1. National Aeronautics and Space Administration www.nasa.gov NAVIGATION & MISSION DESIGN BRANCH NASA GSFC code 595 What is GEONS? Russell Carpenter

2. NAVIGATION & MISSION DESIGN BRANCH, CODE 595 NASA GSFC GEONS Performs Onboard Navigation  Flight-proven  Award-winning  NPR 7150.2 Compliant  UD-Factorized Extended Kalman Filter  ANSI standard C with object- oriented techniques  GPS, TDRSS, DSN/USN/GN, Crosslink, Celestial Object, Accelerometer measurements  One or more user satellites, alone or simultaneously  Earth, Moon, LPOs, Deep Space 2

3. NAVIGATION & MISSION DESIGN BRANCH, CODE 595 NASA GSFC GEONS Core Algorithms and Software have 20+ years of Flight Heritage  Ground-based experiments on Landsats 4 & 5, COBE (1980s) led to series of experiments onboard EUVE (1990s)  EUVE code formed basis for -TDRSS Onboard Navigation System (TONS) now providing operational OD for Terra -Enhanced Onboard Navigation System (EONS) that was integrated into the Command Receiver (forerunner to GD’s MMT) -Celnav that was tested on the ground with POLAR and SOHO data  TONS modified for GPS Enhanced Orbit Determination Experiment (GEODE) on Lewis (1996) -GEODE “Lite” developed for EO-1 Autocon formation flying (2000) -GEODE software licensed to Orbital and Ball, has flown on numerous missions including Microstars, Orbviews, SORCE, CALIPSO -GEODE embedded in ITT Low Power Transceiver and flown on STS-107 CANDOS experiment  GEONS = GEODE + EONS + Celnav (2001 - present) -Simplified software maintenance with one set of source code; compile with only options needed -Integrated with Navigator GPS for MMS and GPM 3

4. NAVIGATION & MISSION DESIGN BRANCH, CODE 595 NASA GSFC Recognition and Compliance  Awards -2000 Runner-up for NASA Software of the Year -2004 Federal Laboratory Consortium Mid-Atlantic Regional Excellence in Technology Transfer Award -2007 NASA Software Release Award  NPR 7150.2 Compliance -Development of all core capabilities occurred prior to NPR 7150.2 (see previous slide)  High-level requirements were documented in the “Software Requirements Specifications”  Detailed requirements were documented in the “Mathematical Specifications”  “As-built” design was documented in the “System Description & User’s Guide” -7150.2 Compliant Software Maintenance Plan currently in effect  Automated SCM, document repository, and issue tracking database in use by all project personnel 4

5. National Aeronautics and Space Administration www.nasa.gov NAVIGATION & MISSION DESIGN BRANCH NASA GSFC code 595 Performance More Details 5

6. NAVIGATION & MISSION DESIGN BRANCH, CODE 595 NASA GSFC Navigator Flight Unit 1A HWIL Testing for MMS Phase 2B 6 Number of GPS 12 10 8 6 4 2 0 MMS Phase 2b, 1.2 x 25Re

7. NAVIGATION & MISSION DESIGN BRANCH, CODE 595 NASA GSFC Cislunar Nav with GPS and Translunar Relay 7 Position and Clock Errors [km] Near L1 Measure- ments GPS Only 25 dB-Hz GPS Only 18 dB-Hz GPS Only 11 dB-Hz GPS 25 dB- Hz, L2 Doppler Radial< 10< 5< 2< 0.5 Cross-track< 1< 0.5< 0.1< 1 Clock Bias< 10< 5< 2< 0.5 Pair of Relay Satellites at L2 provides one-way Doppler Spacecraft receives GPS pseudorange enroute to Moon

8. NAVIGATION & MISSION DESIGN BRANCH, CODE 595 NASA GSFC Celestial Navigation with ACS Sensor Data from HEO Spinner (POLAR) 8 Horizon Sensor Measurement Sun Sensor Measurement  1.8 x 9 Re Orbit, 10 RPM  Limited data: four 1-2 hour contacts over 4 days  “Truth orbit” -Ground-based 2-way Doppler solution -Accuracy ~1 km  Attitude -Ground-based definitive -Accuracy ~6 arcmin  Simulated sensitivity to attitude bias:

9. National Aeronautics and Space Administration www.nasa.gov NAVIGATION & MISSION DESIGN BRANCH NASA GSFC code 595 Algorithms More Details 9

10. NAVIGATION & MISSION DESIGN BRANCH, CODE 595 NASA GSFC Dynamics Models 10 Primary coord sys  Mean equator and equinox of J2000.0 with analytic coordinate transformations Primary time sys  Coordinated universal time (UTC) Numerical integrator  Runge-Kutta 4th-and 8th order Filter spacecraft orbit acceleration model  Joint Gravity Model-2 (JGM-2) geopotential up to degree 30 and order 30  LP100K non-spherical lunar potential model  Other planetary non-spherical potential models  Earth, solar, and lunar point masses with low precision analytic ephemeris or Earth, solar, lunar, and planetary point masses with high precision analytic ephemeris or JPL Developmental Ephemeris  Analytic representation of Harris-Priester atmospheric density  Solar radiation pressure with spherical or multi-plate area model for a spinning  spacecraft  Measured accelerations in RIC, VBN, Spacecraft body, or Mean of J2000.0 frames  Impulsive delta-V maneuver model Spacecraft orbit state transition matrix  Semi-analytic formulation including J2 and Earth and planetary point mass gravity, atmospheric drag, and solar radiation pressure acceleration partial derivatives  Second-order Gauss-Markov orbital covariance artificial damping

11. NAVIGATION & MISSION DESIGN BRANCH, CODE 595 NASA GSFC Estimator Models 11 Estimator  Extended Kalman filter with physically realistic process noise models and factored covariance matrix Orbit estimation state  Position and velocity vectors for local and remote satellites, ground-based receiver or Moon-based receiver, or relative position and velocity vectors for remote satellites  Atmospheric drag coefficient correction for local and remote satellites or relative correction for remote satellites  Solar radiation pressure coefficient correction for local and remote satellites or relative correction for remote satellites  Clock bias, rate, and acceleration for local and remote satellites modeled as random walk, FOGM drift, or FOGM bias and SOGM drift processes, with relativistic correction  Unmodeled acceleration biases in the RIC, VBN, or spacecraft body frame  Pseudorange and Doppler biases for each GPS SV and WAAS GEO  Integrated carrier phase biases for each GPS SV and GPS receiver  Singly-differenced carrier phase biases for each GPS SV and remote GPS receiver with respect to the local receiver  Pseudorange and Doppler biases for each cross-link transmitter  Ground-station-to-satellite range and Doppler biases for each Ground Station  Celestial object sensor biases  Cross-link line-of-sight sensor biases  TDRSS forward-link Doppler bias for each TDRSS satellite

12. NAVIGATION & MISSION DESIGN BRANCH, CODE 595 NASA GSFC Measurement Models and Cold Start 12 Measurement model  Standard and singly differenced GPS pseudorange, Doppler, and integrated carrier phase with GPS receiver time and time bias corrections, single-frequency and dual- frequency ionospheric delay corrections, TASS Differential Corrections, and ICE Differential Correction parameters  Standard and singly differenced WAAS GEO pseudorange and Doppler with GPS receiver time and time bias corrections  Inter-satellite one-way and two-way cross-link pseudorange and Doppler with option to propagate transmitting satellite states if not being estimated  Point solution position and time bias  Ground-station-to-satellite range and Doppler  Line-of-sight vector to a celestial object (3-axis stabilized spacecraft)  Cross-link line-of-sight vector to another satellite (3-axis stabilized spacecraft)  Sun sensor elevation angle (spinning spacecraft)  Earth horizon crossing times (spinning spacecraft)  Near-to-far-body pseudoangle  Near-to-near-body pseudoangle  TDRSS forward-link Doppler Cold Start Initialization  Given nominal shape & orientation of orbit, solves for initial mean longitude using batch of pseudorange and Doppler

13. NAVIGATION & MISSION DESIGN BRANCH, CODE 595 NASA GSFC Other Models 13 Maneuver targeting  Lambert iteration for Earth and planetary orbits “Real-time” state propagation (between filter updates)  Earth point mass + J2 Attitude dynamics model  Gravity gradient and measured torques (math spec only as of Release 2.17) Attitude estimation state  Attitude error, angular rate or gyro bias error, and antenna gain calibration coefficient states for each satellite (math spec only as of Release 2.17) Attitude measurement model  GPS signal-to-noise ratio and double-difference carrier phase (math spec only as of Release 2.17)

14. NAVIGATION & MISSION DESIGN BRANCH, CODE 595 NASA GSFC Benchmarks for GEONS 2.1 (~2003)  GNU Profiler used to obtain average number of FLOPs per state update call over 10 samples in various configurations, compiled with full optimization  Four user satellites in 1.2 x 12 R E orbit with 24-hour period -Up to 12 GPS available below 3 R E ; fewer than 4 GPS above 9 R E  All cases used 10-sec propagation time-step and 35 day time span Four user states estimated, GPS only Four users, GPS only Four users, GPS + all 6 crosslinks Single user, GPS + 3 local crosslinks Seconds between updates 6010 MFLOP per call1.8140.9001.7260.201 CommentsFive prop-only cycles on each call One prop cycle on each call Crosslink processed 10 minutes each hour 14