simultaneous estimations of ground target location and aircraft direction heading via image sequence...
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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
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