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 Hsaio2, Kou-Yuan Huang3, Guo-Shing Huang4, and Fan-Jen Tsai

Dept. of Electrical EngineeringNational Kaohsiung Univ. of Applied Sciences,Kaohsiung,Taiwan,R.O.C.

2Institute of Aeronautics and AstronauticsNational Cheng Kung Univ.,Tainan,Taiwan,R.O.C.

3Dept. of Computer and Information ScienceNational Chiao-Tung Univ.,Hsinchu,Taiwan,R.O.C

4Dept. of Electrical EngineeringNational Chin-Yi Institute of Technology,Taichung,Taiwan,R.O.C.

Introduction

Fundamental Concepts

Simulation Results

Conclusion

Overview

B

xbyb

zb Cxc

yc

zc

xe

yeze

E

P

Target

EPr

CPr

BCr

EBr

Earth'sSurface

Target

Earth'sSurface

CCDCCD

Body coordinate

frame

Camera coordinate

frame

Earch centered, earth fixed coordinate frame

Image plane

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

Earth's Surface

1SA

2SA3SA

4SA

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

1 ( ) i im m

c N Biases

Single Difference Solution

Two stations observe the same SV at the same epoch

)()()(1

)()()( tabj

ftj

abNtj

abtjat

jbt

jab

Double Difference Solution

Two stations observe the same two SVs at the same epoch

)()(1

)( tjkab

Ntjkab

tjkab

Fundamental Concepts

•GPS

•Coordinate Transformation

•Perspective Projection

•EKF

The Homogeneous Transformation

1 1

C

e b Cb C

C

XX

YYT T

ZZ

(1)Earth-Centered-Earth-Fixed (ECEF), i.e., {e} (2)Camera coordinate ,i.e., {c}(3)Body frame ,i.e., {b} (4) [XC YC ZC]T : The target location expressed in {C}

(5) bTC : Transformation between body and camera

(6) eTb : Transformation between earth and body

Note

Coordinate Frames

ECEF and ENU frames(Earth Centered Earth Fixed Cartesian Coordinates)

(East North Up)Body frame

: latitude

: longtitude

: Azimuth Angle

( Pitch , Roll , Yaw) , , Euler Angle

Azimuth Angle

Note: d is a baseline length between two antennas.

[ ] T2 [ d/2 0 0 ]bR

[ ] T1 [ d/2 0 0 ]bR

Fundamental Concepts

•GPS

•Coordinate Transformation

•Perspective Projection

•EKF

3-D to 2-D Perspective Projection

0

0

CPP

CP

CPP

CP

Xi f

Z

Yj f

Z

0

: Image point associated with [ ]

: Focal length.

TP P CP CP CPi j X Y Z

f

CP

CP

CP

X

Y

Z

Fundamental Concepts

•GPS

•Coordinate Transformation

•Perspective Projection

•EKF

Extended Kalman Filter (EKF)

Time Update (Predict)

Measurement Update (Correct)

1 1 1 1ˆˆk k k k kx x K Z Z

1( )k

Tk k k kP A P A Q 1 , 1ˆk kx f x k

1 1 k+1 1( ) ( )k k kP I K H P

-1 1 1 1 1 1 11

( )T Tk k k k k kk

K P H H P H R

State equation & Measurement equation

x k+1 = f(xk,k) + wK, wK ~ N(0,QK)

zk = hk(xk,,k) + vk, vK ~ N(0,RK)

ˆ ( )K

k

fA

x x x

ˆ ( )

KK

k

hH

x x x

112 13 ... Tns

ab ab abx N N N X Y Z

112 13 ...Tns

ab ab abz u v

Define the state:

State Assignment

ijab

NSk

tQCk

tPk

tijab

)()()(

0)][

][

][

][

(c

d)( CS

ejS

ejS

eiS

eiSL

f

ktP .)

][

][

][

][

(d

)(

CSSCS

ejS

ejS

eiS

eiS

cL

f

ktQ

[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

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

Simulation Results

Estimation of azimuth angle using EKF

Simulation Results

Integer ambiguity numbers of N12 ab~ N14 ab using EKF.

Simulation Results

Integer ambiguity numbers of N15 ab~ N18 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.968-976.

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Reference