The Factorized Multi-Carrier Ambiguity Resolution (FAMCAR) Approach for Efficient Carrier-Phase Ambiguity Estimation

Ulrich Vollath

Abstract:	The proposed addition of a third carrier to the modernized GPS as well as the implementation of three carriers in the planned Galileo system will boost the performance of carrier-phase based positioning within the next decade. In principle, highly-reliable instantaneous (one-epoch) ambiguity resolution becomes feasible for a broad range of applications. Beyond the system level developments - regarding the frequency allocation and signal structure - the proposal of three and four carrier frequencies enables new approaches at the processing level. The Factorized Multi-Carrier Ambiguity Resolution (FAMCAR) algorithm introduces a number of new independent linear combinations of carrier-phase observations as well as of carrier-phase and pseudo-range observations. The combinations include the minimumerror geometric carrier-phase combination, the minimumerror ionosphere combination, the new Quintessence combinations and the code-carrier combinations. From these individual estimates, the full floating solution for all carriers is derived. This paper provides a detailed derivation of the approach and the statistical properties of these new linear combinations. Existing standard techniques for multi-carrier ambiguity determination usually apply one big Kalman filter to estimate all unknowns (e.g. position, ambiguities, ionosphere and multipath). The factorization enables the stepwise modeling of each error component and leads therefore to a bank of significantly smaller filters. This approach results in distinct higher computational efficiency for the Kalman filter sets (i.e. float solution) und a better knowledge of each error component for the individual measurements. In addition to the efficient processing of three and four carrier data the new approach is already applicable to a dual-frequency system. Furthermore the decreased computational load enables the use of smaller processor components and therefore provides a significant cost reduction.
Published in:	Proceedings of the 17th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2004) September 21 - 24, 2004 Long Beach Convention Center Long Beach, CA
Pages:	2499 - 2508
Cite this article:	Vollath, Ulrich, "The Factorized Multi-Carrier Ambiguity Resolution (FAMCAR) Approach for Efficient Carrier-Phase Ambiguity Estimation," Proceedings of the 17th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2004), Long Beach, CA, September 2004, pp. 2499-2508.
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