Data Processing for Positioning - A Software-Defined GPS and Galileo Receiver: A Single-Frequency Approach - page 130

20

FIGURE 8.11. The WGS 84 geoid computed for a spherical harmonics expansion includ-
ing terms with degree and order 18. The contour interval is 20 m.

8.11 Time and Coordinate Reference Frames for GPS

and Galileo

GPS uses a time reference frame called GPS Time (GPST), which is steered by a
real-time representation of Coordinated Universal Time (UTC) produced by the
U.S. Naval Observatory. For Galileo an independent time scale, Galileo System
Time (GST) will be established. The offset t between GPST and GST will prob-

ably be in the order of tens of ns.
A combined GPS and Galileo receiver will correct Galileo pseudoranges to
GST and GPS pseudoranges to GPST. The offset t between GST and GPST can

be estimated as an additional unknown in the position solution. Or equivalently
we estimate the receiver clock offset dt to GPST and the receiver clock offset δ t

to GST. Now t .

The linearized system of observation equations for three GPS pseudoranges
and two Galileo pseudoranges is as follows (the proposed RINEX version 3 uses
the letter G for GPS and the letter E for Galileo):

t = dt − δ

⎡ ⎤

X G 1 Y G 1 Z G 1 − X i , 0 − Y i , 0 − Z i , 0

− − − 10

G 1
i

G 1
i

G 1
i

ρ ρ ρ

⎣ ⎦

⎡ ⎤

X G 2 Y G 2 Z G 2

− X i , 0 − Y i , 0 − Z i , 0

X i , 1

− − − 10

G 2
i

G 2
i

G 2
i

ρ ρ ρ

⎣ ⎦

Y i , 1

X G 3 Y G 3 Z G 3

− X i , 0 − Y i , 0 − Z i , 0

A x = − − − 10 Z i , 1

cdt i , 1
c

= b − e .

G 3
i

G 3
i

G 3
i

ρ ρ ρ

X E 1 Y E 1 Z E 1

− X i , 0 − Y i , 0 − Z i , 0

− − − 01

δ t i , 1

E 1
i

E 1
i

E 1
i

ρ ρ ρ

X E 2 Y E 2 Z E 2 − X i , 0 − Y i , 0 − Z i , 0

− − − 01

E 2
i

E 2
i

E 2
i

ρ ρ ρ

(8.45)