Digital Signal Processing Reference
In-Depth Information
which is only available to military equipment with a proper decryption key. The
L1 and L2 signals received from each GPS satellite can be expressed as follows
(Spilker
1980
):
S
L1
.t /
D
p
2C
C=A
D.t/X.t/sin .2f
1
t
C
1
/
C
p
2C
P1
D.t/P.t/cos .2f
1
t
C
1
/
(1.1)
S
L2
.t /
D
p
2C
P2
D.t/P.t/cos .2f
2
t
C
2
/
(1.2)
where
C
C/A
and
C
P1
are the received powers of the in-phase and quadrature
components of the L1 signal, respectively,
C
P2
is the received power of L2,
D
(
t
)
is an amplitude modulation for L1 and L2 containing navigation data,
X
(
t
)isa
pseudorandom sequence of
˙
1, known as clear acquisition or C/A code-modulating
the in-phase component of L1 at a rate of 1.023 MHz, and
P
(
t
) is a pseudorandom
sequence of
˙
1, known as P-code-modulating the quadrature component of L1 and
L2 at a rate of 10.23 MHz.
The C/A-Code and the P-Code are examples of PRN codes. Each satellite
transmits a unique C/A-Code and P-Code sequence (on the same L1 and L2
frequencies), and hence a satellite may be identified according to its “PRN number”,
e.g. PRN2 or PRN14 are particular GPS satellites. The CDMA technique allows
the receiver to recognize multiple satellites on the same frequency with different
PRNs. A GPS receiver will detect amplitude, pseudo-range and phase measurements
for each C/A, L1 P-code (P1) and L2 P-code (P2) signals. The C/A and P1
contained identical information, however, the C/A is preferred over P1 due to
its stronger power and not being encrypted. Note that the pseudo-range is an
absolute measurement of differential group delay between time of transmission and
reception. It is the sum of the actual range between the transmitter and the receiver,
atmospheric and ionospheric delays and transmitter and receiver clocks offsets. Note
that the early GPS included a feature called Selective Availability (SA) that adds
intentional, time varying errors of up to 100 m (328 ft) to the publicly available
navigation signals. This was intended to deny an unauthorized use of GPS signals.
The SA service was eventually terminated in year 2000.
1.3
GNSS Theory and Errors
Navigation, positioning and timing are the main outputs of any global navigation
satellite system and it is achieved by the signals transmitted by the constellation
of satellites. The constellation design and the choice of frequency, modulation
and coding make this technology a superb master piece for applications beyond
imagination. This section discusses the principle, network and applications of
GNSS. The main sources of errors in getting the navigation solution are also
discussed.
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