Multipath Error Reduction in Signal Processing
Alexey Zhdanov, Victor Veitsel, Mark Zhodzishsky and Javad Ashjaee
Javad Positioning Systems
compensate for the imperfections of the above mentioned
strobe methods. It should be noted here that such progress
can be achieved without making any complicated changes
to the receiver design or increasing its power
consumption.
BIOGRAPHY
Alexey Zhdanov is with the JPS research and development
group specializing in GNSS and signal processing. He has
a Ph.D degree in EE.
Victor Veitsel received his Ph.D. and Dr.Sc. in 1955 and
1967, respectively. Pr. Veitsel is presently Consultant at
the Javad Positioning Systems.
INTRODUCTION
In practice, navigation signal processing comprises
accumulation of resulting multiplication products of the
received signal with both the reference carrier and
reference code generated in the receiver. The reference
carrier signal corresponds to the carrier for the given
satellite and the reference code corresponds to the pseudorandom code of the same satellite. Devices that perform
multiplication and accumulation of the products are called
correlators, whereas the corresponding process is called
correlation of both signals.
It is known a lot of ways to design tracking
channels in such a receiver, but the most commonly used
design comprises three or four correlators. The first two
correlators produce in-phase I and quadra-phase Q
correlation signals. These I and Q signals are used to
perform carrier synchronizing. For example, the phase
lock loop (PLL) discriminator can function according to
the algorithm Z d = arctan(Q / I ) . Signal I is used to
demodulate information symbols as well. In different
synchronization systems signal I represents the
normalization signal. In both correlators the reference
code is a replica of the satellite PRN code (Figure 1,a).
Such a reference signal provides the closest to minimal
both variance of the PLL tracking errors and probability of
false demodulation of information symbols.
The third (and fourth) correlator computes the inphase dI (quadra- phase dQ) signal, which is used in the
delay lock loop (DLL) system. A discriminator of the
coherent DLL can operate by the algorithm Z d = dI / I ,
while a discriminator of the noncoherent DLL functions
with the following algorithm Z d = dI ⋅ I + dQ ⋅ Q . For
both correlators the reference code is a strobe sequence,
and hence the correlators are called strobe correlators
Ref.[4].
Mark Zhodzishsky received his Ph.D. and Dr.Sc. in 1965
and 1984, respectively. Pr. Zhodzishsky is presently
Research Group Manager at the Javad Positioning
Systems.
Javad Ashjaee pioneered high Precision GPS at Trimble
Navigation. Dr. Ashjaee is founder of Ashtech (1987).
Later he founded the JPS company, where he is closely
involved in all aspects of product development.
ABSTRACT
The multipath error reduction methods described in
this paper will give you an insight into further
development of the so-called "strobe methods" that have
been used in pseudo random noise (PRN) receivers since
1975 (see Ref.[1]). These methods already proved their
high effectiveness in reducing tracking errors in spreadspectrum (PRN type) digital receivers (see Ref.[2-4]).
However, it should be stressed here that they have some
failings too, for example, the possibility for a DLL to lock
on reflected signals, or problems due to very narrow DLL
lock range. Hopefully we can now offer new techniques
allowing engineers to reduce the failings inherent to the
earlier strobe methods (these new techniques are patent
pending).
The idea of using strobes is based on replacing the
'regular' PRN-code replica in the receiver correlator with
an alternative reference code replica built from a special
series of strobes. In this paper, we will present a new
effective strobe sequence and provide the reader with all
the necessary theoretical information and experimental
data on the expected noise and multipath errors. The new
strobe sequence described below allows developers to
PAGE
To reduce the impact of multipath error due to
varying strobe waveforms it has been suggested in Ref. [4]
to generate relation dI (ε) similar to shown in Figure 2, b.
It should be noted that the strobe, which we get in this
case, is called the complex strobe. Such a shape of relation
dI (ε) provides decreasing both the maximum peak of
multipath error and the reflected signal influence zone.
The maximum peak of multipath error ∆τmax is determined
by the ratio of a value of maximum side peak dImax (see
Figure 2) which is located on the right from the DLL
operating point ε0 to the derivative Kd of dI (ε) with
t
a)
∆
D
t
b)
D
t
c)
D1
d)
D2
t
S1
A
S2
respect to shift ε at the operating point
∆τ max = ±α dI max / K d ,
Figure 1. Reference signals
where α is a ratio of amplitudes for reflected and line of
sight signals. The reflected signal influence zone size is
determined delay range where the multipath error for
reflected signals with preset amplitude exceeds some
threshold value. In Figure 2,b by convention this zone
corresponds to the intervals (ε0 ÷ ε4) and (ε5 ÷ ε6 )].
EMBEDEMBEDFor example, a simple strobe
(Figure 1, b) with duration D that is equal to front duration
(transient process duration) of PRN-code modulating the
incoming correlator signal provides almost minimal
variance of noise errors in DLL tracking, i.e., this strobe is
close to optimal. Note that DLL with simple strobe with
duration D is equivalent early-late DLL with spacing D.
It may be shown that in the quasilinear
approximation the DLL errors are governed only by
statistic of dI. The relation of the mean signal dI on the
time shift ε between a reference and an input PRN code of
this strobe is shown in Figure 2, a. Once being appeared
the reflected signal results in generating a scaled replica of
relation dI (ε) which is shifted to the left since the
reflected signal delays always with respect to the line of
sight signal, and as a rule, the reflected signal is weaker
than the line of sight signal. As a result of adding these
two relations dI (ε) , zero of the sum relation dI (ε) is
offset. It causes offset of the discriminator characteristic
(relation of the mean error signal Z d on the time shift ε)
DISADVANTAGES
OF
THE
DESCRIBED
APPROACH AND WAYS TO THEIR AMENDMENT
The approach described in INTRODUCTION has
two important drawbacks
• narrow DLL lock range;
• possibility of DLL erroneous lock over reflected
signals;
Let us consider these disadvantages one after
another.
The narrow DLL lock range. We mean here the
range of initial errors ε, at which the signals are
synchronized in the operating point ε0 that has been
selected. In Figure 2,b this range is equal to (ε1 ÷ ε2). This
range is narrower than that for the DLL with a simple
strobe (in Figure 2,a that range is equal to ±∆). If under
signal energy search the adjusting delay step is large
enough, for instance, it is ∆, then for correct acquisition a
two-step acquisition procedure has been suggested in
Ref.[4] to be used. After searching had been completed,
we should turn on the DLL with a simple strobe at the first
step of the acquisition procedure. After transient process
in DLL had been completed, we should turn on a complex
strobe at the second step of the acquisition procedure.
Using such a two-step procedure increases acquisition
time and requires extra resources to realize this simple
strobe DLL. Note, that at the first sight we can replace the
described two-step acquisition procedure with an extrasearch procedure, which is carried out after initial rough
searching and has much less delay step. However, such an
approach is inexpedient because there exists the
inadmissibly great possibility to make an incorrect
decision about position of signal’s maximum peak at
extra-search, especially, in respect to the satellites with
low carrier-to-noise power density ratios C/N0. If such a
decision is made there will be an abnormally large error in
pseudorange since in this case the DLL operating point
Z d (ε) operating point, that results in generating the
multipath error.
dI(ε)
b)
∆
∆
ε0 ε3
ε
0
ε1
ε2 ε4
dImax
ε5
(1)
ε6
a)
Figure 2. Possible shapes of relation dI (ε)
PAGE
will not coincide with the desired point ε0, but will be at
either zero point with negative derivative (for example, at
the point ε3 in Figure 2,b).
Possibility of DLL erroneous lock over reflected
signals. Such an erroneous lock may occur when there is a
powerful enough reflected signal at the receiver input.
This reflected signal is delayed by δ related to the line of
sight signal over range (ε2 ÷ ∆) and its carrier phase θ with
respect to carrier phase of the line of sight signal being
close to zero. If C/N0 of the given satellite is low there
exists a possibility of occurring a slip having
approximately δ duration in DLL. As a result, DLL starts
tracking the reflected signal instead of the line of sight
one.
To get rid of the drawbacks above we propose to
synthesize a strobe providing relation dI (ε) of type in
strobe locking type and a strobe shape. Remind that
according to Ref.[4] two locking types are possible. They
are:
• locking with a moment of PRN code sign change,
• locking with a PRN code chip edge.
It should be noted that the strobe sequence of Figure 1, b
has locking with a moment of PRN code sign change.
Let us choose locking type first of all. It is easy to
show that relation dI (ε) of Figure 3 may be only
implemented using locking with a PRN code chip edge.
Either strobe S (t ) having step waveform and total
duration D can be generated from a sequence of n adjacent
to each other rectangular pulses with magnitude Si
(possibly zero) and delay di:
n
S (t ) = ∑ S i ⋅ (h0 (t − d i ) − h0 (t − d i +1 ) ) ,
Figure 3. If we choose ε0 as an operating point the
maximum peak of multipath error will be determined by
dImax [see Eq. (1)], while the reflected signal influence
zone by range (ε0 ÷ ε4).
where h0(t) is unit jump (Heaviside function), dn+1=D + d1.
For example, if n=1 strobe S (t) is a rectangular pulse with
duration D. Then the relation dI (ε) is equal to
dI (ε) =
dI(ε)
ε0 ε3
ε
ε2 ε4
0
k =0
n
T
i =1
0
dI (ε) = ∑ S i
The acquisition range of DLL with such a relation
dI (ε) is wide enough and equal to ∆, hence we need not
employ the two-step acquisition procedure. If a delay step
at the energy search stage is ∆, then after finishing this
stage it is necessary to jump off by ∆/2 along shift ε to the
left toward the flat area of relation dI (ε) . When transient
∑ µ k S (t − k∆) dt
µ
,
(3)
T / ∆ −1
µ k (h0 (t − d i − k∆) −
∫ C (t − ε) ∑
k =0
h0 (t − d i +1 − k∆) )dt
(4)
µ
It is seen from Eq.(4) that for locking with a
moment of PRN code sign change
n
d + d i +1
dI (ε) = ∑ S i ⋅dI S (ε − i
, d i +1 − d i )
(5)
2
i =1
d + d i +1
, d i +1 − d i ) [in such a way
where function dI S (ε − i
2
the multiplier in brackets ⋅ µ Eq.(4) is designed]
process in DLL completes the operating point will be at ε0.
While occurring the reflected signal distorts the left part of
relation dI (ε) but it will not result in appearing extra zero
points with negative derivative and hence in the DLL with
such a relation dI (ε) erroneous lock over reflected signal
will be impossible.
PROVIDING
T / ∆ −1
∫ C (t − ε)
If we use locking with a PRN code chip edge multiplier µ
is equal ±1 dependent on the sign of PRN-code. In the
case of locking with a moment of PRN code sign change if
the sign of PRN-code changes, then µ will be equal to ±1
dependent on the sign. If the sign does not change µ=0.
Substituting Eq.2 in Eq.3 and taking i-sum outside
the integral symbol, we get
dImax
Figure 3. Desired shape of relation dI (ε)
STROBE SYNTHESIS
RELATION dI (ε )
T
where
C(t) is PRN-code passed through the radio frequency (RF)
part and modulating the correlator incoming signal,
T is accumulation time in the correlator,
µ is a sign multiplier,
⋅ µ is ensemble µ average.
∆
0
(2)
i =1
represents nothing else than relation dI (ε) of a simple
strobe (Figure 1, b) shown in Figure 2, a. This function has
d + d i +1
and strobe
two arguments; namely, shift ε − i
2
duration D = d i +1 − d i . So, relation dI (ε) of either strobe
with step waveform can be generated as a linear
combination of some number of simple strobe relation
DESIRED
To synthesize a strobe we will employ a heuristic
approach. The synthesis will include both determination of
PAGE
• providing sufficient suppression of multipath
errors;
• providing a permissible level of energy losses (compared
to the optimal strobe sequence).
dI (ε) with multipliers Si. It is further evident, as function
d i + d i +1
, d i +1 − d i ) (see Figure 2,a) is uneven
2
function, the definite integral of curve dI (ε) (see Eq.5)
dI S (ε −
8
between limits -∝ and ∝ will be equal to zero regardless of
selecting Si and di. But from Figure 3 it can be seen that
the definite integral of desired curve dI (ε) does not have
zero value. So, it is impossible to realize the desired
relation dI (ε) using a strobe having locking with a
moment of PRN code sign change. Therefore, we should
employ locking with a PRN code chip edge.
The simplest variant of the strobe sequence using
locking with a PRN code chip edge is a strobe sequence
shown in Figure 1, c. Such a sequence at duration D=73 ns
(strobe with such duration is close to optimal) provides for
GPS C/A code relation dI (ε) revealed in Figure 4, a. This
4
δ, m
-8
0
0.04
a)
B
0.00
b)
ε, ns
-0.04
400
200
300
400
So it appears to be expedient to set S1=S2 and D1=3D2.
The relation dI (ε) for the case when S1=1 and
D1+D2=146 ns is depicted in Figure 4, b calculated by
'Design Package' (see Ref.[5]). In Figure 5,b multipath
error envelops at ratio of amplitudes α=0.5 for this strobe
sequence is shown as well. For comparison in Figure 5,a
there is multipath error envelopes for strobe showed in
Figure 1,b. Level of synthesized strobe DLL energy losses
compared to the simple strobe DLL (duration D=73 ns) is
5.1 dB. As a result of computation at DLL equivalent
noise band BDLL=0.2 Hz and C/N0=40 dBHz the
synthesized strobe DLL provides standard deviation of
noise error about 0.53 m. In the case of GLONASS СA
code, Figure 5 is valid except standard deviation. It will be
2 greater, i.e.; it will be equal to 0.76 m.
0.08
0
100
Figure 5. Multipath error envelops for strobe sequences
showed in Figure 1, b and Figure 1, d
dI(ε)
-400
b)
-4
0.12
-800
a)
0
relation dI (ε) will be provided if we use SAW-filter
Sawtek 854668 with the bandwidth of 16 MHz at the level
of -3 dB in RF-part. This described filter is employed in
JPS receivers such as Legacy, Odyssey, Regency, and
Eurocard. Figure 4, a shows that the amplitude span of the
relation dI (ε) operating part (that area is designated as
B) is very small and hence if noise is present signal
tracking can be unstable.
-1200
∆τ(δ), m
800
EXPERIMENTAL DATA ON THE SYNTHESIZED
STROBE DLL
1200
Figure 4 The relation dI (ε) for strobe sequences showed
in Figure 1, c and Figure 1, d
The easiest way to increase the amplitude span of
the operating part is adding a negative pulse to the strobe
(that pulse is designated as A in Figure 1, d). By varying
duration D2 and amplitude S2 we can change both spacing
and amplitude span of the operating part correspondingly.
In the synthesis three key points have to be taken into
consideration:
• simplicity of implementing this strobe sequence;
The synthesized strobe DLL has been tested in
static and low kinematic scenarios. The main objective of
testing was to find out to what extent the receiver
performance can be improved by using the synthesized
strobe DLL for the usual simple strobe DDL. Since
multipath error reduction is especially important for
differential tasks, we carried out our tests with the
receivers running in the differential mode (with a few
exceptions, see below). We connected two JPS Legacy
(Ref.[6]) receivers to a common 'base antenna'. In the first
Legacy receiver, the synthesized strobe DDL was enabled.
The other Legacy was using the simple strobe DLL. The
PAGE
'rover antenna' too was connected to (another) pair of
Legacy receivers with similar strobe DLLs.
Static Applications. In these tests, the base and
rover antennas were installed on the roof of a high-rise.
Since the two antennas were spaced several dozen meters
aside there (and at different levels, too), the base and rover
multipath errors could be considered uncorrelated. In fact,
the roof had quite a complex surface with a number of
signal reflecting details. Our preliminary analysis showed
that the multipath delays 0 < δ <30 (meters) and relative
amplitudes 0 < α < 0.5 were characteristic of that
improvised test range.
In our first experiment, all of the receivers were
switched to the code differential mode providing
smoothed GPS/GLONASS C/A pseudo ranges. These
smoothed pseudo ranges were obtained with the help of a
50-second moving average filter where carrier phases were
used for reducing code phase noise. Figures 6 and 7 show
the differential positioning accuracy in plane and height,
respectively. The black triangle
indicates the estimates
obtained for the receivers with the simple strobe DDL,
whereas the gray bullet marks the data obtained with the
use of the synthesized strobe DDL. All the relevant data
were collected over a 14-hour observation interval. To get
these data, we first had to compute a (precise enough)
baseline estimate by using the carrier phase differential,
which was then used as reference. Since the carrier phase
multipath error has a zero mean (assuming a long enough
interval), such a vector estimate can well be used as a
'truth' baseline.
Figure 7. Height positioning errors in code differential
As follows from Figures 6 and 7, the use of the
synthesized strobe allows us to reduce the mean errors: in
latitude, from 0.16 meters down to -0.02 meters, in
longitude, from 0.52 meters to 0.06 meters, in height, from
0.52 meters to 0.04 meters. For standard deviation, this
characteristic changed as follows: in latitude, from 0.89 m
to 0.37 m, in longitude, from 0.52 m to 0.22 m, in height,
from 1.38 m to 0.58 m. For maximal absolute value: in
latitude, from 3.71 m to 1.83 m, in longitude, from 3.22 m
to 1.31 m, in height, from 7.92 m to 2.51 m. Therefore, the
use of the synthesized strobes results in considerable
improving of receiver performance (we gain twice as
much in terms of accuracy).
In our second experiment, we were using the
GPS/GLONASS carrier phase differential based on C/Asignal measurements. The main goal was to find out
whether the code multipath reduction results in a smaller
'time to first fixed solution'. In the course of this 'cyclic'
test, we repeatedly re-set the Real Time Kinematic (RTK)
engine (Ref.[7]) as soon as the engine computed another
fixed ambiguity solution. Both 'receiver pairs' (two
receivers with the simple strobe DDL and another two
with the synthesized strobe DDL), ran simultaneously for
70 hours with an average of 10 satellites being tracked
during this time. Figure 8 shows the 'time to first fixed
solution' histograms based on the collected data. The
histogram shown in black corresponds to the receivers
with the simple strobe DLL whereas the gray histogram
describes the results relating to the synthesized strobe
DDL. As seen from this figure, the use of the synthesized
strobe DDL will also reduce the time it takes the receiver
to fix biases and get a centimeter-level accuracy. In this
experiment it allowed to reduce the mean time to first
fixed solution of 8%.
Figure 6. Plane positioning errors in code differential
PAGE
0.20
2
'Code minus carrier', m
0.16
1
0.12
0
0.08
0.04
-1
time, s
0.00
time, s
0
10
20
30
-2
Figure 8. 'Time to first fixed solution' histograms
0
Low Kinematic Applications. Does a receiver
with the synthesized strobe DDL make difference in low
kinematic? This is a key question. In low kinematic, the
receiver moves so slowly that the mechanism of
"multipath randomization" is not fully enabled. Such
scenarios are not uncommon: imagine a surveyor walking
with his backpack kit in the field or a roller laying asphalt
on the street etc.
In this experiment, the rover antenna was
mounted on the car moving at 4 mph. Again, two 'JPS
Legacy' receivers were connected to this antenna. The next
step to take might be to use a base antenna and another
two receivers, but… Note that in tests like ours it is very
important to assure very low multipath at the base
antenna's location. Otherwise, it will be very difficult, if at
all possible, to distinguish between the rover and base
multipath. Obviously, this is a very tough requirement to
meet. That is why we decided to make do without any base
antenna/receivers in this test. Instead, we decided to use
the so-called 'code minus carrier' combination (the
difference between pseudo range samples and carrier
phase samples expressed in meters) for the rover antenna.
Figure 9 shows the code minus carrier combination based
on the GPS PRN14 C/A-slot measurements from the
receiver with the simple strobe (marked with the black
triangle ) versus the analogous combination for the same
satellite and slot but from the receiver with the synthesized
strobe DLL (marked with the gray bullet ). Please note
that for the sake of convenience the constant offset was
removed from the combinations before drawing these
plots. Figure 10 depicts similar data for another satellite
(specifically, GPS PRN 25 C/A-slot).
As follows from Figures 9 and 10 synthesized
strobe DLL decreases values of code error jump caused be
random reflectors two or more times. Therefore low
kinematic applications, too, will benefit from using the
synthesized strobe DDL since this results in a better signal
tracking performance.
200
400
600
800
Figure 9. Code minus carrier for GPS PRN14 C/A
2
'Code minus carrier', m
1
0
-1
-2
time, s
-3
1200
1400
1600
1800
2000
Figure 10. Code minus carrier for GPS PRN25 C/A
CONCLUSION
The use of the synthesized strobe DDL in
GPS/GLONASS receivers results in a better signal
tracking performance thus leading to higher positioning
accuracies and availability. It resolves problems of the
possibility for a DLL to lock on reflected signals and
narrow DLL lock range.
The conducted experiments showed the accuracy
is improved twice as much in static code differential. The
mean time to first fixed solution is reduced of 8%. The
values of code error jump are decreased two or more times
PAGE
4. Veitsel V., Zhdanov A., Zhodzishsky M. The
mitigation of multipath errors by strobe correlators in
GPS/GLONASS receivers. GPS Solutions, Volume 2,
Number 2, Fall 1998. -pp. 38-45.
5. Zhodzishsky M., Vorobiev M., Zhdanov A and
Ashjaee J. Automated Design of Navigation Receivers.
Proc. of ION GPS-99, The Institute of Navigation,
Nashville, Tennessee.
6.
http://www.javad.com/Products/Hardware/
Legacy.htm.
7.
http://www.javad.com/Products/Applications/
Real%20Time%20Kinematic%20Application.htm.
in low kinematic applications. The gain is especially
obvious in static code differential.
REFERENCES
1. Zhodzishsky M. 1975. Digital PLL systems for
video signal processing. Proc. of 2-nd scientific
conference "PLL systems". Gorky, Russia (in Russian).
2. Garin L., Van Diggelen F. and Rousseau J.M.
Strobe & Edge correlator multipath mitigation for code.
Proc. of ION GPS-96, The Institute of Navigation,
Alexandria, VA, 657-664.
3. Garin L. and Rousseau J.M. Enhanced strobe
correlator multipath rejection for code & carrier. Proc. of
ION GPS-97, The Institute of Navigation, Alexandria,
VA, 559-568.
PAGE