August, 2003 - 1
School of Aeronautics & Astronautics Engineering
Optical Navigation Systems
Takayuki Hoshizaki [email protected]. Dominick Andrisani II
Aaron BraunAde MulyanaProf. James Bethel
School of Civil Engineering
Purdue University
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
August, 2003 - 3
Multiple Ray Intersections
Ground Object
Sequential Images
Tightly Coupled INS/GPS/EO System
August, 2003 - 4
Tightly Coupled INS/GPS/EO:Imaging Geometry for a Frame
Camera(Negative) Image Plane
(Positive) Image Plane
xy
z
Focal Length, f
C
T1T2
T3
Perspective Center, L
t1t2
t3
t1t2
t3
x0y0
Image Coordinate System (c)
ECEF CoordinateSystem (e)
The unknown ground object is assumed to be stationary in this study.
August, 2003 - 5
Image Position Measurements0
0
T L
T Lce
T Lc e
x x X Xy y T Y Y
f Z Z
c
c
c c
x Uy Vf W
Image Position Equations
xy
z
C
T(XT ,YT ,ZT)e
Perspective Center, L (x0 ,y0 ,f )c = T (XL,YL ,ZL)e
t(x,y,0)c
x0y0
f
c
c
Ux fWVy fW
ce
August, 2003 - 6
Linearized State Equations for the Iterated Extended Kalman Filter (IEKF)
Orientation Angle Errors
Velocity Errors
Position ErrorsRate Gyro Biases
Accelerometer Biases
Clock Bias and Drift
Ground Object Coordinate Errors
x F x Gvz H x w
[ , , ,, , ,
, , ,, , ,
, , ,
, ,
, , ]
N E D
x y z
ax ay az
TT T T
xv v v
hB B B
B B B
b d
X Y Z
INS
GPSEO
20 states (with a Single Stationary Ground Object)
August, 2003 - 7
2k+2 Measurements
1
1
1
1
,
,
ˆ
ˆ
ˆ
ˆ
ˆˆ
k
k
GPS
GPS k
GPS
GPS k
c camera c
c camera c
z
x xy y
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
August, 2003 - 8
Schematic Layout of INS/GPS/EO System
(Cessna 182)
IMUNav.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
acce
lera
tions
GPS Receiver
-
+
Image position
Estimates:Aircraft velocity position orientationSensor biasesGround object coordinates
ImagingCamera
Kalman Gain
angu
lar
rate
s
August, 2003 - 9
Simulation I: Traditional INS/GPS System
Objective: Investigation of navigation accuracy for the background studyAssumptions: (1)Straight line of flight (2)Assume INS/GPS performance typical of the
year 2001.(3)Perform 30 random experiments and compute
ensemble averages
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.
August, 2003 - 11
Simulation II: Tightly Coupled INS/GPS/EO System with a Single
Unknown Ground ObjectObjective: Investigation of improvements in navigation accuracyAssumptions: (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.
August, 2003 - 12
Configuration of Simulation
xy
0
(N) (E)h=6096 m
(20000 ft)
VN=61 m/s (200 ft/s)0 sec12
...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)
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 Initializer Tightly Coupled Mode
yaw
(rad) 10-3
time (s)0~19 sec: 20~60 sec:
August, 2003 - 14
Simulation III: Tightly Coupled INS/GPS/EO System with a Single
Control PointObjective: Investigation of improvements in navigation accuracyAssumptions: (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.
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
August, 2003 - 16
Aircraft Navigation Accuracy Comparison
I. INS/GPS II. INS/GPS/EOUGO
III. INS/GPS/EOCP (σ=0.1 m)
vx (m/s) 0.0065/0.0073 0.0040/0.0049 0.0059/0.0043
vy(m/s) 0.0049/0.0059 0.0048/0.0050 0.0040/0.0043
vz(m/s) 0.010/0.010 0.0091/0.0072 0.0066/0.0066
xac(m) 0.42/0.45 0.43/0.45 0.24/0.22
yac(m) 0.43/0.38 0.43/0.38 0.27/0.29
zac(m) 0.81/0.75 0.77/0.70 0.32/0.32
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
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.
August, 2003 - 18
Initialization of Unknown Ground Object Coordinates in the Kalman Filter
LT
LT
LT
c
cT
LT
LT
LT
c
c
ZZYYXX
fyx
M
ZZYYXX
Mf
yx
1
LL
LL
T
T
T
ZcYZcX
ZYX
cc
2
1
2
1
1001
1 image: /1Substituting to the 1st and 2nd rows,
or,
bAAAx T1T
Using more than 2 images, Least Squares Solution of Ground Object Coordinates:
bAx
Separate Batch Processing of a Selected Number of Images
August, 2003 - 19
Pseudo Range, m (σ ) Pseudo Range Rate m/s (σ )6.6 0.05
Sensor Performance
Table 1: GPS Performance
Rate Gyros AccelerometersBias Stability
deg/hr (σ )Random Walk deg/hr/ ( )
Bias Stability 10-6g (σ )
Random Walk 10-6g /
0.003 0.0015 25 5
HzHz PSD
Table 2: INS Performance
Imaging Sensor Performance: White Noise of 5×10-6 m (σ )