite Bias Determination with Global Station Network and Best-Integer Equivariant Estimation

Z. Wen, P. Henkel, A. Brack and C. Gunther

Abstract:	Integer least-squares estimation, e.g. LAMBDA (Leastsquares AMBiguity Decorrelation Adjustment), is widely used for ambiguity fixing as it minimizes the sum of squared ambiguity residuals. However, it does not necessarily minimize the overall mean squared error of both real- and integer-valued parameters as fixed ambiguities are considered as deterministic instead of stochastic quantities in the subsequent least-squares adjustment. The Best Integer Equivariant (BIE) estimator is optimal in the sense of minimizing the overall mean squared error. In this paper, we use the Best-Integer Equivariant estimator to compute a global network solution. As the search process is too complex to be performed in a network solution, we combine the BIE estimator and the sequential least-squares adjustment (bootstrapping, BS). We also use an integer decorrelation to improve efficiency, and a state space model with Kalman filter implementation to compute the float solution. We applied our method to a sparse global network of 17 IGS stations and observed a substantial reduction of the mean squared error due to the combined BIE/BS estimation. The estimated satellite phase biases and satellite clock corrections were very stable with variations of only 5 centimeters within 8 hours.
Published in:	Proceedings of the 25th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2012) September 17 - 21, 2012 Nashville Convention Center, Nashville, Tennessee Nashville, TN
Pages:	3675 - 3682
Cite this article:	Wen, Z., Henkel, P., Brack, A., Gunther, C., "Satellite Bias Determination with Global Station Network and Best-Integer Equivariant Estimation," Proceedings of the 25th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2012), Nashville, TN, September 2012, pp. 3675-3682.
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