Estimation of Satellite-User Ranges Through GNSS Code Phase Measurements - Global Navigation Satellite Systems: Signal,Theory and Applications - page 118

Fig. 7. Pseudorange computation based on “comon tranmission time”, evaluating the
beginning of a subframe for GPS system

Referring to Fig. 7, the satellite tracked on channel 1 is taken as reference, since the
subframe transmitted at GPS

tx t arrives first. In other words this means that the satellite
tracked on channel 1 has the shortest distance respect to the receiver. Since the same
subframe from the other satellites is received at different times, the receiver has to count,
for each tracked satellite, the amount of time past from the reception of the subframe on the
reference channel. Regarding to this concept, it is important to stress that the measurement
of the delay between the reference satellite and the others in view has not necessarily to be
performed on the beginning of a subframe, but it must be computed consistently (i.e. with
respect to the same word or data bit belonging to the same subframe).

When the receiver is able to compute, for each tracked satellite, the relative time difference
with respect to the reference channel, the relative pseudoranges can be evaluated.

In formula this difference can be written as:

R R

δ , = t − t ∀ i = 1,.., 4 (11)

i rx i rx ,1

δ are measured through time counters, that are continuously updated by the tracking
structures of each channel. With these time differences, the set of distances between the
receiver and the satellites can be written as follows:

ρρ = + ⋅ cbc Δ +⋅ δ ∀ i = 1,.., 4 (12)

i 1 i

where:

•

δ are the time differences between the beginning of the subframe received on channel
i and the beginning of the subframe received on the reference channel. δ >0 ∀≠ i 0

i

and δ

1 =0

;