Orbit Determination Issues for Libration Point Orbits

Mark Beckman [email protected] 301-286-8866 Agenda

• Goddard Space Flight Center has designed and supported every libration point mission except the recent Genesis mission out of JPL • This presentation presents published and unpublished orbit determination results from 4 previous LPO missions • ISEE-3 • SOHO • ACE • MAP • The use of advanced technology can improve accuracy and reduce tracking times • CelNav • DDOR 2 International Sun-Earth Explorer-3 (ISEE-3) • Launched in 1978 into large halo orbit about Earth-Sun L1 • Tracking: S-band STDN, 9 x 5 min tracking passes per day, 21 day batch arc

Period Overlap Covariance Compare Analysis (km) (km) A 8.1 6.0

B 9.0 5.5

C 3.6 5.4 3 Solar & Heliospheric Observatory (SOHO) • Launched in 1995 into large halo orbit about Earth-Sun L1 • Tracking: S-band DSN 26-m with some 34-m & 70-m, 5 hrs/day tracking, up to 21 day batch arcs

Data Axis Covariance Maximum Total Error Span Def Period 60d Pred (d) Pos Vel Pos Vel (km) (cm/s) (km) (cm/s) 14 Y 10.1 0.42 17.4 0.79 21 Y 8.6 0.19 8.4 0.34 14 Z 6.6 0.39 20.1 1.05 21 Z 5.7 0.26 11.3 0.06 4 Additional SOHO Results

• Actual definitive overlap comparisons showed 7 km accuracy (14 km after 44 day prediction)

DEF RSS Radial Along- Cross- 44d RSS Radial Along- Cross- track track PRED track track

Pos 7 1 2 7 Pos 14 9 2 11 (km) (km)

Vel 0.4 0.1 0.2 0.3 Vel 0.7 0.2 0.3 0.6 (mm/s) (mm/s)

• Analysis for MAP using real SOHO tracking data showed a degradation of accuracy of less than 2 km when reducing tracking data to 37 min/day 5 Advanced Composition Explorer (ACE) • Launched in 1997 into small Lissajous orbit about Earth-Sun L1 • Tracking: DSN 26-m & 34-m, 3.5 hr/day, 4 to 14 day batch arcs (HGA pointing requirements require attitude maneuvers every 4 to 14 days) RSS Radial Along-trk Cross-trk

Definitive Point Overlap Pos (km) 10 4 5 8

Vel 1.2 0.9 0.1 0.9 (mm/s) 2-Week Predictive Overlap Pos (km) 23 8 6 21

Vel 1.2 0.9 0.1 0.9 6 (mm/s) Maneuver Modeling

• Covariance analysis was performed to determine OD accuracy with modeled maneuvers in the batch data arc • 4 mm/sec maneuvers performed every day over 21 day arc • Thrust modeled with 3% or 5% uncertainty in dV magnitude

Delta-V Pos Error Vel Error Error (km) (cm/sec)

3% 12-47 3.5-4.0

5% 16-78 5.8-6.5

7 Microwave Anisotropy Probe (MAP) • Launched in 2001 into small Lissajous orbit about Earth- Sun L2 • Tracking: S-band DSN 34-m & 70-m, 45 min/day tracking, 14 to 72 day batch arc • Fixed spacecraft area WRT Sun enables consistent estimation of solar pressure forces and allows extension of data arc

8 Additional MAP Results

• Cr estimated to ± 0.005 • Predictive overlaps below from period of low solar activity

RSS Radial Along- Cross- track track 5-Week Predictive Overlap

Pos (km) 2.0 0.3 1.4 2.0

Vel 0.83 0.36 0.40 0.79 (mm/s) 9-Week Predictive Overlap

Pos (km) 6.7 6.2 2.3 1.8

Vel 3.9 3.8 0.4 0.6 9 (mm/s) Celestial Navigator (CelNav)

• GNCC flight algorithms for onboard navigation • Uses standard spacecraft attitude sensors (e.g. DSS, star tracker, Earth sensor, visible camera) and communication components (to extract 1-way forward Doppler) Autonomous Navigation Scenario • Real-time accuracies to 10 km RMS S/C to Sun directional for LPO are achievable using high- measurement Ground Station S/C to Earth to S/C Doppler directional accuracy attitude sensors and one- measurement measurement

way Doppler measurements Earth

10 CelNav Results

_ Addition of more realistic parameters degraded solution accuracy to a range of 14 to 22 km _ noisy USO (10 times the noise sigma) _ reduced Doppler tracking data _ directional measurement biases _ elimination of Earth directional measurements

160 100 160 100 RMS Maximum RMS Maximum 90 140 80 120 70 100 60

80 50 57 40 30 (Kilometers) (Kilometers) 60 46 30 31

40 (Millimeters per Second) (Millimeters per Second) 20 10 4 5 Total Position Error After 7 weeks Total Position Error After 7 weeks

9 Total Velocity Error After 7 weeks Total Position Error After 7 weeks Total Position Error After 7 weeks 20 7 Total Velocity Error After 7 weeks 10 2 0 0 Optimistic Realistic with Sun, Realistic with Sun Optimistic Realistic with Sun, Realistic with Sun Earth, and and Earth Earth, and Doppler and Earth 11 Doppler Delta-Differential One-Way Range (DDOR) • All previous LPO missions have used ground based tracking using range and Doppler measurement types • Both of these measurements give information only along the spacecraft line- of-sight • The radial component of the orbital uncertainty is considerably more accurate than the plane-of-the- sky components. • DDOR is a true VLBI measurement type that is being implemented at the DSN 34-m and 70-m (X- band only) sites as a nominal measurement type by May 2003 • DDOR is obtained by double differencing simultaneous observations of the spacecraft from two widely separated ground sites followed immediately by observations from an angularly 12 nearby quasar DDOR Analysis

• Used operationally before on Voyager, Galileo, and Magellan, and tested on Mars Global Surveyor and Mars Odyssey • DDOR provides relative angular measurement accurate to 5 nrad • Covariance analysis on DDOR for LPOs shows improved accuracy with decreased tracking times

R&D Sch* DDOR Baseline Def Pos Tot DSN Acc (km) Trk Time (hrs/wk)

2 hrs/day None NA 3.8 14

1 hr/3 days None NA 6.5 2.5

1 hr/3 days Once 50% Gds-Mad 2.8 2.5 /day 12% Can-Mad 38% Gds-Can

* Rotating stations each day including both northern/southern hemisphere 13 DDOR Drawbacks

_ For each acquisition during Voyager, 109 bits were reduced to obtain one measurement _ Extensive post-processing typically took up to 24 hrs _ DDOR has been used as a supplemental measurement source with independent solutions obtained from standard measurement types used as references; an increased reliance on DDOR and large reductions in standard tracking would reduce the quality assurance of DDOR

14 Conclusions

• Actual OD results from previous LPO missions indicate a total position uncertainty of 2 km (MAP) to 10 km (ACE) • Accuracy is dependent upon: • Amount and quality of the tracking data • Accurate modeling of solar pressure forces • No spacecraft perturbations within minimum 21 day data arc • CelNav technology can provide real-time onboard OD accurate to 10-22 km depending on attitude sensor quality • DDOR measurement type can improve any tracking scenario while reducing tracking times

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