Global Positioning System Reference
In-Depth Information
3. From the incoming signal to the pseudorange
When the GPS signal arrives at the receiver, it is very weak and the received power,
proportional to the distance between the satellite and the user, is well below the noise floor.
However, GPS receivers are able to compute their position with an accuracy that ranges
from a couple of meters to centimeters in case of carrier-phase measurements. Such
performance are possible thanks to the spread-spectrum nature of GNSS signals. It is useful
to recall that each satellite utilizes Direct Sequence Spread Spectrum (DSSS) modulation
(Kaplan & Hegarty, 2006), broadcasting the navigation message on pseudo random noise
(PRN) spreading codes, over the same frequency. Taking as example the GPS L1 C/A code,
each satellite uses a Gold code, quasi-orthogonal with respect to those used by the other
satellites. Applying signal processing algorithms based on the correlations between the
incoming signal and local replicas, the receiver can de-spread the incoming signal and
retrieve the navigation message. Such algorithms are used to perform two fundamental
processes, commonly known as acquisition and tracking , respectively. The first aims at
roughly estimating the Doppler frequency and the code delay of the received signal. The
tracking phase adjusts the parameters assessed by the acquisition, to finely measure the
phase of each tracked GPS signal, keeping trace of changes in the future. The estimate of the
code delay for all the tracked satellites is at the basis of the pseudoranges computation.
3.1 Signal acquisition
The first task of a GNSS receiver is to detect the presence of the satellites in view. This is
performed by the acquisition system, which also provides a coarse estimate of two
parameters of the received Signal In Space (SIS): the Doppler shift and the delay of the
received spreading code with respect to the local replica. In the next sections, we will see
that the precise alignment between the received and the local spreading codes, is
fundamental for the measure of user-satellites ranges, that is necessary to fix the receiver
position.
There are two mathematical disciplines which govern the operation performed by
acquisition systems: the Estimation theory and the Signal Detection theory . These two extensive
theories are described in various literature, whereas comprehensive analysis and
applications can be found in many papers. For a complete mathematical background of the
operation performed by GNSS signal acquisition, interested readers can refer to (Kay, 1993,
1998).
Keeping our description terse, real acquisition systems search for a satellite in view,
correlating the received signal with a local replica of the spreading code and a local carrier.
The search consists in finding the values of code delay and carrier frequency of the local
signals that maximize the correlation. Exploiting the concepts and the methodology of the
Estimation theory , it is possible to show that the Maximum Likelihood (ML) estimate of the
vector
, whose elements are the two unknowns of the received signal [ ]
p
=
(, )
d
τ
f
y
n , can
IF
be obtained by maximizing the following function
2
L
1
1
ˆ
p
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arg max
y
[
nr
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[
n
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=
arg max
R
(
τ
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f
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(7)
ML
p
IF
IF
p
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0
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