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Performance of Integrated Electro-Optical Navigation Systems. Takayuki Hoshizaki [email protected] Prof. Dominick Andrisani II. Aaron Braun Ade Mulyana Prof. James Bethel. School of Aeronautics & Astronautics Engineering. School of Civil Engineering. Purdue University. Outline. - PowerPoint PPT Presentation
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September, 2003 - 1
School of Aeronautics & Astronautics Engineering
Performance of Integrated Electro-Optical Navigation
Systems Takayuki Hoshizaki [email protected]. Dominick Andrisani II
Aaron BraunAde MulyanaProf. James Bethel
School of Civil Engineering
Purdue University
September, 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
September, 2003 - 3
Multiple Ray Intersections
Ground Object
Sequential Images
Tightly Coupled INS/GPS/EO System
September, 2003 - 4
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)
September, 2003 - 5
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
September, 2003 - 6
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
September, 2003 - 7
Simulation I: Traditional INS/GPS System
Objective: Investigation of navigation accuracy for the background studyAssumptions: (1)Straight line of flight (2)Perform 30 combinations of INS and GPS
performance(3)Perform 30 random experiments and compute
ensemble averages
September, 2003 - 8
Sensor Performance
Table 1: GPS Performance
Notation Pseudo Range, m ( σ )
Pseudo Range Rate m/s ( σ )
RTK1 7.5 × 10-4 0.03RTK2 0.1 0.032001H 6.6 0.052001M 20 0.2752001L 33.3 0.5Broken 1000 1000
September, 2003 - 9
Notation Rate Gyros AccelerometersBias Stability deg/hr ( σ )
Random Walk deg/hr/ ( )
Bias Stability 10-6g ( σ )
Random Walk 10-6g /
2010 0.0001 0.00001 0.1 0.12005 0.001 0.0006 4 1
2001H 0.003 0.0015 25 52001M 0.1765 0.036 37.5 27.52001L 0.35 0.07 50 50
Sensor Performance
HzHz PSD
Table 2: INS Performance
Imaging Sensor Performance: Additive White Noise of 5×10-6 m (σ )
September, 2003 - 10
Aircraft Yaw Angle Determination:INS/GPS
•Aircraft yaw angle accuracy depends mostly on GPS performance for the INS/GPS navigation system.
INS
GPS
September, 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.
(4) The initial σ = 1000 m is given at t=19 sec for an unknown ground object.
September, 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)
September, 2003 - 13
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, 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.
September, 2003 - 15
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, 2003 - 16
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.
ConclusionsAssumptions
• 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, 2003 - 17
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.
September, 2003 - 18
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
September, 2003 - 19
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
September, 2003 - 20
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, 2003 - 21
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)
