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* Corresponding author: brian@fitb.itb.ac.id
Long-range Single Baseline RTK GNSS Positioning for Land
Cadastral Survey Mapping
Brian Bramanto1,*, Irwan Gumilar1, Muhammad Taufik1 and I Made D. A. Hermawan2
1Geodesy Research Group, Institut Teknologi Bandung, Indonesia
2General Technology Indonesia
Abstract. In Indonesia, Global Navigation Satellite System (GNSS) has become one of the important tool
in survey mapping, especially for cadastral purposes like land registration by using Real Time Kinematic
(RTK) GNSS positioning method. The conventional RTK GNSS positioning method ensure high accuracy
GNSS position solution (within several centimeters) for baseline less than 20 kilometers. The problems of
resolving high accuracy position for a greater distance (more than 50 kilometers) becomes greater challenge.
In longer baseline, atmospheric delays is a critical factor that influenced the positioning accuracy. In order to
reduce the error, a modified LAMBDA ambiguity resolution, atmospheric correction and modified kalman
filter were used in this research. Thus, this research aims to investigate the accuracy of estimated position and
area in respect with short baseline RTK and differential GNSS position solution by using NAVCOM SF-
3040. The results indicate that the long-range single baseline RTK accuracy vary from several centimeters to
decimeters due to unresolved biases.
1 Introduction
As a breakthrough technology in position determination,
Global Navigation Satellite System (GNSS) has become
one of the important tool in survey mapping. GNSS term
includes e.g. the GPS (Global Positioning System),
GLONASS (Globalnaya Navigazionnaya Sputnikovaya
Sistema), Galileo, BeiDou and other satellite-based
positioning system. In accordance with its rapid growth,
there is such a huge increase interest in GNSS position
determination, but not limited to, e.g. Automatic Vehicle
Location (AVL) [1, 2], tracking system [3, 4],
geodynamic monitoring [5-7], atmospheric monitoring [8,
9], hazard mitigation [10-12] and so on.
In Indonesia, GNSS is mostly used in surveying and
mapping purposes, especially for cadastral purposes like
land registration by using Real Time Kinematic (RTK)
GNSS positioning method [13-15]. RTK GNSS ensure
the high accuracy in point determination, however, in
conventional RTK GNSS the high accuracy can only be
obtained for baseline less than 20 kilometers [16]. For
medium to long baseline RTK GNSS, the atmospheric
bias is considered as the dominant factor which lead into
unresolved ambiguity resolution. Consider GNSS signal
travelling from a satellite to two receivers that are in a
distant, the signal would be subjected to a different
atmospheric effects. Several approaches have been
proposed to mitigate the atmospheric bias [17-18].
Network RTK is also considered to mitigate the
atmospheric bias [19].
It has been found that atmospheric bias affect more
error in vertical component rather than in horizontal
component which up to several decimeters in RTK GNSS
positioning [20, 21]. Fig. 1 shows the comparison of code
absolute method positioning error using corrected
pseudorange and uncorrected pseudorange. It could be
seen that the deviation could vary up to 20 meters in
vertical component. The corrected terms indicate the used
of troposphere and ionosphere model.
Fig. 1. Error position in absolute positioning method. Red dots
indicate when no atmospheric correction was applied on the
data, while blue dots indicate when atmospheric correction was
applied on the data
Thus, several researches has stated that orbital error
[22] and satellite clock error [23] also indicate as the
problems in GNSS-based positioning system. The orbital
trajectory of GNSS satellites disturbed by surrounding
environments e.g. the Earth’s gravity, the attraction of the
© The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0
(http://creativecommons.org/licenses/by/4.0/).
E3S Web of Conferences 94, 01022 (2019) https://doi.org/10.1051/e3sconf/20199401022
ISGNSS 2018
sun and the moon and as well as solar radiation, while the
satellite clocks are subject to relativistic effects. The
GNSS satellite clock tends to run faster than the clocks in
the receivers.
Fig. 2. GNSS orbital satellite error
In a relatively short baseline, the double difference
(DD) observations could reduce and eliminate both of
orbital and clock satellite error, however, for a far baseline
orbital and clock satellite error still contained on the data
observation. The connection between baseline length,
observing time and rms accuracy were summarize in Fig.
3.
Fig. 3. Accuracy of GNSS static in cm and its correlation with
the baseline length and observing time when using broadcast
orbit and precise orbit [22]
In this research, a relatively new algorithm [23] was
used to enhance the RTK GNSS accuracy in a long
baseline for land cadastral survey mapping. This method
used a modified LAMBDA method which can be
separated into several aspects e.g. modified functional
model to estimate the atmospheric bias, the usage of
precise orbit correction from WADGPS, a modified
Kalman filter and a partial search and ambiguity fixing
strategies.
2 Data and Basic Concept
2.1 Data
Base station was established at the rooftop building.
Bandung, Indonesia, while the land cadastral survey
mapping were simulated on three land parcels in
Pamengpeuk, Indonesia which located for about 85
kilometers away from the base station and has significant
height differences for about 800 meters. Eight
benchmarks were also used to assess the performance of
the algorithm.
Fig. 3. The location of base station (red triangle) and simulated
parcel area (yellow dot)
Fig. 4. The location of land parcels (green dot) and benchmark
(yellow triangle)
Fig. 5. Shows the research methodology. In general,
to assess the performance of the algorithm, the long-range
RTK coordinate results were then compared with a priori
coordinates. The term a priori coordinate refers to
reference coordinate based on static differential
observation method or shorter baseline RTK GNSS
method.
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Long-baseline GNSS
RTK
Point
Coordinates
Differential Static
Observation
Short-baseline GNSS
RTK
Point
Coordinates
Coordinate
Comparison
Analysis
Fig. 5. Research methodology used in this research
2.2 Basic Concept
This section describe the general concept in RTK GNSS
method and the Kalman filter design to enhance the
accuracy of RTK GNSS in long-range baseline.
2.2.1 Observation Models in RTK
The observation model for code and carrier phase
measurement are described as follows:
(1)
(2)
where:
is the measured pseudorange on Li frequency
(i = 1, 2)
is the measured carrier phase on Li frequency
is the true geometric range
is the satellite orbital error
is the tropospheric error
is the ionospheric error
is the speed of light
is the satellite clock error
is the receiver clock error
is the multipath effect on measured code
is the multipath effect on measured phase
is the noise
DD then performed to eliminate the orbital error,
clock error and atmospheric error in short baseline. The
DD () observation model for code and carrier phase
measurement can be described as follows:
(3)
(4)
Linearization of the DD observation then can be
represented as follows:
where V is the residual matrix, A is the design matrix. L is
the observation data and X is the estimated parameters
containing three baseline components and ambiguities. In
a longer baseline the estimated parameters including
residual ionospheric bias and residual tropospheric bias.
2.2.2 General Kalman Filter System Design
Kalman filter predicts the a priori parameters using the
recent estimate of the observation data. The prediction is
based on some assumed model for how the parameters
changes in time [24, 25]. The dynamic model on Kalman
filter can be represented as follows:
(5)
which then continued along with measurement model,
(6)
where:
is the transition matrix (k = epoch)
is the noise from the dynamic model
is the noise from the observation data
Kalman filter also applied recursive least square which
then can be defined into two main parts as follows [26]:
Observation model
(7)
(8)
(9)
Dynamic model
(10)
(11)
where:
is the gain matrix
is the covariance matrix observation model
I is the identity matrix
- is the prediction from previous epoch
is the covariance matrix for dynamic model
is the weighting matrix
The estimated parameter is summarized in Table 1.
Table 1. Parameter estimated in Kalman filter. Superscript (*)
indicates the optional parameter while N is the number of
satellites used
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Parameter in Kalman
Filter
Dimension
Position XYZ
3
Velocity XYZ*
3
Acceleration XYZ*
3
Residual troposphere*
1
Residual DD ionosphere*
N-1
L1 DD ambiguity*
N-1
L2 DD ambiguity*
N-1
2.2.3 Precise Satellite Ephemeris
As stated on the introduction, precise satellite ephemeris
is needed in GNSS-based point positioning for a longer
baseline. In static differential method, the precise satellite
ephemeris can be easily obtained two weeks after the
observation is done. However, in conventional RTK such
a precise ephemeris cannot be obtained. Several
researches indicate that the satellite’s position error might
vary up to 5 meters [22, 27]. The satellite’s position error
is generally the biggest error source after atmospheric bias
is estimated in Kalman filter for long-range RTK.
Thus several GNSS industries have developed their
own system to accommodate the use of precise satellite
ephemeris. John Deere, as one of the GNSS industry has
developed the StarFireTM system which transmits the
needed data correction in near real-time using satellites
communication.
2.2.4 Ambiguity Resolution
The ambiguities are considered as constant. However, due
to remaining tropospheric and ionospheric biases, the
ambiguities can be modeled as a random walk with very
small dynamic noise, such as 0.001 cycle. Thus, the
ambiguities are modeled as constants once the
ambiguities are fixed. The use of these small dynamic
noise is useful in resolving the ambiguities in several
condition, such as bad site condition, excessive multipath,
or the movement of receiver from a severe shading
surrounding to the open sky surrounding.
In a longer baseline, the ambiguities are resolved
improperly due to significant bias. [7] implemented the
modified partial search technique to fixing the
ambiguities. The ambiguity for the L1/L2 signal and its
variance were first converted into L1/Wide Lane (WL) as
described in following vector equation:
(12)
(13)
The used of WL is important due to its wavelength
characteristic. With 0.86 cm wavelength, WL’s
ambiguities are easy to resolve. If the ambiguities are
resolved, the original L1 and L2 ambiguities and the
variance-covariance in the Kalman filter can be recovered
as follows:
(12)
(13)
3 Result and Discussion
Over 1840 epoch were collected within 23 point
observations. Only resolved ambiguities data showed and
considered in further analysis. Coordinates derived from
differential static method were considered as reference
coordinates in bench mark point, while coordinates
derived from short baseline GNSS RTK method were
used as reference coordinates in land parcel point. Short
baseline GNSS RTK (under 3 km) was considered
because in shorter baseline and in the open-sky condition
(Fig. 6) the biases were assumed reduced or eliminated
[28].
Fig. 6. Condition over the simulated area
3.1 Accuracy and Precision
2.2.1 Horizontal Accuracy
Fig 7. shows the overall accuracy for benchmark point,
while Fig 8. shows the overall accuracy for land parcel
point. The accuracy of long-baseline GNSS RTK in
benchmark points were within 3 cm and only 1 point was
slightly worse than the other, however still within RTK
accuracy.
The accuracy of long-baseline GNSS RTK in land
parcel points were within 12 cm. It could be seen that
there was a systematic compared with those for
benchmark point. As mentioned before, coordinate
estimated from short baseline RTK GNSS used to assess
the accuracy of long baseline RTK GNSS in land parcel
points. To evaluate the consistency of the used reference
coordinate on all off the observation method, benchmark
points were also observed using short baseline RTK
GNSS.
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Fig. 7. Overall accuracy of long baseline GNSS RTK for
benchmark points
Fig. 8. Overall accuracy of long baseline GNSS RTK for land
parcel points
Fig. 9. shows the overall accuracy for both short and
long baseline GNSS RTK. It could be seen that there was
a shift tendencies to South-East. It indicates that the
system coordinate might be different.
Fig. 9. Overall accuracy of short baseline (Red Circle) and long
baseline (Blue Circle) GNSS RTK for benchmark points
2.2.2 Vertical Accuracy
Fig 10. shows the overall vertical accuracy for benchmark
point, while Fig 11. shows the overall vertical accuracy
for land parcel point. The accuracy of long-baseline
GNSS RTK in benchmark points were within 15 cm and
the accuracy of long-baseline GNSS RTK in land parcel
points were vary from -20 cm to 15 cm. There is one point
that indicates the unresolved bias. A linear trend of the up
component is found on that point, there is also deviation
in horizontal component as shown on Fig. 7. Further
analysis is needed to explain this phenomenon.
Fig. 10. Overall vertical accuracy of long baseline GNSS RTK
for benchmark points
Fig. 11. Overall vertical accuracy of long baseline GNSS RTK
for land parcel points
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Fig. 12. Selected timeseries of Blue dot, red dot and cyan dot
refer to easting, northing and up component respectively.
Yellow lines indicates the linear trend of up component.
2.2.3 Overall Precision
Table 1. shows the overall precision for long baseline
GNSS RTK. Precision indicated the repeatability of the
estimated coordinate. Over 90% of estimated coordinate
met the 95% of confidence interval as shown on Fig.13.
This indicate that this algorithm is reliable to used.
Table 1. Overall precision for long baseline GNSS RTK
Easting (m)
Northing (m)
Up (m)
Note
0.0055
0.0050
0.0345
BM
0.0020
0.0044
0.0093
BM
0.0028
0.0034
0.0102
BM
0.0045
0.0031
0.0117
BM
0.0044
0.0048
0.0143
BM
0.0029
0.0018
0.0106
BM
0.0036
0.0040
0.0117
BM
0.0021
0.0040
0.0142
BM
0.0026
0.0042
0.0098
Land Parcel
0.0057
0.0083
0.0130
Land Parcel
0.0028
0.0064
0.0138
Land Parcel
0.0031
0.0064
0.0129
Land Parcel
0.0042
0.0066
0.0098
Land Parcel
0.0042
0.0056
0.0114
Land Parcel
0.0039
0.0044
0.0110
Land Parcel
0.0047
0.0046
0.0088
Land Parcel
0.0062
0.0036
0.0195
Land Parcel
0.0049
0.0030
0.0135
Land Parcel
0.0047
0.0050
0.0078
Land Parcel
0.0035
0.0058
0.0203
Land Parcel
0.0054
0.0057
0.0240
Land Parcel
0.0053
0.0050
0.0294
Land Parcel
0.0037
0.0057
0.0408
Land Parcel
Fig. 13. Selected timeseries of estimated coordinate for long
baseline GNSS RTK. Blue dot, red dot and cyan dot refer to
easting, northing and up component respectively. Red lines
indicates the 95% of confident interval.
2.2.1 Area Estimation
Government policy about land and building tax in
Indonesia indicates that the errors tolerances is about
10%. Table.2. shows the differences in calculated area
with the reference area, there is no significant differences
between reference and calculated area. The deviation in
under 0.05% for each area. This result indicates that the
long baseline GNSS RTK algorithm can be used for land
parcel mapping.
Table 2. Area differences
ID
Reference
Area
observed
Area
Area
Differences
%
1
2490.9708
2490.1062
0.8646
0.03%
2
63787.5385
63779.2118
8.3267
0.01%
3
2111.4568
2111.1478
0.309
0.01%
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Fig. 13. Formed area over simulated area. Black lines indicate the reference area while red lines indicate the observed area.
4 Conclusion
The algorithm gives significant improved in long-range
single baseline GNSS RTK for up to 90 km. The accuracy
vary from several centimeters to decimeters due to
unresolved biases. For land cadastral purposes, the
algorithm can be used as one of the method, the observed
area shows no significant difference compared with the
reference area.
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