Note: Descriptions are shown in the official language in which they were submitted.
CA 02507360 2005-05-16
BOG Signal Acquisition and Tracking Method and Apparatus
Inventors: Olivier Julien, Christophe Macabiau, M. Elizabeth Cannon, Gerard
Lachapelle
Assignee: University Technologies International Inc.
FIELD OF THE INVENTION
The present invention relates to a method and apparatus for acquiring and
tracking a
Binary Offset Carrier (BOC) signal as part of a satellite navigation receiver.
BACKGROUND OF THE INVENTION
The vast majority of satellite navigation applications are currently based on
the
Global Positioning System (GPS) controlled by the United States Departments of
Defense and Transportation. This scenario will significantly change with the
advent
of GALILEO.
GALILEO is a European initiative for a global navigation satellite system
(GNSS),
providing a highly accurate global positioning service under civilian control.
While
providing autonomous navigation and positioning services, GALILEO will be
interoperable with GPS and GLONASS, another global satellite navigation
system. A
user will be able to take a position with the same receiver from any of the
satellites in
any combination. By offering dual frequencies as standard, however, GALILEO
may
deliver real-time positioning accuracy down to the metre range. It will strive
to
guarantee availability of the service under all but the most extreme
circumstances
and will inform users within seconds of a failure of any satellite. This will
make it
suitable for applications where safety is crucial, such as running trains,
guiding cars
and landing aircraft. The combined use of GALILEO and other GNSS systems may
offer much improved performance for all kinds of user communities.
In the new generation of GNSSs, attention has been given to have efficient and
spectrally relevant signals. GALILEO and GPS will share two central
frequencies and
will both send several signals on the same carriers. Consequently, new signal
CA 02507360 2005-05-16
modulations had to be studied to minimize inter- and intra-system
interference. One
modulation emerged due to its split spectrum that spectrally isolates the
signal from
the currently used Bi-Phased Shift Keying (BPSK) modulation [Godet et al.,
2002;
Betz, 2002]. This new modulation is known as Binary Offset Carrier (BOC). The
BOC modulation is part of the GALILEO signal plan.
As used herein, "BOC" refers to a signal resulting from a modulation which
multiplies
a pseudo-random noise (PRN) spreading code with a square wave sub-carrier (SC)
that has a frequency multiple of the code rate. It creates a symmetric split
spectrum
with two main lobes shifted from the center frequency by the frequency of the
sub-
carrier. The properties of a BOC signal are dependent on the spreading code
chip
rate, the sub-carrier frequency, and the sub-carrier phasing within one PRN
code
chip. The common notation for BOC-modulated signals in the GNSS field is
BOC(fc,fs) where fc represents the code chip rate, and fs is the frequency of
the sub-
carrier. Both fc and fs are usually noted as a multiple of the reference
frequency
1.023 MHz. BOC(n,m) may then be expressed as PRNmlexSCn.fc.
A BOC signal induces better tracking in white noise and better inherent
multipath
mitigation compared to the spreading code alone. However, it also makes
acquisition
more challenging and tracking potentially ambiguous due to its multiple peak
autocorrelation function. A summary of the basic properties and improvements
brought by BOC signals compared to BPSK signals is given by Betz (2002).
As already mentioned, the presence of a sub-carrier in the BOC signal
introduces
secondary peaks in the range [-1, +1] chip in BOC autocorrelation. The
presence of
these secondary peaks may cause a serious problem if the receiver locks onto a
side peak instead of the main peak. A significant bias of approximately 150 m
would
then be present in the range measurements, which is unacceptable for
navigation
applications.
Several methods have been proposed to track BOC signals without suffering from
any potential tracking bias. Fine and Wilson (1999), Lin et al. (2003), Martin
et al.
(2003) and Ward (2004) are a few examples. They treat the problem of the BOC
2
eV- Vic ___________ =.=====...Irlf*I.O.IPTANVM,1
CA 02507360 2005-05-16
tracking ambiguity in a broad sense, trying to find a solution that could be
applied to
any BOC(n,m) signal. Each of these suffers from various disadvantages.
Therefore, there is a need in the art for efficient methods of acquiring and
tracking a
BOC signal which minimizes potential tracking bias and allows unambiguous
tracking of the signal.
SUMMARY OF THE INVENTION
The methods and apparatuses described and claimed herein may apply to any BOC
signal. In a preferred embodiment, the BOC signal is a sine-B0C(n,n) and more
preferably the BOC signal is a BOC(1,1) signal. The methods utilize a
synthesized
local correlation function.
Therefore, in one aspect, the invention comprises a method of tracking a BOC
signal with a satellite navigation receiver, comprising the steps of:
(a) receiving a BOC signal;
(b) generating an internal BOC replica signal;
(c) generating an internal PRN replica signal;
(d) providing a discriminator for code delay by combining a BOC
autocorrelation function and a BOC/PRN cross-correlation function.
In another aspect, the invention may comprise a method of acquiring a BOC
signal with a satellite navigation receiver comprising the steps of:
(a) receiving a BOC signal;
(b) generating an internal BOC replica signal;
(c) generating an internal PRN replica signal;
(d) obtaining a synthesized acquisition test function by combining a BOC
autocorrelation function and a BOC/PRN cross-correlation function;
(e) if the test realized in (d) is negative, then repeating steps (b) to
(d) until
the test function is passed or the acquisition process is abandoned.
3
CA 02507360 2005-05-16
Preferably, the signal acquisition method is followed by the signal tracking
method.
In another aspect, the invention may comprise a satellite navigation receiver
capable of acquiring a satellite signal, said receiver comprising:
(a) an acquisition test function device comprising a signal input,
computational means for combining the correlation points of a BOC
autocorrelation function and a BOC/PRN cross-correlation function and
means for outputting an acquisition test function including a test
Doppler frequency and a test code delay;
(b) a frequency generator comprising a carrier oscillator and a quadrature
carrier oscillator, having a test frequency input coupled to the
acquisition test function output, and an output coupled to the
acquisition test function device signal input; and
(c) a code generator comprising a code oscillator, a code generator for
generating a PRN replica, a sub-carrier generator for generating a sub-
carrier replica; wherein the code oscillator receives the test code delay
and is coupled to the code generator and the sub-carrier generator,
and wherein the code generator and the sub-carrier generator are each
coupled to the acquisition test device.
Preferably, the acquisition test function device comprises:
(a) an input channel,
(b) first and second secondary channels split from the input channel,
(c) first and second tertiary channels split from the first secondary
channel,
third and fourth tertiary channels split from the second secondary
channel,
(d) and wherein the carrier oscillator is coupled to the first secondary
channel and the quadrature carrier oscillator is coupled to the second
secondary channel; and wherein the code generator is coupled to the
first tertiary channel and also coupled to the third tertiary channel; and
wherein the sub-carrier generator is coupled to the code generator, and
the product of the sub-carrier generator and the code generator is
coupled to the second tertiary channel and the fourth tertiary channel.
4
CA 02507360 2005-05-16
Preferably, the receiver further comprises a code delay estimation device, for
tracking an acquired signal using the computational means.
In another aspect, the invention comprises a satellite navigation receiver
capable of tracking a satellite signal, said receiver comprising:
(a) a code delay estimation device comprising a signal input,
computational means for combining the correlation points of a BOC
autocorrelation function and a BOC/PRN cross-correlation function and
means for outputting a code delay;
(b) a frequency generator comprising a carrier oscillator and a quadrature
carrier oscillator, having a frequency input coupled to an external
speed aid, and an output coupled to the code delay estimation device
signal input; and
(c) a code generator comprising a code oscillator, a code generator for
generating a PRN replica, a sub-carrier generator for generating a sub-
carrier replica; wherein the code oscillator receives the test code delay
and is coupled to the code generator and the sub-carrier generator,
and wherein the code generator and the sub-carrier generator are each
coupled to the code delay estimation device.
Preferably, the sub-carrier generator generates an early, late and prompt sub-
carrier
replica and the code generator generates an early, late and prompt PRN
replica. In
one embodiment, the code delay estimation device comprises:
(a) an input channel,
(b) first and second secondary channels split from the input channel,
(c) first and second tertiary channels split from the first secondary
channel,
third and fourth tertiary channels split from the second secondary
channel,
(d) and wherein the carrier oscillator is coupled to the first secondary
channel and the quadrature carrier oscillator is coupled to the second
secondary channel; and wherein the code generator is coupled to the
first tertiary channel and also coupled to the third tertiary channel; and
wherein the sub-carrier generator is coupled to the code generator, and
the product of the sub-carrier generator and the code generator is
coupled to the second tertiary channel and the fourth tertiary channel.
CA 02507360 2005-05-16
Preferably, the receiver further comprises an acquisition test function
device.
BRIEF DESCRIPTION OF THE DRAWINGS
The invention will now be described with reference to the following diagrams.
Figure 1 shows a normalized autocorrelation for BPSK(1) and sine-phased
BOC(1,1)
Figure 2 shows a standard normalized BOC(1,1) Early-Minus-Late-Power
discriminator for an early-late spacing of 0.2 Chips (6 MHz Double-sided front-
end
filter)
Figure 3 shows the probability of detection of the main and secondary peaks of
the
BOC(1,1) signals for 15, 40 and 60 non-coherent summations and coherent
integration time of 1 ms
Figure 4 shows an example of biased BOC(1,1) tracking on false peak with an
initial
code delay error of -0.5 chips (2 Hz DLL)
Figure 5 shows a normalized squared BOC(1,1) autocorrelation, a normalized
squared BOC(1,1)/PRN correlation, and synthesized correlation obtained by
differencing both (6 MHz Double-Sided Front-End Filter)
Figure 6 shows a normalized squared BOC(1,1) autocorrelation, and synthesized
correlation functions obtained with Beta = 1 and 1.4 (6 MHz Double-Sided Front-
End
Filter)
Figure 7A shows a schematic depiction of an acquisition structure implementing
a
method of the present invention.
Figure 7B shows a schematic depiction of a tracking structure implementing a
method of the present invention.
Figure 8 shows the output of a synthesized EMLP Discriminator Output for the
three
proposed normalizations, and for the original normalized BOC(1,1) EMLP
discriminator for an early-late spacing of 0.2 chips (6 MHz Double-Sided Front-
End
Filter)
Figure 9 shows the output of a dot-product discriminator using the four
different
proposed normalizations (Double-Sided Front-End BW = 50 MHz, Chip Spacing =
0.2 Chips
6
4,====*.=VIVAN^Raerk 1. = new
CA 02507360 2005-05-16
Figure 10 shows the tracking response of the standard BOC(1,1) tracking, and
the
synthesized BOC(1,1) tracking using NORM2 and NORM3 with an initial code delay
of 0.5 chips for a C/No = 40 dB-Hz (10 Hz PLL, 1 Hz DLL, PLL-aided DLL, 1 ms
integration time)
Figure 11 shows the tracking response of the standard BOC(1,1) tracking, and
the
synthesized BOC(1,1) tracking using NORM2 and NORM3 with an initial code delay
of 0.1 chips for a C/No = 40 dB-Hz (10 Hz PLL, 1 Hz DLL, PLL-aided DLL, 1 ms
integration time)
Figure 12 shows the standard deviation of the code tracking errors for the
three
methods considered (10Hz PLL, 1Hz DLL, PLL-aided DLL, 1ms Integration Time)
for
the University of Calgary (Top) and ENAC (Bottom) Simulators
Figure 13 shows the Multipath Envelopes for the Standard BOC(1,1) and new
Synthesized EMLP Discriminators (Beta = 1) for a Single Multipath with Half
the
Power of the Direct Signal and an Early-Late Spacing of 0.2 Chips (6 MHz
Double-
Sided Front-End Filter)
Figure 14 shows the Multipath Envelopes for the Standard BOC(1,1) and new
Synthesized EMLP Discriminators (Beta = 1 and 1.4) for a Single Multipath with
Half
the Power of the Direct Signal and an Early-Late Spacing of 0.2 Chips (6 MHz
Double-Sided Front-End Filter)
Figure 15 illustrates the impact of the coherent integration time and the C/No
on
FOM1 and FOM2
Figure 16 illustrates the probability of detection of the main peak using the
standard
BOC(1,1) and the new acquisition criteria with no non-coherent summations and
coherent integration times of 10, 20 and 30 ms.
Figure 17 illustrates the probability of detection of the main peak using the
standard
BOC(1,1) and the new acquisition criteria with 15, 40 and 60 non-coherent
summations and a coherent integration time of 1 ms.
7
CA 02507360 2005-05-16
DETAILED DESCRIPTION OF THE INVENTION
The present invention relates to a method and an apparatus for acquiring and
unambiguously tracking a BOC signal in a satellite navigation receiver. Unless
otherwise defined herein, the terms used herein shall have the meaning
commonly
understood by those skilled in the art.
The following description refers specifically to a sine-B0C(1,1) signal. It is
to be
understood that the methods of the present invention may be adapted to any BOC
signal. This method can be directly extended to any sine-B0C(n,n) signals as
all
sine-B0C(n,n) share identical correlation properties.
As will be apparent to those skilled in the art, various modifications,
adaptations and
variations of the specific disclosure which follows can be made without
departing
from the scope of the invention claimed herein.
1. BOC(1,1) RANGING AMBIGUITY ISSUE
Figure 1 shows the autocorrelation of a BPSK signal with a 1.023 MHz spreading
code rate and a sine-phased BOC(1,1) with the same spreading code. As
observed,
the BOC autocorrelation presents secondary peaks which can lead to ambiguous
acquisition and tracking problems. Although it is well-known that BOC signals
have a
tracking ambiguity issue, the understanding and quantification of the threat
assists in
understanding the solution the present invention provides.
Two main but not exclusive sources can lead to a ranging ambiguity when using
BOC modulation for ranging:
= A short loss of lock (due to a low C/No for instance) followed by lock,
after a drift
of the code tracking, on a secondary peak (an increase of the C/No shortly
after
the loss of lock)
= An incorrect acquisition that would acquire on the secondary peak of the
autocorrelation function and be followed by ambiguous tracking.
8
CA 02507360 2005-05-16
As the present invention relates to the unambiguous acquisition and tracking
of sine-
BOC(n,n) signals, the two issues mentioned above that could lead to a range
bias
are specifically discussed in the context of a sine-B0C(1,1) signal.
1.1 Tracking Ambiguity
The autocorrelation function of the BOC(n,n) signal with sine phasing, RBoc ,
plotted in
Figure 1, can be written as follows:
RBOCH trio ¨ ¨1 tri ,( --1 tri ,( (1.1)
1 2 1j 2 ¨2-0 )
where tria -Lc is the value in X of a triangular function centred in a with a
base
width of y and a peak magnitude of 1; I' is the code delay in chips.
Assuming that the Delay Lock Loop (DLL) uses an Early-Minus-Late-Power (EMLP)
discriminator, the theoretical expression of the discriminator output is:
vap(62-)= 11/EBoc2 QEBoc21-- LEBoc2 gEBoell (1.2)
Assuming the code tracking error Er is smaller than half the Early-Late
spacing C,,
and that C, is smaller than one chip, the EMLP discriminator expression in the
central region is given by:
A2
vjgfp() ¨ 8C, ¨12k (1.3)
4
for cs < Cs
2 I ¨ 2
where A is the amplitude of the incoming signal.
Normalizing the discriminator is preferred in order to eliminate the
dependency of
that signal upon the received signal power. The normalization typically used
for an
EMLP discriminator is:
NORM =[(IEBoc+ ILBOC)2 -FWEBoc -FQLBocf (1.4)
9
CA 02507360 2005-05-16
As a consequence, assuming a negligible carrier-phase error, the normalized
standard sine-B0C(n,n) EMLP discriminator can be expressed as:
(2 -3Cs deffp (1.5)
rA8r8g/ (er =
(18c -12)NORM
for _ < Cs
2 2
Figure 2 shows the normalized EMLP sine-B0C(1,1) discriminator output for an
early-late spacing of 0.2 chips using a 6 MHz double-sided front-end filter.
The
stability domain is clearly identified around the zero code delay in the [-
0.33; 0.33]
chip region. However, two other stable lock points can be identified around a
code
delay of 0.56 chips. These two false lock points represent the threat of a
tracking
bias. A code tracking error greater than 0.33 chips would lead to a biased
lock.
The two false lock points are not situated exactly at the same code delay as
the
secondary peak (0.5 chips), but slightly beside due to the different slopes
constituting the secondary peaks.
Due to the existence of undesired lock points, high noise or incorrect
acquisition that
leads to a code delay close to a secondary peak, leads to the possibility of
biased
tracking.
1.2 Acquisition Ambiguity
The sine-B0C(1,1) has an autocorrelation function that has secondary peaks
with a
magnitude of 0.5 relative to its main peak, as seen in Figure 1. One skilled
in the art
will realize that this will have an impact on the acquisition performance, as
unlike the
cross-correlation peaks, this relative magnitude will remain constant whatever
the
C/No value. An analysis based upon the theory described by Bastide et al.
(2002)
allows visualization of the probability of acquiring on the secondary peak.
This
method, valid for signals spread by a standard pseudo-random code can be fully
used when a sub-carrier modulates the code because the cross-correlation peaks
of
the BOC signals have the same magnitude as those of the spreading code. In
order
to set the acquisition thresholds, a probability of false alarm (Pth) of 10-3
has been
chosen and an interfering signal with a C/No of 45 dB-Hz has been assumed. The
CA 02507360 2005-05-16
computations assumed the same correlation isolation for the spreading code as
that
of the GPS C/A-code correlation function. Figure 3 shows the probability of
detection
of the main and secondary peaks of the BOC(1,1) signals assuming that neither
Doppler nor code delay error is present, for a coherent integration time of 1
ms and
for 15, 40 and 60 non-coherent summations.
The probabilities of detection of the secondary peaks are offset from the ones
of the
main peak by 6 dB, which is the difference in the correlation power between
the two
peaks. It can be observed from Figure 3 that when the C/No reaches 35 to 40 dB-
Hz,
the secondary peaks can be considered as real threats for acquisition due to
its non-
negligible probability of detection. The 6 dB difference between the curves
corresponding to main and secondary peaks is not the worst case possible.
Indeed,
the search cells could fall slightly on the side of the main peak and so have
a lower
probability of detection that the one indicated in Figure 3 for a given C/No.
Figure 4 shows the results of a simulation in order to illustrate the problem
that the
combination of wrong acquisition followed by ambiguous tracking can provide.
Using
the normalized EMLP discriminator already described, an initial code delay
value of
0.5 chips was fed to the tracking loops (assuming correct Doppler). The sine-
BOC(1,1) signal was simulated using the GPS C/A-code as its spreading code.
The
C/No was chosen to be 40 dB-Hz, the coherent integration time was 1 ms and the
DLL loop filter was set to 2 Hz. As seen in Figure 4, the DLL clearly locks
onto the
secondary peak and remains approximately 0.55 chips away from the true delay,
confirming the stability of the false lock point.
2.0 THE SYNTHESIZED CORRELATION FUNCTION
The present invention comprises an unambiguous synthesized correlation
function
as a solution to the threat created by the sine-B0C(n,n) multi-peak
autocorrelation
function. Since the false lock points described in section 1 are caused by the
secondary peaks of the sine-B0C(n,n) correlation function, the present
invention
comprises a method to synthesize a correlation function without any side
peaks.
11
CA 02507360 2005-05-16
In order to acquire and track a satellite signal, a receiver generates local
replicas of
the code and the carrier, which it then correlates with the received signal.
In an
initial acquisition phase, the receiver operates in open loop to seek the
received
signal by testing several assumptions regarding the position and speed of the
local
code and the local carrier. Once the signal has been acquired, the receiver
operates
in closed loop.
The discrimination function of the present invention was arrived at by
considering the
two following correlation functions:
= Autocorrelation of sine-B0C(n,n) signals, RE0c., whose autocorrelation
function is
given in equation (1.1), considering an infinite front end filter,
= Cross-correlation RBoc pRN of a sine-B0C(n,n) signal with its spreading
code PRN
(without the sub-carrier), which can be expressed as:
tri :51
RBOC PR -trii (2.1) NV = ¨2
2 2
As shown in equations (1.1) and (2.1), the side-peaks of the sine-B0C(n,n)
autocorrelation have the same absolute magnitude and the same location as the
two
peaks of the BOC/PRN cross-correlation function. Thus, in general terms, the
synthesized correlation function of the present invention is obtained by
differencing
the squared correlation points of these two functions. Figure 5 shows the two
squared correlation functions using a 6 MHz double-sided filter and the
resulting
synthesized correlation function. As seen in Figure 5õ the two side-peaks of
the
BOC(1,1) autocorrelation function are almost completely cancelled. The
mismatch is
due to the front-end filter that can have a different effect on each
correlation function.
In order to completely cancel the remainder of the secondary peaks, a
coefficient, p ,
may be introduced into the combination of the two correlation functions. The
synthesized correlation function is then given by:
RsyN(r)= Roar)-13 x IdOC I PR1V(r) (2.2)
The effect of the parameter p is shown by Figure 6. Unless otherwise stated,
the
coefficient p will be assumed to be equal to 1.
12
4=,`,....Aw+mon.sarnyow.rwworw
CA 02507360 2005-05-16
The main peak shown in Figure 5 and Figure 6 maintains the same sharpness. Two
negative side-lobes appear next to the main peak (around 0.35 chips) due to
the
unmatched slopes between the two correlation functions initially considered.
They
bring no threat as potential lock points as they point downwards. The
correlation
values obtained after 0.5 chips are very close to zero.
The expression for the synthesized correlation function in the case of an
infinite
front-end bandwidth is obtained by subtracting the square of equations (1.1)
and
(2.1):
(2.3)
Rsyiv (r) = (trio (-12 - trio (5-) x tri + tri
¨-- 1
2 2
3.0 Sine-B0C(n,n) DLL DISCRIMINATOR DERIVATION
Considering the symmetry and shape of the new synthesized correlation
function, in
a preferred embodiment, the invention may comprise different type of derived
discriminators. Two types of DLL discriminators are considered herein,
referred to as
the modified EMLP and Dot-Product (DP) discriminators, as examples of possible
discriminators resulting from the use of the combination of the BOC
autocorrelation
function, and of the BOC/PRN correlation function.
3.1 The Early-Minus-Late-Power Discriminator
A modified EMLP code tracking discriminator, extrapolated from a conventional
discriminator for a standard sine-B0C(1,1) tracking, may be suitable with the
present
invention.
In order to formulate the discriminator, ideal expressions of the sine-
B0C(1,1)
autocorrelation and BOC/PRN correlation functions are given in the central
region.
For this purpose, assuming that the code tracking error, e, , is smaller than
half the
spacing C., between the early and late correlators, the discrimination
function, in the
absence of filtering and noise, can then be rewritten as follows using
equation (1.1):
13
CA 02507360 2005-05-16
RBOCH = 1 311 for Id -1
(3.1)
2
Similarly, RBoc ARAI (c) can be expressed as:
1
RBOC I PRN(T)=- for iri -2 (sine phasing) (32)
Assuming that V
EBA, Thcp/PRN is the output of the modified EMLP discriminator, it follows
that:
B -TEBoc2 +QEBoc21-kBoc2 Q-LBoc
vEAz pRAT rr
\.-flIVEBocipRAr2 -FQEBOC1 PRN 2h k-LBOCI PRN2 +QLBOCI PRN2
(3.3)
The EMLP discrimination function can then be expressed as:
( CS )2 Cs \ 2
RBOC er +- y " RBOC Er
A2 ,
PRN
VB0(e )=¨ L _
EMLP 2 -
Cs 2 Cs
¨ RBOC,PRN(6r4' ¨27-) RBOC,PRN er
2
_
So, assuming ---<e the final expression of the modified EMLP
discriminator
2 2
is given by:
difiSPRN (6, TN = A2
¨4 08 ¨ fl)Cs ¨12)er (3.5)
for _ <6 <Cs
2¨ 2
In a preferred embodiment, normalizing the discriminator is necessary to
estimate
the amplitude term in the discriminator. However, it is preferred to make sure
that
this normalization does not limit the stability domain of the discriminator.
It is further
preferred to have a normalized discriminator with a 'correct' response for a
code
tracking error as large as possible. The examples of normalizations given
hereafter
use a combination of the BOC autocorrelation function and the BOC/PRN
correlation
function.
14
_______________________________________________________________________________
____ 1...Mi=====
CA 02507360 2005-05-16
In one embodiment, the normalization of the modified EMLP discriminator is
based
on the same method as used by the conventional sine-B0C(1,1) EMLP
discriminator:
NORM= fkIEBoc+/Lsoc)2 +(QEsoc+QLBoc)21 (3.6)
1,
VEBOCI PRN ILBOCI PRWf 4-(QEBOCI PRN+21,BOCI PRN)2
It leads to the following output expression:
- 3C5)2 VEMLP
VNORM1(er)=-- // (3.7)
kk1.8 - /3)Cs -12)NORM1
for _ < <
2 2
In an alternative embodiment, a second expression uses the same normalization
as
the standard sine-B0C(1,1) tracking normalization:
NoRM2=kBoc+140c)2 (QEBoci-Q1Bodi (3.8)
which gives the following normalized output:
(2 -3cs)2 VIP/SPRAT
18fAidT(er)= (3.9)
(k1 8 - /3)C5 - 12)NORM2
for
2 r2
In another embodiment, the normalization comprises a modified version of
expression (3.6), but takes into account the anti-symmetrical property of the
BOC/PRN correlation function:
NORM3= ([0EBoc+/LBocf (QEsoc+Q-LBogi (3.10)
-f-ivEBocipRN- ILBOCI PRIVY +(QEBOCI PRN QLBOCI PRA)2
The normalized discriminator output then becomes:
vpBsioN (sr) =_(µLi I-112C, +v,10C, 2 PRN (3.11)
kk1 8 - - 12)NORM 3
for_ er <Cs
2 2
CA 02507360 2005-05-16
Figure 8 shows the output of each of the three normalized modified EMLP
discriminators (for 13 -1) described as well as the output of the standard
normalized
sine-B0C(1,1) discriminator for an early-late spacing of 0.2 chips and a front-
end
filter of 6 MHz (double-sided). Unlike the standard sine-B0C(1,1)
discriminator that
has a false lock point, there is no such potential problem for the three
exemplary new
discriminators for usual C/No values. For high C/No, there is a potential
problem at
- 0.65 chips as the discriminator output slightly crosses the y-axis 'in the
right
direction'. This problem can be easily removed by slightly increasing the
parameter
,or by choosing a larger front-end filter.
The three exemplary normalizations may lead to different tracking performances
due
to their impact on the discriminator output shape. The first normalization
NORM1
may have weaker performance compared to the two others due to its quick return
to
0 when the code tracking error becomes greater than 0.2 chips. The two other
normalizations, NORM2 and NORM3 , have similar responses and have stability
areas
slightly greater than the standard sine-B0C(1,1) EMLP discriminator: [-0.38;
0.38]
chips compared to [-0.33; 0.33] chips. Accordingly, the modified EMLP
discriminator
of the present invention using one of NORM2 and NORM3 will have a slightly
larger
resistance to tracking errors than pure BOC(1,1) tracking.
3.2 DOT-PRODUCT (DP) TYPE OF DISCRIMINATOR
One alternative discriminator to the modified EMLP discriminator comprises a
modified DP discriminator adapted to the novel sine-B0C(n,n) tracking
technique of
the present invention.
The expression of the modified DP is given by:
((IEBoc H-Boc )/PB oc (QEB oc Q-LBoc )QPB oc
vjvc PRN ( (
-E-
V'130C I PRN BOC I PRN)-1PBOC I PRN
k"
"/". (QEBOC PRN Q1130C / PRN)QPBOC I PRN
(3.12)
16
CA 02507360 2005-05-16
In that case, using the expressions for the correlator outputs, in the absence
of
noise, we have:
A2 - ( C D ( C \
Ve (Er).= ¨4 RBOC ST + - l'BOC Er- --"'""S"' RBOC(ST)
_
(3.13)
A2 - Cs ( Cs \-
--4 RBOC,PRN ST + ¨2 j- /1BOC,PRN ST l`BOC,PRAST)
2
Using the above models for BOC and BOC-PRN correlation functions, the
following
discriminator is arrived at:
2
Vgj C I PRN (6. )=¨ A4- 31 eT I + f3Cjer (3.14)
4
As may be seen, this discriminator does not have a linear variation as a
function of
the code tracking errorcr which decreases the linearity domain of the
discriminator.
Many normalizations may be implemented for the DP discriminator. When
considering the DP discriminator in a traditional sine-B0C(1,1) signal
tracking
application, an interesting aspect of the normalization is that it can help
remove the
multiplicative terms preventing a non-linear variation of the discriminator.
However,
in the case of the present tracking invention, this is difficult since the
strict
multiplicative term (6(1--316,1)+,80 is difficult to synthesize on its own.
One exemplary DP normalization is given by:
(R/EBoc H,Boc )/PBoc (IEBoc H.Boc )IPBocT
NORM1= -
+ ---
(-BOC I PRN 11' BOC I PRN)-1PBOC I PRN (3.15)
(IEBOCI PRN 1LBOC I PRIV)IPBOC I PRN _
A2 1 C s\ ( --
NORM1=¨ R
-BOC Er +¨ -n-BOC Er -- RBOC(ST)
) 2
(3.16)
42 - (
¨4 RBOC,PRN ST + ¨2 RBoc,PRN I - ¨2 RBOC,PRN( T)
(r
NORM1 =4
2 -3C - 314+ 2d) (3.17)
4
17
CA 02507360 2005-05-16
and for Er 0
2
NORM1= A ¨[2 ¨ 3C s] (3.18)
4
The most important term in this normalization is the first term in (3.17)
depending on
( 36,
the value we would like to cancel 1-1-1 , as the second term depends on the
c
squared value of Er , which can be neglected.
(2 - 3rv s )vDBpOCIPRN
vE7PORMi (sr 1 (3.19)
(6+ MNORM1
Another possible DP normalization is derived from the conventional sine-
B0C(1,1)
DP normalization and is given by:
NORM2
=[(--TE
BOC BOC)IPBOC (Q-E BOC + Q1' BOC)QPBOC] (3.20)
2
NORM 2 = A ¨ [2 ¨ 3C si(1. ¨ 318,1) (3.21)
4
( 3er
In this example, this normalization depends on the signal power and on 1-1-1 ,
c
which is a perfect cancellation of the undesired terms in the classical sine-
B0C(1,1)
DP discriminator. However, concerning the modified DP discriminator, it does
not
cancel out completely the quadratic error.
The resulting expression is:
(2 _3covirciPRN
vRm2k)., _______________________________ (3.22)
(6+ C8)NORM2
Yet another possible DP normalization uses only the prompt values of the BOC
autocorrelation function:
NORM3 = [1PB2oc QB20C (3.23)
18
Vra AXT-lX=
CA 02507360 2005-05-16
A 2
11
NORM3 = ¨4 (1 ¨312er i) (3.24)
This example of normalization depends on the signal power, but will not remove
the
terms preventing a non-linear evolution of the discriminator:
B POC I RN
vil Rm3(Er)= __ vDP
(6+ Cs )NORM3
The last DP normalization disclosed herein uses a modified version of DP
NORM3:
NORMA =1.1PB20C +QPB20C IPB20C I PRN QPB20C I PRN J (3.26)
A 2
NORM4 = ¨4 1-616.,_ I + 10Er2 (3.27)
ri-BOC I PRN
V(6)= , __ r DP , (3.28)
(6+ Cs WORM 4
Having described four exemplary DP normalizations, their comparison can be
made.
Figure 9 show the discriminator output for each case, considering a 50 MHz
front-
end filter bandwidth (double-sided), and including the traditional normalized
sine-
BOC(1,1) DP discriminator.
As seen in Figure 9, each of the DP normalizations removes the false lock
point
situated around 0.56 chips. As for the EMLP however, there is a potential
remaining
threat at a code delay of 0.6 chips for high C/No, when limited front-end
filter
bandwidths are used. This can be solved by increasing slightly the value of
the
parameter p . The characteristics of each normalization considered are very
different:
= DP NORM1 offers a limited response when the code delay error approaches
the edge of the stability domain;
19
MN{ JWMIA =awaeaman,
CA 02507360 2005-05-16
= DP NORM4 does not need any extra complex correlators which is a strong
implementation advantage, however, its output on the edge of the stability
domain is weak and might offer less stability when the noise level is high;
= DP NORM2 has a large linearity domain in the stability region compared to
NORM3 and NORM4. However, one more complex correlator is required for
the normalization, as both BOC/BOC early and late correlators output are
needed independently.
= DP NORM3 seems more adapted in this sense, as it uses only the prompt
correlator's output, and as these values are needed anyway for the PLL, it
does not increase the requirement in terms of correlators.
Accordingly, DP NORM2 and DP NORM3 are preferred normalizations for the
methods of the present invention using a DP discriminator. It has the same
characteristic stability domain as the normalized EMLP discriminator described
above.
3.3 Requirements in terms of complex correlators:
For the EMLP discriminator described herein, with the novel sine-B0C(1,1)
unambiguous tracking method described herein, 5 complex correlators are
needed:
Early Boc , LateBoc , Pr ompt Bac (needed for the PLL), EarlyBOC I PRN LateBOC
I PRN
The same 5 complex correlators are required for a DP discriminator with new
BOC(1,1) unambiguous tracking and normalization DP NORM2. If normalization DP
NORM3 is used, 4 complex correlators are needed:
(Early ¨ Late)Boc , Pr omptBoc (needed for the PLL), (Early ¨ Late)BOCI PRN
Pr WnPt BOC I PRN
For the DP with traditional BOC(1,1) tracking using a bump-jumping technique
and
normalization DP NORM3, 4 complex correlators are needed:
(Early ¨ LateLoc , Pr ompt BOC (needed for the PLL), VeryEarly BOC VeryLateBoc
CA 02507360 2005-05-16
Therefore, the signal tracking method using a DP discriminator normalized by
DP
NORM3, does not increase the requirements in terms of complex correlators.
3.4 IMPLEMENTATION OF THE SINE- BOC(1,1) ACQUISITION AND
TRACKING METHOD
As shown in Figure 7A, in acquisition mode, one embodiment of a satellite
receiver
comprises an acquisition decision device (10) having a first input (100) and
three
outputs (S1, S2, S3). A frequency generator (12) and a code generator (14)
provide
inputs to the acquisition decision device (10). The satellite signal is
received on the
first input (100), following filtering, down-conversion, sampling and
quantization.
The acquisition decision device (10) outputs either a positive acquisition
decision
(S1), or a negative decision. If the acquisition decision is negative, the
device (10)
outputs the next set of frequency (S2) and code delay (S3) for trial.
In the code generator (14), the code oscillator (16) receives the code delay
(S3) to
use for the next acquisition trial. This code oscillator (16) drives the code
generator
(18) and the sub-carrier generator (20). The code generator (18) outputs a
code
replica (22) with the correct code delay received from (S3). The sub-carrier
generator
(20) outputs the sub-carrier with the correct code delay received from (S3)
that is
then multiplied with the code replica (22) to provide the BOC replica (24)
with the
correct code delay (S3).
In the frequency generator (12), the carrier oscillator (26) receives the
frequency
(S2) to use for the next acquisition trial and outputs a carrier signal (28)
and a carrier
signal phase-shifted by 900 (30).
The incoming signal (100) is multiplied by the carrier signal on a first
secondary
channel (201) and by the quadrature carrier signal on the second secondary
channel
(202). Each of the secondary channels is then split into two tertiary
channels.
The first tertiary channel (301) results from the first secondary channel
(201) and is
multiplied by the code replica signal (22). The second tertiary channel (302)
is
multiplied by the BOC replica signal (24). The third tertiary channel (303)
results
21
õ
CA 02507360 2005-05-16
from the second secondary channel (202) and is multiplied by the code replica
signal
(22). The fourth tertiary channel (304) is multiplied by the BOC replica
signal (24).
The signals obtained on each of the four tertiary channels is processed by an
integrate and dump device (40), then processed by a squaring device (42) and
then
combined by a combination device (44) by means of reproducing the synthesized
correlation function described herein. The combination device outputs a
synthesized
correlation value (401) that is input in a summation device (50) that
accumulates
several synthesized correlation values before outputting the acquisition test
value
(501). This acquisition test value (501) is then input in the decision test
device (60)
that takes the decision of declaring successful acquisition (S1) or continuing
the
acquisition process with the next frequency (S2) and code delay (S3).
Once the signal is acquired, the device may go into tracking mode, as
described
herein. Figure 7B illustrates a receiver tracking structure of one embodiment
of the
present invention. The device comprises a receiver comprising a code delay
estimation device (10') having a first input (100) and an output (S'). A phase
and/or
frequency lock loop (12') and a code loop (14') provide inputs to the code
delay
estimation device (10'). The satellite signal is received on a first input
(100),
following filtering, down-conversion, sampling and quantization.
The code delay estimation device (10') outputs discrimination information (S')
which
is used by the code loop (14'). Specifically, the Delay Lock Loop or DLL (16')
which
operates as a code corrector, calculates the code correction information or
the code
Doppler estimate and adds it (with a scaling factor) to the external speed
reference
(18') from the PLL (or FLL), which is then used by the code oscillator (20').
The code
oscillator (20') controls the sub-carrier signal generator (22') and the code
signal
generator (24'). The code signal generator (24') outputs an early, late and
prompt
spreading code replica signal (26') while the sub-carrier signal generator
(22')
outputs an early, late and prompt sub-carrier replica signal which is
multiplied by the
code replica (26') to produce the BOC replica signal (28').
22
CA 02507360 2005-05-16
In the phase and/or frequency lock loop (12'), the carrier oscillator (30')
receives the
external speed reference (18') and outputs a carrier signal (32') and a
carrier signal
phase-shifted by 90 (34').
The incoming signal (100) is multiplied by the carrier signal on a first
secondary
channel (201') and by the quadrature carrier signal on the second secondary
channel
(202'). Each of the secondary channels is then split into two tertiary
channels.
The first tertiary channel (301') results from the first secondary channel
(201') and is
multiplied by the early, late and prompt code replica signals (26'). The
second tertiary
channel (302') is multiplied by the early, late and prompt BOC replica signals
(28').
The third tertiary channel (303') results from the second secondary channel
(202')
and is multiplied by the early, late and prompt spreading code replicas (26').
The
fourth tertiary channel (304') is multiplied by the early, late and prompt BOC
replicas
(28 ).
The signals obtained on each of the four tertiary channels is processed by an
integrate and dump device (40') and the channel outputs are combined in the
discriminator (42') which produces the discrimination information or raw code
delay
by means of the synthesized correlation function described herein.
4.0 EXAMPLES (Simulation Results)
The following examples describe test results and are intended to illustrate
the
invention and not to limit the claimed invention.
The test results are the result of investigations into the effect of two of
the main
sources of error in GNSSs: thermal noise and multipath. Simulation results
comparing tracking in white thermal noise the traditional sine-B0C(1,1)
tracking
technique and the present invention are shown.
4.1 OBSERVED SINE-B0C(1,1) UNAMBIGUOUS TRACKING
PERFORMANCE
23
CA 02507360 2005-05-16
The normalized discriminators described herein appear to have an asymptotic
behaviour at the edge of their tracking region. As a consequence, in order to
avoid
large tracking jumps due to large discriminator output, a cut-off value
dependent
upon Cs may be necessary.
The PLL needs to have the correct phase information on both the in-phase and
quadra-phase channels in order to consistently estimate the phase offset. As a
consequence, the PLL is run using the prompt values of the standard sine-
B0C(1,1)
correlators. Therefore, the PLL is exactly the same as the PLL in a
conventional
sine-B0C(1,1) tracking system.
A first test confirmed that a discriminator of the present invention avoids
any false
lock points. For this example, the three different normalized EMLP
discriminators
described in section 3.1 were compared. The first one used the standard
normalized
sine-B0C(1,1) EMLP discriminator. The two others used the modified EMLP
discriminators with two different normalizations: NORM2 and NORM3 . A PLL-
aided
DLL was used. A cut-off value was set for the three discriminators' outputs.
By using
a 0.2 chip early-late spacing, the discriminator output was set to 0.4 chips
whenever
the actual absolute value of the absolute output was greater than 0.4 chips.
The
front-end filter has a double-sided bandwidth of 6 MHz. The DLL and PLL loop
bandwidths were set to 1 and 10 Hz respectively. The integration time was
chosen to
be 1 ms and the initial =code delay was set to 0.5 chips, assuming an
acquisition on
the side peak. The C/No was 40 dB-Hz. The results are shown in Figure 10.
Figure 10 shows that unlike a prior art sine-B0C(1,1) standard discriminator,
the two
others do not make the DLL lock on any offset stable point, confirming the
results
shown in Figure 8. The use of the same PLL as in standard sine-B0C(1,1)
tracking
could have raised a concern as the PLL aiding uses standard sine-B0C(1,1)
prompt
correlation values. Figure 10 demonstrates that the PLL does not limit the
drift from
the biased initial code delay, following the estimation coming from the PLL.
It is important to note again that for high C/No, and for a limited front-end
filter
bandwidth, there may still be a chance of tracking the secondary peak, as
discussed
24
CA 02507360 2005-05-16
above. To solve this problem, 13 can be chosen to have a value greater than 1.
The
minimum value to use depends on the front-end filter, but also on the early-
late
spacing.
4.2 STUDY OF THE IMPACT OF THERMAL NOISE ON THE
PROPOSED METHOD
4.2.1 STUDY OF THE EMLP DISCRIMINATORS
The tests were run with the same settings as described previously. In this
example,
however, the initial code delay was set to 0.1 chips in order to observe the
convergence toward zero, a strong clue for correct tracking, as well as to
study the
code tracking noise when convergence is achieved. The simulations were run
over
20 seconds of simulated data. The exact same tracking parameters as the ones
used to obtain Figure 10 were chosen. Figure 11 shows the results of one of
the
simulations for a signal with a C/No of 40 dB-Hz using the EMLP discriminator
implementations.
The convergence period in Figure 11 takes approximately 1 second. The standard
deviation of the code tracking error is computed for all the output obtained
after two
seconds of data processed in order to make sure that the values used are taken
after the convergence period. For the EMLP discriminators, in order to have a
reliable analysis, tests were done independently on two different software
receivers:
one developed by ENAC, Toulouse, France, and one developed at the University
of
Calgary, Canada. 12 summarizes the results obtained during the simulation
campaign. For all the cases considered, convergence was obtained.
Figure 12 shows consistent results, which tends to confirm the correctness of
the
implementation, particularly with C/No greater than 30 dB-Hz. Comparing the
two
new EMLP normalized discriminators, the one using N0RM3 appears to outperform
the one using NORM2 . Although the difference is very small for high C/No, it
increases as the signal strength decreases. Consequently, NORM3 is a preferred
normalization selected as a preferred modified EMLP discriminator.
CA 02507360 2005-05-16
However, its noise mitigation performance is still slightly worse than for
code tracking
using the standard normalized sine-B0C(1,1) discriminator. The main reason can
be
explained when viewing the new synthesized discriminator as the difference of
two
EMLP discriminators: one associated with the pure sine-B0C(1,1)
autocorrelation,
and the other one with the BOC/PRN correlation. This linear combination brings
extra noise that is partially cancelled by the correlation of both pairs'
noise values.
However, there is still extra noise entering the tracking loops. The ratio
between the
code tracking error standard deviations is between 1.07 and 1.22 (excluding 30
dB-
Hz results) according to the tests considered, which is very small. When
looking at
= Figure 12, this represents a loss in C/No of less than 1 dB.
4.3.2 STUDY OF THE DP DISCRIMINATORS
Using the exact same settings, the performance of the normalized DP
discriminators
has been compared with the conventional sine-B0C(1,1) DP discriminator using
also
DP NORM2 and DP NORM3 as a normalization. The tests were based on a 20
second signal. The results are shown in Table 4.1.
Table 4.1 ¨ Standard Deviation of the Code Tracking Error for Different C/No
for
the Different DP Tracking Techniques
Traditional Traditional.
C/No (dB-Hz) BOC(1,1) BOC(1,1) DP NORM2 DP NORM3
NORM2 NORM3
32 0.00525 0.00663 0.00678 0.00599
35 0.00312 0.00326 0.00370 0.00375
It can be seen that in the case of the traditional sine-B0C(1,1) tracking,
using a DP
discriminator, there is a better noise mitigation using NORM2. However, this
difference between the two proposed normalizations decreases as the C/No
increases.
Concerning the novel method of the present invention, it has a slightly worse
performance than traditional tracking. However, the degradation is typically
less than
1 dB.
26
CA 02507360 2005-05-16
The implementation of the synthesized method, using NORM3 may easily be
implemented on a sine-B0C(1,1) platform by those skilled in the art as it uses
the
same number of complex correlators as the traditional DP (when bump jumping
(Fine and Wilson, 1999) is implemented) and does not require extra
computations.
4.3 SINE-B0C(1,1) MULTIPATH MITIGATION PERFORMANCE
Another important performance parameter when studying a tracking technique is
its
inherent resistance to multipath. Although only the EMLP discriminator will be
discussed in this section, one skilled in the art will realize the results can
be directly
transposed to the DP case.
As discussed above, the synthesized correlation function has a support
function
smaller than that of the sine-B0C(1,1) autocorrelation function. In the ideal
case of
infinite bandwidth, it has non-zero values only within 0.5 chips. However,
due to
the use of a non-linear combination of correlators output to form the
discriminators, it
does not imply that the impact of long delay multipath is cancelled. Figure 13
shows
the multipath envelope of the standard and synthesized EMLP discriminators
(for
p =1) for a received multipath of half the direct signal amplitude and an
early-late
spacing of 0.2 chips. The front-end filter used has a 6 MHz double-sided
bandwidth.
The multipath envelope of a novel method of the present invention has the same
shape as the one of the traditional sine-B0C(1,1) tracking method. However,
they
have two main differences: (1) the first lobe of the new method is slightly
wider for
multipath delays between 0.25 and 0.55 chips; (2) the second lobe for the new
tracking method is narrower, implying a better multipath rejection for long
delay
multipath. It has to be noticed that the choices of the front-end filter
bandwidth and of
the early-late spacing have an impact in the magnitude of the difference
between the
two methods. However, it gives the same general shape. The new synthesized
method appears to offer good resistance to long delay multipath while giving
reliable
measurements. The use of slightly greater parameter p does not modify the
general
shape of the multipath envelope, as shown in Figure 14. It is also important
to note
two drawbacks of the traditional sine-B0C(1,1) tracking technique when
multipath
are present. First, the multipath envelope plotted in Figure 13 is not
realistic, as it
27
CA 02507360 2005-05-16
assumes a correct tracking which might not be occurring. Secondly, it has to
be
noticed that using the traditional method, it is possible that a strong
multipath creates
an interfering correlation peak that is higher or as high as the secondary
peak of the
sine-B0C(1,1) autocorrelation function. In such a case, if the receiver is
tracking the
secondary peak, this can dangerously mislead the receiver.
5.0 DEMONSTRATION OF THE SINE- BOC(1,1) ACQUISITION METHOD
As demonstrated herein, the stability domain of a novel discriminator of the
present
invention is slightly greater than the one associated with the standard EMLP
sine-
BOC(1,1) discriminator. Its tracking performance is quasi-equivalent to
standard
sine-B0C(1,1) tracking. Finally, it has a better inherent mitigation of long-
delay
multipath. However, if the initial tracking error is greater than
approximately 0.35
chips the discriminator will not be able to converge toward zero code delay,
and the
loop will lose lock. Note that the behavior of pure sine-B0C(1,1) tracking in
that case
would be to slide to a false lock point as presented in the first section.
This means
that in order to make sure that the receiver using the new tracking technique
succeeds in tracking the incoming signal it has to acquire the signal
relatively close
to the main peak. As already seen, this may be a problem when using a
conventional
acquisition technique based on a search of the maximum energy using the
autocorrelation power due to the presence of the side peaks. For this reason,
an
investigation of an acquisition technique using the synthesized correlation
function is
done hereafter.
The following assess the performance of the new acquisition scheme.
Assuming that M is the number of non-coherent summations, the signal power at
the output of the synthesized correlation is given by:
P
+ n2 (12 2 )) (5.1)
Bock OCk BOC I PRNk n I PRNk
k=1
Since the noise power at each correlator's output is the same, it is possible
to have
the following acquisition criterion:
28
CA 02507360 2005-05-16
-, _________________________ =,2 -
kl¨CTP RBOC(es)SitZfDTP) (
COS EA+ n IBOC
No , 7 DTp J
N 2
_
+ (il¨CTP RBOC(gr)sink.DTP)sin(68)+ QBOC n (5.2)
P M No
afDrp
i
--i- ¨ 1
fliCTP __ \sink 2
DDTp) ( \
"BOC I PRN ( let- 1 COSkeo )+ nIBOC I PRN
No ______ nf DT p
\
( ______
, \sink T ) 2
- \I-CTP RBoc 1 PRNl6r I _,. D P sin(60) nQBOCIPRN
No ifI DTp
_ \ -
where an2 is the variance of the correlator's output noise with power___9_N ;
Tp is the
47p
coherent integration time; C is the signal power at the output of the receiver
antenna; nIBOC 1 nQB0C I n IBOCI PRN and nIBOCIPRN are centred Gaussian noise
with a
unity variance; 60 is the phase error; and f'D is the frequency error.
The acquisition criterion can be seen as the difference between two non-
central Chi-
square distributions. Consequently, the acquisition criterion can be defined
as:
P
Tnew = ¨27 = A , BOC ¨ MOGI PRN (5.3)
Cn
where
,( _______
i _______ .
CT, õsin( \2
DTP nfDTp) r 1,
i RBOCt8r ) - COSkEtil 4- nIBOC (5.4)
71f
TBOC = Ail \ N /
N 2
k=1 l IICTp f IsinkDT )
----RBOCl6r / _,.D' ,p P sin(60)+ nQB0C
No 'Y
\ ,.. / ,I
and
((( CT, \ 2 N
i , 'n To , .,
(CT
ker ) SI _6"D, " )COSVO ] + n IBOC I PRN
M NO iy Di p i
TBOC I PRN = I \..
\ 2
" (i/Crp I ) \sin(prp) µ ,
+ ¨RBOC PRN ler sinteo /1-11Q/30c / PRN
No ' izfDT,
Since the acquisition criterion is the difference between two Chi-square
distributions,
its expected value can be expressed as:
(Tnew) := (TBOC) ¨ (TBOC I PRN) (5.6)
29
CA 02507360 2005-05-16
It has been determined that the two distributions T.Boc and T Boc pRN can be
assumed
as independent when no front-end filter was used as the correlation between
the two
correlators' noise considered is null. Empirically, this covariance has been
determined to be very low when using a front-end filter, so that:
a2 r,r 2 fr 2
rnm (5.7)
TBOC TBOC I PRN
From equations (5.6) and (5.7), it is possible to compare the mean and
variance of
the new acquisition criterion with the values of the standard acquisition
criterion
(symbolized by T ). For this purpose, two figures of merit have been defined:
the
ratio of the means (Fomi), and the ratio of the variances (Fom2). These two
figures
of merit can be expressed using equations nT)
p(5: - 5'7) as:
FOM1 =
CTp
_______ kkRB0C \\2 kRBOC,PRiV(er ))2µ(
No //fp Tp (5.8)
CT
P (RBOC(er))2 (sin(ilfDTP).\ 2 + 2
No 1DTp
and,
( in (rif D Tp
4 CT----I1RBOC (er))2 (RBOC,PRAErk)s __ + 2
NO )µ XfDrp (5.9)
FOM2=
CT
¨1-1.(RBOC(E,D2( sir4fDTP 2 +1
N0 if DTI)
From equations (5.6) and (5.7), it can be seen that both figures of merit
favour the
standard acquisition criterion. Indeed, the ratio of the means will always be
smaller
than 1, meaning that (Tne,õ) will always be smaller than (TB0c) when the same
acquisition parameters are used. Similarly, FOM2 will always be greater than
1,
meaning that o will always be larger thancf-7.2 . Due to the relatively
small value
of (RBOC,PRN(Er))2 compared to (RBoc.(632 around 6, =O, its impact on the
acquisition
performance will be small.
The number of non-coherent summations appears to have no impact on the two
figures of merit. This means that the difference between the two criteria
cannot be
bridged using a large number of non-coherent summations. Equations (5.6) and
(5.7)
CA 02507360 2013-02-27
also show that the difference between the two acquisition criteria is reduced
when
the value of CTp increases. The impact of the C/No and Tp on the two figures
of merit
is represented in Figure 15.
Knowing that the difference between two independent random variables has a
distribution which is the convolution between the first variable distribution
and the
opposite of the second variable distribution [Papoulls, 1991], it can be
written that:
(x)?--- p0c (7C)* P rfioc Pm x) (5.10)
where pc, is the distribution of the random variable a .
As a consequence, it is possible to model through simulations the distribution
of Tõ.,
as a non-central Chi-square distribution. Therefore, the probability of
detection of the
main peak using the new acquisition criteria can be estimated. Making the same
assumptions as in the sections above, Figures 16 and 17 are obtained.
As expected, the coherent integration time has a greater effect on the
acquisition
performance than the non-coherent summation number compared to the original
BOC(1,1) acquisition strategy. For long coherent integrations, the new method
even
outperforms the standard BOC(1,1) method. One skilled in the art may realize
the
importance of this as new GNSS civil signal will have a dataless channel
authorizing
longer coherent integrations.
REFERENCES= .
Bastide, F., O. Julien, C. Macabiau, and B. Roturier (2002), Analysis of L5/E5
Acquisition, Tracking and Data Demodulation Thresholds, Proceedings of U.S.
Institute of Navigation GPS (Portland, OR, USA, Sept. 24-27), pp. 2196-2207.
31
CA 02507360 2005-05-16
Betz, J.W. (2002), Binary Offset Carrier Modulations for Radionavigation,
Navigation,
Journal of the Institute of Navigation, Winter 2001-2002, Vol. 48, Number 4,
pp. 227-
246.
Fine, P., and W. Wilson (1999), Tracking Algorithm for GPS Offset Carrier
Signals,
Proceedings of U.S. Institute of Navigation NTM (San Diego, CA, USA, Jan. 25-
27),
pp. 671-676.
Gibbon, G (2004), Welcome Progress in GNSS Talks, GPS World, February issue.
Godet, J., J.C. de Mateo, P. Erhard, and O. Nouvel (2002), Assessing the Radio
Frequency Compatibility between GPS and Galileo, Proceedings of U.S. Institute
of
Navigation GPS (Portland, OR, USA, Sept. 24-27), pp. 1260-1269.
Lin, V.S, P.A. Dafesh, A. Wu, and C.R. Cahn (2003), Study of the Impact of
False
Lock Points on Subcarrier Modulated Ranging Signals and Recommended Mitigation
Approaches, Proceedings of U.S. Institute of Navigation AM (Albuquerque, NM,
USA, June 23-25), pp. 156-165.
Martin, N., V. Leblond, G. Guillotel, and V. Heiries (2003), BOC(x,y) Signal
Acquisition Techniques and Performances, Proceedings of U.S. Institute of
Navigation GPS/GNSS (Portland, OR, USA, Sept. 9-12), pp. 188-198.
Papoulis, A. (1991), Probability, Random Variables and Stochastic Processes,
Third
Edition, McGraw Hill International Editions.
Ward, P. (2004), A Design Technique to Remove the Correlation Ambiguity in
Binary
Offset Carrier (BOC) Spread Spectrum Signals (Revised Version), Proceedings of
U.S. Institute of Navigation NTM (San Diego, CA, USA, Jan. 26-28), pp. 886-
896.
32
WW as- am a
