Mars Odyssey Navigation

1. Mars Odyssey Navigation Moriba Jah Jet Propulsion Laboratory California Institute of Technology

2. Spacecraft Mission • Investigate the Martian environment on a global scale, over a period of 917 Earth days. • Serve as a relay for information to Earth, following the science phase.

3. Spacecraft Mission constraints • To achieve the mission, the spacecraft must: • Be injected into an orbit with a period of less than 22 hours, while having a 300 km periapse altitude (+/- 25 km) and an inclination of 93.5º (+/- 0.2º), including MOI burn execution errors. This is equivalent to hitting a golf ball from NY to Paris and making it in the hole in only 4 swings. (achieved: 18:36 period 300.75 km and 93.51º) • Employ aerobraking over a 3-month period (walk-in, main phase, end-game/walk-out) in order to maximize payload mass and minimize propellant expense. • By the end of aerobraking, stabilize in a 400 km “circular”, frozen, sun-synchronous orbit with a 2PM LMST AEQUAX.

4. Trajectory Selection: Pork-Chop plot Courtesy of Rodney Anderson

5. Interplanetary Trajectory 10 day time ticks

6. Collecting Navigation Data

7. Collecting Navigation Data • Radiometric Data Types • Doppler • Measurements are comparisons of transmitted frequency (from ground station or spacecraft) with received frequency on ground; typical frequencies are at S-band (2 GHz) and X-band (7-8 GHz) • Highly reliable; used in all interplanetary missions to date • Range • Measurements are typically two-way light time for radio signal to propagate between ground stations and spacecraft with a turn-around time; typical frequencies are also at S- and X-band • Used in nearly all interplanetary missions since late 1960s

8. Range and Doppler Tracking

9. Radial vs Angular Measurements • For most interplanetary missions, S/C position uncertainty is much smaller in Earth-spacecraft (“radial”) direction than in any angular (“plane-of-sky”) direction • Radial components of position and velocity are directly measured by range and Doppler observations • In absence of other data, angular components are much more difficult to determine -- they require either changes in geometry between observer and spacecraft or additional simultaneous observer, neither of which is logistically simple to accomplish • Angular errors are more than 1000 x radial errors even under the most favorable conditions (see below) when depending on range and Doppler measurements 1999 Capability Position Velocity Radial Error 2 m 0.1 mm/s Angular Error (at 1 AU) 3 km* 0.1 m/s *Equivalent to angle subtended by quarter atop Washington Monument as viewed from Chicago

10. Navigation Data Types • Delta Differential One-Way Range (DDOR) • DDOR is a measurement technique that utilizes two ground stations to simultaneously view the spacecraft and then a known radio source (quasar or another S/C) to provide an angular position determination • Two stations viewing the same signal allows for geometric plane-of-sky angular position measurement (Differential) • By viewing two sources, common errors cancel and the angular separation can be calculated (Delta)

11. Very Long Baseline Interferometry - ΔDOR

12. DDOR Campaign • Project requirement to use DDOR as independent data type • VLBI implementation effort led by Jean Patterson and Jim Border • 9 successful MGS demonstrations (Jan 2001) • 5 more scheduled on MGS (Aug-Sep 2001) • North-South baseline only geometric opportunity for majority of cruise • Provides critical plane-of-sky information • East-West measurements possible beginning in October • Campaign began as soon as geometrically possible • Two measurements per week started 04-June-01 • All opportunities successful (except for E-W baseline “low elevation”) • Total of 45 measurements scheduled (40 N-S, 5 E-W) • Traditional S/C-Quasar-S/C Measurements • Measurement Accuracy 0.12 nsec (0.27 km - 1s)

13. DSN Viewperiods

14. Navigation Processes • Trajectory/Mission Design • Orbit Determination • Maneuver Design & Analysis

15. Trajectory Targeting Process • Targets are designed pre-launch, updated as necessary • Cruise Targets (encounter at Mars) usually defined with Closest Approach metrics • Orbiter: Radius (Altitude) of Periapse, Inclination, Time • Lander: Entry Radius, Entry Latitude, Entry Flight Path Angle, Time • Can be expressed in other coordinates (B-plane) • Aerobraking trajectory defined by a “corridor” • Corridor defined by spacecraft and trajectory constraints • Dynamic Pressure (structural), Heat Rate (Thermal), Density (Trajectory) • Target Altitude and Time at Periapsis • Mapping Orbit Targets are usually orbital elements • Semi-Major Axis, Eccentricity, Longitude on Asc/Desc Node • Node often described via True or Local Mean Solar Time • Orbit can be described via orbit Beta angle

16. Our Targeting Plane: B-plane

17. Orbit Determination • Orbit Determination is the process of adjusting trajectory models/apriori information to best match the observed tracking data, and quantify the error associated with the trajectory estimate • The collected tracking data are the actual or Observed measurements • Trajectory models produce predicted or Computed measurements • Data Residuals = Observed – Computed • OD method is to minimize residuals by adjusting the trajectory models • Minimized in a weighted least-squares sense (square-root information filter) • OD filter accounts for measurement and apriori state parameter accuracies • OD products: • OPTG & SPK • P-file

18. What will our spacecraft experience? • Satellite motion is determined by a number of forces that act on the spacecraft: • Gravitational Forces • Central body force • Third-body force (other planets, moons) • Central body gravity field asymmetries • General relativistic effects • Non-gravitational Forces • Thruster Firings • Trajectory correction maneuvers (TCMs) • Attitude control thrusting • Angular Momentum Desaturations (AMDs) • Solar Radiation Pressure • Aerodynamic Drag • Gas Leaks

19. Spacecraft Configuration (cruise) +Z Earth +X Solar Array Normal Sun

20. Thruster Configuration TCM-2 TCM-3 RCS-2 RCS-3 AACS Cruise Coordinate Frame (Same as Mechanical Frame) RCS-4 RCS-1 TCM-4 TCM-1

21. Models That May Be Estimated • Trajectory Force Models • Initial S/C position and velocity (State at Epoch) • 6 components of cartesian state • Any S/C thrusting events • 3 components (DVx,DVy,DVz or |DV|, RA, DEC) for each discrete event • Many events over course of cruise trajectory: TCMs, AMDs • Solar Radiation Pressure • Dependent on attitude profile and component orientation (solar panel) • Specular • Diffuse • Planet and Satellite Ephemerides and Gravity Fields • Gravity Field of Mars: MGS75C • Atmospheric Density • Due to drag pass during aerobraking

22. Models That May Be Estimated • Measurement or Signal Path Models • Earth Platform Parameters • Tracking Station Locations • Earth Rotation and Pole Nutation (Timing and Polar Motion) • Tracking Data Calibration Parameters • Signal delays induced by Ionosphere and Troposphere • Measurement Biases • Range Biases due to hardware delays • One-way doppler bias due to oscillator frequency drift

23. Trajectory Prediction • All planning is based on predictive capabilities, not real-time spacecraft location • Trajectory Prediction involves accurately modeling and estimating all past events, as well as predicting all future events • During the cruise to Mars, Nav must model all future events such as: • Solar Pressure - Attitude profile and component orientations • Thrusting - Angular Momentum Desaturations, or thruster slews • Unmodeled forces must eventually be compensated with maneuvers • Solar pressure mismodeling can contribute ~ 10,000 km trajectory error • AMD mismodeling can contribute ~ 7,000 km trajectory error • These effects are inexpensive at TCMs-1,2, but can be costly at TCMs-3,4

24. Low-Torque Attitude • Low-torque configuration starting at MOI - 50 days • Reduces desat frequency from ~1/day to ~1/week • Desat DV per event drops from ~ 8 mm/s to ~2 mm/s • Deterministic trajectory change per event decreases significantly • Minimizes predict bias error • At the time of TCM-4 Design (MOI-16 days) the deterministic altitude change remaining due to predicted AMDs : • Original Torque Profile: -80 km (Altitude Drop) • Low-Torque Profile: 5 km (Altitude Raise)

25. Maneuver Design • Clean up Injection Errors from Upper Stage • Remove Injection Bias • Correct Targeting Errors • Maneuver execution errors • Orbit Determination errors • Satisfy Planetary Quarantine (PQ) Requirements • Achieve Injection Conditions Trajectory Correction Maneuvers (TCMs)

26. Maneuver Analysis • Statistical propellant usage calculated via Monte-Carlo analysis based on the nominal trajectory, and expected trajectory dispersions, due to • Launch vehicle injection dispersions • Orbit Determination errors • Maneuver execution errors • Usually quoted as DV99 (99% of cases require no more than) • PQ analysis is the calculation of aimpoint biases required to ensure that the probability of impacting a planetary body is sufficiently small • Probability of Impact calculated on each trajectory leg • Includes probability of not being able to perform another maneuver • Based on expected trajectory dispersions • Generally presented in terms of B-plane aimpoints and dispersion ellipses

27. Planetary Protection Requirements • COSPAR 1964: • “… a sterilization level such that the probability of a single viable organism aboard any spacecraft intended for planetary landing or atmospheric penetration would be less than 1 x 10-4 … “ • “… a probability limit for accidental planetary impact by unsterilized fly-by or orbiting spacecraft of 3 x 10-5 or less … “ • At that time, it was thought that Mars had a life-harboring environment • Liquid water on the surface • Water ice caps • Atmospheric pressure ~ 85 mbar • This led COSPAR to assign a probability of 1.0 that a terrestrial organism would grow on the planet • NASA’s requirements for the Viking missions: • 10-3 or less of contaminating Mars. Combination of the following probabilities: • Survival of organisms in space vacuum, temperature, and UV flux • Arrival of organisms at Mars • Survival or organisms through atmospheric entry • Release of organisms from the lander • Growth and proliferation of terrestrial organisms on Mars

28. Planetary Protection Requirements • NASA’s Revisions 1988: • Category I: Spacecraft targets such as the Moon or Sun • Category II, III, IV: Flybys, orbiters, landers, and probes sent to planets or targets with increasing exobiological interest • Category V: Sample return missions • Specific Missions: • Viking 1 and 2 Landers: Substantial heating to produce P ~ 10-6 or less of contamination • Mars Observer: Category III orbiter • Launch aimpoint bias P ~ 10-5 or less • Spacecraft maneuvers P ~ 10-4 or less • Orbit maintained until Dec. 31, 2008; P > 0.95 of impact until Dec. 31, 2038 • Mars Global Surveyor: Category III orbiter • Mars Pathfinder: Category IV lander • Mars ’96: Category IV lander

29. Mars Odyssey Navigation Navigation Major Events • Injection • TCM-1 • TCM-2 • TCM-3 • TCM-4 • TCM-5 (Contingency) • MOI • Period Reduction Maneuver

30. Interplanetary Trajectory 10 day time ticks

31. The B-plane

32. Mars Odyssey Navigation

33. Mars Odyssey Navigation TCM-1 Execution Date: 23-May-01

34. Mars Odyssey Navigation TCM-2 Execution Date: 02-July-01

35. Mars Odyssey Navigation TCM-3 Execution Date: 17-Sept-01

36. Mars Odyssey Navigation TCM-4 Execution Date: 12-Oct-01 Target Alt: 300 km Inc: 93.47˚ Current Estimate (OD034) Alt: 324.1±11 km Inc: 94.10˚±0.2˚ Current Miss (Est-Target) Alt: +24 km Inc: +0.6˚ TCM-4 to Correct Miss DV: 0.08 m/s

37. Data Type Contributions to the Solution OD Knowledge at the time ofTCM-4 Design (3s)

38. MOI Configuration Thrust Vector Velocity

39. Mars Odyssey Navigation • MOI and PRM • MOI • Burn to Oxidizer depletion to minimize Capture Orbit Period • Main Engine Thrust: 694.7 N • Oxidizer mass available: 121.3 kg ==> 1183 sec burn • Design • Start time: 24-OCT-2001 02:26:19 UTC - ERT • Magnitude: 1426 m/s • Pitch rate: 0.03727 deg/sec (44.1 deg in 1183 sec) • Expected Capture Orbit • 300 km post-MOI periapsis altitude • 19.9 hour period • PRM • Period Reduction Maneuver Scheduled for 3rd Periapsis after MOI (P4) • Perform PRM (if necessary) to ensure completion of Aerobraking • If post-MOI orbit period < 22 hrs => No PRM • If post-MOI orbit period > 22 hrs => PRM to reduce period to 20 hrs

40. Mars Orbit Insertion

41. MOI - View from Earth Goal: Altitude: 300 km ± 25 km Inclination: 93.5° ± 0.2° Achieved: Altitude: 300.75 km Inclination: 93.51°

42. Aerobraking Nav Prediction Accuracy • Requirement • Must predict Periapsis Time to within 225 sec • Must predict Periapsis Altitude to within 1.5 km • Capability • Altitude requirement easily met with MGS gravity field (Nav Plan) • Timing requirement uncertainty dominated by assumption on future drag pass atmospheric uncertainty • Atmospheric Variability • Total Orbit-to-Orbit Atmospheric variability: 80% (MGS: 90%) • Periapsis timing prediction • To first order, the expected change in orbit period per drag pass will indicate how well future periapses can be predicted • This simplifying assumption is supported by OD covariance analysis

43. Nav Predict Capability • Example • Total expected Period change for a given drag pass is 1000 seconds • Atmosphere could change density by 80% • Resulting Period change could be off by 80% = 800 sec • If orbit Period is different by 800 seconds, then the time of the next periapsis will be different by 800 seconds • This fails to meet the 225 sec requirement • Large Period Orbits • Period change per rev is large • Therefore can never predict more than 1 periapsis ahead within the 225 sec requirement with any confidence • Small Period Orbits • Period change per rev is small (for example 30 seconds) • Therefore can predict several periapses in the future to within the 225 second requirement • Example: 80% uncertainty (24 sec) will allow a 9 rev predict

44. Aerobraking Navigation Process Long Orbits Drag Pass A2 A1 P1 P2 P3 Collect Tracking Data Tp < 225 sec Tp > 225 sec Analysis And Uplink Drag Pass (No Comm) A1 Collect Tracking Data Nav Analysis Sequence Update & Uplink P1

45. Navigation Process Short Orbits An A1 A2 …. P1 P2 P3 Pn Pn+1 Tp < 225 sec Tp > 225 sec Collect Tracking Data Nav Analysis Sequence Update & Uplink

46. What contributed to MOI success? • A Baseline set of Navigation solution strategies were identified • Varied data arcs, data types, data weights, parameter estimates, a-prioris • These solutions were regularly performed and trended • Built a time history of trajectory solutions • Trended evolution of parameter estimates and encounter conditions • Lessons learned from MCO and MPL • Regularly demonstrate consistency to Project and NAG • Weekly Status Reports • Daily Status after TCM-4 (MOI-12 days) “Daily Show” • Shadow navigators • Independent solutions run by Sec312 personnel (Bhaskaran, Portock)

47. Conclusions Questions, comments, etc.