Galileo Down to the Millimeter

Galileo Down to the Millimeter Analyzing a GIOVE-A/B Double Difference ESA photos ESA 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.

Christian Tiberius, Hans van der Marel On the evening of July 6, we did just to a receiver, and errors in the clock of Delft University of Technology that, using a static baseline set-up to the satellite and the receiver will directly Jean-Marie Sleewaegen, Frank Boon collect measurements from GIOVE-A affect the observed range. In the double- Septentrio Satellite Navigation and GIOVE-B together. This enabled us difference combination of measure- to make a first attempt to fix a Galileo ments, the clock errors are eliminated. n December 2005 the first Galileo double-difference carrier phase cycle At the outset the satellite clock errors prototype satellite, GIOVE-A, was ambiguity and analyze the carrier phase are unknown and receiver clock errors launched. Then, on April 26, 2008, measurement noise. are highly time varying, the latter being Ia second satellite — GIOVE-B — typically based on quartz oscillators. was successfully put into orbit and soon Double-Difference Technique If we deploy the two receivers close began transmitting a variety of signals. The double-difference technique is com- together — just a few meters apart — With two operational satellites in monly used in relative positioning for atmospheric delays in the satellite signals place, and having two receivers available, high precision applications. The double to both receivers will be the same. There- which can track both satellites’ signals at difference is a particular combination of fore, these common delays are excluded the same time (using omni-directional ranges observed between two satellites in the double-difference combination. antennas), one can perform a Galileo- and two receivers. What remains is the satellite-receiver only double-difference calculation and Ranging is accomplished by measur- geometry, from which under operational analysis. ing the signal travel time from a satellite circumstances the baseline vector coor-

40 InsideGNSS september/october 2008 www.insidegnss.com dinates are determined (through linear- Baseline in the dark. The ization of the ranges into coordinates). measurements were taken Because the Galileo satellites were not out in the field from 22:12h yet transmitting navigation data at the to 23:48h local time. 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 expla- nation of geometry-free and geometry- based GNSS techniques, see the article by D. Odijk listed in the Additional Resources section at the end of this col- umn.) 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.

Measurement Set-Up We should note that the collected On the date of the experiment With two identical 24-channel receivers, data — from the point of view of our reported here, GIOVE-A transmit- we established a short baseline in the flat intended analysis — is sub-optimal ted a BOC(1,1) modulation on L1, and and open Delfland area of The Nether- because of a not too favorable geometry GIOVE-B an MBOC modulation. The lands, allowing for a clear reception of (in particular through the low elevation L1-BC code and carrier phase measure- GNSS signals in space. (See the accom- of GIOVE-A). On the other hand, wait- ments used in our analysis have been panying photo of the receiver set-up.) A ing for a favorable geometry from the obtained by tracking both satellites with 360-degree visibility extended virtually current Galileo constellation may take a BOC(1,1) replica. down to the horizon with only a few some time, especially since the satellites Regarding code tracking perfor- trees and farmhouses at several kilome- were not yet transmitting 24/7. mance, the main benefit of the BOC(1,1) ters distance. The experiment required careful GIOVE-A/B satellite-visibility planning, and some Signals in initial attempts turned out to be less Space successful. Finally, on July 6, GIOVE-B The signals trans- appeared, transmitting, above the south- mitted by GIOVE- ern horizon on its way to reach nearly A and -B are largely local zenith around 23:00 UTC. We representative of the began tracking its signals at 19:45 UTC future Galileo sig- (and in the lower-left corner of Figure 1, nals. On the L1 car- one can indeed see that the screen-shot rier at 1575.42MHz, is taken at 19:45 and that a clear green the Open Service is signal bar appears for Galileo E31, 43 transmitted through dB-Hz). the so-called B and Meanwhile, GIOVE-A was on the C signal compo- way down, eastwards, and both receivers nents (respectively, lost its signal around 21:50 UTC. So, the data and pilot chan- FIGURE 1 The ultimate “Yes!” moment. For the first time we observed baseline was measured for slightly more nels), which we refer both GIOVE-A and GIOVE-B at the same time (indicated by E32 and E31, than 1 hour and 36 minutes (20:12–21:48 to as L1-BC in this respectively). Shown is a screenshot of the graphical user interface to the L1 24-channel GNSS receiver. UTC). article. www.insidegnss.com september/october 2008 InsideGNSS 41 galileo down to the millimeter

modulation with respect to the BPSK(1) multipath delays larger than 150 meters, PRN C/N0 [dB-Hz] st. dev. [m] modulation of the L1 GPS C/A-code which rarely occur in practice. 24 49-48-47 0.16 (GPS-CA) signal comes from the reduc- Carrier phase tracking noise is not 31 49-47-45 0.16 tion of tracking noise. In terms of code dependent on the modulation type. So, 16 47-49-49 0.16 multipath, which is typically the largest for this reason, GIOVE-L1BC and GPS- source of GNSS error, BOC(1,1) does CA are expected to experience about the 21 47-49-48 0.16 not perform significantly better than same level of tracking noise for an equal 29 49-48-45 0.17 BPSK(1). This is because the multipath value of the carrier-to-noise-density GIOVE-B 43-45-46 0.18 advantage of BOC(1,1) only begins at ratio C/N0. 06 40-42-46 0.25 30 46-42-38 0.26 Estimated DD ambiguity (cyc) GIOVE 10 Double- 10 39-39-38 0.32 5 Difference GIOVE-A 38-37-35 0.42 Ambiguity TABLE 1. Standard deviation of the pseudo- 0 Resolution range measurement noise estimated from single differences. The standard deviation –5 We used the mea- is given in terms of undifferenced measure- ments, for eight GPS satellites (L1-CA), –10 surements across two Galileo satel- and for GIOVE-A and B (L1-BC). The middle column gives the C/N (three values) during –15 0 lites and two receiv- the survey, at epoch 1000, 3000, and 5000 –20 ers to form a pure seconds. Galileo double dif- –25 ference. Employ- pseudorange code measurements. For –30 ing the geometry- one combination of two satellites, the 0 1000 2000 3000 4000 5000 free approach, we model for one epoch of measurements (seconds) can estimate the reads FIGURE 2 GIOVE-A/B double-difference (DD) carrier phase ambiguity GIOVE-A–GIOVE- estimated using the corresponding pseudorange code measurements. B double-difference The ambiguity is estimated anew each epoch (sampled at a one-second interval). The float ambiguity estimate over the full time span is -9.05, carrier phase cycle which is fixed to the integer value -9, with large confidence. ambiguity using the where P is the double-difference pseu- dorange measurement, Φ is the double- 50 difference carrier phase measurement (expressed in units of range), ρ is the 40 double-difference geometric range, λ is the L1 wavelength, and N is the double-

(dB-Hz) 30 GIOVE-B GIOVE-A difference ambiguity. E denotes the 20 mathematical expectation operator. 0 1000 2000 3000 4000 5000 With single-frequency measure- 0 ments, redundancy only arises from –2 using multiple epochs, because the ambiguity is a constant as long as no (mz) –4 cycle slips or signal tracking interrup- tions occur. Figure 2 shows the epoch- 0 1000 2000 3000 4000 5000 wise ambiguity estimates . The empiri- –2 cal standard deviation is 3.4 cycles (on L1), which reflects the double-difference –4 pseudorange code noise. (m) –6 Pseudorange Code 0 1000 2000 3000 4000 5000 Measurement Noise (seconds) The pseudorange measurement noise can be assessed at the single-difference FIGURE 3 Single-difference code-minus-carrier phase measurements demonstrate the pseudorange level, per satellite, with two receivers. measurement noise — in the middle panel for GIOVE-B, in the lower panel for GIOVE-A (same scale). Note that GIOVE-A was observed at low elevation, resulting in larger measurement noise. The top The carrier phase acts as a ground-truth

panel presents the carrier-to-noise-density ratio (C/N0) in dB-Hz (data shown for receiver 1, (with a constant offset due to the ambi- which were very similar for receiver 2). guity). Figure 3 shows the single-differ-

42 InsideGNSS september/october 2008 www.insidegnss.com PRN C/N0 [dB-Hz] st.dev. [m] by a second-order 0.015 21-24 47-48-47 0.0007 polynomial, each 21-31 47-47-45 0.0008 time in a span of 0.010 16-29 47-48-45 0.0008 typically between 5 and 10 minutes. 0.005 16-30 46-42-38 0.0013 Figure 4 shows the 10-16 39-39-38 0.0016 phase residuals of 0.000 A-B 38-37-35 0.0016 two successive time meters 10-06 39-39-38 0.0018 spans. –0.005 Table 2 shows TABLE 2. Standard deviations of carrier phase measurement noise estimated from double the empirical stan- –0.010 differences. The standard deviation is given dard deviation of in terms of undifferenced measurements, for six GPS combinations and for the GIOVE-A/B the carrier phase –0.015 m e a s u r e m e n t s , 1200 1300 1400 1500 1600 1700 1800 combination. The middle column presents (seconds) the C/N0 (three values) during the survey, at expressed in terms epoch 1000, 3000, and 5000 seconds, each of undifferenced FIGURE 4 GIOVE-A/B double-difference L1 phase residual at a 1-second time for the lowest of the two satellites. interval for a 12-minute slice of data. In addition to the noise, a low measurements — periodic effect is also present, most likely due to carrier multipath. The ence pseudorange code, with respect the obtained dou- estimated (all-in) standard deviation is 2.7 millimeters (in terms of to the carrier phase, for GIOVE-B and ble-difference (DD) double difference). GIOVE-A. Table 1 shows the empirical estimate is evenly standard deviation of the pseudorange distributed across the two identical ematical observation model, taking code measurements, expressed in terms receivers, and across the two satellites receiver design into account (consider- of undifferenced measurements (the (also assumed equally); σ = sDD /2. ing such factors as RF bandwidth and obtained single-difference estimate is As expected, the carrier phase mea- correlator spacing), for the joint use of evenly distributed across the two iden- surements of both GPS and Galileo have GPS and Galileo in high-precision rela- tical receivers; ). similar precision, around 1-2 millime- tive positioning. Table 1 presents the measurements ter (standard deviation; undifferenced). for selected satellites, including eight Taking into account the C/N0 values, one Concluding Remarks GPS spacecraft, in order of increasing could say that the Galileo combination Taking advantage of the availability of standard deviations of the pseudorange seems to slightly outperform the others two Galileo signal-in-space feeds, a first code measurements and display a clear in this experiment. assessment has been made of the high- inverse relationship with the C/N0 val- precision relative positioning capability ues. Outlook of Galileo. A short baseline between two The superior performance of Gali- This short article reports on only an ini- receivers was measured to experience leo with respect to GPS-CA is less pro- tial experiment with the first two Gali- carrier phase ambiguity resolution with nounced in this experiment than in pre- leo satellites. It is just the start of the use GIOVE-A and B. vious independent studies, such as the of Galileo for high-precision relative With this set-up, we obtained a first one reported in the article by A. Simsky positioning applications. Many aspects impression of the measurement preci- et alia cited in Additional Resources. A remain to be addressed and experiment- sion, under real-life circumstances, in the likely explanation is to be found in the ed with. field — both for pseudorange code and receiver RF-bandwidth. Due to a larg- We used here only single-frequency carrier phase. As for Galileo, the obser- er RF bandwidth, up to 40 MHz, the measurements. However, Galileo offers vation geometry was not very favorable high-end receiver used in the research signals in three frequency bands. Earlier in this experiment; the C/N0 values have described by Simsky is able to take more design studies have shown that tracking to be properly taken into account when advantage of the Galileo modulation multiple frequencies simultaneously will interpreting the obtained results. characteristics, and thereby allows for be very beneficial to carrier phase ambi- even better multipath rejection. guity resolution, for instance, in terms of Manufacturers success rate. The baseline experiment used two Carrier Phase Noise In addition to this aspect, we very AsteRx1 24-channel L1 GNSS receivers, In order to assess phase measurement much want to look into interoperabil- together with PolaNt survey antennas, noise, the double-difference combina- ity: the use of GPS and Galileo together from Septentrio Satellite Navigation tion is really needed. Figure 4 shows an in one integral, high-precision posi- NV, Leuven, Belgium. The high-end example of the GIOVE-A/B double-dif- tion solution. Will there be intersystem receiver used in the research described ference phase residual. The double-dif- biases? Research and experiments are in the article by A. Simsky et alia was the ference geometry is piecewise modeled needed to develop an adequate math- GeNeRx from Septentrio. www.insidegnss.com september/october 2008 InsideGNSS 43 galileo down to the millimeter

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 Sig- nals Transmitted by GIOVE-A,” Proceedings of the ION GNSS 2007, Forth Worth, Texas, USA, Septem- ber 25–28, 2007

Authors Christian Tiberius received his Ph.D. degree from the Delft University of Technology, The Nether- lands, for his thesis on “Recursive data process- ing for kinematic GPS surveying.” He is an assistant professor with the Delft Institute for Earth Observation and Space Systems (DEOS) and involved in research on enhanced GNSS positioning, such as precise point positioning and satellite-based augmentation systems, and on data quality control. Hans van der Marel re- ceived his Ph.D. degree from the Delft University of Technology with a thesis on “The great circle reduction in the data analysis for the astrometric satellite Hipparcos.” He is an assistant professor with the Delft Institute for Earth Obser- vation and Space Systems (DEOS) and involved in research on high-precision GNSS positioning, sci- entific, and meteorological applications of GNSS. Jean-Marie Sleewaegen is responsible for GNSS signal processing, sys- tem architecture, and technology development at Septentrio Satellite Navigation, Leuven, Bel- gium. He received his M.Sc. and Ph.D. in electrical engineering from the University of Brussels. He received the Institute of Navigation’s Burka Award in 1999. Frank Boon is head of Septentrio’s research department. He received his M.Sc. in aero- space engineering from Delft University of Technology.

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