Fundamentals of Satellite Navigation - Understanding GPS: Principles and Applications - page 61

&

& & &

dxayaz act
j

= + + −

u xj u yj u zj u

, &

uuuu which can be solved by using
measurements from four satellites. As before, we calculate the unknown quantities
by solving the set of linear equations using matrix algebra. The matrix/vector
scheme is

We now have four unknowns: u & = xyzt & , & , &

a

a

a 1

1

d
d
d
d

x
y
z

&
&
&

y 1 z 1

x 1

1 u

a

a

a

y 2

z 2

x 2

2 u

d = H = g =

a

a a

1
1

y 3

z 3

3 x 3 u

&

a − ct

a

a

4 y 4 u

x 4 z 4

Note that H is identical to the matrix used in Section 2.4.2 in the formulation
for the user position determination. In matrix notation,

dHg =

and the solution for the velocity and time drift are obtained as

− 1

gHd =

The phase measurements that lead to the frequency estimates used in the veloc-
ity formulation are corrupted by errors such as measurement noise and multipath.
Furthermore, the computation of user velocity is dependent on user position accu-
racy and correct knowledge of satellite ephemeris and satellite velocity. The rela-
tionship between the errors contributed by these parameters in the computation of
user velocity is similar to (2.35). If measurements are made to more than four satel-
lites, least squares estimation techniques can be employed to obtain improved esti-
mates of the unknowns.

2.6 Time and GPS

GPS disseminates a realization of coordinated universal time (UTC) that provides
the capability for time synchronization of users worldwide. Applications range
from data time tagging to communications system packet switching synchroniza-
tion. Worldwide time dissemination is an especially useful feature in military fre-
quency hopping communications systems, where time synchronization permits all
users to change frequencies simultaneously.

2.6.1 UTC Generation
UTC is a composite time scale. That is, UTC is comprised of inputs from a time scale
derived from atomic clocks and information regarding the Earth's rotation rate.
The time scale based on atomic standards is called International Atomic Time
(TAI). TAI is a uniform time scale based on the atomic second, which is defined as
the fundamental unit of time in the International System of Units. The atomic sec-