Sequential Best Integer-Equivariant Estimation for Geodetic Network Solutions

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

Abstract:	The key to high precision parameter estimation (e.g., positioning) in global navigation satellite system (GNSS) applications is to take the integer nature of the carrierphase ambiguities into account. The class of integer estimators, like integer bootstrapping (BS) or integer leastsquares (ILS), fixes the ambiguities to integer values, which can also decrease the precision of the estimates of the nonambiguity parameters, if the probability of wrong fixing is not sufficiently small. The best integer-equivariant (BIE) estimator is optimal in the sense of minimizing the meansquared error (MSE) of both the integer and real valued parameters, regardless of the precision of the float solution. However, like ILS, the BIE estimator comprises a search in the integer space of ambiguities, whose complexity grows exponentially with the number of ambiguities, which is not feasible for large-scale network solutions. To overcome this problem, a sequential BIE (SBIE) algorithm is proposed, which shows close to optimal performancewhile being part of the class with complexity of linear order. Numerical simulations are used to verify the performance of the SBIE algorithm.
Published in:	Proceedings of the 2013 International Technical Meeting of The Institute of Navigation January 29 - 27, 2013 Catamaran Resort Hotel San Diego, California
Pages:	310 - 317
Cite this article:	Brack, A., Henkel, P., Gunther, C., "Sequential Best Integer-Equivariant Estimation for Geodetic Network Solutions," Proceedings of the 2013 International Technical Meeting of The Institute of Navigation, San Diego, California, January 2013, pp. 310-317.
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