GPS Software Receivers - Fundamentals of Global Positioning System Receivers: A Software Approach - page 202

9.10 GPS SYSTEM TIME AT TIME OF TRANSMISSION CORRECTED BY
TRANSIT TIME (t c )

Since time is a variable in the earth-centered, earth-fixed coordinate system, to
determine the user position a time must be given. All the GPS signals from
different satellites are transmitted at the same time except for the satellite clock
error. However, all the signals arrive at the receiver at different times because
of the different pseudoranges. The receiving time is equal to the transmission
time plus the transit time. The transit time is the time the signal travels from
the satellite to the user, which is equal to the pseudorange divided by the speed
of light. It is reasonable to select one time (time of receiving) to measure the
user position. Once a time of receiving is selected as a reference, the time of
transmission can be obtained by subtracting the transit time from the time of
receiving. Since the transit time for different satellites is different, the time of
transmission for different satellites is also different. This seems unreasonable
because all the times of transmission for different satellites are very close together.
These differences can be explained as that selecting a receiving time as a reference
causes the time of transmission to be different. This time of transmission can be
referred to as time of transmission corrected by transit time and represented by t c .
As discussed in the previous section, the transit time cannot be measured because
the user clock bias is unknown. Only the relative transit times among different
satellites can be measured. The time t c can be found from the relative transit time
and the time of the week (TOW), which has a time resolution of seconds. The
TOWs obtained from different satellites should have the same values because the
time resolution is 6 seconds and the transit time is only 67 - 86 milliseconds. The
time t c can be obtained by subtracting the relative transit time from the TOW as
shown in the following equation:

t c = TOW − relative transit time = TOW − diff of dat × 200 × 10 − 9 ( 9 . 6 )

In this equation the subtracting implies that the time of transmission is before
the receiving time. The relative transit time is the same as the difference in
digitized data points ( diff of dat ). The factor 200

10 − 9

× is the time between

digitized points.

9.11 CALCULATION OF SATELLITE POSITION

Most of the equations used to find the satellite positions are from Chapter 4. In
order to refer to these equations easily, they will be listed here again. However,
the explanations of these equations will not be included here.
Let us use the obtained data to calculate the mean motion as shown in
Equation (4.33):

µ
a s + n

n = ( 9 . 7 )