Inter-spacecraft Ranging and Relative Navigation

1. Inter-spacecraft Ranging and Relative Navigation SIRA Workshop 5/14/2003 Russell Carpenter, GSFC

2. Orbit Uncertainty Ellipses SIRA Ranging Requirements • Science requirements: • 12-16 s/c in 50 km spherical shell, 3 m ranging resolution • Baseline relative metrology is scalar ranging only (?) • No real-time relative navigation requirement (?) • Orientation of baselines less- or un- important (?) • Flight Dynamics may dictate additional requirements… Ground OD may not constrain orientation of baselines

3. Relative Trilateration (cross-link range and Doppler) Does not directly estimate relative position vectors Accuracy Fundamentally depends on wavelength Noise and power requirements increase with distance One-way Similar to GPS Biased by errors in onboard clocks Must estimate clock errors Two-way Round-trip, so clock bias cancels Relative Triangulation (relative bearing angles) Passive angular measurements, made optically, e.g. by star tracker Typically requires favorable lighting conditions Ranging Options: Direct Relative State Measurements One-way Ranging Two-way Ranging Relative Angles

4. Relative Navigation Flight Performance: “Heritage” Systems Relative GPS (RGPS) Flight Experiments Performance Survey Performance of Existing Shuttle Rendezvous System on STS-80 State Vector Differencing Performance During STS-80 RGPS State Vector Differencing Performance Derived From Space Shuttle Absolute State GPS Flight Data through 1998

5. Ranging Systems: State of the Art • GRACE (flying) • Low Earth orbit • 1 micron range change, (“relative, not absolute, range between spacecraft”) over few hundred km • MMS (2009 launch) • Highly elliptical (1.2x12 - 10x50 Re) • Absolute range between spacecraft to 1% over 10 km - 1000 km • 3 candidate ranging systems identified • TRL 6 by FY05 • Techsat-21 (recently canceled) • Low Earth orbit • 3-D relative position, velocity to 10 cm, 5 mm/sec with carrier differential GPS (CDGPS) • ST-9 (Proposed) • Low Earth orbit • Relative position < 2 cm in real-time, likely w/CDGPS

6. GPS Weak signal tracking technology may allow significant high altitude coverage Unmodified receivers have tracked at 9-10 Re (limited OD) “Black” GEO program admits using GPS for ground OD Must propagate through long outages above the GPS Most SIRA concepts are probably too far out One-way Doppler SN (TDRSS) or GN Requires long tracking arc, simultaneous with uplink Celestial LOS to planetary bodies and/or angles between bodies and distant stars Backup to ground on Apollo AF demo (STEP) mid-80’s Satellite-to-Sun directional measurements Ground-Station-to-Satellite Doppler measurements Satellite-to-Earth directional measurements Ranging Options: Differential Absolute State Measurements All produce 3-D relative state vectors indep. of distance More Accurate Accuracy Less Less accurate data useful to complement ranging

7. Need large angles between targets for best absolute navigation accuracy Useful in any orbit Celestial Navigation Concept • Uses hardware already onboard for other functions (attitude, comm)

8. One-way Doppler Results for SOHO (L1) • Successful in current use by Terra (TDRSS-based), 8m accuracy • Requires ultra stable oscillator onboard • Decreased accuracy when range-rate relative to Earth is small (e.g. libration points)

9. Real Sun and Horizon Sensor Results from POLAR • Celestial navigation technique successfully used by Apollo, Shuttle, and DS-1 • Important issue is sensor calibration; very sensitive to bias errors

10. Some Combinations of Measurements • Ongoing simulation study of relative orbit determination for libration point mission -- preliminary results:

11. Formations require precise control of the relative orbits Example: nearly all formations require a common semi-major axis Otherwise, period differences cause the spacecraft to rapidly drift apart: along-track drift per orbit ≈ -3p x SMA difference (low e) Fundamental limit on degree of “period maintenance” is knowledge of the relative semi-major axes Relative SMA knowledge requires knowledge of a well-correlated 3-D relative state vector Aside: Frequent station-keeping of multiple satellites would be operationally less complex to support with an onboard OD capability Impact of OD onRelative Station-keeping Concept for Coordinated Maneuvering by LEO spacecraft

12. Formations require precise control of the relative orbits Control accuracy is limited by navigation error, since knowledge errors are “locked in” by maneuvers Example: nearly all formations require a common semi-major axis Otherwise, period differences cause the spacecraft to rapidly drift apart: along-track drift per orbit at apogee along-track drift per orbit at perigee For MMS Phase 1, e ~ .8, and period is about a day, so apogee drift ~ -p m/day per meter of SMA difference perigee drift ~ -9p m/day per meter of SMA difference SMA error typically not constant around the orbit (peak at perigee) Drift due to Orbit Differences

13. Landsat-7 & EO-1 Scaling Problem for Precision Formation Flying How do we get there… … from where we are today?

14. “Sub-formations” “Sub-formations” a) Centralized Control b) Decentralized Control c) Hybrid Control Example f) Hybrid Navigation Example d) Centralized Navigation e) Decentralized Navigation Architecture Comparison

15. One (of Many) Fundamental Questions • Goal: achieve specified reliability at minimal cost • Trades • Centralized architecture with highly reliable supervisor (e.g. multiple “strings”) • Some level of decentralization, with lower spacecraft-level reliability • Context here is the GNC system, but may be applicable to entire spacecraft How many supervisory nodes should the formation possess?

16. Optimization Problem • Given • Failure probabilities for supervisor and subordinate spacecraft individually, qc and qs, • Total number, k, and minimal number, kmin, of spacecraft • Required mission reliability, rM, • Choose number of supervisors, l, and number of strings, n and m, to minimize cost subject to constraint that

17. Results Summary: Only a Few Sub-Formations Are Enough

18. Summary • Many options exist to support relative navigation for formation flying, but … • … formation flying requires more than just precise relative positioning • Relative SMA is one of the more sensitive parameters; non-zero values lead to order of magnitude larger along-track drifts per orbit • Flight data indicate that relative SMA has been difficult to determine to levels comparable to relative position knowledge • Large formations pose flight dynamics architecture challenges • Onboard navigation based on celestial navigation in combination with a “3-D” ranging system (distance and bearing) may be a feasible approach • Relatively small number of “supervisor” spacecraft achieve high reliability