Fundamentals of Satellite Navigation - Understanding GPS: Principles and Applications - page 62

ond is defined as “the duration of 9,192,631,770 periods of the radiation corre-
sponding to the transition between two hyperfine levels of the ground state of the
cesium 133 atom” [24]. The Bureau International des Poids et Mesures (BIPM) is the
international body responsible for computing TAI. TAI is derived from an ensemble
of atomic standards located at more than 50 timing laboratories in various coun-
tries. The BIPM statistically processes these inputs to calculate definitive TAI [25].
TAI is referred to as a “paper” time scale since it is not kept by a physical clock.
The other time scale used to form UTC is called Universal Time 1 (UT1). UT1 is
a measure of the Earth's rotation angle with respect to the Sun. It is one component
of the Earth orientation parameters that define the actual orientation of the ECEF
coordinate system with respect to space and celestial bodies and is treated as a time
scale in celestial navigation [24]. UT1 remains a nonuniform time scale due to varia-
tions in the Earth's rotation. Also, UT1 drifts with respect to atomic time. This is on
the order of several milliseconds per day and can accumulate to 1 second in a 1-year
period. The International Earth Rotation and Reference System Service (IERS) is
responsible for definitively determining UT1. Civil and military timekeeping appli-
cations require knowledge of the Earth's orientation as well as a uniform time scale.
UTC is a time scale with these characteristics. The IERS determines when to add or
subtract leap seconds to UTC such that the difference between UTC and UT1 does
not exceed 0.9 second. Thus, UTC is synchronized with solar time [25] at the level of
approximately 1 second. The USNO maintains an ensemble of approximately 50
cesium standards and forms its own version of UTC, denoted as UTC (USNO) that
is kept to within 50 ns of the international standard UTC, provided by the BIPM
approximately 1 month in arrears.

2.6.2 GPS System Time
GPS system time (previously referred to as system time) is referenced to UTC
(USNO).
GPS system time is also a paper time scale; it is based on statistically processed
readings from the atomic clocks in the satellites and at various ground control seg-
ment components. GPS system time is a continuous time scale that is not adjusted
for leap seconds. GPS system time and UTC (USNO) were coincident at 0h January
6, 1980. At the time of this writing, GPS system time led UTC (USNO) by 13 sec-
onds. The GPS control segment is required to steer GPS system time within 1

sof
UTC (USNO) (modulo 1 second) [26], but the difference is typically within 50 ns
(modulo 1 second). An epoch in GPS system time is distinguished by the number of
seconds that have elapsed since Saturday/Sunday midnight and the GPS week num-
ber. GPS weeks are numbered sequentially and originate with week 0, which began
at 0h January 6, 1980 [25].

µ

2.6.3 Receiver Computation of UTC (USNO)
2.6.3.1 Static Users
It can be observed from (2.20) that if the user's position ( x u , y u , z u ) and satellite
ephemerides ( x 1 , y 1 , z 1 ) are known, a static receiver can solve for t u by making a single
pseudorange measurement,

1 . Once t u is determined, it can be subtracted from the