1. August, 2003 - 1 School of Aeronautics & Astronautics Engineering Optical Navigation Systems Takayuki Hoshizaki hoshizak@purdue.edu Prof. Dominick Andrisani II Aaron Braun Ade Mulyana Prof. James Bethel School of Civil Engineering Purdue University

2. August, 2003 - 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. August, 2003 - 3 Multiple Ray Intersections Ground Object Sequential Images Tightly Coupled INS/GPS/EO System

4. August, 2003 - 4 Tightly Coupled INS/GPS/EO: Imaging Geometry for a Frame Camera (Negative) Image Plane (Positive) Image Plane x y z Focal Length, f T1T1 T2T2 T3T3 Perspective Center, L t1t1 t2t2 t3t3 t1t1 t2t2 t3t3 x0x0 y0y0 Image Coordinate System (c) ECEF Coordinate System (e) The unknown ground object is assumed to be stationary in this study.

5. August, 2003 - 5 Image Position Measurements Image Position Equations x y z T(X T,Y T,Z T ) e Perspective Center, L (x 0,y 0,f ) c = T (X L,Y L,Z L ) e t(x,y,0) c x0x0 y0y0 f ce

6. August, 2003 - 6 Linearized State Equations for the Iterated Extended Kalman Filter (IEKF) Orientation Angle Errors Velocity Errors Position Errors Rate Gyro Biases Accelerometer Biases Clock Bias and Drift Ground Object Coordinate Errors INS GPS EO 20 states (with a Single Stationary Ground Object)

7. August, 2003 - 7 2k+2 Measurements Pseudoranges in which geometric ranges are linearized Pseudorange rates in which geometric range rates are linearized Linearized image position measurements = Geometric range k = Number of visible satellites (11 in the simulation) GPS EO Sensor = Geometric range rate

8. August, 2003 - 8 Schematic Layout of INS/GPS/EO System (Cessna 182) IMU Nav.Eq. IEKF - + Aircraft velocity, Ground object coordinates Corrections: IMU biases Pseudorange Pseudorange rate UAV Model Covariance INS/GPS/EO Ellipsoidal- Earth Based 6 DOF Dynamics position, orientation accelerations GPS Receiver - + Image position Estimates: Aircraft velocity position orientation Sensor biases Ground object coordinates Imaging Camera Kalman Gain angular rates

9. August, 2003 - 9 Simulation I: Traditional INS/GPS System Objective: Investigation of navigation accuracy for the background study Assumptions: (1)Straight line of flight (2)Assume INS/GPS performance typical of the year 2001. (3)Perform 30 random experiments and compute ensemble averages

10. August, 2003 - 10 Aircraft Yaw Angle Determination time (s) yaw (rad) 10 -3 The initial error size of σ = 0.002 (rad) is not reduced during 60 seconds for the INS/GPS system.

11. August, 2003 - 11 Simulation II: Tightly Coupled INS/GPS/EO System with a Single Unknown Ground Object Objective: Investigation of improvements in navigation accuracy Assumptions: (1)Straight line of flight with a good aircraft/ground object geometry. (2)The imager is always bore-sighting the unknown ground object for 60 sec and images at 1 Hz. (3)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. August, 2003 - 12 Configuration of Simulation x y 0 (N) (E) h=6096 m (20000 ft) V N =61 m/s (200 ft/s) 0 sec 1 2... 60 sec 1829 m (6000 ft) 3048 m (10000 ft) ▪ Good aircraft/ground object geometry ▪ 60 seconds of imaging at 1 Hz z 1829 m (6000 ft)

13. August, 2003 - 13 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. Aircraft Yaw Angle Determination Batch Process InitializerTightly Coupled Mode yaw (rad) 10 -3 time (s) 0~19 sec:20~60 sec:

14. August, 2003 - 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. August, 2003 - 15 Aircraft Yaw Angle Determination 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 %. time (s) yaw (rad) 10 -3

16. August, 2003 - 16 Aircraft Navigation Accuracy Comparison I. INS/GPSII. INS/GPS/EO UGO III. INS/GPS/EO CP (σ=0.1 m) v x (m/s)0.0065/0.00730.0040/0.00490.0059/0.0043 v y (m/s)0.0049/0.00590.0048/0.00500.0040/0.0043 v z (m/s)0.010/0.0100.0091/0.00720.0066/0.0066 x ac (m)0.42/0.450.43/0.450.24/0.22 y ac (m)0.43/0.38 0.27/0.29 z ac (m)0.81/0.750.77/0.700.32/0.32 Roll (rad)3.1×10 -5 /2.9×10 -5 2.6×10 -5 /2.4×10 -5 2.5×10 -5 /2.2×10 -5 Pitch (rad)2.6×10 -5 /2.9×10 -5 2.4×10 -5 /2.7×10 -5 2.3×10 -5 /2.3×10 -5 Yaw (rad)2.1×10 -3 /1.9×10 -3 9.1×10 -5 /8.9×10 -5 6.7×10 -5 /6.6×10 -5 (Ensemble Average σ / theoretical σ ) Aircraft position accuracy is 2 times better in Simulation III than Simulation I and II

17. August, 2003 - 17 Conclusions i.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. ii.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. 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.

18. August, 2003 - 18 Initialization of Unknown Ground Object Coordinates in the Kalman Filter 1 image:Substituting to the 1 st and 2 nd rows, or, Using more than 2 images, Least Squares Solution of Ground Object Coordinates: Separate Batch Processing of a Selected Number of Images

19. August, 2003 - 19 Pseudo Range, m (σ )Pseudo Range Rate m/s (σ ) 6.60.05 Sensor Performance Table 1: GPS Performance Rate GyrosAccelerometers Bias Stability deg/hr (σ ) Random Walk deg/hr/ ( ) Bias Stability 10 -6 g (σ ) Random Walk 10 -6 g / 0.0030.0015255 Table 2: INS Performance Imaging Sensor Performance: White Noise of 5×10 -6 m (σ )