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Galileo Down to a Millimeter: Analyzing the GIOVE-A/B Double Difference

Third of three stories about Galileo's new signals in space

With only two spacecraft in orbit for the Galileo constellation that will eventually have 30 satellites, having enough observation time to track and analyze the new signals can pose a challenge. Using a short baseline set-up and a late-night session, however, these authors were able to collect simultaneous measurements from both satellites, perform a double-difference resolution of the carrier phase cycle ambiguity, and assess the measurement noise.

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In December 2005 the first Galileo prototype satellite, GIOVE-A, was launched. Then, on April 26, 2008, a second satellite — GIOVE-B — was successfully put into orbit and soon began transmitting a variety of signals.

With two operational satellites in place, and having two receivers available, which can track both satellites’ signals at the same time (using omni-directional antennas), one can perform a Galileo-only double-difference calculation and analysis.

On the evening of July 6, we did just that, using a static baseline set-up to collect measurements from GIOVE-A and GIOVE-B together. This enabled us to make a first attempt to fix a Galileo double-difference carrier phase cycle ambiguity and analyze the carrier phase measurement noise.

Double-Difference Technique
The double-difference technique is commonly used in relative positioning for high precision applications. The double difference is a particular combination of ranges observed between two satellites and two receivers.

Ranging is accomplished by measuring the signal travel time from a satellite to a receiver, and errors in the clock of the satellite and the receiver will directly affect the observed range. In the double-difference combination of measurements, the clock errors are eliminated. At the outset the satellite clock errors are unknown and receiver clock errors are highly time varying, the latter being typically based on quartz oscillators.

If we deploy the two receivers close together — just a few meters apart — atmospheric delays in the satellite signals to both receivers will be the same. Therefore, these common delays are excluded in the double-difference combination.

What remains is the satellite-receiver geometry, from which under operational circumstances the baseline vector coordinates are determined (through linearization of the ranges into coordinates). Because the Galileo satellites were not yet transmitting navigation data at the time of our observations, we followed the so-called geometry-free approach. This implies that the geometry in the double difference measurement remains parameterized in terms of ranges, rather than baseline coordinates.

(For an explanation of geometry-free and geometry-based GNSS techniques, please use the link to the article by D. Odijk listed in the Additional Resources section, below.)

To analyze the noise in the carrier phase measurements, we modeled the remaining double-difference range term, piecewise in time, through a low-order polynomial. With our receivers both static on the Earth’s surface and the satellites in high-altitude orbits with smooth dynamics, we found this an appropriate modeling method.

. . . The experiment required careful satellite-visibility planning, and some initial attempts turned out to be less successful. Finally, on July 6, GIOVE-B appeared, transmitting, above the southern horizon on its way to reach nearly local zenith around 23:00 UTC.

. . . The signals transmitted by GIOVE-A and -B are largely representative of the future Galileo signals. On the L1 carrier at 1575.42MHz, the Open Service is transmitted through the so-called B and C signal.

. . . We used the measurements across two Galileo satellites and two receivers to form a pure Galileo double difference. Employing the geometry-free approach, we can estimate the GIOVE-A–GIOVE-B double-difference carrier phase cycle ambiguity using the pseudorange code measurements.

. . . In addition to this aspect, we very much want to look into interoperability: the use of GPS and Galileo together in one integral, high-precision position solution. Will there be intersystem biases? Research and experiments are needed to develop an adequate mathematical observation model, taking receiver design into account (considering such factors as RF bandwidth and correlator spacing), for the joint use of GPS and Galileo in high-precision relative positioning.

For the complete story, including figures, graphs, and images, please download the PDF of the article, above.

Additional Resources
[1] Odijk, D., “What does “geometry-based” and “geometry-free” mean in the context of GNSS?GNSS Solutions column, Inside GNSS, March/April, 2008, pp. 22-24
[2] Simsky, A., and D. Mertens, J.-M. Sleewaegen, T. Willems, M. Hollreiser, and M. Crisci, “Multipath and Tracking Performance of Galileo Ranging Signals Transmitted by GIOVE-A,”  Proceedings of the ION GNSS 2007, Forth Worth, Texas, USA, September 25–28, 2007


The baseline experiment used two AsteRx1 24-channel L1 GNSS receivers, together with PolaNt survey antennas, from Septentrio Satellite Navigation NV, Leuven, Belgium. The high-end receiver used in the research described in the article by A. Simsky et alia was the GeNeRx from Septentrio.

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