Optimal Estimation of Dynamic Systems, 2nd Edition

Review of Dynamic Systems 625

Prime

Meridian

Plane

Equatorial

Plane

2

ˆ

e

33

ˆ

ˆ

,ie

ˆ

n

ˆ

e

1

ˆ

e

GPS Satellite

ˆ

d

R

r

1

ˆ

i

2

ˆ

i

Inertial

Reference

Direction

Figure A.10: Definitions of Various Reference Frames

Earth turns relative to this frame.

42

Vectors described using ECI coordinates

will have a superscript I (e.g., r

I

).

• Earth-Centered-Earth-Fixed (ECEF) Frame: denoted by {

ˆ

e

1

,

ˆ

e

2

,

ˆ

e

3

}.This

frame is similar to the ECI frame with

ˆ

e

3

=

ˆ

i

3

;however,the

ˆ

e

1

axis points

in the direction of the Earth’s prime meridian, and the

ˆ

e

2

axis completes the

right-handed system. Unlike the ECI frame, the ECEF frame rotates with the

Earth. The rotation angle is denoted by Θ in Figure A.10.