Antti Lehtinen Doppler Positioning with GPS - Matematiikan laitos

of the PRN codes is crucial because all the satellites transmit at the same frequency.
The PRN codes are used to differentiate the satellite signals from each
other. The PRN codes have been designed to have extremely low cross-correlation
[GPS 1995]. With their wide spectra and low cross-correlations, the PRN codes
are ideally suited for makingthe difference between the satellite signals. Systems
like the GPS, which transmit different data at the same frequency, are called code
division multiple access systems.
The satellites transmit also navigation data which is modulated to the C/A signal
at 50 Hz frequency. The navigation data is organised in superframes, frames and
subframes. The superframes, frames and subframes last 12.5 minutes, 30 seconds
and 6 seconds, respectively.
The navigation message contains for example the ephemeris. The ephemeris is a
set of time varyingparameters that are used to calculate the position and velocity
of the satellite. The satellite positions can be computed accurately or approximated
[Korvenoja & Piché]. The knowledge of satellite’s position is crucial for
the positioning, as can be seen from the Figure 3.1. If the satellite position is
biased, also the receiver position will be incorrectly determined. The ephemeris
contains also some correction terms that pass the user information for example
about the satellite clock drift.
One of the most important things that the navigation data contains, is the time.
The time in the navigation message is the time of transmission of the beginning
of each subframe. Thus, the time information is sent in the navigation message
once in 6 seconds.
3.2.4 Pseudorange and Delta Range
Above, the GPS was stated to be a time-of-arrival positioningsystem. The way
to measure the propagation times of the signals is based on the PRN codes.
The satellite PRN code is replicated in the receiver. Retardingthe replica code
and performinga correlation process with the received signal yields △ti, the
signal propagation time from the ith satellite. This can be obtained because the
user knows both the time of the beginning of each subframe from the navigation
message and the time of signal reception from the correlation process. The GPS
signals travel at the speed of light c. Thus, the satellite-to-user range can be
computed with
ri − ru = c△ti
(3.1)
where ri is the satellite position vector, ru is the receiver position vector, c is the
speed of light and △ti is the signal propagation time.
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