Summary of doctor thesis le van hung

MINISTRY OF EDUCATION AND TRAINING
HANOI UNIVERSITY OF MINING AND GEOLOGY

The dissertation has been completed at the Department of
Engineering surveying, of Surveying Faculty, Hanoi University of
Mining and Geology.

Scientific Supervisors:
1. Assoc. Prof. Dr. Dang Nam Chinh

LE VAN HUNG

Hanoi university of Mining and Geology
2. Assoc. Prof. Dr. Nguyen Quang Phuc
Hanoi university of Mining and Geology

STUDY OF ADJUSTING COMBINATION OF GPS AND
TERRESTRIAL OBSERVATIONS IN THE LOCAL
TOPOCENTRIC COORDINATE SYSTEM APPLIED FOR
ENGINEERING SURVEY NETWORK

Examiner 1: Assoc. Prof. Dr. Nguyen Quang Tac
Hanoi Architectural University
Examiner 2: Dr. Dương Chi Cong
VietNam Institute of Geodesy and cartography

Study field: Geodesy and mapping
Code:

62520503

SUMMARY OF DOCTORAL DISSERTATION

Examiner 3: Dr. Nguyen Van Van
Military map service of general staff of Viet Nam army

The dissertation will be defended at the University
examination Council at the Hanoi University of Mining and
Geology , at….. h, ……………… 2014

This dissertation can be referenced at the National library
Ha Noi – 2014

or at the library of the Hanoi University of Mining and Geology.


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INTRODUCTION
The importance of dissertation
For engineering survey (TðCT), we are likely to encounter
cases where control networks are built in region not convenient for
GPS observation due to limited satellite transmission signal; therefore,
replying on only GPS technology for establishment of control network
is not sufficient. In such cases, it is essential for combination of GPS
and terrestrial observations in order to enhance feasibility and
effectiveness in establishment of engineering control network. On the
basis of the abovementioned practical requirements, it is prerequisite
for studying means of adjusting combination of GPS and terrestrial

observations and selecting the coordinate system which can be used in
certain limitation as the basic coordinate system for engineering
survey. Using the local topocentric coordinate system whose datum
point is established at the center of control network area can mitigate
both abovementioned issues.
2. Objective, subjective and scope of the dissertation
- Studying methods for establishment of the local topocentric coordinate
system whose datum point is located at the center of the Works;
completing procedures for transformation and conversion between the
local topocentric coordinate system and other popular systems;
- Determining the appropriate regions for local coordinate system to be
used for civil and industrial engineering surveys;
- Completing the theoretical basis and proposal of procedures for
closely adjusting combination of GPS and terrestrial observations;
- Establishing the software for adjusting combination of GPS
observation and angular-side measurement, this has highly relevent
application in the context of Viet Nam;
- Evaluating the accuracy of software performance.
3. Content of dissertation
- General study of GPS technology and total station (TððT) in order
to establish engineering control network;
- Study of the local topocentric coordinate system, conversion from the
local topocentric coordinate system to geodetic coordinate system and
to rectangular coordinate system in UTM projection;

- Determination of usage limit of the local topocentric coordinate
system in engineering survey;
- Calculation of weight of relative measurement in adjustment of GPS
network;
- Study of adjusting GPS network in geocentric coordinates system

(X,Y,Z) and the local topocentric coordinate system;
- Study of adjusting combination of GPS observation and angular- side
measurement in the local topocentric coordinate system;
- Study of establishing computer programs to adjust combination of
GPS observation and angular- side measurement.
4. Scientific and practical meaning of dissertation
- Findings of the study provide the basis for adjusting combination of
GPS and terrestrial observations in the local topocentric coordinate
system applying for engineering high precision network.
- Proposal to use the local topocentric coordinate system as the basic
coordinate system and replacement of rectangular coordinate system in
UTM projection in civil and industrial engineering survey;
- Algorithms and procedures are converted into combined adjustment
softwares that are applicable to practical engineering survey in Viet Nam.
- Findings of the dissertation can be applicable in the field of
education, teaching, scientific research and manufacturing.
5. Rational arguments:
- First argument: It is significant for calculation of weight in GPS
network and combination of GPS network and terrestrial observation.
Weight of GPS network should be standardized in accordance with
two-step adjustment procedure.
- Second argument: It is required to calculate angle distort for
adjusting the measured angle before adjustment combination of GPS
and terrestrial observations. Factors (i.e dimensions) of the network
after adjustment ensure the best suitability with field factors. These
factors are necessary for the design works, construction of civil and
industrial works that requires high accuracy.
- Third argument: The local topocentric coordinate system can be used
as basic coordinate system, which is the replacement of rectangular
coordinate system in UTM projection in order to serve for surveying

1.


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stage (large scale ratio), design, and construction works. Scope
(radius) of using the local topocentric coordinate system is estimated
according to the requirements of angle distor and length distort.
6. New contributions
- Completing the formulation system in order to determine appropriate
region for the local topocentric coordinate system to be used in
engineering surveying;
- Introducing the formula for calculation of the horizontal angle distort
when adjusting combination of GPS and terrestrial observations in the
local topocentric coordinate system.
- Establishing Data Processing Software called ADGT (ADjustment
GPS Topography) including transformation module, conversion
module, module for analyzing side processing data, module for
adjusting combination of GPS and terrestrial observations in the local
topocentric coordinate system applying for engineering surveying.
7. Quantity and structure of dissertation
Content of dissertation is presented on 118 pages, 39 drawings
and diagrams, 21 tables.

in order to avoid the impact of weather conditions and meteorology on
the measurement result.
1.1.2. GPS observation method

Based on specific parameters a, b of GPS satellite and total
station, draw the diagram (Figure 1.1) to compare visually the
accuracy of side length measurement by GPS ( mD-GPS) and
accuracy of side measurement by total station (mD-TD). According to
the diagram, at the distance of D <2,3 km, side length error by GPS is
larger than that by total station.

CHAPTER 1
OVERVIEW OF APPLICATION OF GPS TECHNOLOGY IN
ESTABLISHMENT OF ENGINEERING CONTROL NETWORK
AND ADJUSTMENT OF GPS NETWORK
1.1. METHODS FOR ESTABLISHMENT OF GEODETIC NETWORK

Two common methods for establishment of horizontal control
network as well as engineering surveying network are use of terrestrial
observation (traditional) and satellite positioning (GNSS). Each
method has its own advantages and disadvantages and requires
specific conditions for measurement and establishment of the network.
1.1.1. Terrestrial observation method
In the past, in order to establish engineering control network, we
mainly use total stations. However, this method is not fully efficient in
complicated topography and poor sky visibility. In addition, one
disadvantage is that performance of terrestrial observation only can be
delivered in the appropriate weather conditions and appropriate times

Figure 1.1 - Comparison of side length error by GPS and by total station
1.1.3. Combination of GPS and terrestrial observations
The control network used in engineering surveying requires high
accuracy, specific selection of appropriate location and construction
time of the network. If only using one method for establishment of

network (either terrestrial observation or GPS observation), difficulties
can arise due to the certain disadvantages of each method. Therefore,
combination of both methods for establishment of the control network
will gain advantages, overcome drawbacks of each method, improve
the efficiency and shorten construction duration of the network.
1.2. OVERVIEW OF APPLICATION OF GPS TECHNOLOGY IN
ESTABLISHMENT OF ENGINEERING CONTROL NETWORK

1.2.1. Application of GPS technology in establishment of
engineering control network in foreign countries
In foreign countries, geodesists early made applications of GPS
technology for engineering survey and results indicate that accuracy
(plan, elevation) in short distance can be from 2mm to 5mm.
1.2.2. Application of GPS technology in establishment of
engineering control network in Viet Nam.


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In engineering survey, GPS technology has been researched to
be applicable for each stage of design, construction and operation.
GPS technology was used for establishment of geodetic networks for
the following works: Dung Quat Industrial Zone, National
Convention Center, My Dinh National Stadium, But Son Cement
Plant, Thai Nguyen Cement Plant, Bai Chay Bridge, Thanh Tri Bridge,
Yen Phong Industrial Zone…

- Software MOVE3 v.4.0.2 made in Netherlands

- Software COLUMBUS v.3.8 made in United States. etc.
General comments:
Findings of above-mentioned foreign and domestic studies
indicate that application of GPS technology for establishment of
geodetic control network in general and engineering control networks
in particularly has become popular. For engineering survey (TðCT),
we are likely to encounter cases where the Works are implemented in
region not convenient for GPS observation due to limited satellite
transmission signal. Moreover, it is difficult to apply only GPS
technology for establishment of network when the Works are built in
adjacent to each other or in the area with barriers and signal jamming
factors. In such cases, GPS and terrestrial observations are combined
in order to improve the feasibility and effectiveness for establishment
of engineering control network.
For GPS network, (3D) three-dimensional coordinate network,
the network is adjusted in the geocentric coordinate system (X,Y,Z) or
geodetic coordinate system (B,L,H) and then transformed to
rectangular coordinate system in UTM projection. The calculation
procedure above is entirely reasonable when being applied for the
national coordinate system, all over the country. For engineering
surveying network with small scope of control, using
the local topocentric coordinate system to process GPS network are
mentioned in some studies, including adjustment combination of GPS
observation and distance measurement by total station. In fact, there
have not been any in-depth researches into above issue.
Regarding to the local topocentric coordinate system, it is
required to clarify some issues in order to apply the system
appropriately and determine the largest area for using the
the local topocentric coordinate system as basic coordinate system for
engineering surveying during the process of surveying, design,

construction and resolutions of relationship between the
local topocentric coordinate system and national coordinate system. A
number of studies relating to adjustment of combination of GPS and

1.3. OVERVIEW OF PROCESSING DATA ON COMBINATION OF
GPS AND TERRESTRIAL OBSERVATIONS IN ENGINEERING
SURVEY

1.3.1. Processing data on combination of GPS and terrestrial
observations for enginneering survey in foreign countries.
The Observations in the GPS network is correlative
measurement [54] and posterior covariance matrix after baselines
solutions will be apriori covariance matrix of the adjustment GPS
network [64]. This is the difference between calculation of adjustment
of modern three-dimensional coordination network and traditional
two-dimensional rectangular coordination network. Adjusting
combination of GPS and traditional terrestrial observation in
the local topocentric coordinate system was studied by Slawomir
Cellmer and Zofia Rzepecka since 2008 [65]; however, mentioned
terrestrial observation was only the length of sides measured by total
station, but not horizontal angle measurment.
1.3.2. Processing data on combination of GPS and terrestrial
observations in engineering survey in Viet Nam.
A number of studies related to this subject were conducted;
however, mostly in geodetic coordinate system and resolutions for
large network.
1.4. ADJUSTMENT SOFTWARE FOR GEODETIC NETWORK IN
FOREIGN COUNTRIES

Besides a number of data processing softwares together with

GPS sattelites from well-known manufacturers such as Trimble, Leica,
there are some other softwares introduced in the websites of
Geoinformatics Software Development Companies:
- Software STAR*NET v.7.1 (2012) made in Canada


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terrestrial observations were conducted; however, mostly with
geodetic coordinate system and resolutions for large network. Now,
usage of the rectangular coordinate system in UTM projection is not
conformed to the major Works that set high requirement for the level
of distort of the reference grid. Therefore, research and selection of a
coordinate system that is conformed to the Works and completion of
procedures for processing measurement data in that coordinate system
is a practical requirement of engineering surveying in our country.
Regarding to softwares, besides some data processing softwares
for GPS observation such as GPSurvey 2.35, TTC, TBC, etc..., together
with adjustment module of GPS network, there will be adjustment
softwares for engineering surveying such as STAR*NET, MOVE3 and
COLUMBUS which are dedicated adjustment softwares for all geodetic
networks (1D, 2D, 3D). Similarities of these softwares are that results
are recorded in the form set by programmer and explained in English.
Until now most manufacturers in our country has not used these
softwares, but applied the adjustment module of data processing
softwares of Global Navigation Satellite System (GNSS). Therefore, it
is crucial to establish computation programs for calculating adjustment
of combination of GPS and terrestrial observations in engineering

surveying for practical application in Viet Nam.

Correction to the measured edge length when calculated
according to the UTM projection

CHAPTER 2
THE LOCAL TOPOCENTRIC COORDINATE SYSTEM AND
APPLICATION IN THE ENGINEERING SURVEY
2.1. REQUIREMENTS OF REFERENCE SYSTEM FOR GEODETIC
HORIZONTAL CONTROL NETWORK

When carrying out the establishment of engineering control
network, it is required that distance between points in the network
after adjustment shall be conformed to the actual dimension on the
field. Because of the above requirements, selection of reference scale
(mo), central meridian (Lo) when using UTM projection is significant
to process the engineering control network.
2.1.1. Correction horizontal projection

∆ S UTM = ( m 0 − 1 +

y 2m
).S '
2 .R 2m

(2.1)

With zone 30 (m0=0,9999) and the relative distortion length limit is
1 / T = 1/200000, calculate ymax=92,3 km and ymin=87,8 km. Such areas
with distortion smaller than 1/200000 is only 4,5 km wide.

With zone 60 (m0=0,9996) and the relative distortion length limit is
1 / T = 1/200000, calculate ymax=181,3 km and ymin=179,1 km. Such areas
with distortion smaller than1/200000 is only 2,25 km wide.
2.1.2. Correction for elevation compared with the reference
Ellipsoid
Correction for elevation calculated by the formula:
∆SH = −

Hm
.S
Rm

(2.2)

In order to reduce this distortion, choosing one projection surface
elevation of approximately average height measured region.
2.2. LOCAL TOPOCENTRIC COORDINATE SYSTEM
2.2.1. Establishment of the local topocentric coordinate system
The local topocentric coordinate system is used in the satelite
geodesy, geodetic astronomy, for determining the instantaneous
position of satelite or space objects (coordinates of satellites or space
objects continously change in the topocentric coordinate system and
z
therefore, it is necessary to take consideration
x
Z
y
into the time factor) in the coordinate
G
system establised at the observing position

H
on the earth surface. The topocentric
Gr
coordinate system is also used for
O B
Y
transforming the equations of 3D
L
coordinate system, which is mentioned in
X
the dissertation. [58],[62].
Figure 2.1- The local topocentric coordinate system
G

G


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2.2.2. Transformation and conversion
When establishing the rectangular coordinate system and using
this system in engineering surveying- map, it is the priority to build and
complete the equation for conversion of coordinates from this
coordinate system to different popular coordinate system. The equation
for conversion of the coordinate (in the forward direction and reverse)
ensures accuracy, about 0,”00001 for geodetic coordinates B, L.
For example: Conversion from geodetic coordinates to the local
topocentric coordinate system presented in this dissertation.

Comment: After conversion from geographical ellipsoidal coordinates
(B, L, H) into the local topocentric coordinate system (x, y, z) and vice
versa, it is indicated that calculated error is only 0,00001”, which
satisfies the calculations requiring high accuracy. Elliposidal height (H)
completely coincides with the initial value.
2.2.3. Measurement of coordinate and elevation to the control
network.
According to the requirements stated in current standards and
codes and national management works, it is necessary for measurement
of national coordinates to the control network in order to:
- Carry out construction works in accordacne with the general planing;
inspect the red line boundary and construction boundary line.
- Uniform the elevation system of the control network with national
elavation system, meeting the requirements of space planning, water
supply and drainage works for the works.
- Manage the Works by national geographic database.

in which the basic plane is close to normal horizontal plane of the
building. This is necessary for small area and high-altitude building in
mountainous areas such as hydroelectric projects, industrial zones, etc.

2.3.DETERMINATION OF THE LIMITATION WHEN USING OF
LOCAL GEODETIC COORDINATE SYSTEM FOR ENGINEERING
SURVEY

2.3.1.Theoretical basis
Basic plane playing an important role in the local topocentric
coordinate system is horizontal plane (horizon plane) which is
perpendicular to the normal direction of Ellipsoid at the reference
point. On that horizontal plane, a rectangular coordinate system x, y

(or N, E) is established and can be used as ground coordinates of the
building. Using this method, we can set a cartesian coordinate system

Figure 2.2- Options for establishment of topocentric coordinate system
For three cases shown in the Figure 2.2, the length L in the
horizon plane will be compared with the length of S geodetic line on
the Ellipsoid which replaced by the length of large semi- circle with
the radius Rm+HG (Figure 2.2.b). In the third case (Figure 2.2.c), the
position of point on relief plan is projected toward normal direction at
G on the horizontal plane without using practical ellipsoid.
2.3.2.Determination of radius of area to be used for the local
topocentric coordinate system
1.Calculation of scope of measurED area acoording to length
distortion limit
- For the case that the distortion of the length L is based on the
datum: L ≤ 15,6 km;
- For the case that the distortion of the length L is not based on the
datum: L ≤ 20,1km;
- For general case (estimated according to the requirement on
distort): L≤ 2,45.R. 1 /T
2. The equation for calculating
the horizontal angle distort
Adjustment of the horizontal
angle distort due to elevation
differences between points is
the difference:
Figure 2.3 - Adjustment of the horizontal angle distort
∆ β = δ P − δT =

ρ "  ∆z P LP sin Φ P ∆zT LT sin Φ T


−
Rm 
dP
dT






(2.3)


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2.3.3.Surveying horizontal angle distort
It can be realized that in the case, measured angle is far from the
reference point of the topocentric coordinate system with a distance of L=
1km and elevation difference of 55m (200m long side), horizonal angle
distort due to elevation difference of points is 13”. If the length of side is
greater, the horizontal angle distort will be smaller in accordance with the
inverse proportion. In general, this quite big distort should be taken
consideration into when adjusting combination of horizontal angle
measurement and GPS observation in the topocentric coordinate system.
Table 2.1- Deformation values of horizontal angle δβ and correction of
deformation ∆ β

According to the result of table 2.2, it can be seen that, so that
angle distort (or error after adjustment) is no more than 0”,2 equivalent
to 20% of accurate horizontal angle measurement error (taking of 1”),
radius (L) in the topocentric coordinate system can be 13 km if
measured area is plain. For the of difference in height, scope of usage
is smaller, only using in the radius of 9 km and calculating adjustment
of horizontal angle distort according to the equation (2.1).
2.3.5. Comments:
1. The local topocentric coordinate system is established on the principle of
orthogonal projection representing the ground surface onto the horizontal
plane (Local topocentric coordinate system) at the reference point (the
datum). The length of side will not change when changing the elevation of
local topocentric coordinate system according to normal at initial point.
2. In case that elevation of points is considerably different from each
other, it is necessary to take consideration into the angle distort for
adjustment into measured angle before adjustment combination of GPS
and terrestrial observations.
3. Equations for conversion from geodetic coordinate system to
topocentric coordinate system, as well as local topocentric coordinate
system are exactly determined in the aspect of mathematics, which is
convenient for programming on the computer in order for automation of
conversion and transformation between local coordinate system and
national coordinate system.
4. Topocentric coordinate system is also a means of representing the
positions in national coordinate system, similar to rectangular coordinate
system in UTM projection in which central meridian LO is not defined
according the general regulations. [41].
5. Scope (radius) of using the local topocentric coordinate system in
engineering survey is estimated according to requirements on distortion
by the equation: L≤ 2,45.R. 1 /T

Angle symbol
(T – M – P)

No.

1
2
3
4
5
6
7

2
3
4
5
6
2
1

-

1 - 3
1 - 4
1 - 5
1- 6
1 - 2
6 - 1

2 - 6

Angle on
Ellipsoid ( β )

90
60
30
59
120
30
29

00
00
00
59
00
00
59

Angle on plane
( β' )

00.00
00.00
00.00
59.92
00.08
00.00

59.92

90 00 08.89
60 00 06.65
30 00 01.43
59 59 56.08
119 59 46.95
30 00 04.43
30 00 08.63

δβ

(“)

∆ β (“)

8.89
6.65
1.43
-3.84
-13.13
4.43
8.71

8.90
6.66
1.43
-3.85
-13.15
4.43

8.72

Sum of three numbers of angle distort adjustment ∆ β in the
triangle 1-2-6 are checked in the three last rows of table 2.1 and have
the value of 0, which is completely matched with spherical excess that
is appropriately 0 in this case.
2.3.4. Calculation of scope of measured area according to
horizontal angle distort limit.
Table 2.2- Deformation value after using topocentric coordinate system
Option

L (km)

Case A : δ
β

1
2
3
4
5
6
7

1
5
9
10
13
15

20

0”,00
0”,03
0”,09
0”,11
0”,19
0”,25
0”,45

Case B:

δ β( H )

0”,02
0”,08
0”,20
0”,23
0”,35
0”,44
0”,70

2.4. USING THE LOCAL TOPOCENTRIC COORDINATE SYSTEM
AS REPLACEMENT OF UTM PROJECT IN CIVIL AND INDUSTRY
ENGINEERING SURVEYING

2.4.1. Comparison between UTM horizontal network and the local
topocentric coordinate system

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For example: Thanh Hoa Province. According to above calculation,
only a narrow 4.5km-wide strip, which is in symmetric position and 90
km far from the prime meridian, varies in length with less than
1/200000 (Figure 2.5). All zones beyond two above narrow strips bear
the variation in length with over 1/200000 due to UTM projection,
such variation scale is too
great in engineering surveying
and exceed the requirement in
the Standard 309:2004 [3].
Obviously, according to the
regulation, cadastral
map
separated into plot plans is not
suitable
for
large-scale
topographic map in design and
Figure 2.5- Thanh Hoa Map and Position of
construction
of
works.
prime meridian (Lo=105o)
Therefore, a separated prime
meridian is used so as to gurantee that length distort varies slightly.
Using a separated prime meridian by UTM projection, it also means
that a topocentric coordinate system is set up.
For above reasons, technically speaking, using the topocentric
coordinates is as meaningful as using UTM projection with a separated

prime meridian (as appropriate) and the advantage is that while the
width of an area is greater, length distort is still ensured to be
1/1000000 and height distort of measured area (if considering into
mountainous areas) is corrected.
2.4.2. Advantages and disadvantages of using local topocentric
coordinate system
1.Processing GPS and terrestrial observations is convenient in a
appropriate region.
2. Direction of the x-axis of the topocentric coordinate system is
northern direction and coincides with the meridian passing the datum of
the topocentric coordinate system. However, direction of the x-axis in
UTM projection is the direction of the meridian of zone.
3.The local topocentric coordinate system is 3D Coordinates system,
with the third axis z (or U) containing information about the elevation,

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which is more preeminent than a grid azimuth, 2D coordinate system.
4. By measurement of national coordinates to the datum point of
topocentric coordinate, conversion from topocentric coordinate system
to geodetic coordinate system and national coordinate system is
accurately defined by rigorous formulas; moreover, meeting the
requirement of managing positions in national coordinate system.
2.4.3. Remarks of using the local topocentric coordinate system
1. Objects of usage: For civil and industry egineering surveying (in the
area of about 250 km2), the local topocentric whose datum located
adjacent to the center of the Works can be used as the basic coordinate
system for engineering survey serving for design and construction.
2. The local topocentric coordinate system shall be established and used at
the stage of drawing the large-scale topographic map serving for deign

works, construction works until the as-built drawing of completed Works.
Coordinate transformation and conversion from the local coordinate
system to UTM rectangular coordinate systems and vice versa will be
calculated via geographical ellipsoidal coordinates(B,L,H) by close
formulas. In the case of transformation from the topocentric coordinate
system into local coordinate system, a number of common points will be
used for determining the transformation parameters on the basis of some
algorithms like Helmert, Affine transformation vv...
3.In order to ensure angle and length distort, for the flat terrain, the
measured radius can be up to 13km. For the unflat terrain (slope of
0,275), the measured radius can be 9 km (diameter of 18 km) and
before adjustment combination of horizontal angle measurement and
GPS observation in the local topocentric coordinate system, it is
essential to calculate the adjusment of horizontal angle distort due to
elevation difference in the value of measured angle.
4. When using the topocentric coordinate system for layout of the
Works, it should be avoided to use point of sight with high elevation
difference in order to prevent angle distort adjusment in layout angle.
5. In order to calculate the elevation of adjusted points GPS network, it
is necessary to transform the local topocentric coordinate system to
geographical ellipsoidal coordinates (B, L, H) and determine
differential leveling on the basis of Geoid model or using common
points - GPS leveling to interpolate anomalous elevation.


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CHAPTER 3

ADJUSTMENT COMBINATION OF GPS AND TERRESTRIAL
OBSERVATIONS IN THE LOCAL TOPOCENTRIC
COORDINATE SYSTEM
3.1. MEASUREMENT IN GPS NETWORK

3.1.1. GPS Baselines vector and effects of covariance matrix in
adjustment of GPS network
1. When carrying out close adjustment of GPS network (option
1) , in which the weight of baselines vector is the inverse of covariance
matrix Cxyz , mean square error of unit weight µ after adjustment will
be many times greater than 1 and verification Chi-squared test is
failed. This indicates that covariance matrix Cxyz of baselines vector
only shows the correlation relationship (dependent) of elements of
baselines vector, but not accurately shows the value of actual
adjustment and covariance matrix. This remark should be taken
consideration into when weight calculation for adjustment
combination of GPS and terrestrial observations.
2. When using simple weight without the correlation component
(option 2) and considered equal weight (option 3), not only result of
accuracy assessment, but also coordinates, elevation, side length and
azimuthal side after adjustment can be changed.
3. To get close and highly reliable adjustment results, when
adjusting the network, it is required to take full consideration into
covariance matrix Cxyz of measurement. Covariance elements in
covariance matrix Cxyz can be omitted or weight matrix can be used in
the case of approximate adjustment of GPS network.
3.1.2. Checking loop of closure in GPS Network.
Checking measurement value before adjustment by loop of
closure limit is to discover and detect gross error. This is a significant
work to be implemented before adjustment of the network so that

result adjustment will be accurate and reliable.
3.2. ADJUSTMENT OF
COORDINATES SYSTEM

GPS

NETWORK

IN

GEOCENTRIC

Indirect adjustment of GPS network in topocentric coordinate
system will be carried out in the following steps:

Step 1: Process baselines
Step 2: Check loop of closure before adjustment
Step 3: Establish equation of correction
Step 4: Calculate the weight matrix P of the system of equations
Step 5: Establish the standard equation
Step 6: Solve the system of standard equations
Step 7: Calculate correction for measurement
Step 8: Evaluate accuracy after adjustment
3.3. ADJUSTMENT OF COMBINATION OF GPS AND
TERRESTRIAL OBSERVATIONS IN THE LOCAL TOPOCENTRIC
COORDINATE SYSTEM.

3.3.1. GPS network adjustment in the local topocentric coordinate system
1. Calculation of the approximate coordinates of GPS points
2. Equation for measurement correction in the local topocentric

coordinate system
V = AX + L
(3.1)
3. Estabishment and solution of standard equation
Based on correction equation (3.1) and covariance matrix, the
standard equation is established as follow:
ATPA.X + ATPL =0
(3.2)
With P is diagonal block matrix, Pi is the inverse matrix of covariance
matrix
Mxyz(3x3): Pi = M i−1
(3.3)
In which: M = R T C xyz R , R is rotation matrix.
With the equation (3.3), actually take constant c = 1 for
calculating the weight in network adjustment.
Standard equation (3.2) will be solved in the normal method:
(3.4)
X = −(A T PA) −1 A T PL
4. Calculation of measurement after adjustment and assessment of
accuracy
Assessing the accuracy of the network after adjustment includes:
- Mean square error of unit weight µ ; error of position.
- Mean square error of weight function side and weight function
azimuthal side


17

18

3.3.2.Adjustment combination of GPS and terrestrial observations
in the local topocentric coordinate system.
Terrestrial observation values are adjusted in combination with
GPS observation includes: Value of horizontal angle measurement,
value of side length measurement.
3.3.2.1. Horizontal angle measurement
Equation of linear angular correction as follow:
vβ = (am,p − am,t )dxm + (bm,p − bm,t )dym −am,pdxp − bm,pdyp + am,t dxt + bm,t dyt + lβ (3.5)

Step 1: Using the equation of correction GPS Observations, the priori
covariance matrix of weight Mxyz and coordinate of datum point C to adjust
only GPS in topocentric coordinate system in order to get first adjustment
coordinate of points and mean square error of unit weight µ GPS .
Step 2: Adjustment of combination of GPS observation and angularside measurement. The weight of the GPS basseline in this step must
be calculated by the following the formula:
−1
1
~
(3.11)
P = (µ 2 M ) =
M −1

It should be noticed that horizontal angle will be deformed due
to orthogonal projection on the plane when points are different in
elevation. For this case, it is essential to calculate correction of
deformation ∆ β in measured angle β in the following formula (2.1):
∆β = δp − δ t

(3.6)

3.3.2.2. Side length measurement
Equation of horizontal angle correction as follow:
v k ,i = −

(yo − yo )
(x o − x o )
(yo − yo )
( x oi − x ok )
dx k − i o k dy k + i o k dx i + i o k dy i + l k ,i
o
D k ,i
D k ,i
D k ,i
D k ,i

A T PL = A TGPS PGPSL GPS + A TMD PMD L MD

Values of

µ GPS

(3.10)

Solving the standard equation (3.8) will reveal the unknown
quanity of combination adjusment calculation.
When only adjusting GPS network, mean square error of unit
weight µ GPS is many times bigger than 1; this indicates that covariance
matrix CXYZ of sides has not truely reflects GPS observation error.
Chi-squared test are usually not passed.
For processing weight in adjustment combination, steps are performed

as follow:

GPS

xyz

xyz

2
µ GPS

is the basis for estimating the priori covariance

matrix of weight, when weight of GPS observation is compatible with
angular- side measurement.
3.3.2.4. Assessment of accuracy
Assessment of accuracy of adjustment result includes:
1. Calculation of unit reference standard deviation

(3.7)

The length of incline side also can be used for establishment of
correction equation.
3.3.2.3. Establishment and solution of common standard equation
(3.8)
A T PA .X + A T PL = 0
Standard equation of coefficient matrix is established in the
following formula:
(3.9)
A T PA = A TGPS PGPSA GPS + A TMD PMD A MD

and:

GPS

µ=

V T PV
3n + n 1 + n 2 − t

(3.12)

2. Assessment of accuracy of point location and mutual accuracy
Mean square error of position:
(3.13)
m p = m 2x + m 2y = µ Q xx + Q yy
Mean square error of side: mS = µ QS
Standard deviation of the bearings m α = µ Q α

(3.14)
(3.15)

3.3.3. Application of Kalman filter in combination adjustment
(divided into several stages)
The multi-stage consecutive adjustment step using Kalman
filtering solution as follows:
Step 1: Use the measurement step (i) and adjusted unknowns in step
(i-1) to calculate the free class L(i) . Gain matrix K(i) is based on coweight matrix Q X of previous stages (i-1), weight matrix additional
( i −1 )

measurement stages (i) P(i) and matrix system A number of (i) the

correction equation measurement stages (i).
(3.16)
K i = Q X A T( i ) ( P(−i )1 + A ( i )Q X A T( i ) ) −1
( i −1)

( i −1)


19

20

Step 2: Use the gain matrix K (i) to update unknowns and update the
co-weight matrix of the unknown:
(3.17)
X ( i ) = X (i−1) + K ( i ) .L (i )
Q X ( i ) = Q X( i −1) − K (i ) A (i ) Q X( i −1)

BEGIN
Input

(3.18)

3.3.4. Adjustment combination of (3D) coordinate system and (2D)
coordinate system.
Adjustment procedures includes 02 steps as follow:
Step 1: Based on GPS observation value, the first adjustment is
carried out in the topocentric coordinate system in order to determine
the approximate coordinates for location of GPS receiver. Mean
square error of unit weight µ GPS is determined in order to normalize

X

Y

Z

N

E

U

BG LG HG

Terrestrial
observations

Mxyz

Establish equation of
correction GPS, P GPS

Establish and Solve the system
of standard equations GPS

Calculate ( x,y,z )

1

Calculate

CXYZ multiplying with µ 2GPS determined in the previous step.

GPS
GPS

GPS

Calculate

B

Calculate L

CHAPTER 4
ESTABLISHMENT OF SOFTWARE FOR ADJUSTMENT
COMBINATION OF GPS AND TERRESTRIAL OBSERVATIONS
IN LOCAL TOPOCENTRIC COORDINATE SYSTEM

C xyz

Rotation
matrix RG

Check loop of closure
in the LTCS

the weight for adjustment combination with terrestrial observation
value. Using approximate coordinates (x,y) of associated points and

terrestrial observation value are to calculate the approximate
coordinates for the 2D grid points.
Step 2. Correction equation for terrestrial observation value is
established in order to adjust combination with GPS observation.
Weight of GPS observation is calculated based on covariance matrix
The solution of the standard equations and calculations of correction,
adjustment and evaluation of accuracy are performed in sequence as
the other networks.

xG , yG , HG

M§

>1

1

Establishment of common
standard equation

Establishment and solution
of common standard equation

NOTE:
LTCS: local topocentric coordinate system

4.1. PROGRAME FOR COMBINATION ADJUSMENT

Procedures for adjusting combination of GPS observation and
angular-side measurement in the local topocentric coordinate system is

performed in the following procedures:

Assessment
of accuracy

END

Figure 4.1 - A block diagram for computer program


21

22

4.2. ESTABLISHMENT OF SOFTWARE FOR ADJUSTMENT
COMBINATION OF GPS AND TERRESTRIAL OBSERVATIONS IN
LOCAL TOPOCENTRIC COORDINATE SYSTEM.

4.3.2.Field claculation of adjusment combination of GPS and
terrestrial observations for Thai Nguyen Cement Plant
Engineering control network of Thai Nguyen Cement Plant
includes 21 points to be determined, 04 outer control points called
from GPS-01 to GPS-04, 13 control points on the construction plane
called TN-01 to TN-13, 51 basesides measured by GPS, 26 sides and
19 angles measured by electric total station.

Result on adjustment of GPS network by softwares including
ADGT, TBC, GPSurvey 2.35 indicates that:
• Difference in the geodetic coordinates between software ADGT
and TBC, GPSurvey 2.35 is similar to that between software TBC
and GPSurvey 2.35.

• Mean square error of position between software ADGT and
GPSurvey 2.35 is about 0,1mm. Besides, difference in plane is
about 1,5mm between software ADGT and TBC;

Adjustment combination of GPS and terrestrial observations by
software ADGT:
• Combination of GPS and terrestrial observation enhances the
accuracy of the network;
• Compatibility of two technologies is proved and reliability of
results is enhanced.
4.3.3. General comments
1. Covariance matrix of GPS vectors received from side solutions only
reflects error of each separated vectors, but not present the quality of
whole measurement of GPS network; therefore, adjustment
combination of GPS observation and angular-side measurement should
be carried out two-step processing procedures. After the first step,

For processing geodetic data, the most significant requirement is
to ensure the accuracy of results; therefore it is required to select the
appropriate algorithm and proper processing procedures. Based on the
algorithm and procedures at section 4.1, for adjustment combination of
GPS and terrestrial observations in the topocentric coordinate system,
these steps should be followed sequentially:
Step 1: Use a software with GPS receiver to import and process GPS
observation value such as GPSurvey 2.35, TGO, TTC, TBC, etc.
Step 2: Establish the adjustment software in combination with
ADGT.EXE
“ADGT (ADjustment GPS Topography) software: includes 4 modules
with an user-friendly design, Vietnamese language, simplicity, direct
data imported on Windows platform, good operation on Windows-8
operating system with fast processor speed and results are exported in

Vietnamese forms.
4.3. FIELD CALCULATION

4.3.1. Field claculation of adjusment combination of GPS and
terrestrial observations for Dung Quat Oil Refinery Plant
Engineering control network of Dung Quat Oil Refinery Plant includes
01 datum point, 14 points to be determined, 34 baselines, 04 angles
and 08 sides.

Result on adjustment of GPS network by softwares including
ADGT, TBC, GPSurvey 2.35 indicates that:
• Difference in the geodetic coordinates between softwares ADGT
and TBC, GPSurvey 2.35 is similar to that between softwares TBC
and GPSurvey 2.35.
• Mean square error of position between softwa re ADGT and
GPSurvey 2.35 is all the same. Besides, difference in plane is
about 3mm between software ADGT and GPSurvey 2.35;

Adjustment combination of GPS and terrestrial observations by
software ADGT:
• Angular-side measurement is well performed in additional area;
• Compatibility of two technologies is proved and reliability of
results is enhanced.

µ

mean square error of unit weight GPS , will be determined, which is
the basis for estimating the covariance matrix of a priori weight to
standardize GPS observation in the second step.
2. Adjustment combination of GPS and angular-side measurement in
the local topocentric coordinate system whose datum is established in

23

24

the center of network with proper control scope will simplify procedures
of adjustment calculation, ensure coherence and meet the requirement of
network deformation. The factors (i.e dimension) of network after
adjustment ensure the best conformity to field factors. This is critical to
design work, construction of civil and industrial works requiring high
accuracy level.
3.In the local topocentric coordinate system, it is possible to adjust
combination of GPS network (3D) and terrestrial network (2D) if GPS
receiver cannot be placed in some network points, but angular-side
measurement are carried out by classical observations.

stages of survey (large scale), design and construction. The scope
(radius) of using the topocentric coordinate system is calculated by
required deformation and by the formula L≤ 2,45.R. 1/T .
5. Within the scale of defined area, the elements (dimension) of
network after adjustment ensure the best suitability for field factors.
This is necessary for the design, construction of civil and industrial
works which requires high accuracy.
6. ADGT software is reliable enough to use for the adjusting
combination of GPS and terrestrial observations in engineering survey
in Vietnam.
B. Recomendations
1. In the actual engineering survey for civil and industrial works, it is
able to combine GPS technology and electric total station to establish
geodetic network and process adjustment in the local topocentric

coordinate system in order to meet technical requirements and improve
the reliability of network.
2. In the local topocentric coordinate system, it is possible to adjust
GPS network (3D) and terrestrial network (2D) if some points are not
in good conditions for placing GPS receiver.
3. When establishing the local topocentric coordinate system, it is
necessary to select the datum suitable for a receiver to be placed on
and adjacent to network centre. This coordinate system utilizes
orthogonal projection; therefore, if elevation of points are significantly
different, angle distort must be calculated in the formula (2.1) to adjust
the measured angle before adjustment.
4. To determine exactly the weight of GPS observation when adjusting
combination with angular- side measurement, it is required to apply
two-step adjustment procedure. In the first step, the adjustment of only
GPS observation value is defined in order to determine approximate

CONCLUSION AND RECOMMENDATIONS
A. Conclusion
1.In fact, adjustment combination of GPS network and terrestrial
observations in the local topocentric coordinate system is the
adjustment in the three-dimensional coordinate system (3D) with
rigorous algorithm and adjustment procedures. The coordinate
components z of topocentric coordinate system enables calculation and
determination of geodetic height H of network points after adjustment.
2. Covariance matrix CXYZ of GPS vectors only represents the
correlative relationship of measurement value, but the increments of
their variance and covariance; mean square error of unit weight µ GPS
after adjustment of only GPS network is much greater than 1. The
value µ GPS is required to be determined in order to re-estimate
covariance matrix of GPS vectors when adjusting combination of GPS

and terrestrial observations.
3. It is required to calculate angle distort in order to correct the angles
before the adjustment combination with GPS observation value. This
is critical for measured angles between points of significantly different
elevation.
4. The topocentric coordinate system may be used as a basis instead of
plane rectangular coordinate system in UTM projection, serving for

coordinates and mean sqaure error of unit weight

µ GPS , which is the

basis for re-estimate covariance matrix of GPS observation value in
the second step of adjustment. When calculating weight of
measurement value, Constant C=1 is taken.


LIST OF PUBLICATIONS RELATED TO THE DISSERTATION
1. Le Van Hung (2008), “ Economic efficiency - the use of the
technique combined Trimble5602 electronic total station and Trimble
R3 GPS monitoring in shift work”, Building science and technology
journal, (No 2), Ha Noi.
2. Le Van Hung (2008), “ Reasonable solution to the axis moving
high in the construction of tall buildings”, Building science and
technology journal, (No 3), Ha Noi.
3. Ngo Xuan The, Nguyen Xuan Hoa, Le Van Hung (2010), “
Establishment of software systems for transformation from GPS
coordinates to the coordinate system works”, Building science and
technology journal, (No 3), Ha Noi.
4. Dang Nam Chinh, Le Van Hung (2011),“ Adjustment in multiple

phases and approach to Kalman filter” Science - technical journal of
mining and geology, (No 35), Ha Noi.
5. Le Van Hung (2012), “ Difference between the UTM plane
rectangular coordinates system and local topocentric coordinate
system”, Building science and technology journal, (No 3), Ha Noi.
6. Dang Nam Chinh, Le Van Hung (2013), “ Determination of
the limit when using of local topocentric coordinate system for
engineering surveying”, Science - technical journal of mining and
geology, (No 41), Special issue for 40 years of Department of
Geodesy, Ha Noi.
7. Nguyen Xuan Hoa, Le Van Hung (2013), “ Establishment of
interpolation formula for the elevation anomalous in the local
topocentric coordinate system” Building science and technology
journal, (No 2), Ha Noi.
8. Dang Nam Chinh, Nguyen Quang Phuc, Le Van Hung (2013),
“Adjustment combination of GPS observables and measurements by
electronic total station in the local topocentric coordinate system”,
Proceeding of conference on the 50th anniversary of establishment of
Viet Nam institute for Building science and technology, Geotechnical
– Surveying engineering, (ISBN 978-604-82-0021-3), Construction
Publishing House, Ha Noi.