- Email: [email protected]
Commercial Use of GNSS Signals in GEO
ELSEVIER
Copyright © IFAC Automatic Control in Aerospace, Saint-Petersburg, Russia, 2004
IFAC PUBLICATIONS www.elsevier.comllocate/ifac
COMMERCIAL USE OF GNSS SIGNALS IN GEO M. Mittnacht l ), E. Gottzein I), M. Hartrampf l ), A. Konrad I), P.A. Krauss I), C. KOhl l ) D. MarareskouI 1), A. Grechkoseev 1), E. Islentjev 1)
1) EADS Astrium GmbH, 81663 Munich, Germany, e-mail: [email protected] 2) NPO PM, 662972, Lenina 52, Zheleznogorsk, Krasnoyarsk region, Russia, e-mail: [email protected]
Abstract: Geostationary orbit detennination using GNSS (GPS/GLONASS) signals is an attractive option compared to existing ground based orbit detennination techniques. This paper addresses the commercial application of GNSS receivers for geostationary navigation. The major issues of geostationary GNSS navigation are weak signal-to-noisedensity ratio and poor geometrical satellite distribution and visibility. The investigations and system trade-offs presented here are based on the MosaicGNSS receiver (EADS Astrium GmbH) and the ARN GEO receiver (NPO-PM). The receiver hardware is outlined and a review of the properties of a geostationary mission with respect to GNSS applications is given. Copyright © 2004 IFAC Keywords: Autonomous, GEO, GLONASS , GNSS, GPS, Orbit Determination
detennination using GNSS. A geostationary, near circular orbit with a 3-axis stabilized, Earth oriented spacecraft with the GNSS receiver antenna mounted on the Earth panel of the spacecraft is used to demonstrate those properties.
I . INTRODUCTION
1.1 Motivation and Background The use of GNSS receivers for navigation purposes in satellites beyond low Earth orbits has been considered for some time (Ananda and Jorgensen, 1985). The orbital maintenance based on GNSS signals gives the following advantages: increase of detennination accuracy, increase of satellite autonomy, decrease of cost and complexity of ground segment, reduced influence of the human factor and simplification of the satellite control technology. The use of relative navigation opens new possibilities for co-positioning of satellites in one GEO slot. In highly elliptical orbits non-military experiments were already perfonned and evaluated, see e.g. (Balbach, 0., et aI., 1998). In the geostationary case GPS pseudorange data was already used routinely for orbit detennination in military applications (Kronman, 2000). This paper addresses techniques for orbit detennination of commercial geostationary satellites using GNSS. Two receivers will be introduced, which are tailored for GEO applications.
2.1 Geometrical Configuration and Implications The geostationary orbit (GEO) altitude is about 36000 km, i.e. geostationary satellites fly above the GNSS altitude (-20000km) and thus, they receive only signals from GNSS satellites beyond the Earth.
Fig. 1. Geometrical configuration of geostationary GPS/GLONASS application.
2. CONDITIONS IN GEOSTATIONARY ORBIT
a
Figure I shows the geometrical configuration. This has the following major impacts on GNSS based navigation:
This section emphasizes the special properties of a geostationary scenario with respect to orbit
1097
•
•
Weak signal-to-noise-density ratio of the received GNSS signal due to the long distance between GNSS satellite and receiver and the GNSS transmit antenna characteristics. Poor geometrical distribution of visible GNSS satellites. As seen from a geostationary orbit the distribution of the visible GNSS satellites is constrained to a small "ring" around the Earth with an angular width of about two degrees (high geometric delusion of precision; GOOP). In GEO usually less than 4 GNSS satellites are visible.
GLONASS and GLONASSIGPS satellite visibility The number of tracked GNSS satellites depends very much on the acquisition threshold Qtr=C/N threshold. The signal detection and acquisition without a priori information is possible if the C/N ratio is greater than 30 dBHz. The signal tracking after acquisition is possible down to an CIN ratio of 25-30 dBHz.
2.2 Ionospheric Effects
GNSS signals received in the geostationary orbit may pass through large portions of the ionosphere which leads to inaccurate results. In order to eliminate ionospheric effects, the Earth radius will be artificially increased in the navigation planning module of the receiver by about 1000 km. This reduces the "geometric" visibility due to the "larger" Earth disk. 2.3 Link Budget Link Budget GEO - GPSIGLONASS The following effects were considered for link budget calculations:
• • • • • • •
_. 12
"
Fig. 2. Number of visible GLONASS and GPS satellites for Qtr=30dBHz The orbit motion is repeatable and predictable. This allows to support the search and acquisition process under worst conditions by using dynamic models. 2.5 Relative Dynamics GEO-GPS Table 2 summarizes the relative dynamics parameters of a receiver on a 3-axis stabilized Earth oriented spacecraft. The values are very low (comparable to that of static terrestrial GPS user) and thus, do not introduce specific requirements for the geostationary application.
Transmit signal power (EIRP) Relative GPS/GLONASS antenna gain Space loss Polarization loss (3.4 dB max.) Receiver antenna gain LNA noise figure (1.5dB) Antenna noise and ambient temperature of 300 K and 290 K, respectively
Table 2: Relative dynamics GEO relative velocity Doppler shift
A low noise amplifier (LNA) must be implemented close to the antenna. Then the noise contributions after the LNA are negligible.
GPS satellites. relative acc.
Crn/s1
[k!IzJ
Cm/s 2]
+1255
±6.6
±O.24
GEO - GLONASS The GLONASS and GPS constellations are similar. Therefore the relative dynamics conditions for GLONASS are similar to those of GPS.
2.4 GNSS Satellite Visibility
GPS satellite visibility Detailed investigations have shown that the visibility does depend on the nominal longitude of the GEO satellite. Due to the inertial drift of the GPS constellation, worst case situations will be encountered by every GEO communications spacecraft, even with constant geostationary longitude.
3. RECEIVER HARDWARE
3. I MosaicGNSS Receiver Overview The MosaicGNSS receiver (Figure 4) is a radiation tolerant (up to 100 krad) GPS single board receiver for applications in LEO, MEO and GEO (Krauss, 2002). It is a LI CIA code receiver, which is capable of acquiring and independently tracking of up to eight GPS satellites. A key feature of this receiver is the implementation of main parts of the signal processing in software (Botchkovski, et aI., 1999). This permits flexible control of the processor load (i.e. reduction of channels or partial correlation). The receiver is designed to process weak signals and its dynamic navigation solution provides PVT (position,
Table I: GPS satellite visibility in percent of time. Longitude 0°, 0 visible >0 visible >1 visible 24 hours satellites satellite satellite antenna gain 17.5% 48.5% 10 dB 51.5% 26.1% 6.4% 73.9% 5dB 2.7% 14.5% 3dB 85 .5% Table 1 summarizes the results with different receiver antenna gains.
1098
the order of 30 dBHz. This means, that the acquisition techniques have to be adjusted for the weak signals in order to ensure a successful receiver operation.
Velocity, Time), even in situations where less than four satellites are visible. A sequential estimation algorithm with a high precision orbit model is used to form the dynamic solution. Synchronization to GPS time is provided by a one Hertz Time Mark Pulse. Figure 3 shows the block diagram of the hardware components of the MosaicGNSS receiver. GPS receiver performance data (rrns) is given in Table 3.
Table 4 shows estimated CIN density and signal dynamics for several satellite orbits. The MosaicGNSS receiver with its software correlation has been initially developed for LEO applications, where high dynamics and standard C/N have to be taken into account. In the case of a GEO scenario the GPS signals with lower C/N have to be coped with, while on the other hand the receiver experiences less dynamics relative to the GPS satellites. Thus, the Doppler uncertainty range can be reduced. An additional reduction of the Doppler uncertainty range can be achieved using better Doppler predictions based on the initial PVT knowledge and the GPS almanac data. Table 4: Signal-to-noise ration for space applications Parameter LEO MEO GEO Doppler 50 kHz 20 kHz 6.6 kHz 10 HzJs 7 HzJs Doppler-Rate 60 HzJs C/N Density 45 dBHz 35 dBHz 30 dBHz
Fig. 3. MosaicGNSS Receiver block diagram Table 3: MosaicGNSS Receiver Performance Data Accuracy. 3D. no SA Position Velocity Time
< 8 min
The acquisition algorithms of the MosaicGNSS receiver are originally designed as a two step search procedure. The first step is used only in the case of no (suitable) predicted Doppler-shift and consists of the Fast Fourier Transformation (FFT) of the signal samples. The second step is based on the conventional real-time signal search, where the twodimensional search area (frequency and code phase) is sequentially checked. This search procedure was then extended by a procedure for acquisition of weak signals. Since the real-time search can not be optimized for both weak and normal GPS signals at the same time, the algorithm is designed to analyze the uncertainty of the Doppler prediction first. If the uncertainty is small enough (about 2 kHz), the search is conducted as a two-pass procedure. This means, if the GPS signal is not found during the first pass, which is parameterized for strong GPS signals with a minimum C/N of 37 dBHz, the search parameters (threshold and analysis time at a specific code phase) are readjusted for weak signals with C/N of down to 30d.BHz. The drawback of the ability to detect weak signals during the second pass is an increase in search time by the factor of 5 to fmish a search over the full ClA code epoch in one Doppler bin.
Warm start < 4 min
• aJbhlde 10000 kiI1
Figure 4 shows the "slide in module" version of the receiver, scheduled to fly on the TerraSAR satellite, while another version, the redundant "stand alone box" configuration including power converter, is going to fly on the SAR-Lupe satellites.
3.2 ARN GEO Receiver Overview The methods of digital signals processing are realised in the receiver. Part of the spectrum shifts are done in the digital module. The correlation of the signal is mainly done in software. In the HF section the GLONASS and GPS spectrum are shifted to a low intermediate frequency. The signals frequency separation and primary signal correlation processing are executed in the digital-processing module, which is a chip developed by NPO PM. The final digital signal processing, search, filtration, selections of
Signal Acquisition In the case of a GPS receiver for space applications lower C/N must be taken into account for some missions compared to terrestrial GPS receivers. In the case of a GPS receiver on board of a GEO satellite the additional degradation of the C/N caused by the signal propagation in space may be as high as 15 dB, so that the worst case of signal to noise ratio (CIN) (as seen by the receiver software) may be of 1099
navigational parameters and navigational message is done in the computer module. The current ARN-GEO calculates and telemetries the pseudorange, Doppler shift and time shift from GLONASS, GPS and UTC scale. The navigation determination is realised on the main onboard computer in the software navigation module. In the next generation, the navigational module is implemented in the internal ARN-GEO computer module. Optional ARN-GEO provides precise time signals for I Hz, I KHz and 5 MHz synchronized with GLONASS or GPS time. Directional antenna To improve the tracking capability, a directional antenna with 15 dB gain is used. The antenna mass is 0.7 kg. Antenna size: base diameter - 180 mm, length 660 mm, top diameter 50 mm. Acquisition Techniques To improve the search performance, the ARN-GEO receiver is supported by information from the navigation and orbit prediction software. In steady state of the navigation determination, the support data for signal search are known with an accuracy for the Doppler shift < 1 Hz, and for the ARN time scale shift and pseudorange < 500 m.This allows to reduce the search range search time in each search position. As a result the tracking performance is better in steady state then in initial state.
Power voltage, V: 25.28 Supply power, W: 20 Pseudorange measuring error, RMS, m: 3 Interface: MIL-STD 15538 Life time, year: 10 Redundancy: cold, (2 units) 4. NAVIGATION STRATEGIES IN GEO
A kinematic solution requires four or more visible navigation satellites at the same time to calculate the four unknowns (position vector and clock bias). In the geostationary orbit usually less than 4 satellites are visible simultaneously and thus, a kinematic solution is not possible. Therefore, sequential estimation methods must be applied, e.g. Kalman filtering. These methods require a model of the system (user) dynamics and statistical knowledge of the process and measurement noise. 4.1 Model of the User Dynamics
The satellite motion of a geostationary satellite can be expressed using the linear and time invariant Hill's equation. The system state describes the relative motion of the satellite with respect to a nominal geostationary orbit. The discrete system model (1 )
To maintain the time scale stability during GNSS satellites visibility gaps, a highly stable TCXO clock (GK54-TC) is installed in the HF module. At present, NPO PM is developing a flight model of the ARN-GEO based on the current laboratory model. Figure 5 shows the block diagram and Figure 6 the DSP unit of the ARN-GEO laboratory model.
is used for orbit propagation. tJ)S,k is the 6 x 6 transition matrix, As,Jc is the 6 x 3 input matrix and WS,k is additional noise, The 6-dimensional state XI comprises the relative position and velocity with reference to the nominal orbit. The axis related accelerations, which are composed of natural disturbance accelerations (such as solar pressure and luni-solar attraction as well as thruster accelerations), are represented by the input vector Uk. The in-plane motion and the out-of-plane motion of the satellite are decoupled. The receiver clock is modeled as a two state random process. The state is comprised of the clock phase and frequency error.
- .. ,
Fig. 5. ARN-GEO block diagram 4.2 MosaicGNSS Navigation Algorithms
Two navigation approaches have been investigated: the first one uses pseudorange measurements for Kalman filter updates, the second one uses differences of pseudoranges (A verin, et aI., 1996). Pseudorange Measurements A pseudorange measurement is composed of the satellite-ta-user range, the clock bias in meter and additional noise. The measurement equation can then be linearized around the best position and clock bias estimate. When pseudoranges are used, Kalman filter updates can be performed with only one or more visible navigation satellite(s). In this case the state vector is comprised of the six states of the user dynamics and the two receiver clock states, i.e. a motion model of the geostationary satellite as well as a receiver clock model is required. Compared to the
The ARG-GEO performances: Ll (GLONASS&GPS) Received signals: Number of channel: 8 Mass (without antenna, 2 units), kg: 6 Size, mm: 300x250x200
1100
well known satellite dynamics the clock model is relative uncertain which limits the navigation accuracy. It is well known that the performance is sensitive to clock uncertainties, see e.g. (Ananda and Jorgensen, 1985). High performance clocks are therefore required for this approach.
Pseudorange Differences The second navigation method eliminates the clock bias using single differences of pseudoranges for Kalman filter updates. The filter model is composed only of the well known orbit dynamics, i.e. this approach is completely independent of (robust with respect to) clock uncertainties. Therefore a relatively inexpensive standard clock (TCXO) can be used with a typical drift of 10-7 (long-term stability). The drawback of this method is that two navigation satellites must be visible simultaneously, which leads to longer gaps without any measurements. Therefore, this approach is sensitive to the link budget. Single differences of pseudorange measurements are given by
0i
= Pm -
Pi
= (If -l~)r+vi ' i = I to m-I ,
(2)
where r is the position deviations from the reference values, -lj is the unit vector from the receiver to the ith GNSS satellite and Vj is a (noise) disturbance of the i-th pseudorange measurement. or in matrix form with (noise) disturbance
Pm -: PI
0=
[
1f Jr -l~ 1·r+vo , = :
Pm - Pm-I
5. TEST ENVIRONMENT 5.1 MosaicGNSS Rx Test Environment The real-time closed loop test environment (Figure 7) comprises the MosaicGNSS receiver, a simulation computer, which calculates the orbit and attitude of the user satellite and a 2 times 12 channel GPS RF signal simulator. The term 'closed loop' is used here in the sense of a closed loop test system and not in the sense of a closed control loop. All simulation equipment is timely synchronized with the GPS RF signal simulator. The orbit and attitude data of the user satellite is fed to the GPS RF signal simulator unit, which stimulates the GPS receiver. The MosaicGNSS receiver calculates the PVT and sends it back to the simulation computer for further analysis, visualization and storage.
(3) . ...... . ...... -. . . : RIui ·nrr:* Td!i&f~Jtot~
1~_1 -I~
o is
the single differences measurement and m denotes the number of pseudorange measurements. This method reduces the number of "actual" measurements by one. Despite this fact, it turns out that the elimination of the clock model improves the overall performance and reduces the computational effort. Note, that the covariance matrix of the noise in equation (3) has non-zero off-diagonal elements, caused by the differences. Using the navigation solution the receiver clock bias can be calculated by I m • bca1c =-LPi -di
process an estimation of the GEO position is made based on the received measurements. Corrections to the current position, calculated by a high-precision propagator, are made by calculating the estimation errors. At the end of the improvement process, the estimated position vector can be used for further calculation of the GEO position by the propagator. The determination of the current position is improved by corrections from the measurements. The duration of the improvement process lasts 24 hours. Therefore, each 24 hours the initial conditions for the propagator are corrected.
(4)
mi=1
i' I=::~-'--" }':~~~i~~~~: ' :! ~-~l ~~
I: ! i
'!
.1 I
,--
. . . -- , . ~
.
..
- .-~,,- -- -; . . -..- ... .... ... - ... .
,, ~
. . _- ..
~- ,,-- ~--~--
Fig, 7, GPS Test Facility
5.2 ARN GEO Test Environment For ground tests of the ARN-GEO hardware and software a test bench has been created. The core of this bench is the GLOASS/GPS signal simulator from Krasnoyarsk SRI "Radiotechnika". The conditions of orbital flights are simulated with a stimulation of all satellite subsystems. For this purpose a software model of ARN-GEO has been created.
where d j is the estimated value of the distance between the i-th navigation satellite and the receiver and m denotes the number of measurements.
4.3 ARN-GEO Navigation algorithm
6. PERFORMANCE RESULTS
The ARN-GEO uses pseudorange differences as input for the navigation filter (2).
6.1 Performance Results with MosaicGNSS Receiver Real-time runs were performed with a geographical longitude with worst case visibility conditions in the geostationary orbit and a receiver antenna gain of 5 dB . A mismatch of the model and the "real" natural forces has been taken into account. The uncertainty of the solar pressure is assumed to be 10 % of its
The calculated position is given as corrections to an initial GEO satellite position. This initial position is fixed at the reference time. The measurements are then fed into a Kalman filter. During the navigation
llOI
nominal value, whereas the uncertamttes of the gravity of sun and moon, the triaxiality, and oblateness of the Earth are modeled to be 5% of its nominal value with additional random noise effects. The initial position error has been set to the limits of a station-keeping window (± 37.5 km). Selective availability (SA) has been switched off. The Kalman filter converges even if e.g. no solar pressure is modeled at all . Table 5: Performance results (SA oft) Single differences GPS ESTIMATION STD MEAN RMS ERROR [m] [m] [m] Along track 52.90 1.52 52.92 Cross track 18.34 -3.56 18.68 Radial 27.31 -2.95 27.47
The accuracy of the GEO satellite orbit navigation with GLONASS/GPS (model data) is shown in Table 6; Table 7, Figure 9 and Figure 10. Table 7: Position error (GLONASS + GPS) (SA oq) Along track Cross track Radius RMS 72 m 53 m 41 m MAX 262 m 168 m 148 m
..... ..... ~--~----~+----+------4--+~ .1,00
Figure 8 and Table 5 show the obtained results (steady state).
o
1121IJr1
••
CZ
'hno, h
Fig. 10. Estimation errors with GLONASS + GPS
Estimation Error 3D and axis related
7. CONCLUSION The dependence of receiver performance on HW (LNA, antenna, etc.) and SW implementation (signal processing, CIN threshold) has been shown. Performance results from worst case simulation are given and show the applicability of GNSS receivers for orbit determination of GEO telecommunications satellites. Timc(h]
REFERENCES
Fig. 8. 3D/axis related errors with MosaicGNSS receiver and GPS simulator in the loop, SA off.
6.2 Performance Results ARN GEO Receiver A mathematical model was built for the estimation of precise GEO satellite positioning. For modeling purposes the navigation measurements and system models of the GLONASS and GPS navigation systems were created. The initial position error was set to ±40 km and Selective Availability for the GPS system was turned on.
..,.. ""'~---r-+--'-------~1rr-+-~~
o
•
n
~
M
•
•
G
•
M
•
•
n
'hno, h
Fig. 9. Estimation errors with 24 GLONASS satellites Table 6: Position error with 24 GLONASS satellites Along track Cross track Radius RMS 69 m 46 m 42 m 184 m 347 m MAX 259 m
1102
Ananda, M.P. and P.S. Jorgensen (1985). Orbit Determination of Geostationary Satellites Using the Global Positioning System, Proceedings of the Symposium on Space Dynamics for Geostationary Satellites, CNES, Toulouse, France, Aug. 1985. Averin, S., V. Vinogradov, N. Ivanov and V. SaIischev (1996). Application of Differential Method for Relative Positioning of Geostationary Satellites with use of GLONASS and GPS Navigation Signals, Proceedings of the fifth international conference on differential navigation DSNS-06, Vol. 2,1996. Balbach, 0., et a!. (1998). Tracking of GPS Above GPS Satellite Altitude: Results of the GPS Experiment on the HEO Mission Equator-S, Proceedings of the Institute of Navigation GPS 98 Conference, Nashville, TN, 1998. Botchkovski, A. V. et al. (1999). Softflex: An Advanced Approach to Design of GNSS Receiver with Software Correlator, Proceedings of the 12th International Technical Meeting of The Institute of Navigation, ION-GPS99, Nashville, Tennessee, 1999. Krauss, P. A.. (2002). EADS Astrium GmbH MosaicGNSS Receiver Flyer, peter.a.krauss @astrium.eads.net Kronman, 1.D. (2000). Experience Using GPS for Orbit Determination of a Geosynchronous Satellite, Abstracts for the ION GPS 2000 conference, SaIt Lake City, Sept. 2000.
Copyright © IFAC Automatic Control in Aerospace, Saint-Petersburg, Russia, 2004
IFAC PUBLICATIONS www.elsevier.comllocate/ifac
COMMERCIAL USE OF GNSS SIGNALS IN GEO M. Mittnacht l ), E. Gottzein I), M. Hartrampf l ), A. Konrad I), P.A. Krauss I), C. KOhl l ) D. MarareskouI 1), A. Grechkoseev 1), E. Islentjev 1)
1) EADS Astrium GmbH, 81663 Munich, Germany, e-mail: [email protected] 2) NPO PM, 662972, Lenina 52, Zheleznogorsk, Krasnoyarsk region, Russia, e-mail: [email protected]
Abstract: Geostationary orbit detennination using GNSS (GPS/GLONASS) signals is an attractive option compared to existing ground based orbit detennination techniques. This paper addresses the commercial application of GNSS receivers for geostationary navigation. The major issues of geostationary GNSS navigation are weak signal-to-noisedensity ratio and poor geometrical satellite distribution and visibility. The investigations and system trade-offs presented here are based on the MosaicGNSS receiver (EADS Astrium GmbH) and the ARN GEO receiver (NPO-PM). The receiver hardware is outlined and a review of the properties of a geostationary mission with respect to GNSS applications is given. Copyright © 2004 IFAC Keywords: Autonomous, GEO, GLONASS , GNSS, GPS, Orbit Determination
detennination using GNSS. A geostationary, near circular orbit with a 3-axis stabilized, Earth oriented spacecraft with the GNSS receiver antenna mounted on the Earth panel of the spacecraft is used to demonstrate those properties.
I . INTRODUCTION
1.1 Motivation and Background The use of GNSS receivers for navigation purposes in satellites beyond low Earth orbits has been considered for some time (Ananda and Jorgensen, 1985). The orbital maintenance based on GNSS signals gives the following advantages: increase of detennination accuracy, increase of satellite autonomy, decrease of cost and complexity of ground segment, reduced influence of the human factor and simplification of the satellite control technology. The use of relative navigation opens new possibilities for co-positioning of satellites in one GEO slot. In highly elliptical orbits non-military experiments were already perfonned and evaluated, see e.g. (Balbach, 0., et aI., 1998). In the geostationary case GPS pseudorange data was already used routinely for orbit detennination in military applications (Kronman, 2000). This paper addresses techniques for orbit detennination of commercial geostationary satellites using GNSS. Two receivers will be introduced, which are tailored for GEO applications.
2.1 Geometrical Configuration and Implications The geostationary orbit (GEO) altitude is about 36000 km, i.e. geostationary satellites fly above the GNSS altitude (-20000km) and thus, they receive only signals from GNSS satellites beyond the Earth.
Fig. 1. Geometrical configuration of geostationary GPS/GLONASS application.
2. CONDITIONS IN GEOSTATIONARY ORBIT
a
Figure I shows the geometrical configuration. This has the following major impacts on GNSS based navigation:
This section emphasizes the special properties of a geostationary scenario with respect to orbit
1097
•
•
Weak signal-to-noise-density ratio of the received GNSS signal due to the long distance between GNSS satellite and receiver and the GNSS transmit antenna characteristics. Poor geometrical distribution of visible GNSS satellites. As seen from a geostationary orbit the distribution of the visible GNSS satellites is constrained to a small "ring" around the Earth with an angular width of about two degrees (high geometric delusion of precision; GOOP). In GEO usually less than 4 GNSS satellites are visible.
GLONASS and GLONASSIGPS satellite visibility The number of tracked GNSS satellites depends very much on the acquisition threshold Qtr=C/N threshold. The signal detection and acquisition without a priori information is possible if the C/N ratio is greater than 30 dBHz. The signal tracking after acquisition is possible down to an CIN ratio of 25-30 dBHz.
2.2 Ionospheric Effects
GNSS signals received in the geostationary orbit may pass through large portions of the ionosphere which leads to inaccurate results. In order to eliminate ionospheric effects, the Earth radius will be artificially increased in the navigation planning module of the receiver by about 1000 km. This reduces the "geometric" visibility due to the "larger" Earth disk. 2.3 Link Budget Link Budget GEO - GPSIGLONASS The following effects were considered for link budget calculations:
• • • • • • •
_. 12
"
Fig. 2. Number of visible GLONASS and GPS satellites for Qtr=30dBHz The orbit motion is repeatable and predictable. This allows to support the search and acquisition process under worst conditions by using dynamic models. 2.5 Relative Dynamics GEO-GPS Table 2 summarizes the relative dynamics parameters of a receiver on a 3-axis stabilized Earth oriented spacecraft. The values are very low (comparable to that of static terrestrial GPS user) and thus, do not introduce specific requirements for the geostationary application.
Transmit signal power (EIRP) Relative GPS/GLONASS antenna gain Space loss Polarization loss (3.4 dB max.) Receiver antenna gain LNA noise figure (1.5dB) Antenna noise and ambient temperature of 300 K and 290 K, respectively
Table 2: Relative dynamics GEO relative velocity Doppler shift
A low noise amplifier (LNA) must be implemented close to the antenna. Then the noise contributions after the LNA are negligible.
GPS satellites. relative acc.
Crn/s1
[k!IzJ
Cm/s 2]
+1255
±6.6
±O.24
GEO - GLONASS The GLONASS and GPS constellations are similar. Therefore the relative dynamics conditions for GLONASS are similar to those of GPS.
2.4 GNSS Satellite Visibility
GPS satellite visibility Detailed investigations have shown that the visibility does depend on the nominal longitude of the GEO satellite. Due to the inertial drift of the GPS constellation, worst case situations will be encountered by every GEO communications spacecraft, even with constant geostationary longitude.
3. RECEIVER HARDWARE
3. I MosaicGNSS Receiver Overview The MosaicGNSS receiver (Figure 4) is a radiation tolerant (up to 100 krad) GPS single board receiver for applications in LEO, MEO and GEO (Krauss, 2002). It is a LI CIA code receiver, which is capable of acquiring and independently tracking of up to eight GPS satellites. A key feature of this receiver is the implementation of main parts of the signal processing in software (Botchkovski, et aI., 1999). This permits flexible control of the processor load (i.e. reduction of channels or partial correlation). The receiver is designed to process weak signals and its dynamic navigation solution provides PVT (position,
Table I: GPS satellite visibility in percent of time. Longitude 0°, 0 visible >0 visible >1 visible 24 hours satellites satellite satellite antenna gain 17.5% 48.5% 10 dB 51.5% 26.1% 6.4% 73.9% 5dB 2.7% 14.5% 3dB 85 .5% Table 1 summarizes the results with different receiver antenna gains.
1098
the order of 30 dBHz. This means, that the acquisition techniques have to be adjusted for the weak signals in order to ensure a successful receiver operation.
Velocity, Time), even in situations where less than four satellites are visible. A sequential estimation algorithm with a high precision orbit model is used to form the dynamic solution. Synchronization to GPS time is provided by a one Hertz Time Mark Pulse. Figure 3 shows the block diagram of the hardware components of the MosaicGNSS receiver. GPS receiver performance data (rrns) is given in Table 3.
Table 4 shows estimated CIN density and signal dynamics for several satellite orbits. The MosaicGNSS receiver with its software correlation has been initially developed for LEO applications, where high dynamics and standard C/N have to be taken into account. In the case of a GEO scenario the GPS signals with lower C/N have to be coped with, while on the other hand the receiver experiences less dynamics relative to the GPS satellites. Thus, the Doppler uncertainty range can be reduced. An additional reduction of the Doppler uncertainty range can be achieved using better Doppler predictions based on the initial PVT knowledge and the GPS almanac data. Table 4: Signal-to-noise ration for space applications Parameter LEO MEO GEO Doppler 50 kHz 20 kHz 6.6 kHz 10 HzJs 7 HzJs Doppler-Rate 60 HzJs C/N Density 45 dBHz 35 dBHz 30 dBHz
Fig. 3. MosaicGNSS Receiver block diagram Table 3: MosaicGNSS Receiver Performance Data Accuracy. 3D. no SA Position Velocity Time
< 8 min
The acquisition algorithms of the MosaicGNSS receiver are originally designed as a two step search procedure. The first step is used only in the case of no (suitable) predicted Doppler-shift and consists of the Fast Fourier Transformation (FFT) of the signal samples. The second step is based on the conventional real-time signal search, where the twodimensional search area (frequency and code phase) is sequentially checked. This search procedure was then extended by a procedure for acquisition of weak signals. Since the real-time search can not be optimized for both weak and normal GPS signals at the same time, the algorithm is designed to analyze the uncertainty of the Doppler prediction first. If the uncertainty is small enough (about 2 kHz), the search is conducted as a two-pass procedure. This means, if the GPS signal is not found during the first pass, which is parameterized for strong GPS signals with a minimum C/N of 37 dBHz, the search parameters (threshold and analysis time at a specific code phase) are readjusted for weak signals with C/N of down to 30d.BHz. The drawback of the ability to detect weak signals during the second pass is an increase in search time by the factor of 5 to fmish a search over the full ClA code epoch in one Doppler bin.
Warm start < 4 min
• aJbhlde 10000 kiI1
Figure 4 shows the "slide in module" version of the receiver, scheduled to fly on the TerraSAR satellite, while another version, the redundant "stand alone box" configuration including power converter, is going to fly on the SAR-Lupe satellites.
3.2 ARN GEO Receiver Overview The methods of digital signals processing are realised in the receiver. Part of the spectrum shifts are done in the digital module. The correlation of the signal is mainly done in software. In the HF section the GLONASS and GPS spectrum are shifted to a low intermediate frequency. The signals frequency separation and primary signal correlation processing are executed in the digital-processing module, which is a chip developed by NPO PM. The final digital signal processing, search, filtration, selections of
Signal Acquisition In the case of a GPS receiver for space applications lower C/N must be taken into account for some missions compared to terrestrial GPS receivers. In the case of a GPS receiver on board of a GEO satellite the additional degradation of the C/N caused by the signal propagation in space may be as high as 15 dB, so that the worst case of signal to noise ratio (CIN) (as seen by the receiver software) may be of 1099
navigational parameters and navigational message is done in the computer module. The current ARN-GEO calculates and telemetries the pseudorange, Doppler shift and time shift from GLONASS, GPS and UTC scale. The navigation determination is realised on the main onboard computer in the software navigation module. In the next generation, the navigational module is implemented in the internal ARN-GEO computer module. Optional ARN-GEO provides precise time signals for I Hz, I KHz and 5 MHz synchronized with GLONASS or GPS time. Directional antenna To improve the tracking capability, a directional antenna with 15 dB gain is used. The antenna mass is 0.7 kg. Antenna size: base diameter - 180 mm, length 660 mm, top diameter 50 mm. Acquisition Techniques To improve the search performance, the ARN-GEO receiver is supported by information from the navigation and orbit prediction software. In steady state of the navigation determination, the support data for signal search are known with an accuracy for the Doppler shift < 1 Hz, and for the ARN time scale shift and pseudorange < 500 m.This allows to reduce the search range search time in each search position. As a result the tracking performance is better in steady state then in initial state.
Power voltage, V: 25.28 Supply power, W: 20 Pseudorange measuring error, RMS, m: 3 Interface: MIL-STD 15538 Life time, year: 10 Redundancy: cold, (2 units) 4. NAVIGATION STRATEGIES IN GEO
A kinematic solution requires four or more visible navigation satellites at the same time to calculate the four unknowns (position vector and clock bias). In the geostationary orbit usually less than 4 satellites are visible simultaneously and thus, a kinematic solution is not possible. Therefore, sequential estimation methods must be applied, e.g. Kalman filtering. These methods require a model of the system (user) dynamics and statistical knowledge of the process and measurement noise. 4.1 Model of the User Dynamics
The satellite motion of a geostationary satellite can be expressed using the linear and time invariant Hill's equation. The system state describes the relative motion of the satellite with respect to a nominal geostationary orbit. The discrete system model (1 )
To maintain the time scale stability during GNSS satellites visibility gaps, a highly stable TCXO clock (GK54-TC) is installed in the HF module. At present, NPO PM is developing a flight model of the ARN-GEO based on the current laboratory model. Figure 5 shows the block diagram and Figure 6 the DSP unit of the ARN-GEO laboratory model.
is used for orbit propagation. tJ)S,k is the 6 x 6 transition matrix, As,Jc is the 6 x 3 input matrix and WS,k is additional noise, The 6-dimensional state XI comprises the relative position and velocity with reference to the nominal orbit. The axis related accelerations, which are composed of natural disturbance accelerations (such as solar pressure and luni-solar attraction as well as thruster accelerations), are represented by the input vector Uk. The in-plane motion and the out-of-plane motion of the satellite are decoupled. The receiver clock is modeled as a two state random process. The state is comprised of the clock phase and frequency error.
- .. ,
Fig. 5. ARN-GEO block diagram 4.2 MosaicGNSS Navigation Algorithms
Two navigation approaches have been investigated: the first one uses pseudorange measurements for Kalman filter updates, the second one uses differences of pseudoranges (A verin, et aI., 1996). Pseudorange Measurements A pseudorange measurement is composed of the satellite-ta-user range, the clock bias in meter and additional noise. The measurement equation can then be linearized around the best position and clock bias estimate. When pseudoranges are used, Kalman filter updates can be performed with only one or more visible navigation satellite(s). In this case the state vector is comprised of the six states of the user dynamics and the two receiver clock states, i.e. a motion model of the geostationary satellite as well as a receiver clock model is required. Compared to the
The ARG-GEO performances: Ll (GLONASS&GPS) Received signals: Number of channel: 8 Mass (without antenna, 2 units), kg: 6 Size, mm: 300x250x200
1100
well known satellite dynamics the clock model is relative uncertain which limits the navigation accuracy. It is well known that the performance is sensitive to clock uncertainties, see e.g. (Ananda and Jorgensen, 1985). High performance clocks are therefore required for this approach.
Pseudorange Differences The second navigation method eliminates the clock bias using single differences of pseudoranges for Kalman filter updates. The filter model is composed only of the well known orbit dynamics, i.e. this approach is completely independent of (robust with respect to) clock uncertainties. Therefore a relatively inexpensive standard clock (TCXO) can be used with a typical drift of 10-7 (long-term stability). The drawback of this method is that two navigation satellites must be visible simultaneously, which leads to longer gaps without any measurements. Therefore, this approach is sensitive to the link budget. Single differences of pseudorange measurements are given by
0i
= Pm -
Pi
= (If -l~)r+vi ' i = I to m-I ,
(2)
where r is the position deviations from the reference values, -lj is the unit vector from the receiver to the ith GNSS satellite and Vj is a (noise) disturbance of the i-th pseudorange measurement. or in matrix form with (noise) disturbance
Pm -: PI
0=
[
1f Jr -l~ 1·r+vo , = :
Pm - Pm-I
5. TEST ENVIRONMENT 5.1 MosaicGNSS Rx Test Environment The real-time closed loop test environment (Figure 7) comprises the MosaicGNSS receiver, a simulation computer, which calculates the orbit and attitude of the user satellite and a 2 times 12 channel GPS RF signal simulator. The term 'closed loop' is used here in the sense of a closed loop test system and not in the sense of a closed control loop. All simulation equipment is timely synchronized with the GPS RF signal simulator. The orbit and attitude data of the user satellite is fed to the GPS RF signal simulator unit, which stimulates the GPS receiver. The MosaicGNSS receiver calculates the PVT and sends it back to the simulation computer for further analysis, visualization and storage.
(3) . ...... . ...... -. . . : RIui ·nrr:* Td!i&f~Jtot~
1~_1 -I~
o is
the single differences measurement and m denotes the number of pseudorange measurements. This method reduces the number of "actual" measurements by one. Despite this fact, it turns out that the elimination of the clock model improves the overall performance and reduces the computational effort. Note, that the covariance matrix of the noise in equation (3) has non-zero off-diagonal elements, caused by the differences. Using the navigation solution the receiver clock bias can be calculated by I m • bca1c =-LPi -di
process an estimation of the GEO position is made based on the received measurements. Corrections to the current position, calculated by a high-precision propagator, are made by calculating the estimation errors. At the end of the improvement process, the estimated position vector can be used for further calculation of the GEO position by the propagator. The determination of the current position is improved by corrections from the measurements. The duration of the improvement process lasts 24 hours. Therefore, each 24 hours the initial conditions for the propagator are corrected.
(4)
mi=1
i' I=::~-'--" }':~~~i~~~~: ' :! ~-~l ~~
I: ! i
'!
.1 I
,--
. . . -- , . ~
.
..
- .-~,,- -- -; . . -..- ... .... ... - ... .
,, ~
. . _- ..
~- ,,-- ~--~--
Fig, 7, GPS Test Facility
5.2 ARN GEO Test Environment For ground tests of the ARN-GEO hardware and software a test bench has been created. The core of this bench is the GLOASS/GPS signal simulator from Krasnoyarsk SRI "Radiotechnika". The conditions of orbital flights are simulated with a stimulation of all satellite subsystems. For this purpose a software model of ARN-GEO has been created.
where d j is the estimated value of the distance between the i-th navigation satellite and the receiver and m denotes the number of measurements.
4.3 ARN-GEO Navigation algorithm
6. PERFORMANCE RESULTS
The ARN-GEO uses pseudorange differences as input for the navigation filter (2).
6.1 Performance Results with MosaicGNSS Receiver Real-time runs were performed with a geographical longitude with worst case visibility conditions in the geostationary orbit and a receiver antenna gain of 5 dB . A mismatch of the model and the "real" natural forces has been taken into account. The uncertainty of the solar pressure is assumed to be 10 % of its
The calculated position is given as corrections to an initial GEO satellite position. This initial position is fixed at the reference time. The measurements are then fed into a Kalman filter. During the navigation
llOI
nominal value, whereas the uncertamttes of the gravity of sun and moon, the triaxiality, and oblateness of the Earth are modeled to be 5% of its nominal value with additional random noise effects. The initial position error has been set to the limits of a station-keeping window (± 37.5 km). Selective availability (SA) has been switched off. The Kalman filter converges even if e.g. no solar pressure is modeled at all . Table 5: Performance results (SA oft) Single differences GPS ESTIMATION STD MEAN RMS ERROR [m] [m] [m] Along track 52.90 1.52 52.92 Cross track 18.34 -3.56 18.68 Radial 27.31 -2.95 27.47
The accuracy of the GEO satellite orbit navigation with GLONASS/GPS (model data) is shown in Table 6; Table 7, Figure 9 and Figure 10. Table 7: Position error (GLONASS + GPS) (SA oq) Along track Cross track Radius RMS 72 m 53 m 41 m MAX 262 m 168 m 148 m
..... ..... ~--~----~+----+------4--+~ .1,00
Figure 8 and Table 5 show the obtained results (steady state).
o
1121IJr1
••
CZ
'hno, h
Fig. 10. Estimation errors with GLONASS + GPS
Estimation Error 3D and axis related
7. CONCLUSION The dependence of receiver performance on HW (LNA, antenna, etc.) and SW implementation (signal processing, CIN threshold) has been shown. Performance results from worst case simulation are given and show the applicability of GNSS receivers for orbit determination of GEO telecommunications satellites. Timc(h]
REFERENCES
Fig. 8. 3D/axis related errors with MosaicGNSS receiver and GPS simulator in the loop, SA off.
6.2 Performance Results ARN GEO Receiver A mathematical model was built for the estimation of precise GEO satellite positioning. For modeling purposes the navigation measurements and system models of the GLONASS and GPS navigation systems were created. The initial position error was set to ±40 km and Selective Availability for the GPS system was turned on.
..,.. ""'~---r-+--'-------~1rr-+-~~
o
•
n
~
M
•
•
G
•
M
•
•
n
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Fig. 9. Estimation errors with 24 GLONASS satellites Table 6: Position error with 24 GLONASS satellites Along track Cross track Radius RMS 69 m 46 m 42 m 184 m 347 m MAX 259 m
1102
Ananda, M.P. and P.S. Jorgensen (1985). Orbit Determination of Geostationary Satellites Using the Global Positioning System, Proceedings of the Symposium on Space Dynamics for Geostationary Satellites, CNES, Toulouse, France, Aug. 1985. Averin, S., V. Vinogradov, N. Ivanov and V. SaIischev (1996). Application of Differential Method for Relative Positioning of Geostationary Satellites with use of GLONASS and GPS Navigation Signals, Proceedings of the fifth international conference on differential navigation DSNS-06, Vol. 2,1996. Balbach, 0., et a!. (1998). Tracking of GPS Above GPS Satellite Altitude: Results of the GPS Experiment on the HEO Mission Equator-S, Proceedings of the Institute of Navigation GPS 98 Conference, Nashville, TN, 1998. Botchkovski, A. V. et al. (1999). Softflex: An Advanced Approach to Design of GNSS Receiver with Software Correlator, Proceedings of the 12th International Technical Meeting of The Institute of Navigation, ION-GPS99, Nashville, Tennessee, 1999. Krauss, P. A.. (2002). EADS Astrium GmbH MosaicGNSS Receiver Flyer, peter.a.krauss @astrium.eads.net Kronman, 1.D. (2000). Experience Using GPS for Orbit Determination of a Geosynchronous Satellite, Abstracts for the ION GPS 2000 conference, SaIt Lake City, Sept. 2000.