final presentation

Robust Spacecraft Attitude Determination Using Global Positioning System Receivers: 

J.D. Madsen The University of Texas at Austin Robust Spacecraft Attitude Determination Using Global Positioning System Receivers

Motivation: 

Motivation

Background: 

Background SNR Methods Axelrad & Behre (‘99) Dunn & Duncan (‘98) Lightsey & Madsen (‘00,‘01,‘03) Carrier Phase Axelrad & Ward (‘96) Lightsey (‘97) Carpenter & Hain (‘97) Um & Lightsey (‘01)

Contributions: 

Contributions Three-axis SNR Attitude Determination Combined Filter On-board SNR Calibration Improved Integer Resolution Improved Robustness Incorporate Additional Sensors

Outline: 

Outline Combine Methods via an Extended Kalman Filter Develop state, dynamics, and measurement model equations. Test filter performance via simulation and rooftop experimentation. Convert to flight ready code. Further utilize filter design to incorporate other measurement sources (Magnetometer). Conclusions Future Work

Extended Kalman Filtering: 

Extended Kalman Filtering

State Vector: 

State Vector Quaternion

Dynamics: 

Dynamics Quaternion Propagation

Dynamics: 

Dynamics Euler’s Equations

SNR Theory: 

SNR Theory

SNR Filter Equations: 

SNR Filter Equations

3 Axis SNR Solutions: 

3 Axis SNR Solutions Canting Angle Coverage vs. Accuracy

Results (FOAM)(Simulation): 

Results (FOAM) (Simulation)

Carrier Phase Theory: 

Carrier Phase Theory

Carrier Phase Filter Equations: 

Carrier Phase Filter Equations

InitialCombined Algorithm Logic: 

Initial Combined Algorithm Logic Measurements are ordered – SNR first

Experimentation Setup: 

Experimentation Setup Simulation

Rooftop: 

Rooftop

Integer Resolution: 

Integer Resolution Required accuracy a function of geometry and measurement noise.

Resolution Procedure: 

Resolution Procedure Integers estimated through rounding and augmented to measurement equation (h). Augmented measurements used to update temporary state. Residuals of temporary state calculated.

Threshold Tests (15 deg, 3 Antennas, Roof): 

Threshold Tests (15 deg, 3 Antennas, Roof)

Incorrect Assignment Detection: 

Incorrect Assignment Detection Standard deviation of residuals during correct assignment.

Detection Logic: 

Detection Logic

False Detection Test: 

False Detection Test Assign Integers when incorrect and below false detection threshold (rooftop test). Record time to detection.

First Guess: 

First Guess Initial Estimate – Point at Satellite (start with 900 yaw error for testing)

SNR Tuning Results(Rooftop Test): 

SNR Tuning Results (Rooftop Test)

Receiver Comparison: 

Receiver Comparison SIGI quantizes SNR measurements into bins. Measures AMU’s instead of dB.

Carrier Phase Tuning: 

Carrier Phase Tuning

SNR Trade Study: 

SNR Trade Study SNR Degrades Carrier Phase Solutions

Final Logic Flow Chart: 

Final Logic Flow Chart

Final Results : 

Final Results

GEONS Implementation: 

GEONS Implementation GPS Enhanced Orbit Navigation System NASA flight ready GPS navigation code with 1 error = 20m. Multiple Satellite, WAAS, inter-satellite link capabilities. Original MATLAB code converted to C and integrated in GEONS. Line of Sight vectors now computed from GEONS solutions (not by receiver). Interface is multiple RINEX files (one for each antenna).

Results – GEONS: 

Results – GEONS

Magnetometer: 

Magnetometer Three-axis Magnetometer (TAM) Two Setups Single GPS antenna (SNR only) Multiple canted antennas Truth – 10th order IGRF 2000 model Measurements – 6th order IGRF 1995 model plus 0.3mG measurement noise.

Equations: 

Equations

Results – Magnetometer: 

Results – Magnetometer

Magnetometer, SNR, and Carrier Phase: 

Magnetometer, SNR, and Carrier Phase

Conclusions: 

Conclusions Algorithm can provide attitude information at the sub-degree accuracy level. Canted Antennas appear to have little effect on the double differenced carrier phase measurements. EKF facilitates sensor integration. Performance is a function of the model accuracy. Magnetometer improves integer resolution. Magnetometer could allow for integer resolution on aligned array. Achieved 100% availability

Future Work: 

Future Work Validate performance with a more suitable receiver. Improve coverage Improve accuracy Approach 100% correct integer estimation. Filtering techniques – line bias estimation, multipath modeling, exponentially correlated random variables. Judicious choice of order of carrier phase updates may improve integer resolution.

Questions?: 

Questions?

Plot – Attitude - Roof: 

Plot – Attitude - Roof

Plot – Quaternion – Roof: 

Plot – Quaternion – Roof

Plot – Body Rates – Roof: 

Plot – Body Rates – Roof

Plot – Attitude – 6 hour: 

Plot – Attitude – 6 hour

Plot – Quaternion – 6 hour: 

Plot – Quaternion – 6 hour

Plot – Body Rates – 6 hour: 

Plot – Body Rates – 6 hour

Plot – Attitude – 19 hour: 

Plot – Attitude – 19 hour

Plot – Quaternion – 19 hour: 

Plot – Quaternion – 19 hour

Plot – Body Rates – 19 hour: 

Plot – Body Rates – 19 hour

Plot – Attitude – 30 deg: 

Plot – Attitude – 30 deg

Plot – Quaternion –30 deg: 

Plot – Quaternion –30 deg

Plot – Body Rates – 30 deg: 

Plot – Body Rates – 30 deg

Plot – Attitude - Simulation: 

Plot – Attitude - Simulation

Plot – Quaternion – Simulation: 

Plot – Quaternion – Simulation

Plot – Body Rates – Simulation: 

Plot – Body Rates – Simulation

Plot – Attitude – GEONS: 

Plot – Attitude – GEONS

Plot – Quaternion - GEONS: 

Plot – Quaternion - GEONS

Plot – Body Rates - GEONS: 

Plot – Body Rates - GEONS

Plot – Attitude – Magnetometer: 

Plot – Attitude – Magnetometer

Plot – Body Rates – Magnetometer: 

Plot – Body Rates – Magnetometer

Plot – Quaternion – Magnetometer: 

Plot – Quaternion – Magnetometer

Plot – Nonzero Rates: 

Plot – Nonzero Rates

Carrier Phase Tuning: 

Carrier Phase Tuning

Investigate SNR Simulation Validity: 

Investigate SNR Simulation Validity Antenna gain pattern Qualitative multipath effects.

Results: 

Results

Investigate Carrier Phase Simulation: 

Investigate Carrier Phase Simulation Effects of Using Non-aligned antennas Qualitative multipath effects

Results: 

Results

Residuals: 

Residuals