Estimation of Satellite-User Ranges Through GNSS Code Phase Measurements - Global Navigation Satellite Systems: Signal,Theory and Applications - page 120

Δ δδ = −∀ i =1,..,4 (14)

i i 1

and consequently, by modifying equation (12), the pseudoranges can be written as:

ρρ Δ Δ = +⋅ +⋅ ∀ cbc i = 1,.., 4 (15)

i 1 i

where, as in the case of “common transmission time”:

•

ρ is the reference pseudorange ;

• Δ represents the clock bias between the one on board of the satellite and the receiver's

one.

This second method is usually employed in commercial GPS receivers. The main reason
behind this choice is the relative simplicity and suitability of that approach in real-time
implementations, since it does not require to wait until all the channels have received the
same data bit (e.g. the beginning of the same subframe) to compute the pseudoranges. This
concept gets more clear if we consider that, during the data demodulation and the tracking
process, the receiver continously counts the number of samples processed on that channels,
as well as the number of frames, subframes and data bits decoded. As a consequence,
through a system of counters, it becomes easy to compute the time difference

Δ among the

R
u

channels at a certain t .

4.2 Computation of the subsequent sets of pseudoranges

Once the initial set ot pseudoranges has been computed, subsequent pseudoranges can be
estimated. In this case, the computation of the reference pseudorange (i.e. ρ ) can be
refined with respect to the approximated value set during the first estimate (see section 4.1.1
for details). In fact, at this stage, the receiver has already computed the first estimate of its
position and is able to accurately calculate the geometrical distance between the satellite and
itself.

As far as the pseudoranges of the other satellites in view is concerned, let suppose that the
receiver performs a new PVT every second.

According to the method based on common transmission time, the receiver has to measure a
delay of 1s for the reference channel. By considering that a GPS navigation data lasts for 20
ms, it means that, after 1 second, 50 bits have been decoded for the reference satellite,
starting from the beginning of the subframe. In order to estimate the time difference, the
receiver must wait until each channel has demodulated 50 bits after the beginning of the
subframe. Then, the pseudoranges can be computed as stated in equation (6) and the
process repeats over time.
On the contrary, if the receiver follows the”common reception time”, it moves ahead u t of
1s, before measuring the time difference among the channels. Again, it is important to stress
that this reception time is fixed by the receiver and it is independent from the number of
navigation bits have been read for each tracked satellite.

The receiver can compute the user's position estimation at a rate much higher than 1 Hz. If
we consider as the reference time the beginning of a new C/A code (i.e. every ms), the
receiver can update the PVT at a 100 Hz rate.