Zero-difference Ambiguity Fixing for Spaceborne GPS Receivers

D. Laurichesse, F. Mercier, J.P. Berthias, P. Broca, L. Cerri

Abstract:	Integer ambiguity fixing is routinely applied on double differenced phase measurements to achieve precise positioning of receiver antennas. This method removes most of the common errors between the different signal paths. It also minimizes the size of the problem to be solved by removing all clock contributions. Using added pseudo-range information, it is possible to directly fix integer ambiguities on zero-difference phase measurements, for dual-frequency problems without using any ionosphere model. Phase measurements then become unambiguous and similar to pseudo-range measurements with millimeter noise level. We have already shown that these zero-difference phase measurements allow the positioning of dual-frequency receivers using a PPP-like method in the integer domain, with centimeter level precision. We have also previously shown that this method can be implemented in real-time. In this paper, we address zero difference ambiguity fixing issues for high precision spaceborne GPS receivers. GPS based precise orbit determination for low Earth orbiters is usually performed on zero-difference measurements nowadays. However, attempts to fix ambiguities have so far been only marginally successful, in part because the standard ambiguity fixing step requires double difference processing. Our approach to ambiguity fixing which applies directly to zero difference measurements is thus much better suited for low Earth satellite orbit determination. In the zero-difference approach, after a first step consisting of fixing the zero-difference widelane ambiguity using specific GPS satellite biases, it is possible to use the satellite clocks, named ´integer´ clocks, estimated over a global network of ground stations as part of a global zero-difference ambiguity fixing for the GPS constellation. These clocks have the property of keeping the integer nature of the zerodifference narrowlane ambiguities, for any ground or spaceborne GPS measurements. A first example is given by the Grace mission. This mission consists of two identical spacecraft flying in near polar low earth orbit. Each satellite carries a NASA/JPL BlackJack GPS dual-frequency receiver. These receivers are shown to be compatible with zero-difference widelane ambiguity fixing in the same way as ground receivers. Given an initial floating solution for the absolute orbits, the narrowlane ambiguities fixing problem is more complex but can be solved independently on each satellite. The relative position of the satellites obtained with resulting absolute orbits (after zero difference ambiguity fixing) can then be computed with an accuracy of around 2 mm RMS (validated using the K-band intersatellite range measurements), close to the state of the art for this formation flying experiment. A second example is given by the Jason mission. The onboard receiver (also a NASA/JPL BlackJack receiver) appears to be compatible with the zero-difference widelane ambiguity fixing method. Narrowlane ambiguity fixing between Jason and a ground receiver is difficult due to the non-cancellation of common errors sources between the different propagation paths (troposphere effect only on one receiver, complexity of antennas phase maps). Also, the quality of absolute orbits cannot be as good as the quality of relative orbits for close satellites because of modeling limitations. Using single or double difference measurements, narrowlane ambiguities can be fixed between Jason and a network of ground stations. However the geometry of the problem leads to many discontinuous passes on each station, thus the observability of baselines is very different than in the two nearby satellite case. The observability is also reduced due to the need to solve for a station clock at each epoch using the satellite clock as a reference. We will address the different ambiguity fixing issues and the corresponding success rates. We will also compare orbits resulting from standard floating precise orbit determination with orbit computed using fixed ambiguity measurements.
Published in:	Proceedings of the 21st International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2008) September 16 - 19, 2008 Savannah International Convention Center Savannah, GA
Pages:	758 - 768
Cite this article:	Laurichesse, D., Mercier, F., Berthias, J.P., Broca, P., Cerri, L., "Zero-difference Ambiguity Fixing for Spaceborne GPS Receivers," Proceedings of the 21st International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2008), Savannah, GA, September 2008, pp. 758-768.
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