Simultaneous Estimations of Ground Target Location and Aircraft Direction Heading via Image Sequence and GPS Carrier-Phase Data Luke K.Wang, Shan-Chih Hsieh, Fei-Bin Hsaio 2, Kou-Yuan Huang 3, Guo-Shing Huang 4, and Fan-Jen Tsai Dept. of Electrical Engineering National Kaohsiung Univ. of Applied Sciences,Kaohsiung,Taiwan,R.O.C. 2 Institute of Aeronautics and Astronautics National Cheng Kung Univ.,Tainan,Taiwan,R.O.C. 3 Dept. of Computer and Information Science National Chiao-Tung Univ.,Hsinchu,Taiwan,R.O.C 4 Dept. of Electrical Engineering National Chin-Yi Institute of Technology,Taichung,Taiwan,R.O.C.

 Introduction  Fundamental Concepts  Simulation Results  Conclusion Overview

Introduction {c} {b} {e}

GPS CARD IMAGE EKF ESTIMATED POSITION FEATURE EXTRACTION Initial State & Error Covariance Measurement & Process Error CAMERA POSITION AND ORIENTATION

Fundamental Concepts GPS Coordinate Transformation Perspective Projection EKF

Control Segment Space Segment User Segment Three Segments of GPS

Sources of Signal Interference Troposphere Ionosphere

GPS receiver GPS satellite wave length actual distance between receiver and satellite receiver‘s clock error satellite‘s clock error speed of light Integer ambiguity accounts for ionospheric, tropospheric delays The Carrier-Phase Measurements

Single Difference Solution Two stations observe the same SV at the same epoch

Double Difference Solution Two stations observe the same two SVs at the same epoch

Fundamental Concepts GPS Coordinate Transformation Perspective Projection EKF

The Homogeneous Transformation (1)Earth-Centered-Earth-Fixed (ECEF), i.e., {e} (2)Camera coordinate,i.e., {c} (3)Body frame,i.e., {b} (4) [X C Y C Z C ] T : The target location expressed in {C} (5) b T C : Transformation between body and camera (6) e T b : Transformation between earth and body Note

Coordinate Frames ECEF and ENU frames (Earth Centered Earth Fixed Cartesian Coordinates) (East North Up) Body frame

Azimuth Angle Note: d is a baseline length between two antennas.

Fundamental Concepts GPS Coordinate Transformation Perspective Projection EKF

3-D to 2-D Perspective Projection

Fundamental Concepts GPS Coordinate Transformation Perspective Projection EKF

Extended Kalman Filter (EKF) Time Update (Predict) Measurement Update (Correct) State equation & Measurement equation x k+1 = f(x k,k) + w K, w K ~ N(0,Q K ) z k = h k (x k,,k) + v k, v K ~ N(0,R K )

Define the state: State Assignment [2]

Outline  Introduction  Fundamental Concepts  Simulation Results  Conclusion  Reference

Simulation Steps Step1: Obtaining carrier phase data from two GPS receivers. There are eight satellites being observed. Thus, according to double difference method, seven double differences are recorded. Step2: Given a known trajectory of the target, the image point sequences [u, v] are obtained. Step3: Given a sequence of noisy image point [u, v], we use Kalman filter technique to estimate the ground target position and azimuth angle. Step4: Compare the errors between true and estimated target positions.

Simulation Results

Root-mean-square mismatch of the target using EKF

The estimation errors for ground target in x-, y-, and z-direction. Simulation Results

Estimation of azimuth angle using EKF

Simulation Results Integer ambiguity numbers of N 12 ab ~ N 14 ab using EKF.

Simulation Results Integer ambiguity numbers of N 15 ab ~ N 18 ab using EKF.

Outline  Introduction  Fundamental Concepts  Simulation Results  Conclusion

The proposed filter is verified by utilizing actual GPS carrier-phase measurement data. The root-mean-square error of ground target coordinate is substantially reduced to less than 1 meter and 0.2 deg. for position and azimuth angle, respectively. The worst case in position estimation is in z direction(elevation) according to simulation. The benefits of using the proposed scheme are due to its low cost and simplicity to implement on wing tips. Conclusion

Thank you ！

[2]J.C. Juang and G. S. Huang," Development of GPS-Based Attitude Determination Algorithm," IEEE Trans. on Aerospace and Electronic Systems, Vol.33, No.3, 1997, pp Back Reference