GPS+BDS RTK: A low-cost single-frequency positioning approach

Full text

50 GPS WORLD WWW.GPSWORLD.COM
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SEPTEMBER 2017
WITH RICHARD B. LANGLEY
GPS+BDS RTK
GPS has been the number-one positioning tool
for a range of applications during the past
few decades. The integration of the emerging
global navigation satellite systems, such as the
Chinese BeiDou Navigation Satellite System (BDS), can give
improved precise (millimeter- to centimeter-level) real-time
kinematic (RTK) positioning. When BDS is combined with
GPS, about double the number of satellites are visible in the
Asia-Pacific region, which can make single-frequency RTK
and low-cost receiver RTK positioning possible.
In this article, we will analyze the performance of L1
GPS + B1 BDS in Dunedin, New Zealand, using low-cost
receivers. We compare their performance to that of L1+L2
GPS survey-grade receivers.
First, we describe the GPS+BDS functional and stochastic
models and the data used for our evaluations. Least-squares
variance component estimation (LS-VCE) is used as a means
to determine the code and phase (co)variances to formulate
a realistic stochastic model. (An incorrect stochastic model
will deteriorate the ambiguity resolution and consequently
the achievable positioning precisions.) Having correctly
defined the stochastic model, we focus on the positioning
performance. We investigated the ambiguity resolution and
positioning performance, both formally and empirically, for
customary and high-elevation cut-off angles. The high cut-
off angles are used to mimic situations when low-elevation
multipath is to be avoided. Lastly, we compared all our results
between using low-cost and survey-grade antennas.
GPS+BDS POSITIONING MODEL
The model that we used for positioning is given as follows.
Assume that sG + 1 GPS satellites are tracked on fG frequencies
and sB + 1 BDS satellites on fB frequencies. As we apply
system-specific double-differencing (DD), one pivot satellite
is used per system. The total number of DD phase and code
observations per epoch then equals 2 fG sG + 2 fB sB. We assume
for now that cross-correlation between frequencies as well
as code and phase is absent. The combined multi-frequency
short-baseline GPS+BDS model is then defined as follows.
The system-specific DD phase and code observation
vectors are denoted as and , respectively, with * = {G, B}
where G = GPS and B = BDS. The single-epoch GNSS model
of the combined system is given as
(1)
and
(2)
in which
is the combined phase vector,
is the combined code vector,
is the combined integer
ambiguity vector,
is the real-valued baseline vector,
is the combined phase random
observation noise vector,
is the combined code random
observation noise vector, and
denotes the dispersion operator.
The entries of the baseline design and wavelength matrices
are given as
A Low-Cost Single-Frequency Positioning Approach
BY Robert Odolinski and Peter J.G. Teunissen
FIGURE 1 Low-cost single-frequency receivers collecting GPS+BDS data for
single-baseline RTK, with patch antennas (left) and survey-grade antennas
(right) on Jan. 4–6 and Jan. 6–8, 2016, respectively. Survey-grade dual-
frequency GPS receivers were connected to the same survey-grade antennas
simultaneously to truly track the same GPS constellation.

SEPTEMBER 2017
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WWW.GPSWORLD.COM GPS WORLD 51
where is the vector of 1s, is the
differencing matrix, is the unit matrix,
the geometry-matrices and contain the undifferenced
receiver-satellite unit direction vectors for GPS and BDS,
respectively, is the wavelength of frequency , denotes
the Kronecker product, and “diag” and “blkdiag” indicate
diagonal and block diagonal matrices, respectively. The
entries of the positive definite variance matrices are given as
(3)
where denote the phase and code standard
deviation, respectively, and the satellite elevation-angle-
dependent weight.
The model in Equation 1 applies to short baselines, and
thus the ionospheric and tropospheric delays are assumed
absent. The broadcast ephemerides are used to obtain the
satellite coordinates. Further, the Least-squares AMBiguity
Decorrelation Adjustment (LAMBDA) technique is used
to estimate the integer ambiguities a. The observation noise
vectors ε and e, respectively, are zero-mean vectors, provided
that no multipath is present in Equation 1.
EXPERIMENT SETUP
The GNSS receivers we used are depicted in FIGURE 1. Firstly,
two low-cost single-frequency receivers were set up to collect
L1+B1 GPS+BDS data for two days. These receivers cost a
few hundred U.S. dollars. Since the patch antennas we used
have been shown to have less effective signal reception
and multipath suppression in comparison to survey-grade
antennas, the receivers that collected data for two days were
additionally connected to such antennas. These antennas
have a cost of slightly more than US$1,000 per antenna. To
compare the low-cost solution to a survey-grade receiver-
solution, two such receivers (which cost several thousand
U.S. dollars) were connected to the same survey-grade
ALL GOOD THINGS ARE CHEAP; ALL BAD
ARE VERY DEAR. That’s what the famous
American essayist (and surveyor) Henry
David Thoreau wrote in his diary on March
3, 1841. He was likely referring, in part,
to the cheapness of the things he came
across in nature such as birdsong or the
plants and trees on the shores of Walden
Pond and the dearness of some luxuries
and comforts of civilization, which he
tended to eschew. But what has that got
to do with GPS, you might ask?
When they were first introduced in the
late 1970s and early 1980s, GPS receiv-
ers were very dear. Many of them sold
for anywhere from $50,000 to $250,000,
which would be equivalent to about twice
those amounts in today’s dollars. The
first civilian receivers were large bulky
affairs. As I documented in this column
in April 1990 (“Smaller and Smaller: The
Evolution of the GPS Receiver”), the “first
commercially available GPS receiver was
the STI-5010 built by Stanford Telecom-
munications Inc. It was a dual-frequency,
C/A- and P-code, slow-sequencing
receiver. Cycling through four satellites
took about five minutes, and the receiver
unit alone required about 30 centimeters
of rack space. External counters, also
requiring rack space, made pseudorange
measurements. An external computer
controlled the receiver and computed
positions.” While it could be transported in
a small truck (and some were), it was not
designed for portability and ease of use by
surveyors or geodesists.
Then, in 1982, Texas Instruments
introduced the first relatively compact
civil GPS receiver, the TI 4100, also
known as the Navstar Navigator. And as
I also noted in that column more than
15 years ago, this “receiver could make
both C/A- and P-code measurements
along with carrier-phase measurements
on both L1 and L2 frequencies. Its single
hardware channel could track four
satellites simultaneously through a
multiplexing arrangement. The 37 × 45 ×
21–centimeter receiver/processor had a
handheld control and display unit and an
optional dual-cassette data recorder for
saving measurements for postprocessing.
The unit, although portable, weighed 25
kilograms and consumed 110 watts of
power (the receiver doubled as a hand
warmer). Field operation required a
supply of automobile batteries.”
My, how things have changed.
Beginning around 1990, receivers steadily
got smaller and smaller and cheaper and
cheaper. Survey-grade GNSS (not just
GPS) receivers can now be purchased
for well under $10,000 and consumer-
grade units sell for as little as a hundred
dollars or less. And, of course, the GNSS
modules inside smartphones and other
devices cost manufacturers only a couple
of dollars or so. But even a GNSS receiver
that can supply raw pseudorange and
carrier-phase measurments now costs
only a few hundred dollars, and in this
month’s column, a couple of researchers
from Down Under pit a couple of these
receivers up against a couple of survey-
grade receivers. Did this cheap receiver
turn out to be a good thing? Read on to
find out.
INNOVATION INSIGHTS
BY RICHARD B. LANGLEY

52 GPS WORLD WWW.GPSWORLD.COM
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SEPTEMBER 2017
antennas through splitters and
collected L1+L2 GPS data. A detection,
identification and adaption procedure
was used to eliminate any outliers.
FIGURE 2 depicts the corresponding
redundancy of the two receiver models
(that is, the number of observations
minus the number of estimated
unknowns) together with the number
of satellites over 48 hours (30-second
epoch interval). The number of BDS
satellites (magenta lines) is overall
smaller than when compared to GPS
(blue lines) in Dunedin. However,
Figure 2 also shows that the model
strength of L1+B1 GPS+BDS, as
measured by its redundancy, is almost
similar to that of L1+L2 GPS except
for some hours at the middle of the
two days. This implies that the two
receiver models can potentially give
competitive RTK ambiguity resolution
and positioning performance. This is
however only true if the receiver code
and phase observation noise would
be of similar magnitude between the
receivers used, hence the need for an
analysis of the receiver observation
precision.
In our receiver evaluations,
we determined a set of reference
ambiguities by using a known baseline
and treating them as time-constant
parameters over the two days in a
dynamic model.
LOW-COST RTK POSITIONING
The code and phase variances were
estimated by LS-VCE using data
independent from the data used for
the following positioning analysis.
The variances are needed to formulate
a realistic stochastic model, whereas
an incorrect stochastic model will
deteriorate the ambiguity resolution
and consequently the achievable
positioning precisions. TABLE 1 depicts
the corresponding estimated standard
deviations (STDs) used for our
positioning models.
Table 1 shows that the code
precision of L1 GPS and B1 BDS
improves significantly when the
survey-grade antennas are used instead
of patch antennas (49 centimeters
STD for L1/B1 that decreases to
about 30 centimeters), due to their
better signal reception and multipath
suppression abilities. For testing our
stochastic model, we used data that
is independent from the data used to
estimate the code/phase precision.
Positioning Performance. Th e
single-epoch (instantaneous) RTK
positioning results for 24 hours data
are shown in FIGURE 3, with ambiguity-
float solutions shown at the top and
ambiguity-fixed solutions at the
0 1440 2880 4320 5760
0
4
8
12
16
20
24
28
32
Redundancy
Number of epochs (30 seconds)
L1 GPS + B1 BDS
L1+L2 GPS
0 1440 2880 4320 5760
0
4
8
12
16
20
24
28
32
Number of epochs (30 seconds)
Number of satellites
GPS sat.
BDS sat.
Total sat.
−4 −2 02 4
−4
−2
0
2
4
East error (m)
North error (m)
Emp. σN = 0.70 m σE = 0.62 m
Mean error N = 0.03 m E =−0.02 m
Emp. 95% ellipse
Form. 95% ellipse
720 1440 2160 2880
−5
0
5
No. of epochs (30 s)
Up error (m)
Emp. σU = 1.43 m
Mean error U = −0.00 m
Emp. 95% conf. level
Form. 95% conf. level
−0.02 00.02
−0.02
0
0.02
East error (m)
North error (m)
Emp. σN = 0.002 m σE = 0.002 m
Mean error N = −0.000 m E =−0.000 m
Emp. 95% ellipse
Form. 95% ellipse
720 1440 2160 2880
−0.05
0
0.05
No. of epochs (30 s)
Up error (m)
Emp. σU = 0.005 m
Mean error U = 0.000 m
Emp. 95% conf. level
Form. 95% conf. level
(a) Low-cost receiver + patch antenna: L1+B1 GPS+BDS
−4 −2 02 4
−4
−2
0
2
4
East error (m)
North error (m)
Emp. σN = 0.42 m σE = 0.40 m
Mean error N = 0.10 m E =−0.03 m
Emp. 95% ellipse
Form. 95% ellipse
720 1440 2160 2880
−5
0
5
No. of epochs (30 s)
Up error (m)
Emp. σU = 0.90 m
Mean error U = −0.03 m
Emp. 95% conf. level
Form. 95% conf. level
−0.02 00.02
−0.02
0
0.02
East error (m)
North error (m)
Emp. σN = 0.002 m σE = 0.001 m
Mean error N = 0.001 m E =−0.000 m
Emp. 95% ellipse
Form. 95% ellipse
720 1440 2160 2880
−0.05
0
0.05
No. of epochs (30 s)
Up error (m)
Emp. σU = 0.004 m
Mean error U = 0.001 m
Emp. 95% conf. level
Form. 95% conf. level
(b) Low-cost receiver + survey-grade antenna: L1+B1 GPS+BDS
0
0
0
0
FIGURE 2 Redundancy (left) and number of satellites (right) of L1+B1 GPS+BDS and L1+L2 GPS during Jan.
6–8, 2016, (48 hours) for an elevation cut-off angle of 10°.
FIGURE 3 Horizontal (north (N), east (E)) position scatter and corresponding vertical (U) time series of the float (top) and correctly fixed (bottom) L1+B1 GPS+BDS
single-epoch RTK solutions for an elevation cut-off angle of 10°. The 95% empirical and formal confidence ellipses and intervals are shown in green and red,
respectively. The 24 hour (30 second) period is 22:00-22:00 UTC Jan. 5-6, 2016, for patch antennas in (a) and 21:48-21:48 UTC Jan. 8-9, 2016, for survey-grade
antennas in (b), which are periods independent of the periods used to determine the stochastic model through the code/phase STDs in Table 1.

bottom. Only the correctly fixed solutions are depicted as
determined by comparing the instantaneously estimated
ambiguities to the set of reference ambiguities. The 95%
empirical and formal confidence ellipses and intervals are
shown in green and red, respectively. They were computed
from the empirical and formal position variance matrices.
The empirical variance matrix was estimated from the
positioning errors as obtained from comparing the estimated
positions to precise benchmark coordinates. The formal
variance matrix used was determined from the mean of all
single-epoch formal variance matrices.
Figure 3 shows a good fit between the formal and empirical
confidence ellipses/intervals, which thus illustrates realistic
LS-VCE STDs in Table 1 that were used in the stochastic
model. Note also the two-order of magnitude improvement
when going from float to fixed solutions, and that the low-
cost receiver plus survey-grade antenna has the most precise
ambiguity-float positioning solutions.
Ambiguity Resolution and Positioning Performance for Higher Cut-
Off Angles. We subsequently investigated the low-cost L1+B1
GPS+BDS performance for high elevation cut-off angles,
so as to mimic situations in urban canyon environments or
when low-elevation-angle multipath is present and is to be
avoided. We have made comparisons to the survey-grade
L1+L2 GPS results. It has been shown that a good ambiguity
resolution performance does not necessarily imply a good
positioning performance, so we investigated what effect this
has on our positioning models.
The following integer least-squares (ILS) success
rates (SRs) are thus computed based on epochs with the
condition of positional dilution of precision (PDOP) ≤
10 and averaged over all epochs over two days of data. By
including and excluding epochs with large PDOPs, we can
show how the positioning performance of the different
models is affected by poor receiver-satellite geometries. To
better understand how this exclusion of epochs with large
PDOPs also influenced the empirical ambiguity-correctly-
fixed positioning performance, we constructed TABLE 2,
which shows the corresponding positioning STDs for two
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SEPTEMBER 2017
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WWW.GPSWORLD.COM GPS WORLD 53
Receiver/
antenna System Frequency STD code
(cm) STD phase
(mm)
Survey-grade/
survey-grade GPS L1
L2 18
20 2
2
Low-cost/
survey-grade GPS
BDS L1
B1 31
30 2
2
Low-cost/patch GPS
BDS L1
B1 49
49 2
2
TABLE 1 Zenith-referenced undifferenced code and phase standard deviations
estimated by least-squares variance component estimation.

54 GPS WORLD WWW.GPSWORLD.COM
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SEPTEMBER 2017
−5 05
−6
−4
−2
0
2
4
6
East error (meters)
North error (meters)
Float solution
Wrongly fixed solution
Correctly fixed solution
00.02
−0.02
0
0.02
L1 GPS + B1 BDS (10°)
1440 2880 4320 5760
−5
0
5
10
# of e ochs 30 s
01440 2880 4320 5760
−0.05
0
0.05
−5 05
−6
−4
−2
0
2
4
6
East error (meters)
North error (meters)
Float solution
Wrongly fixed solution
Correctly fixed solution
00.02
−0.02
0
0.02
L1 GPS +B1 BDS (10°)
1440 2880 4320 5760
−5
0
5
10
# of e
p
ochs
[
30 s
01440 2880 4320 5760
−0.05
0
0.05
−5 05
−6
−4
−2
0
2
4
6
East error (meters)
North error (meters)
Float solution
Wrongly fixed solution
Correctly fixed solution
00.02
−0.02
0
0.02
1440 2880 4320 5760
−5
0
5
10
# of e
p
ochs
[
30 s
01440 2880 4320 5760
−0.05
0
0.05
L1+L 2GPS (10°)
1440 2880 4320 5760
0
0.5
No. of epochs (30 seconds)
ADOP (cyc)
0
5
10
STD U [m]
1440 2880 4320 5760
0
0.5
No. of epochs (30 seconds)
ADOP (cyc)
0
5
10
STD U [m]
1440 2880 4320 5760
0
0.5
No. of epochs (30 seconds)
ADOP (cyc)
0
5
10
STD U (m)
−5 05
−6
−4
−2
0
2
4
6
East error (meters)
North error (meters)
Float solution
Wrongly fixed solution
Correctly fixed solution
00.02
−0.02
0
0.02
1440 2880 4320 5760
−5
0
5
10
# of e
p
ochs
[
30 s
01440 2880 4320 5760
−0.05
0
0.05
L1 G PS + B 1 BDS (25°)
−5 05
−6
−4
−2
0
2
4
6
East error (meters)
North error (meters)
Float solution
Wrongly fixed solution
Correctly fixed solution
00.02
−0.02
0
0.02
L1 G PS + B 1 BDS (25°)
1440 2880 4320 5760
−5
0
5
10
# of e
p
ochs
[
30 s
01440 2880 4320 5760
−0.05
0
0.05
1440 2880 4320 5760
0
0.5
No. of epochs (30 seconds)
ADOP (cyc)
0
10
20
30
40
STD U [m]
−5 05
−6
−4
−2
0
2
4
6
East error (meters)
North error (meters)
Float solution
Wrongly fixed solution
Correctly fixed solution
00.02
−0.02
0
0.02
L1+L 2 GPS (25°)
1440 2880 4320 5760
−5
0
5
10
# of e
p
ochs
[
30 s
01440 2880 4320 5760
−0.05
0
0.05
1440 2880 4320 5760
0
0.5
No. of epochs (30 seconds)
ADOP (cyc)
0
10
20
30
40
STD U [m]
1440 2880 4320 5760
0
0.5
No. of epochs (30 seconds)
ADOP (cyc)
0
10
20
30
40
STD U (m)
Up error (meters)
Up error (meters)
0 0
Up error (meters)
0
Up error (meters)
Up error (meters)
Up error (meters)
0 0 0
−0.02 −0.02 −0.02
−0.02−0.02−0.02
FIGURE 4 Horizontal (N, E) scatterplots and vertical (U) time series for L1+B1 low-cost receiver with patch antenna (first column) with 99.5% (89.8%) ILS
SR, L1+B1 low-cost receiver with survey-grade antenna (second column) with 100% (97.8%) ILS SR, and survey-grade L1+L2 GPS (third column) with 100%
(94.1%) ILS SR, using 10° (top two rows) and 25° (bottom two rows) cut-off angles respectively (Jan. 4–6, 2016, for low-cost receiver with patch antenna
and Jan. 7–8, 2016, for the low-cost and survey-grade receivers with survey-grade antennas). The SRs are conditioned on PDOP ) 10 and computed based
on all epochs. Below the vertical time series, the ADOP is depicted in blue color, the 0.12-cycles level as red, and ambiguity-float vertical formal STDs are
shown in gray.

days of data. These STDs were computed by comparing the
estimated positions to precise benchmark coordinates. In
addition to the positioning performance, we depict in Table
2 the corresponding empirical ILS SR for full ambiguity-
resolution, which is given by the ratio of the number of
correctly fixed epochs to the total number of epochs.
Table 2 shows that the L1+B1 low-cost receiver plus
patch antenna combination has (as expected) smaller SRs in
comparison to those when the survey-grade antenna is used.
This latter combination has comparable SRs to the (PDOP-
conditioned) SRs of the survey-grade L1+L2 GPS receiver
for cut-off angles up to 25°.
In support of better understanding Table 2, FIGURE 4 shows
typical positioning results for the different receiver and
antenna combinations with elevation cut-off angles of 10°
(top two rows) and 25° (bottom two rows). The first and
third rows show the local horizontal (N, E) positioning
scatterplots and the second and fourth rows the vertical
(U) time series over two days of data. The float solutions
are depicted in gray, and incorrectly and correctly fixed
solutions in red and green, respectively. The zoom-in
is given to better show the spread of the correctly fixed
solutions with millimeter-centimeter level precisions. The
formal ambiguity-float STDs are also shown under the up
time series to reflect consistency between the empirical and
formal positioning results.
We also depict in Figure 4 the ambiguity dilution of
precision (ADOP) as an easy-to-compute scalar diagnostic
to measure the intrinsic model strength for successful
ambiguity resolution. The ADOP is defined as
(cycles) (4)
with n being the dimension of the ambiguity vector,
the ambiguity variance matrix, and |.| denoting the
determinant. ADOP gives a good approximation to the
average precision of the ambiguities, and it also provides for
a good approximation to the ILS SR. The rule-of-thumb is
that an ADOP smaller than about 0.12 cycles corresponds
to an ambiguity SR larger than 99.9%.
Figure 4 shows that more solutions are incorrectly
fixed (red dots) when the ADOPs (blue lines) are larger
than the 0.12 cycle level (red dashed lines). The figure also
reveals that the L1+B1 low-cost receiver plus patch antenna
combination achieves an ILS SR (99.5%) similar to that of
the survey-grade L1+L2 GPS receiver (SR of 100%) for
the cut-off angle of 10°. This ILS SR corresponds to the
availability of correctly fixed solutions (green dots) with
millimeter-centimeter level positioning precision over the
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WWW.GPSWORLD.COM GPS WORLD 55
Positioning model Empirical STDs (mm), ILS SR (%)
Cut-off (°): 20 25 30 35
N E U SR N E U SR N E U SR N E U SR
L1+L2 survey-grade 3 2 7 99.9 90 23 114 99.4 73 27 195 93.0 75 37 229 80.2
PDOP ) 10 3 2 6 99.5 3 38 94.1 4 39 81.8 5 311 64.1
L1+B1 low-cost receiver and
survey-grade antenna 2 1 4 99.8 2 25 97.8 2 26 77. 3 2 27 50.3
PDOP ) 10 2 2 6 76.7 2 26 48.8
L1+B1 low-cost receiver and
patch antenna 2 2 6 96.9 3 27 89.8 3 28 57.3 3 412 25.0
PDOP ) 10 3 2 8 57. 0 3 310 24.9
TABLE 2 Single-epoch empirical STDs (N, E, U) of correctly fixed positions for the three positioning models together with their ILS SR for four elevation cut-off angles
and 48 hours of data (Jan. 4–6 and Jan. 6–8, 2016). The empirical STDs and ILS SRs are also shown when conditioned on PDOP ) 10.

two days. The L1+L2 GPS receiver has, moreover, large
ambiguity-fixed positioning excursions at the same time
as the formal STDs are large for the cut-off angle of 25° due
the poor GPS-only receiver-satellite geometry for this high
cut-off angle. This is also reflected by the corresponding
relatively large ambiguity-fixed STDs depicted in Table
2 that are improved from decimeter- to millimeter-level
when the PDOP ≤ 10 condition is applied. Figure 4 also
shows that the L1+B1 low-cost receiver with the survey-
grade antenna has a larger SR of 97.8% when compared
to the PDOP-conditioned SR for L1+L2 GPS of 94.1% for
the cut-off angle of 25° (see also Table 2), owing to the use
of BDS that significantly improves the receiver-satellite
ge o metr y.
Finally, we also tested the low-cost receiver-solution (with
survey-grade antennas) for a baseline length of 7 kilometers,
where (small) residual slant ionospheric delays are present.
It was shown that this combination still has the potential to
achieve ambiguity resolution and positioning performance
competitive with the survey-grade receiver-solution.
CONCLUSIONS
In this article, we evaluated a low-cost L1+B1 GPS+BDS RTK
setup and compared its ambiguity resolution and positioning
performance to a survey-grade L1+L2 GPS solution in
Dunedin, New Zealand. The LS-VCE procedure was used
to determine the variances of the low-cost receivers. The
estimated variances are needed so as to formulate a realistic
stochastic model, otherwise the ambiguity resolution
and hence the achievable positioning precisions would
deteriorate.
Since we analyzed a short baseline, the LS-VCE variances
were shown to likely be affected by multipath. To mitigate
multipath we connected the low-cost receivers to survey-
grade antennas with better signal reception and multipath
suppression abilities. It was shown that the survey-grade
antennas can significantly improve the performance for the
low-cost receivers so that the code/phase noise estimates
more resemble that of survey-grade receivers. The LS-VCE
STDs were furthermore shown to be realistically estimated
for an independent time period.
We also demonstrated that the low-cost receivers can
give competitive instantaneous ambiguity resolution
and positioning performance to that of the survey-grade
receivers. This is particularly true when the low-cost
receivers are connected to survey-grade antennas.
ACKNOWLEDGMENTS
Ryan Cambridge at the School of Surveying, University of
Otago, collected the low-cost receiver data. Author Peter J.G.
Teunissen was supported by an Australian Research Council
Federation Fellowship. All of this support is gratefully
acknowledged.
MANUFACTURERS
The low-cost receivers used in the research were u-blox
(www.u-blox.com) EVK-M8T receivers. The survey-grade
receivers were Trimble (www.trimble.com) NetRS receivers.
The patch antennas were u-blox ANN-MS antennas, while
the survey-grade antennas were Trimble Zephyr 2 GNSS
antennas.
ROBERT ODOLINSKI conducted his Ph.D. studies at Curtin University, Perth,
Australia, from 2011 to 2014. His research focus is next-generation multi-
GNSS integer ambiguity resolution enabled precise positioning. In 2015,
Odolinski started his position as a lecturer/research fellow in geodesy/
GNSS at the School of Surveying, University of Otago, New Zealand.
PETER J.G. TEUNISSEN is a professor of geodesy and navigation and the
head of the Curtin GNSS Research Centre, Curtin University. He is also with
the Department of Geoscience and Remote Sensing, Delft University of
Technology, Delft, The Netherlands. His research interests include multiple
GNSS and the modeling of next-generation GNSS for high-precision
positioning, navigation and timing applications.
Further Reading
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