Data Processing for Positioning - A Software-Defined GPS and Galileo Receiver: A Single-Frequency Approach - page 117

When computing the subsequent pseudoranges, keep track of two issues. The
first issue is the difference in ms between the start of the subframe compared to
the reference satellite. The second issue is the start of the C/A code, which gives
the exact pseudorange for the channel .
When the receiver is computing the subsequent pseudoranges, the receiver
moves all the indexes 100 ms. (The receiver moves the indexes 100 ms if the re-
ceiver is set up to compute positions 10 times per s.) Then the start of the C/A
code is found for all the new indexes for all the tracked channels. In this way it
is possible to produce pseudoranges every millisecond and the receiver computes
positions 1000 times per s.

8.5 Computation of Receiver Position

8.5.1 Time
The traveling time between satellite k and receiver i is denoted

k
i

τ .Let c denote

the velocity of light in vacuum, and the pseudorange P i

is defined as

t k

k
i

P i /

t i − = τ = c . (8.9)

Let any epoch in GPS time (GPST) be called t GPS . The clock at satellite k and the
clock at receiver i do not run perfectly aligned with GPST. Thus, we introduce
clock offsets defined as

t GPS t i = + dt i , (8.10)

t k

k GPS

dt k = ( t i − τ

i )

+ . (8.11)

In the latter equation we substitute dt k t k

= a 0 + a 1 ( − t oe ) +··· as given from

the ephemeris:

− a 0 + t oe ) +··· .

k gps

t k t k

( t i − τ

i )

= a 1 ( − (8.12)

The left term is used as argument when computing the satellite position. Rear-
ranging Equation (8.9), we get

t k P i /

= t i − c . (8.13)

One way of using this equation is to consider t i as given. That is the epoch time
as defined in terms of the receiver clock. The pseudorange P i is likewise known
as an observable. Hence t k can be computed, and after correcting for the satellite
clock offset dt k we obtain the transmit time in GPST. This is the procedure used
for hardware receivers.
For software receivers the situation is a little different. The time t common com-
mon to all pseudorange observations is defined as the time of transmission at the
satellites. Hence the computation of position of satellite k is done at
t k dt k = t common − . (8.14)