Worst-Case GPS Constellation for Testing Navigation at Geosynchronous Orbit for GOES-R Kristin Larson, Dave Gaylor, and Stephen Winkler Emergent Space Technologies and Lockheed Martin Space Systems 36 th ANNUAL AAS GUIDANCE AND CONTROL CONFERENCE February 1 - February 6, 2013 Breckenridge, Colorado Sponsored by Rocky Mountain Section AAS Publications Office, P.O. Box 28130 - San Diego, California 92198
WORST-CASE GPS CONSTELLATION FOR TESTING NAVIGATION AT GEOSYNCHRONOUS ORBIT FOR GOES-R Kristin Larson, * Dave Gaylor, and Stephen Winkler The Geostationary Operational Environmental Satellite R Series (GOES-R) is the next generation NOAA weather satellite to be launched in 2015. GOES-R will use an L1 C/A GPS receiver (GPSR) to receive both GPS main beam and side lobe signals. The quality and availability of GPS signals at geosynchronous orbit (GEO) strongly impact navigation accuracy. For the GOES-R program, navigation accuracy requirements must be maintained during nominal operation of the spacecraft including station-keeping maneuvers. The GPSR solution 3- sigma accuracy requirement in position knowledge is 75 meters for the in-track and cross-track directions, and 100 meters for radial direction. Since maneuvers are not modeled in the onboard GPSR software, accuracy can degrade significantly during a maneuver. In order to verify that the GOES-R GPS navigation system can meet the stringent accuracy requirements during station-keeping maneuvers, a worst-case test scenario was developed for receiver testing. To find this scenario, we developed a simulation that models the GPS constellation and a GPS receiver and determines whether each GPS space vehicle (SV) can be tracked based on a high fidelity link budget model. Using this simulation, we modified the position of the GPS constellation relative to the Earth to find the scenario with the fewest number of trackable SVs during a North-South stationkeeping maneuver. The lowest visibility cases were found to be dependent on the right ascension, and occurred at 6 different shifts in right ascension. GPS receiver results from the Engineering Development Unit (EDU) are provided for both nominal and worst-case performance. INTRODUCTION GPS signals reach GEO over Earth s limbs, or from the transmitter side lobes. The strongest signals at GEO are approximately 10 db weaker than those seen at low Earth orbit (LEO). 1 High altitude GPS receivers require improved sensitivity to acquire and track weak signals including the side lobe signals as shown in Figure 1. GOES-R will use an L1 C/A GPS receiver (GPSR) to receive both GPS main beam and side lobe signals. The GPS receiver features that have the most impact on navigation accuracy are: The number of GPS SVs that are being tracked, The geometry of the SVs being tracked, The receive antenna pattern and RF losses, The acquisition and tracking thresholds and time to acquire, * GPS Engineer, Emergent Space Technologies, 355 S. Teller St, Lakewood, CO 80226. Vice President, Emergent Space Technologies, 355 S. Teller St, Lakewood, CO 80226. Certified Principal Engineer Space GPS Receivers, Space Systems, Lockheed Martin, Denver, CO. 1
The clock stability, The Kalman filter design and tuning. AAS 13-064 Side Lobe Signal GEO Satellite Main Lobe Signal Earth Blockage Cone GPS Satellite Figure 1: GPS at GEO For the purposes of identifying the worst-case constellation for navigation performance, we will look at both the number of SVs that are being tracked and the geometry of the SVs being tracked. ORBIT DETERMINATION TOOLBOX SIMULATION This worst-case analysis was performed using NASA GSFC Orbit Determination Toolbox (ODTBX). This is an open source set of tools written in MATLAB that simulates the GPS constellation and computes the link budget. ODTBX is freely available under the NASA Open Source Agreement at http://sourceforge.net/project/odtbx. Simulated Visibility Results From a GEO orbit, the GPS SVs appear within a donut centered on the Earth between about 9 degrees to 40 degrees off the nadir (earth pointing) vector as shown in Figure 2. To maximize the number of GPS SVs tracked, the receive antenna should be pointed toward nadir and optimized to receive signals in the donut. The GOES-R GPS receive antenna is designed to receive GPS signals to 32 degrees from nadir, however, trackable signals are present in between 32 and 40 degrees from nadir. 2
Figure 2: Visible GPS signals from GEO (Blue dots indicate RF visible signals during a 3 day GEO scenario using an OMNI RX antenna) Antenna Patterns The IIR-M GPS transmit pattern was used for all GPS SVs for this analysis, since the simulation is currently only capable of supporting only one transmit pattern. This is not entirely realistic as the GPS constellation current consists of IIA, IIR, IIR-M, and IIF GPS SVs. GPS IIIA SVs will be added to the constellation beginning in 2013. The IIR-M was chosen because it represents a more conservative test case between 23 and 43 degrees from bore-sight as shown in Figure 3. Figure 3: Mean Antenna Gain for GPS SVs The measured worst-case gain values at each elevation from the symmetrically designed GOES-R antenna EDU were used for the GPS receive antenna pattern. ODTBX Link Budget GPS signal availability is based upon received signal strength computed using Eq. (1). 3
Where: CN 0 P SV G SV L fs L at G r L i (1) P sv = nominal IIR-M GPS broadcast power: 10.1 dbw G sv = gain from the transmitter gain pattern (computed) L fs = free space loss of the signal (computed) L at = loss due to atmospheric effects: 0 (due to ionosphere masking) G r = gain from the receiver gain pattern (computed) L i = Receive System Noise Density: 204.4 dbw/hz AAS 13-064 The nominal IIR-M GPS broadcast power is a derived value backed out from the specified minimum received power at the ground in the GPS ICD 200. The receiver is required to exclude all SVs from the solution that are below a given ionospheric exclusion altitude; therefore, the loss due to the atmospheric effects will be zero. The receiver system noise density is a computed value based on the receiver source temperature, the receiver passive losses, and the receiver noise figure. These values are based on the flight configuration and are: Receiver source temperature in the lab: 30K Receiver passive losses: 1.81dB (before the LNA) Receiver noise figure: 1.2dB For the ODTBX simulation it was assumed that the receiver would minimally meet the specified acquisition and tracking thresholds, and acquire all SVs above -144dBm and track all SVs down to -148dBm, which correspond to a C/N0 of 30dB-Hz and 26dB-Hz, respectively. GPS Constellation The GPS constellation consists of 6 equally spaced orbital planes each with 4 baseline slots for GPS SVs, however, more than 24 SVs are available. On June 15, 2011, the Air Force completed the transition to a 24+3 or Expandable 24 configuration that has 3 expanded slots to improve GPS coverage. For this analysis, we used a 24+3 constellation from November 7, 2011. This Yuma file contained 30 SVs, so two SVs that were not in nominal slots (PRN 10 in slot E6 an PRN 6 in slot C5) were marked as unhealthy, and one SV was deleted (PRN 32 in slot E5). This became the 24+3 constellation used in our worst-case scenario search. The constellation was the shifted in one degree increments along the longitude of the ascending node axis as well as the argument of latitude axis. The original constellation is shown in Figure 4. http://www.gps.gov/systems/gps/space/ 4
Figure 4: Nominal 24+3 Constellation with 2 Unhealthy SVs ODTBX WORST-CASE ANALYSIS For the GOES-R program, navigation accuracy requirements must be maintained during nominal operation of the spacecraft including station-keeping maneuvers. To determine the worstcase constellation scenario to test the stringent navigation accuracy requirements, a 24-hour scenario was used assuming that a North-South station-keeping (NSSK) maneuver would occur 12 hours into the scenario (one revolution of the Earth for the GOES-R satellite and two revolutions for the GPS SVs). The constellation was incremented in right ascension from 0 to 359 degrees, and then incremented in mean anomaly from 0 to 359 degrees, for a total of 129600 cases. Two different metrics were used for each constellation shift to characterize the worst-case during the time of the maneuver. The first one is the number of SVs tracked during a given period, the second one is the sum of the angle off nadir of each SV being tracked, which considers the DOP of the tracked SVs. Number of SVs Tracked Metric The first metric that was studied was the number of SVs tracked during a maneuver. The number of tracked SVs was computed once per minute during the simulation. Since a maneuver is approximately an hour long, the sum of the number of SVs tracked for one hour between the 12 th and the 13 th hour was taken to create a worst-case metric. The lowest visibility metric value is 77 and occurs at a right ascension shift from the nominal location at the time of the broadcast ephemeris file of 234 and 237 degrees, and at a mean anomaly shift of 313 and 310 degrees, respectively. The visibility metric is shown with respect to a shift in mean anomaly in Figure 5, and with respect to right ascension in Figure 6. The lowest visibility metric is marked with a red line. The number of SVs tracked is more dependent on right ascension variation, with 6 different shifts in the right ascension about 60 degrees apart resulting in a very low visibility metric. 5
Figure 5: Visibility Metric with respect to Mean Anomaly DOP Metric Figure 6: Visibility Metric with respect to Right Ascension The second metric considered the geometry of the constellation. The DOP metric defines a constellation that is more representative of the worst case because it combines both the number of visible SVs and their geometry into one metric. The sum of the angle from nadir of each tracked SV was computed once per minute during the simulation, and the sum of the data points between the 12 th and the 13 th hour was taken to create a worst-case metric. A low value would indicate that all of the tracked SVs are very close to the Earth, creating a poor geometry. The lowest value of the DOP metric is 22.3, which occurs at a right ascension shift of 236 degrees and a mean anomaly shift of 312 degrees. The visibility metric at this shift in the constellation is equal to 78. The DOP metric is show with respect to shifts in mean anomaly in Figure 7, and with respect to shifts in right ascension in Figure 8. The minimum values are marked with a red line. 6
Figure 7: DOP Metric with respect to Mean Anomaly Figure 8: DOP Metric with respect to Right Ascension The visible SVs during the maneuver for the constellation shift that causes the minimum DOP metric are shown in Figure 9. Only six SV signals are visible, they are mostly on the same half of the sky-plot, and all trackable signals are less than 26 degrees from the antenna bore-sight. By contrast, the visible SVs during the maneuver for the constellation shift that causes the maximum DOP metric of 165.3 is shown in Figure 10 and there is very good geometry of SVs for that case. The blue dashed line indicates the ionospheric exclusion zone. 7
Figure 9: Visible SVs during maneuver for Worst-Case DOP Metric Figure 10: Visible SVs during maneuver for Best-Case DOP Metric Dependency on Right Ascension The GPS constellation consists of six orbital planes that are separated by 60 0 in right ascension of the ascending node. This explains why the worst-case metrics occur at 6 different shifts in right ascension. The minimum visibility metric for each of these six different shifts range from 77 to 126. The visibility metric is below 126 for only 0.5% of the manufactured cases. The DOP metric ranges from 22.3 to 38.3, although the dependency on shift in right ascension is less apparent. The DOP metric is below 38.3 for only 0.5% of the cases. There is no correlation with a shift in mean anomaly, which is different for each of these cases. SPIRENT GPS SIMULATION A Spirent GSS8000 system, consisting of a controller running Spirent SimGEN software and a GSS8000 signal generator, is used for real time testing of the actual GPS receiver. The SimGEN software accepts many user-defined parameters to create a detailed test scenario, including trajectory, constellation, and antenna patterns. A Spirent scenario was created to correspond with the worst-case test scenario found using the ODTBX analysis, however, a few modifications were 8
necessary to the ODTBX software so that the ODTBX results would better match the hardware testing (using the Spirent). GPS Attitude Yaw Model The attitude yaw of the GPS SVs affects the number of SVs tracked by a GPS receiver at GEO due to the extreme difference in gain for a given azimuth (up to 30dB) of GPS transmit antenna pattern gain at the side lobes. ODTBX implements a realistic model of the GPS SV nominal yaw attitude, which is determined by satisfying the two constraints that the GPS transmit antenna is nadir pointing, and the solar array is pointed towards the Sun. 2 The Spirent GPS simulator uses a much simpler attitude yaw model of having zero azimuth always pointed north. The Spirent model was implemented as an option in ODTBX so that the simulated results would better match hardware testing. ODTBX vs. Spirent Simulated Results The number of trackable SVs during a 1-day scenario for both the Spirent and ODTBX simulations is shown in Figure 11, with Figure 12 showing that the same SVs were being simulated. Figure 11 also shows a zoom-in the number of SVs tracked during the NSSK maneuver. Results are consistent between Spirent SimGEN software and updated ODTBX software. 9
Figure 11: Number of SVs Tracked for both ODTBX and Spirent SimGEN Figure 12: Tracked SVs for both ODTBX and Spirent SimGEN A similar plot is shown in Figure 13, except this time the accurate ODTBX attitude model is implemented. During this time, the realistic attitude yaw model used for ODTBX reports more SVs being tracked than with the Spirent SimGEN software. Since the SimGEN software attitude model is not modifiable, this analysis serves as a conservative baseline for the space system. 10
Figure 13: Number of SVs Tracked for Spirent SimGEN and ODTBX with an Accurate Attitude Model NAVIGATION PERFORMANCE A Spirent scenario was created to correspond to the lowest visibility worst-case, and run with the EDU GPS receiver. The EDU GPS receiver is an 8-channel, L1 C/A receiver. The GPSR accuracy requirement is that 3-sigma position knowledge over 24 hours is within 75 meters for the in-track and cross-track directions, and within 100 meters for radial direction, even during station-keeping maneuvers. The statistics for the 1-day scenario in Table 1 show that the EDU receiver does not meet the stringent GOES-R requirements during the worst-case scenario, with the largest error being in the radial direction. The Viceroy 4 receiver that will be used on the GOES-R mission is a more advanced receiver than the EDU, with more channels and an acquisition processor that will improve performance. If the Viceroy 4 can meet the position accuracy requirements for this worst-case scenario, then it is very likely that the Viceroy 4 will be able to meet the mission accuracy requirements. 11
Table 1: EDU Statistics for a Single 24-hour Run AAS 13-064 EKF Velocity Errors (cm/s) Requirement (3-sigma over 24 hours) Maximum 3-sigma ECEF R 6 184 66 ECEF I 6 186 25 ECEF C 6 115 16 EKF Position Errors (m) ECEF R 100 1186 268 ECEF I 75 373 52 ECEF C 75 219 35 The velocity error for each axis is shown in Figure 14 and the position error for each axis is shown in Figure 15. Figure 14: EDU Velocity Error 12
Figure 15: EDU Position Error The EDU GPS receiver sometimes tracked fewer and sometimes tracked more SVs than theoretically predicted possible based on the truth data as shown in Figure 16. This is because of several factors. The GPS EDU receiver sometimes performed better than the acquisition and tracking thresholds were assumed for the theoretical performance. Also, for theoretical performance, it was assumed that the receiver would acquire 100% of the SVs above the acquisition threshold, and track 100% of the SVs down to the tracking threshold, which is not the case for the actual receiver. The EDU tracked as few as zero SVs during the maneuver. The location of the SVs tracked during the maneuver in the antenna frame is shown in Figure 17. The EDU performed better than predicted at some points during the maneuver, tracking SVs below the specified thresholds, and worse than expected at other point during the maneuver, tracking as few as zero SVs. 13
Figure 16: Number of SVs Tracked by the EDU AAS 13-064 Figure 17: Sky-plot of SVs Predicted Tracked based on Spirent Truth (blue) and Tracked by the EDU (green) during the NSSK maneuver CONCLUSION A worst-case test scenario was created by looking at the visibility and geometry of GPS SVs at GEO. A worst-case constellation for GPS performance occurs at 6 different shifts in the right ascension of the constellation due to the 6 different orbital planes at a different shift in mean anomaly for each case. Worst-case constellations during maneuver occur for only about 0.5% of the manufactured cases. Due to limitations of the Spirent, it was not possible to test the EDU with a realistic GPS SV yaw model. The EDU was tested against the worst-case was found using the SV yaw model implemented in the Spirent SimGEN software. If the GOES-R GPS receiver is able to meet the stringent GOES-R accuracy requirements during this worst-case scenario, it is very likely that the GPSR can satisfy the mission navigation accuracy requirement. REFERENCES 1 Bamford, W. et al., "Navigation Performance in High Earth Orbits using Navigator GPS Receiver," 29th Annual Guidance and Control Conference, Breckenridge, Colorado, February 4-8, 2006 2 Y.E. Bar-Server, "A New Model for Yaw Attitude of Global Positioning System Satellites." TDA Progress Report 42-123 Tracking Systems and Applications Section. 2005, pp. 37 46. 14