School of Aeronautics & Astronautics Engineering

1. Performance of Integrated Electro-Optical Navigation Systems 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 INS/GPS/EO (Electro Optical System) system • Simulation results: • Traditional INS/GPS • Tightly coupled INS/GPS/EO focusing on a single unknown ground object • Tightly coupled INS/GPS/EO focusing on a single control point (known ground object) • Conclusions

3. Multiple Ray Intersections Tightly CoupledINS/GPS/EO System Sequential Images Ground Object

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

5. 2k+2 Measurements Pseudoranges in which geometric ranges are linearized GPS Pseudorange rates in which geometric range rates are linearized Linearized image position measurements EO Sensor = Geometric range = Geometric range rate k = Number of visible satellites (11 in the simulation)

6. Nav.Eq. Schematic Layout of INS/GPS/EO System UAV Model accelerations angular rates INS/GPS/EO Estimates: Aircraft velocity position orientation Sensor biases Ground object coordinates 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 Imaging

7. Simulation I: Traditional INS/GPS System • Objective: • Investigation of navigation accuracy for the • background study • Assumptions: • Straight line of flight • Perform 30 combinations of INS and GPS performance • Perform 30 random experiments and compute ensemble averages

8. Sensor Performance Table 1: GPS Performance

9. Sensor Performance Table 2: INS Performance Imaging Sensor Performance: Additive White Noise of 5×10-6 m (σ )

10. Aircraft Yaw Angle Determination:INS/GPS GPS INS • Aircraft yaw angle accuracy depends mostly on GPS performance for the INS/GPS navigation system.

11. Simulation II: Tightly Coupled INS/GPS/EO System with a Single Unknown Ground Object • Objective: • Investigation of improvements in navigation accuracy • Assumptions: • Straight line of flight with a good aircraft/ground object geometry. • The imager is always bore-sighting the unknown ground object for 60 sec and images at 1 Hz. • A separate batch system is used to estimate initial ground object coordinates using the first 20 images. The remaining 41 images are used for the INS/GPS/EO based on an IEKF. • The initial σ = 1000 m is given at t=19 sec for an unknown ground object.

12. Configuration of Simulation ▪ Good aircraft/ground object 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

13. Aircraft Yaw Angle Determination:INS/GPS/EO with an Unknown Ground Object GPS INS • INS/GPS/EO yaw accuracy is significantly better than • INS/GPS yaw accuracy.

14. Simulation III: Tightly Coupled INS/GPS/EO System with a Single Control Point Objective: Investigation of improvements in navigation accuracy Assumptions: (1) The same set-up as Simulation II (2) The imager is always bore-sighting a single control point whose location is known with the accuracy of σ = 0.1 m. (Initial σ = 1000 m previously) (3) The INS/GPS/EO based on an IEKF is activated throughout 0 – 60 seconds.

15. Aircraft Yaw Angle Determination:INS/GPS/EO with Control Point GPS INS • INS/GPS/EO+CP is more accurate than almost all • performance combination of INS/GPS.

16. Conclusions • Assumptions • Straight line of flight with a good aircraft/ground object geometry. • The imager is always bore-sighting the unknown ground object for 60 seconds and images at 1 Hz. • The accuracy of the control point is σ = 0.1 m. • The use of the tightly coupled INS/GPS/EO system focusing on an unknown ground object results in a significant improvement in yaw angle accuracy mainly in the range where the GPS is working. • Tight coupling the EO system focusing on a control point is a potential alternative of the broken GPS in the INS/GPS system.

17. Tightly Coupled INS/GPS/EO:Imaging Geometry for a Frame Camera t1 t2 (Negative) Image Plane t3 z Image Coordinate System (c) Perspective Center, L Focal Length,f x y ECEF Coordinate System (e) t3 y0 x0 t2 t1 (Positive) Image Plane T3 T2 T1 The unknown ground object is assumed to be stationary in this study.

18. Image Position Measurements Perspective Center, L (x0 ,y0 ,f )c= T(XL,YL ,ZL)e ce z f x y y0 x0 t(x,y,0)c T(XT ,YT ,ZT)e Image Position Equations

19. Substituting to the 1st and 2nd rows, Initialization of Unknown Ground Object 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 Ground Object Coordinates:

20. Simulation I (INS/GPS) / Simulation II (INS/GPS/EO+UGO) Improvement Factor: A/C Yaw Accuracy, INS/GPS vs. INS/GPS/EO+UGO GPS INS • Major improvements in yaw angle accuracy result in the range where the GPS is working. Improvement factor is 23 for (INS, GPS)=(2001H, 2001H).

21. Simulation II (INS/GPS/EO+UGO) / Simulation III (INS/GPS/EO+CP) Improvement Factor: A/C Yaw Accuracy, INS/GPS/EO+UGO vs. INS/GPS/EO+CP GPS INS • A control point is more valuable than an UGO for all • performance combination. • As GPS performance degrades, the value of the CP increases.