School of Aeronautics & Astronautics Engineering

1. Sun-Tracking INS/GPS/EO System for Improved Targeting and Navigation Performance Takayuki Hoshizaki hoshizak@purdue.edu Prof. Dominick Andrisani II Aaron Braun Ade Mulyana Prof. James Bethel School of Aeronautics & Astronautics Engineering School of Civil Engineering Purdue University

2. Outline • Implementation of the tightly coupled Sun-Tracking INS/GPS/EO system • Simulation results: • Tightly coupled INS/GPS/EO with an unknown target • Tightly coupled Sun-Tracking INS/GPS/EO with an unknown target • Conclusions

3. Simultaneous Tracking of the Sun and a Target Sequential Images Ground Target

4. Tight Coupling of New Measurements: Solar Angles, η & ε Sun Tracker or Camera Pod for Sun Tracking (assumed to be mounted on top of the aircraft for this study) xb η ε Aircraft Body yb zb η : Azimuth angle of the sun, relative to the Aircraft Body-Fixed Coordinate System. ε : Elevation angle of the sun

5. Measurement Equations for η & ε Imaginary “Gnomon” (height = 1) xb η α :Right Ascension of the Sun δ : Declination of the Sun [1] [2] ε y Aircraft Body x yb Solar Angles: zb Error Model: Additive White Noise of 0.1 deg (σ ) on η and ε

6. Effect of Atmospheric Refraction apparent sun actual sun zp Atmospheric refraction is ignorable refr z Thermosphere (Ionosphere) Z=Zp+refr 80 km temperature model for refraction computation Atmospheric refraction is SIGNIFICANT The original figure can be found in Ref. [3].

7. Effect of Atmospheric Refraction Mean Value and Uncertainty Model of Refraction Angle Mean value + random noise refraction angle, refr (deg) Mean value of refraction angle [4] σ value of uncertainty (deg) σ=25% of mean value σ=5% of mean value true solar zenith angle, Z (deg)

8. Nav.Eq. Schematic Layout of Sun-Tracking INS/GPS/EO System UAV Model accelerations angular rates Estimates: Aircraft velocity position orientation Sensor biases Ground object coordinates Sun-Tracking INS/GPS/EO IMU Ellipsoidal-Earth Based 6 DOFDynamics Corrections: Aircraft velocity, IMU biases position, orientation Ground object coordinates - (Cessna 182) - Covariance Kalman Gain + - + GPS Receiver + IEKF Pseudorange Pseudorange rate Image position Camera Solar angles Imaging Sun Tracker

9. Simulation I: Tightly Coupled INS/GPS/EO System with a Single Unknown Target • Objective: • Investigation of prototype targeting performance • Assumptions: • Straight line of flight with a good aircraft/target geometry • 1 Hz measurements for 60 sec: pseudoranges, pseudorage rates, bore-sighted target image positions • A separate batch system estimates initial target coordinates using the first 20 images. The INS/GPS/EO based on an IEKF uses the remaining 41 images. • The initial σ = 1000 m for an unknown target at the time = 19 sec.

10. Configuration of Simulation ▪ Good aircraft/target geometry ▪ 60 seconds of imaging at 1 Hz z 60 sec ... VN=61 m/s (200 ft/s) 2 1 0 sec 1829 m (6000 ft) y x (E) 1829 m (6000 ft) (N) h=6096 m (20000 ft) 3048 m (10000 ft) 0

11. Target Location Error: INS/GPS/EO with an Unknown Target GPS • CE90 (ft) at the time=60 sec • Computed from ensemble averages of actual errors INS • Navigation sensor performance can be chosen according to the targeting performance goal. • If the GPS is lost, both of platform and target locations are lost.

12. Simulation II: Tightly Coupled Sun-Tracking INS/GPS/EO System with an Unknown Target Objective: Investigation of improvements in targeting accuracy Assumptions: (1) The same set-up as Simulation I (2) Extra 1 Hz measurements: solar angles (accuracy: σ = 0.1 deg)

13. Target Location Error: Sun-Tracking INS/GPS/EO with an Unknown Target GPS • CE90 (ft) at the time=60 sec • Computed from ensemble averages of actual errors INS • Significant improvements result in the range where the GPS is broken or degraded.

14. Conclusions • Assumptions • Straight line of flight with a good aircraft/target geometry. • The imager is always bore-sighting the unknown target for 60 seconds and images at 1 Hz. • The accuracy of the sun tracker is σ = 0.1 deg. Tightly coupling sun tracking with the INS/GPS/EO system results in improved targeting accuracy in the range where the GPS is broken or degraded.

15. Future Directions • Sun pointing accuracy of 1/60 ° is achievable • and will be studied. • Effect of time of day • Model the effects of EO pointing biases and the • benefits of a Sun tracker mounted on the EO • boresight • Develop a dynamic model of the EO pointing • system

16. Statement of Work • INS/GPS • INS/GPS/EO + UGO • INS/GPS/EO + CP(0.1m) • INS/GPS/EO + Sun Tracker • INS/GPS/EO + Sun Tracker + UGO • INS/GPS/EO + S-Turn + Very Far UGO • INS/GPS/EO + S-Turn + Moving UGO (constant velocity) • INS/GPS/EO + 2 UGOs • INS/GPS/EO + Very Far UGO + CP(0.1m) • 1 min of INS/GPS/EO + UGO & 9 min of INS/GPS • 1 min of INS/GPS/EO + CP(0.1m) & 9 min of INS/GPS

17. Separate Sun Tracker Mounted on the Aircraft Line of site of separate Sun tracker Line of site of primary sensor • Calibration of aircraft heading angle is expected. • (Not for primary sensor’s boresight misalignment.)

18. Use of the Primary Sensor as the Sun Tracker with Maneuvers Line of site of Sun tracker Line of site of primary sensor • Calibration of: 1. aircraft heading angle; 2. boresight misalignment (beneficial for targeting), is expected.

19. Use of the Sun Tracker Fixed to the Primary Sensor with Maneuvers Line of site of separate Sun tracker known angle Line of site of primary sensor • Calibration of: 1. aircraft heading angle; 2. boresight misalignment (beneficial for targeting), is expected.

20. Existing Airborne Sun Photometer (Containing Sun Tracker) Ref. [5]

21. References Computation of the solar direction: [1] Bretagnon, P. and Simon, J-L., Planetary Programs and Table from -4000 to 2800, William-Bell, Inc., Richmond, VA, 1986. Computation of celestial longitude of the Earth: [2]The Naval Observatory, The Astronomical Almanac For The Year 2003, United States Government Printing Office, Washington, D.C., 2003. Structure of the Earth atmosphere: [3] Lutgens, F. K. and Tarbuck, E. J., The Atmosphere (8th Edition), Prentice Hall, Upper Saddle River, NJ, 2001. Computation of atmospheric refraction: [4] Noerdlinger, P. D., Atmospheric refraction effects in Earth remote sensing, ISPRS Journal of Photogrammetry & Remote Sensing 54, 1999, pp. 360-373. Sun Photometer: [5] Russell, P. B., Livingston, J. M., Schmid, B., and Eilers, J. A., Ames Airborne Tracking Sunphotometers, AATS-6 and AATS-14, NASA Ames Research Center, 2003.

22. Linearized State Equations for the Iterated Extended Kalman Filter (IEKF) 20 states (with a Single Stationary Target) Orientation Angle Errors Velocity Errors Position Errors INS Rate Gyro Biases Accelerometer Biases Clock Bias and Drift GPS Target Coordinate Errors EO

23. 2k+4 Measurements Pseudoranges in which geometric ranges are linearized Pseudorange rates in which geometric range rates are linearized GPS Linearized image position measurements EO Sensor Sun Tracker Linearized solar angle measurements = Geometric range = Geometric range rate k = Number of visible satellites (11 in the simulation)

24. Sensor Performance Table 1: GPS Performance

25. Sensor Performance Table 2: INS Performance Imaging Sensor Error Model: Additive White Noise of 5×10-6 m (σ ) Sun Tracker Error Model: Additive White Noise of 0.1 deg (σ )

26. Target Location Error, LE90 (ft) Sun-Tracking INS/GPS/EO INS/GPS/EO No improvements: sun tracking improves directional navigation accuracy, which is related to CE90, rather than LE90.

27. Substituting to the 1st and 2nd rows, Initialization of Unknown Target Coordinates in the Kalman Filter Separate Batch Processing of a Selected Number of Images 1 image: or, Using more than 2 images, Least Squares Solution of Target Coordinates: