August, 2003 - 1

School of Aeronautics & Astronautics Engineering

Optical Navigation Systems

Takayuki Hoshizaki hoshizak@purdue.eduProf. 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 )