School of Aeronautics & Astronautics Engineering

1. 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. 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.

5. 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

6. 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

7. 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)

8. 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

9. Simulation I: Traditional INS/GPS System • Objective: • Investigation of navigation accuracy for the • background study • Assumptions: • Straight line of flight • Assume INS/GPS performance typical of the year 2001. • Perform 30 random experiments and compute ensemble averages

10. Aircraft Yaw Angle Determination (rad) 10-3 yaw time (s) • The initial error size of σ= 0.002 (rad) is not reduced during 60 seconds for the INS/GPS 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.

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 (rad) 10-3 yaw time (s) 0~19 sec: 20~60 sec: Batch Process Initializer Tightly Coupled Mode • The initial error size of σ = 0.002 (rad)is reduced to σ = 9.1×10-5 (rad) after 60 seconds.Imaging a single unknown ground object has a huge benefit on yaw angle determination.

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 (rad) 10-3 yaw time (s) • The initial error size of σ = 0.002 (rad)is now reduced to σ = 6.7×10-5 (rad) after 60 seconds.Imaging a single control point results in a further reduction of yaw angle determination error by another 26 %.

16. Aircraft Navigation Accuracy Comparison (Ensemble Average σ/ theoretical σ ) Aircraft position accuracy is 2 times better in Simulation III than Simulation I and II

17. 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. • Using the tightly coupled INS/GPS/EO system, yaw angle accuracy becomes 20 times better by focusing on an unknown ground object, and 30 times better by focusing on a control point, compared with an ordinary INS/GPS navigation system. • Focusing on a control point with the tightly coupled INS/GPS/EO system gives two times better aircraft position accuracy than the ordinary INS/GPS system or when focusing on an unknown ground object with the INS/GPS/EO system.

18. 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:

19. Sensor Performance Table 1: GPS Performance Table 2: INS Performance Imaging Sensor Performance: White Noise of 5×10-6 m (σ )