September, School of Aeronautics & Astronautics Engineering Performance of Integrated Electro-Optical Navigation Systems Takayuki Hoshizaki Prof. Dominick Andrisani II Aaron Braun Ade Mulyana Prof. James Bethel School of Civil Engineering Purdue University

September, 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

September, Multiple Ray Intersections Ground Object Sequential Images Tightly Coupled INS/GPS/EO System

September, 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)

September, k+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

September, 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

September, Simulation I: Traditional INS/GPS System Objective: Investigation of navigation accuracy for the background study Assumptions: (1)Straight line of flight (2)Perform 30 combinations of INS and GPS performance (3)Perform 30 random experiments and compute ensemble averages

September, Sensor Performance Table 1: GPS Performance NotationPseudo Range, m ( σ ) Pseudo Range Rate m/s ( σ ) RTK17.5 × RTK H M L Broken1000

September, NotationRate GyrosAccelerometers Bias Stability deg/hr ( σ ) Random Walk deg/hr/ ( ) Bias Stability g ( σ ) Random Walk g / H M L Sensor Performance Table 2: INS Performance Imaging Sensor Performance: Additive White Noise of 5×10 -6 m (σ )

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

September, 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. (4)The initial σ = 1000 m is given at t=19 sec for an unknown ground object.

September, Configuration of Simulation x y 0 (N) (E) h=6096 m (20000 ft) V N =61 m/s (200 ft/s) 0 sec 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)

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

September, 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.

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

September, i.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. ii.Tight coupling the EO system focusing on a control point is a potential alternative of the broken GPS in the INS/GPS system. 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.

September, 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.

September, 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

September, 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

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

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