Estimation of the GPS to Galileo Time Offset and its validation on a mass market receiver Ciro Gioia, Joaquim Fortuny-Guasch, Borio Daniele European Commission, Joint Research Centre (JRC), Institute for the Protection and Security of the Citizen (IPSC), Security Technologies Assessment Unit, Via Enrico Fermi 2749, 21027 Ispra VA, Italy{ciro.gioia, joaquim.fortuny, daniele.borio}@jrc.ec.europa.eu Abstract — The European GNSS, Galileo is currently in its InOrbit Validation (IOV) phase where four satellites are available for computing the user position. Galileo E1 OS and GPS C/A represent a very effective constellation pair in a consumer grade receiver: the signals are conveyed on the same analog path and measurements can be combined in a single position, velocity and time (PVT) solution, provided that the Galileo to GPS Time Offset (GGTO) is available. Algorithms for GGTO estimation are presented in this paper, including a real-time implementation on a compact hardware receiver, based on the Teseo-II chipset. Experimental results are provided, showing the benefit in terms of accuracy and availability of the Galileo plus GPS multiconstellation solution respect to the GPS only case. Also analyzed are the effects on the GGTO estimate of different ionospheric models, namely: GPS Klobuchar and Galileo NeQuick. Both simulated scenarios and real, recorded Galileo IOV samples from a roof antenna are used in the validation of the proposed algorithms. Keywords –Galileo, pseudorange, NeQuick
I.
In-Orbit
Validation,
IOV,
GGTO,
INTRODUCTION
GNSS are worldwide, all-weather navigation systems able to provide tridimensional position, velocity and time synchronization to UTC (Universal Time Coordinated) scale [1, 2, 3]. Currently, only GPS and GLONASS are globally operational. The Chinese BeiDou has started its regional service on December 2012. At the end of 2013 Galileo successfully completed its In-Orbit Validation (IOV) phase; with a total of four satellites. In March 2013, for the first time a Galileo receiver got a Position Velocity and Time (PVT) solution using the signals broadcast by the four IOV satellites. Following the declaration of the Early Services of Galileo foreseen at the end of 2014 a wide-spread use of combined GPS/GLONASS/Galileo receivers in mass-market application is expected [4]. Noting this evolution of the GNSS market, Galileo can be considered a prime candidate for a multiconstellation system together with GPS. The multiconstellation approach, combining different GNSS, such as GPS and Galileo, increases the available measurements, facilitating a more continuous and accurate PVT solution [4]. However, one must keep in mind that when GPS
Fabio Pisoni ST Microelectronics Milano, Italy
[email protected]
measurements are used along with Galileo observables, the GPS to Galileo Time Offset (GGTO) or difference between the system time scales must be precisely estimated, thus limiting the full usage of multi-constellation, since one observation has to be “sacrificed” to estimate the additional unknown as detailed in Section II.A. The methodology proposed in this paper is based on the single point positioning using GPS and Galileo observables and focuses on the impact of the intersystem bias between GPS and Galileo time scales. The device adopted to test the methodology is the Teseo-II chipset, manufactured by ST Microelectronics, and the algorithm proposed is implemented within the above mentioned receiver. Mass market receivers are typically used for land navigation in signal degraded scenarios, such as in urban canyons, where measurements are strongly affected by gross errors, and a degradation of the navigation solution can be observed. This requires a severe quality check on the measurements to ensure the maximum accuracy of the PVT solution. The remainder of this paper is organized as follows. The navigation solution is described in Section II along with the GGTO estimation algorithm and the quality check developed. The experimental setup adopted for the analysis is detailed in Section III, including some details of the Teseo-II embedded implementation. Experimental results are then described in Section IV and finally Section V concludes. II.
NAVIGATION SOLUTION AND ALGHORITM DESCRIPTION
GNSS satellites continuously broadcast signals that enable users to determine their three-dimensional position, velocity and time synchronization with respect to UTC. A. Navigation solution GNSS positioning is based on the one-way ranging technique: the time of travel of a signal, transmitted by a satellite, is measured and scaled by the speed of light to obtain the Pseudorange (PR) whose equation is:
d c tu c ts Where
(1)
is the PR measurement, d is the geometric distance
receiver–satellite,
c ts is the satellite clock error, ctu is the
receiver clock offset scaled by the speed of light
c and
contains the residual errors after atmospheric and satelliterelated corrections [1, 2, 3]. Eq. (1) holds for both single GNSS (i.e. GPS or Galileo only) and ctu is referred to the time scale of the considered system. GNSS receivers are able to provide Doppler measurements, related to the relative motion between receiver and satellites [1, 2, 3]. Doppler observable can be converted in PR-rate whose measurement equation is [2]:
d c tu c ts
(2)
d is the time derivative of the geometric distance receiver – satellite, ctu Where
is the PR rate measurement,
is the receiver clock drift,
contains
the
c tu is the satellite clock drift and
residual
errors
after
satellite-based
corrections. The measurement model consists of equations as (1) and (2), linearized for the unknowns, and assume the following expression:
H x
H v Where
(3)
is the difference between actual and predicted
is the vector containing the PR-rate measurements, H H are the design matrix, and are the residual error vectors, x v and are the state vector, measurements,
different master clocks, producing a further difference of typically less than 100 ns; this difference is broadcast to the users in the navigation message [5]. TABLE I: GPS AND GALILEO DIFFERENCES GPS Galileo 27 Operational Number of SV 24 Expandable + 3 spares Orbital Planes 6 3 Orbit Altitude 20200 km 23222 km Constellation Orbit 55 deg 56 deg Inclination Ground Track 1 Sideral Day 10 Sideral Days period 1575.42 MHz 1575.420 MHz Carrier 1227.60 MHz 1191.795 MHz Frequencies 1176.45 MHz 1278.750 MHz Multiple Signal CDMA CDMA Access Broadcast Keplerian Keplerian Ephemerides Reference WGS84 GTRF Frame System Reference Time GPS Time GST
Galileo System Time (GST) is a continuous time scale maintained by the Galileo Mission System (GMS) and synchronized to the Temps Atomique International (TAI) [6]. The time difference between GPS and Galileo time scales is broadcast within the Galileo navigation message, and therefore it is possible to align GPS and Galileo measurements with respect to a common time scale using parameters such as the Galileo to GPS Time offset (GGTO). The relationship between the two system time scales is:
tSystem tGal tGPS tSystem A0G A1G t
detailed below:
x P cdtuGPS v V
cdtuGPS
Where (4)
In the multi-constellation case a further unknown, representing the inter-system time offset, must be estimated. GPS and Galileo are herein considered; they are similar in many aspects, such as the operational principle described above, but with some meaningful differences that can be classified in terms of constellation, signal and reference system and are summarized in TABLE I. The most significant term for the scope of this paper is that related to the time scale, i.e. GPS and Galileo systems adopting different reference time scales, connected with different UTC realizations. More precisely, GPS time is connected with UTC (USNO), the UTC maintained by US Naval Observatory; UTC scale is connected to the astronomical definition of time by occasionally adjusting it of one second to keep the scale close to the mean solar time. The GPS time scale is, however, continuous and so the GPS time scale and UTC (USNO) differ for an integer number of seconds (called leap seconds, currently 16 s). Moreover GPS time and UTC (USNO) are maintained by
(5)
tGal is the GST, tGPS is the GPS system time, A0G is
the constant term of the GGTO, broadcast within the Galileo navigation message, A1G is the rate of change of the GGTO, broadcast within the Galileo navigation message, and t TOW t0G 604800 WN WN0G mod 64 ,
TOW is the Time of the week, t0G is the reference time for GGTO,
WN is the GST Week Number and WN0G is the
Week Number of the GGTO reference. The broadcast GGTO parameters only corrects for timing differences originated at the satellite transmit side. Other inter system biases introduced by the receiver, like group delay differences [14] or delays generated during the baseband or DSP processing, cannot instead be directly recovered. For this reason, an estimator is proposed, as a complement to the broadcast information. A solution to the estimation problem is the inclusion of two additional unknowns, representing the bias and drift between GPS time and GST, which need to be estimated. In this way, the position and velocity state vector are:
where
cdt
GPS GAL
x P cdtuGPS
GPS cdtGAL
v V
GPS cdtGAL
cdtuGPS
navigation message [2], Iono is the accuracy related to ionosphere error after ionospheric model application [10], 2
(6)
GPS and cdtGAL are the bias and the drift between
GPS time and GST, respectively, hence one Galileo observation has to be “sacrificed” to estimate the additional unknown presented above. B. Alghortim Description In the proposed algorithm, a PVT (Position-Velocity-Time) estimator and a quality check (detailed in Figure 1) are developed to process GNSS data in single point mode. Main inputs of the navigation algorithm are GPS and Galileo raw measurements, i.e. PR and PR-rate, and the GNSS ephemerides. The ephemerides are used to compute satellite position and velocity; an orbital propagator is implemented for the considered GNSS; GPS orbital propagator is extensively treated in [5], while for Galileo the main reference is [6]. Measurements are corrected for satellite clock and atmospheric errors, specifically Klobuchar\NeQuick [1, 3, 8, 9] and Hopfield models are adopted to reduce ionosphere and troposphere delays respectively [1, 3].
2 Tropo
is the accuracy related to troposphere delay after
correction model application [10] and
2 mp
is the accuracy
related to multipath error [10]. PR-rate accuracy is simply assumed to be inversely proportional to sin(elv), where elv is the satellite elevation angle, because the main error terms affecting Doppler observables (orbital, atmospheric, multipath) can be neglected. C. Quality check The mass market receiver used for validation purposes is tailored for navigation (vehicular or pedestrian applications) in signal degraded scenarios, such us urban canyons. In order to perform a quality check on the measurement set, a block for the quality check is introduced in the navigation algorithm. Although this block adds complexity to the navigation algorithm, it is an essential part for the reliability assurance. The test is carried out to verify the measurement set consistency and is called Global Test (GT) [11, 12]. In the GT, the null-hypothesis assumes that the adjustment model is correct and the distributional assumptions meet reality; the errors are assumed to be Gaussian with zero mean. The alternative hypothesis assumes that the adjustment model is not correct. In the GT, the statistical variable, D, used to test the null hypothesis, is the quadratic form of the residual, r , weighted by the weighting matrix W (weighting matrix representing the different accuracy of the measurements
2 , PR
2 PR rate ) [13].
D r TWr
(8)
D is compared with a threshold, T , which is usually related
to the probability of false alarm, , and to the redundancy (defined as the difference between the number of measurements m and the number of the state n ), as shown below:
T 12 , mn where
the
notation
12 , mn
corresponding to a probability value of
The adopted estimator is a Weighted Least Squares (WLS) and 2 the PR accuracy model, PR , is dependent on satellite elevation: (7)
where URA is the User Range Accuracy (URA) related to the satellite ephemeris and clock, broadcast in the Galileo/GPS 2
indicates
the
abscissa
1 of a 2 distribution
m n order.
If D exceeds the threshold T the measurement set is declared inconsistent and the solution is flagged as unreliable.
Figure 1. Navigation Algorithm
2 2 2 2 2 PR URA Iono Tropo mp
(9)
III.
EXPERIMENTAL SETUP
The validation has been conducted on a compact evaluation board based on the multi-constellation chipset Teseo-II. The receiver software supports GPS, Galileo and GLONASS plus regional augmentation systems. Its main positioning algorithm combines the measurements from all the constellations into a single PVT solution, taking the GGTO as a given parameter. GPS GPS The corrections cdtGAL and cdtGAL are applied upfront, to the
Galileo pseudorange and frequency measurements respectively. A position least-squares algorithm is then executed, as part of the Teseo-II software. Two different modes of producing the GGTO information have been considered:
use of the broadcast GGTO, downloaded from the navigation message estimation by the PVT algorithm, described in the previous section
The receiver software architecture is shown in Figure 2. It presents some advantages respect to a single PVT algorithm (implemented through an extended state vector). The Teseo-II positioning software could be reused; in addition, since the GGTO parameters are slowly varying with time, the GGTO PVT estimator can be executed at a much slower rate, with a reduction in the processing load. The GGTO can be estimated at epochs where visibility is good, then propagated and assumed as a known parameter, such that no additional satellites are required. Since availability is not critical, then a strict quality check could be implemented.
When the GGTO is estimated, instead all these biases are automatically accounted as inter-system time offset, even if their actual origin is different. As a result the estimated and broadcast GGTO can take different values, usually in the range of few meters, in our experiments. A. Configuration of the GGTO Estimator Only the position WLS of Figure 1 has been implemented in the real-time software, whereas the A1G parameter was always set to zero. This simplification has little impact on the final accuracy as long as the GGTO fix rate is kept sufficiently high (e.g. every 30s). The estimator parameters have been chosen as from Table II and are the result of a general trade-off between estimation noise, error susceptibility to multi-path and fix availability. TABLE II: GGTO ESTIMATOR PARAMETERS Parameter GPS Galileo Min. Number of SVs to fix 4 1 Min. Signal Strength (CN0) 30 dBHz 30 dBHz Min. Elevation Mask 10 deg 10 deg Default URA 2.2 2.2 Min. Time to Track 250 ms 500 ms GGTO Expiration Interval 900 s Max. number of WLS Iterations 2 Max. Position Shift Squared 25 m2
The Teseo-II software implements both GPS Klobuchar and Galileo NeQuick ionospheric models. Model selection is available through NMEA sentences and applies to all the constellations. If SBAS is present, then the iono-grid delay overrides any previously selected model. If a prior user position is available from the main PVT solution, then it is used to initialize the H matrix.
Figure 2. Teseo-II GGTO Architecture
Each of the two supported modes (broadcast and estimated) has some specific pro and cons. The broadcast GGTO introduces virtually no estimation error but requires an accurate knowledge of all the other possible pseudorange and velocity biases introduced by the receiver. The Teseo-II chipset convey GPS and Galileo signals through the same RF path, such that the pseudorange biases induced by the total transfer function of analog plus IF filters, at the receiver side, are negligible [14]. Additional analog filters were inserted by the front-end of the sample record & replay device, which was used as signal generator. The Teseo-II digital baseband also introduces some small differences in the propagation delay, which however are constant and can be measured. The remaining biases are caused by differences in the DSP algorithms for channel tracking. Relevant parameters are, for example, the E-L spacing or the noise bandwidth of the loops.
The GGTO WLS is iterated up to a predefined number of times until position is stabilized within a predefined threshold (Table II). Pseudorange modulus is set to 1ms on the first iteration and to 100ms on the next iterations. To have a valid pseudorange over a 100ms modulus, a satellite is requested to have locked the preamble (GPS) or to have acquired the secondary code phase (Galileo). In most of the real cases, a 1ms modulus will be sufficient to achieve a fix rapidly, whereas in bad prior position conditions, 100ms will be necessary, which in turn will require more time for the bit phase alignment of the tracking channel to be reached. The Global Test (9) is applied to the residuals only after the position shift has stabilized below threshold. Both the broadcast navigation message and the estimator produce a pair of GGTO coefficients A0G, A1G tagged with a GST system time. If the Global Test rejects the fix, the main Teseo-II PVT will continue to provide a valid position by propagating the old estimate at the new epoch. IV.
EXPERIMENTAL RESULTS
The first validation scenario was generated by a signal simulator, with 10×GPS + 10×Galileo visible satellites. The simulator was configured to apply an ideal GGTO as follows: A0G=3E-8s ≈ 9m, A1G=8.3E-12s/s. Notice that, the A1G value
was intentionally programmed outside the maximum range allowed by the corresponding field in the navigation message, with the purpose of making the drift clearly visible in the plots. The receiver has run for about 700s under stable, clear sky, conditions producing the GGTO estimate shown in Figure 3.
GGTO estimation in the combined Galileo+GPS PVT solution, with respect to the GPS only case. The Cumulative Distribution Function (CDF) of the horizontal and vertical errors respect to the true antenna position, for the two constellation configurations are plotted in Figures 5. The NeQuick model for all SVs was adopted. A slight improvement for both the horizontal and vertical components can be noted when GPS and Galileo measurements are used together. In Figure 6 the CN0 and the elevations of the visible Galileo IOVs (PRN11, 12, 19, 20) are plotted vs. time; whereas the number of tracked SVs and HDOP are shown in Figure 7.
Figure 3. GGTO Estimation (simulator)
In the second experiment, a record & replay instrument was employed to capture the GPS C/A and Galileo E1 OS signals from a roof antenna. The data were collected during a period where the 4×IOV Galileo satellites were all visible at the same time. The objective of the test was to evaluate the effects of the ionospheric model on the GGTO estimation. Three replays of the same samples were done, where the receiver was programmed to apply respectively: 1) the NeQuick model on all SVs, 2) the GPS Klobuchar model on all SVs, 3) Klobuchar on GPS and NeQuick on Galileo (mixed). The resulting GGTO in the three cases are all very close and in good agreement, as shown in Figure 4.
Figure 5. Horizontal and Vertical Error CDF
Figure 6. CN0 and Elevation for Galileo SVs
Figure 8 shows the scatter plot around the true antenna location at the ST labs in Arzano (NA), Italy, where the scenario was recorded. The corresponding horizontal and vertical error components vs. time are plotted on Figure 9. Figure 4. Effects of Iono Model on GGTO
The same data samples were replayed also in the third experiment. The objective was to evaluate the benefits of
Figure 7. Tracked #SVs and HDOP vs. time
Figure 9. Horizontal and Vertical Errors vs. time, Galileo+GPS
REFERENCES [1] B. Hoffmann-Wellenhof, H. Lichtenegger and J. Collins, “Global Positioning System: Theory and Practice”. Springer New York, 1992.
Figure 8. Scatter plot at ST labs: Galileo + GPS
V.
CONCLUSIONS
An algorithm for the estimation of the Galileo to GPS Time Offset (GGTO), including a weighted least-squares and a global integrity test has been presented. Practical real-time implementation and integration have been proven on a consumer grade GNSS hardware receiver, based on the TeseoII chipset. Experiments have been conducted using a GNSS simulator and a live, recorded scenario with 9×GPS and 4× Galileo IOVs visible at the same time. Results have shown that, with this specific setup, GGTO estimation was effective and allowed for the combination of Galileo plus GPS measurements into a single PVT solution, with comparable or better accuracy respect to GPS only. Different ionospheric models (Klobuchar and NeQuick) have been applied on the same recorded IOV scenario, showing comparable results. Respect to the direct application of the broadcast GGTO (from the I/NAV message), the use of an estimator has the advantage that other biases introduced by the receiver and not necessarily related to system times differences, are also captured in a single correction term. Future developments will include: tuning of the integrity thresholds and the introduction of a local integrity test, validation in presence of reflections and multipath and further reduction of the GGTO fix rate by direct estimation of the A1G coefficient.
[2] E.D. Kaplan and J. Hegarty, “Fundamentals of Satellite Navigation. Kaplan, E.D. ed., Understanding GPS: Principles and Applications” (second edition), Artech House Mobile Communications Series, 2006. [3] B. Parkinson and J.J.Jr Spilker, “Global Positioning System: Theory And Applications”, volumes 1-2, American Institute of Aeronautics and Astronautics, Inc., Washington D.C., USA,1996. [4] C. Gioia, D. Borio, A. Angrisano, S. Gaglione, and J. Fortuny-Guasch, "Testing the test satellites: the Galileo IOV measurement accuracy," Proc. of the International Conference on Localization and GNSS (ICL-GNSS 2013 Torino), pp.1-6, June 2013 [5] IS-GPS-200, Navstar GPS Space Segment/Navigation User Interfaces, Revision D, ARINC Research Corporation, El Segundo, CA, 2004. [6] European GNSS (Galileo) open service, signal in space interface control document, European Union and European Space Agency (ESA), Tech. Rep. Ref: OS SIS ICD, Issue 1, Feb. 2010. [7] A. Angrisano, S. Gaglione, C. Gioia, U. Robustelli, and M. Vultaggio, “GIOVE satellites pseudorange error assessment,” The Journal of Navigation, vol. 65, no. 1, pp. 29–40, 2012 [8] S. M. Radicella, The NeQuick model genesis, uses and evolution. Annals of Geophysics, Vol. 52, N. 3/4, June/August 2009, 417-422. [9] A. Angrisano, S. Gaglione, C. Gioia, M. Massaro, S. Troisi, Benefit of the NeQuick Galileo version in GNSS single-point positioning (2013) International Journal of Navigation and Observation, 2013, art. no. 302947. [10] SC-159 of the RTCA, Minimum Operational Performance Standards for Global Positioning System/Wide Area augmentation system airborne equipment, RTCA - Washington DC, Document DO-229D, December 13, 2006. [11] A. K. Brown. Receiver autonomous integrity monitoring using a 24satellite GPS constellation. Papers published in NAVIGATION, Journal of The Institute of Navigation,V:21–33, 1998. Red Book of RAIM. [12] H. Kuusniemi, A.Wieser, G. Lachapelle, and J. Takala. User-level reliability monitoring in urban personal satellite-navigation. IEEE Trans. Aerospace and Electronic Systems, 2004. [13] A.Angrisano., C. Gioia, S. Gaglione, G. Del Core, GNSS reliability testing in signal-degraded scenario (2013) International Journal of Navigation and Observation, art. no. 870365. [14] Pisoni, F.; Mattos, P.G.; “Correction of pseudorange errors in Galileo and GLONASS caused by biases in group delay”, 6th ESA Workshop on GNSS Signals and Signal Processing, (NAVITEC), December 201
