Data Processing for Positioning - A Software-Defined GPS and Galileo Receiver: A Single-Frequency Approach - page 121

TABLE 8.6. Typical standard deviations for pseudorange measurement

Error source σ [m]

Satellite clock and orbit 1-2

Atmospheric modeling 4

Multipath and receiver noise 1

The next iteration restarts from (8.26) to (8.29) with i , 0 substituted by i , 1 .These
iterations continue until the solution Z i , 1 is at meter level. Often

two to three iterations are sufficient to obtain that goal; refer to Strang & Borre
(1997).
If the observations (pseudoranges) and ephemerides are stored for later post-
processing, a popular storage format is RINEX. A description of this can be found
at http://www.ngs.noaa.gov/CORS/instructions2/.
When starting from RINEX format, the following M -files can be used for com-
putation of the receiver position: easy3 , get_eph , anheader , fepoch_0 , fobs_typ ,
recpo_ls , find_eph , check_t , satpos , e_r_corr , topocent , tropo ,and frgeod .

X i , 1 , Y i , 1 ,

8.5.4 Real-Time Positioning Accuracy
A pseudorange observation on L 1 is typically influenced by several error sources:
the broadcast orbits and the satellite clock offsets are not exact, the signal prop-
agation through the atmosphere may only partly be modeled correctly, and the
receiver adds some noise, and finally, signal multipath plays a role.
It is difficult to give precise estimates for the various errors; however, Table 8.6
indicates typical standard deviations for the said contributions.

8.6 Time Systems Relevant for GPS

The fundamental time interval unit is one SI second. The SI second was defined
at the 13th general conference of the International Committee of Weights and
Measures in 1967, as the “duration of 9,192,631,770 periods of the radiation cor-
responding to the transition between the two hyperfine levels of the ground state
of the cesium 133 atom.” The SI day is defined as 86,400 seconds and the Julian
century as 36,525 days.
Since the apparent revolution of the sun about the Earth is nonuniform (this
follows from Kepler's second law) a fictitious mean sun is defined that moves
along the equator with uniform velocity. The hour angle of this fictitious sun is
called Universal Time (UT).
The time epoch denoted by the Julian Date (JD) is expressed by a certain num-
ber of days and fraction of a day after a fundamental epoch sufficiently in the past