Nghiên cứu phương pháp thiết kế tối ưu và bình sai hỗn hợp lưới tự do mặt đất GPS trong điều kiện việt nam tt tiếng anh

MINISTRY OF EDUCATION AND TRAINING
HANOI UNIVERSITY OF MINING AND GEOLOGY

LUU ANH TUAN

RESEARCHING OPTIMAL DESIGN METHOD AND
ADJUSTMENT OF FREE COMBINED GPS TERROTORIAL NETWORKS IN CONDITIONS OF
VIETNAM

Major :
Code :

Survey and mapping
9520503

ABSTRACT OF THESIS FOR DOCTOR OF
TECHNICAL SCIENCE

HANOI - 2019


The work was finished at: Subject of Plane Surveying and
Deviation, Faculty of Survey - Mapping and Land
Administration, Hanoi University of Mining and Geology,
Hanoi
Supervisor:
Prof.D.Sc. Hoang Ngoc Ha

Reviewer 1: Dr. Dao Quang Hieu
Reviewer 2: Assoc.Prof.Dr. Duong Van Phong
Reviewer 3: Prof.Dr. Vo Chi My

The dissertation will be defensed in front of the University
Dissertation Assessment Committee at Hanoi University of
Mining and Geology
At time of…

The dissertation could be retrieved from:
- Vietnam National Library.
- Library of Hanoi University of Mining and
Geology


1
PREFACE
1. The urgency of the topic
Modern adjustment theory has been investigating the extent of
the effect of rough errors on post-adjustment results and methods of
treatment. In actual measurement, geodetic data obtained through
statistics and analysis show that the probability of rough errors
accounts for about 1% ÷ 10% (Tukey, 1962) [51]. Rough errors often
have a great value compared to random errors, so when processing
geodetic data, rough errors greatly affect the adjustment results.
In Vietnam, the establishment of geodetic coordinates control
network combined with traditional measurements and GPS
measurements is a necessary and topical issue, etc. However, the
issue of analyzing the quality of geodetic network with different
types of measurements, even in the case measurements contain rough
errors in Vietnam, is almost not studied. The thesis studied the
optimal design according to the redundancy level of the measurement
quantity and applied a robust estimation method to process and

analyze the free combined GPS - territorial networks even in the case
measurements contain rough errors. These studies allow the
processing and analysis of geodetic networks, especially for large
ones. On the other hand, the application of the achievements of
statistical mathematics allows to expand the analysis of explicit and
intuitive adjustment results that the classical methods do not mention.
2. Purposes, objects and scope of the dissertation
- Purpose of the research: Develop a model of optimal design
and robust estimation for processing and analyzing data of the free
combined GPS - territorial networks even in the case measurements
contain rough errors.
- Objects of the study: Optimal design method, processing and
analyzing data of the free combined GPS - territorial networks in
conditions of Vietnam.
- Scope of the study: Researching Optimal design method,
processing and analyzing data of the free combined GPS - territorial
networks for some large geodesic networks in Vietnam.
3. The contents of the research
- Research overview of geodetic network construction work in
Vietnam.


2
- Research the optimal design methods for geodetic networks,
propose the optimal design of combined GPS - territorial networks
according to the redundancy of measurement quantities.
- Research methods of processing geodetic data in case
measurements contain rough errors.
- Research and apply robust estimation method, propose to use
the extended Huber weight function to process and analyze large

geodetic networks of free combined GPS - territorial networks in
conditions of Vietnam.
- Research to computer programming, serving optimal design
and data processing.
4. Research Methods
- Search methods: Search, collect documents and update
information on the Internet and libraries.
- Analysis method: Use facilities and utilities, collect related
documents to solve related issues.
- Statistical method: Collect, synthesize and process
relevant data.
- Comparative method: Summarize results, compare, evaluate
and draw conclusions for raised issues.
- General method: Summarize the research results, evaluate
and check the accuracy of the given algorithm.
- Expert method: Receive opinions of instructors, consult
scientists, production units, colleagues on the issues of the research.
5. Scientific and practical significance of the research
Scientific significance:
- Research results of optimal design and processing, analyzing
data of free combined GPS - territorial networks even with rough
errors contribute to develop optimal design theory and processing
data of large geodesic networks with many different types of
measurements in Vietnam.
Practical significance:
- Research results of optimal design and processing, analyzing
data of free combined GPS - territorial networks serve the work of
improvement and construction of control geodesic coordinate
network in Vietnam and a number of specialized geodetic networks.
6. Defensed points

3
- Point 1: The optimal design according to redundancy level of
measurement is suitable for large free combined GPS - territorial
networks in Vietnam.
- Point 2: Application of robust estimation method with the
selection of appropriate weight function is an effective solution for
processing and analyzing free combined GPS - territorial networks
even in the case measurements contain rough errors.
7. New points of the research
- Propose an optimal design method of free combined GPS territorial networks according to the excessive measure of
measurement quantity.
- Apply robust estimation method for processing and analyzing
the data of free combined GPS - territorial networks even in cases
measurement contains rough errors.
- Develop an optimal computer program designed, analyze and
process the data of free combined GPS - territorial networks even in
cases measurement contains rough errors.
8. The structure and content of the dissertation
The structure of the dissertation consists of three parts:
1 Introduction: Introduce the urgency, purpose, object and
scope of the research, offer defensed points and new points.
2. The content is presented in 4 chapters
Chapter 1: Overview of optimal design and data processing of
control geodetic coordinate network.
Chapter 2: Optimal design of free combined GPS - territorial
networks
Chapter 3: Research and apply robust estimation method for
processing and analyzing data of free combined GPS - territorial

networks
Chapter 4: Experiment optimal design and data processing of
free combined GPS - territorial networks


4
Chapter 1
OVERVIEW OF OPTIMAL DESIGN AND DATA
PROCESSING OF CONTROL GEODETIC COORDINATE
NETWORK
1.1 Overview of geodetic control network
1.1.1 Overview of foreign geodetic control network
Countries around the world have also gone through the stages
of building and developing geodetic coordinates networks with
different measurement methods such as astronomical measurement
method, triangle method, polygon method, edge measurement
triangle method, triangle angle measurement method, angle-side
triangle measurement method, GNSS technology application method.
In the field of geodetic networks, many countries have successfully
applied GPS technology very early, for example, the United States,
Germany and China. In addition, some countries such as Australia ,
New Zealand, Greece, Poland, Latvia, Indonesia, etc. have applied
GPS technology to improve the network of their national control
coordinate networks.
1.1.2 Overview and status of establishing geodetic control networks
in Vietnam
The Vietnam National Coordinate Network is a unified
network covering the whole territory and territorial waters of
Vietnam and was built in a long time with different conditions and
technologies. However, so far, a number of national waypoints have

been lost, shifted and fluctuated, many of which are located on high
mountains, which are not convenient for use. In addition, when
establishing the national reference system and national coordinate
system according to the dynamic viewpoint, the selection of
technology solution must inherit the results from VN2000 system and
ensure the ability to transform into VN2000 system with
homogeneous accuracy throughout the country. Therefore,
improvements are needed to enhance the accuracy of the existing
national network.
1.2 Overview of optimal geodetic network design
1.2.1 Overview of foreign optimal design
The work of optimal geodetic network design has been studied
and applied by many scientists in the world such as Helmert (1868),


5
Schreiber (1882). In particular, Grafarend, E proposed four types of
optimal geodetic design that are widely and effectively used until the
present. Recent published results of researches in optimal geodetic
network designs have focused on the tendency of combining
electronic computers and modern algorithms to make optimal design
simple and efficient. One of the most prominent researches in the
world in recent years has been the application of redundancy level of
measurement quantities in the optimal design of networks. M.Yetkin,
Berber, M (2012) or Amiri - Simkooei, A. R, (2001) could be named
as some famous examples.
1.2.2 Overview of domestic optimum design
In Vietnam, optimal geodetic network design largely follows
the traditional method, and current regulations only specify a number
of basic characteristics of networks such as location error, weakness,

relative error of weak length, weakest mutual errors, etc.
1.2.3 Trends and optimal design solutions for large geodesic
networks in conditions of Vietnam
From the review of foreign and domestic studies, the optimal
design problems still have the following shortcomings:
Shortcomings: The studies have not mentioned the optimal
design solution for large geodetic networks and different types of
measurement such as free combined GPS - territorial networks.
Solutions: Research the optimal design problem based on the
redundancy level of measurement quantity for large geodetic
networks such as free combined GPS - territorial networks in
conditions of Vietnam.
1.3 Overview of data processing methods for geodetic networks
containing rough errors
1.3.1 Foreign studies
Geodetic surveyors around the world have been focusing on
studying geodetic data processing algorithms when measurements
contain rough errors. For example, Kalman RE and Bucy RS (1961)
proposed Kalman filter or Markuze YI (1986) was based on
Kalman filter to develop regressive adjustment method. Most
notably, Huber, P. J laid the ground for the Robust Estimation
method bystudying methods of statistical stability evaluation
methods (Huber, P.J .1964) . Nowadays, many published applications


6
use robust estimation method to process geodetic data when the
measurements contain rough errors.
1.3.2 Domestic studies
In Vietnam, geodetic network adjustment is done according to the

traditional method, which is the adjustment methods are based on the
principle of least squares with measurements that contain random errors
only. Therefore, when evaluating accuracy of the networks, studies only
consider local factors in the networks such as mean error of position
point, mean error of edge azimuth, relative error of edge length, etc.
1.3.3. Trends and solutions for processing and analyzing geodetic
networks in conditions of Vietnam
Shortcomings of foreign and domestic studies:
Shortcomings: Processing and analysis of large geodetic
networks and networks with different measurement types such as the
free combined GPS - territorial networks have not been researched.
Solutions: Research and apply Robust estimation method for
processing and analyzing large geodetic networks such as free
combined GPS - territorial networks in conditions of Vietnam.
Chapter 2
OPTIMAL DESIGN OF FREE COMBINED GPS –
TERRITORIAL NETWORKS
2.1 General optimal problem
The most general optimal problem could be represented as
follows [4]:


min f(X)
X  Rn

g i (X)  0, i  1,2,...,m 
h j (X)  0 , j  1,2,...,l 
in which:

(2.1)

X is a vector vector space with n R n dimensions
f, g i , h j are continuous real equations of X
f(X) is target equation
gi (X)  0 is constrained inequality

h j (X)  0 is constrained inequality


7
Variable X is a set of qualities to be found in the optimal
problem, a determined value set is a specific plan, often taking nonminus values of that variable set.
2.2 Quality standard of control network
2.2.1 Local accuracy
a. Root mean square error of point position

mpi   Qxxi  Qyyi

(2.5)

m X i   Qxxi ; m Yi   Qyyi

(2.6)

in which: Q xx , Q yy is the matrix of converse weight of unknowns
i

i

xi and yi of point pi.

b. Root mean square error of edge length

m Sij   Q FS

(2.7)
ij

QFS  fSTij Q x fSij

(2.8)

ij

in which:

fSij is coefficient vector of weighting function of

edge length Ssij

fSij  (  cos  ij  sin  ij cos  ij sin  ij )T
Qxx is the matrix of converse weight of unknowns
c. Root mean square error of edge azimuth

m ij   Q F

(2.9)
ij

QF  fTij Q xxfij

(2.10)

ij

in which:

fij is coefficient vector of weighting function of

edge azimuth Sij

fij  (a ij

bij

 a ij

d. Root mean square error of mutual points

 bij )T

(2.11)


8

mTH
  Qxx  Qyy
ij

(2.12)

mxij   Qxx ; m yij   Qyy

(2.13)

in which:

Qxx  Qxi xi  Qxi xi  2Qxi xj

(2.14)

Qyy  Qyi yi  Qyi yi  2Qyi y j

(2.15)

e.Ellipse error of point position

E

F

Q xx  Q yy  p
2

Qxx  Q yy  p
2

2
P  (Qxx  Q yy )2  4Qxy

in which:

tg(2. 0 ) 

2.Q xy
Q xx  Q yy

(2.16)

(2.17)
(2.18)
(2.19)

f.Ellipse mutual error of point position


2

2


F 
2

2

E2 
2

Q

Q

xx

 Q yy  (Q xx  Q yy )2  4Q 2 xy

(2.20)

xx

 Q yy  (Q xx  Q yy )2  4Q 2xy

(2.21)

tg(2. 0 ) 
in which:

2.Q xy
Q xx  Qyy

(2.22)

Qxx  Qxi xi  2Qx x  Qx jx j

(2.23)

Qyy  Qyi yi  2Qy y  Qy jy j

(2.24)

Qxy  Qxi yi  2Qx y  Qx jy j

(2.25)

i j

i j

i j


9
2.2.2 General accuracy
Criteria for assessing optimal design [4]:
a. Optimal of A grade: min(S pQ xx )
b. Optimal of D grade: min(det Qxx )
c. Optimal of E grade: min max  Q xx 
d. Optimal of I grade: min

max Q xx 
min  Q xx 

e. Optimal of G grade: min max (Q xx )ii 
2.2.3. Measured redundancy
Reliability criteria of control network, the relationship between
measured redundancy r in the network with measured redundancy rii of
each measurement are presented in the following formula [7]:

r

ii

 nt  r

(2.36)

in which, n is total measurements and t is the unknown to be found in
the network.
From formula (2.36), total measured redundancy in the
network is distributed for each measurement at level rii , abbreviated
as ri (0  ri  1) . Therefore, the smaller ri is, the greater the effect of
measurement i is, vice versa, the greater the ri is, the smaller the
effect of of measurement i is. When ri  0 , this measurement is
important and must be measured, and when ri  1 , then it is not
necessary to measure this.
2.4. Propose optimal design for free combined GPS – territorial
networks according to redundancy level of measurement
quantities
- Selected design variables are measurement quantities
- Selected target function is expenses of measuring geodesic
networks


10
- Constrained conditions are accuracy and reliability of
networks
Model of the problem of optimal design for free combined GPS –
territorial networks is as follows:
- Design variables yi

- Target functions:
m

m

nj

nS

j1

j1

i 1

i 1

Z   U j   C j  (1  y ji )   CSi (1  ySi )  min
Max(m P )  (m P )CF

n
- Constrained conditions: 
1.5t

y i  c.t


i 1

in which, respective Max(mP), (mP)CF are maximum root mean square

error of point position as allowed by norms, c.t < n (n: possible
number of measurements of geodesic networks), t is the necessary
measurement, c is a constant.


11
Block diagram of optimal design of free combined GPS – territorial
network
Start

Establish initial parameters

Build equation system of correction number of
possible measurements

Calculate matrix

Calculate rii and arrange measurement quantities

Adjust plan
Initial

Initial

Call adjustment number equation

Calculate matrix

Save results of plans

Incorrect

Correct

Fail
Pass
Choose optimal plan

End


12
Figure 2.1: Block diagram of optimal design of free combined
GPS – territorial network
2.4.1 Investigate the role of measurable quantities according to
redundancy in optimal design
2.4.1.1 Experimental geodetic networks in Lang Son and Bac Ninh
provinces
Lang Son experimental network contained 6 points to
determine coordinates , the average edge length in the network was
1400m. When surveying the experimental network, an electronic
total station with accuracy m β = 3 '' , m S = (2 + 2ppm) and GPS with
an accuracy of = 5, b = 1 were chosen; Based on the network diagram
to design, possible measurements of free combined GPS - territorial
network were 21 angles and 26 GPS measurement quantities.
Bac Ninh experimental network had 36 points to determine
coordinates, the average edge length in the network was 1050m.
When surveying the experimental network, an electronic total station
with accuracy m β = 3 '' , m S = (2 + 2ppm) and GPS with an accuracy
of = 5, b = 1 were chosen; Based on the network diagram to design,

possible measurements of free combined GPS - territorial network
were 162 angles and 178 GPS measurement quantities.

Figure 2.3: Experimental network in Bac Ninh province
2.4.1.2. Compare and comment
The experimental calculations of two cases, arranging
measurement quantities in two groups, the group of measurements


13
with low redundancy (Option 1) and the group of measurement with
high redundancy (Option 2) shows:
Lang Son experimental network: Two options had equal
measurements of 21 angles and 5 baselines but different redundancy
levels. Experiments showed that results of option 1 were better than
those of option 2. Specifically, the maximum position error was 5.50
mm for option 1 and 13.16mm for option 2. The relative square error
of the edge length was 1/161464 for option 1 and 1/82864 for option
2. In addition, typical quantities for network accuracy such as, weak
square azimuth errors, reciprocal squares of reciprocal weaknesses,
optimal A, G of option 1 were also better than those of option 2.
Bac Ninh experimental network: Two options had equal
measurements of 162 angles and 72 baselines but different
redundancy levels. Experiments showed that results of option 1 were
better than those of option 2. Specifically, the maximum position
error was 3.92 mm for option 1 and 14.17mm for option 2, the
relative square error of the edge length was 1/140650 for option 1
and 1/46437 for option 2. In addition, typical quantities for network
accuracy such as, weak square azimuth errors, reciprocal squares of
reciprocal weaknesses, optimal A, G of option 1 were also better than

those of option 2.
Comment:
The position and role of the measurements in the geodetic
networks depend on the excess level of the measurement quantities.
Qualities of distance measurement at the edge of the networks
often have lower redundancy levels than those of other measurements
in the networks.
Chapter 3
RESEARCH THE APPLICATION OF ROBUST ESTIMATION
METHOD FOR PROCESSING AND ANALYZING DATA OF
FREE COMBINED GPS – TERRITORIAL NETWORKS
3.1 Overview of robust estimation
The basic principle of a robust estimation is to consider that the
existence of rough errors in the measurement range is unavoidable,
selecting the most appropriate estimation method so that the estimation
is not affected by rough error and obtains the best results.


14
The principle of the largest natural robust estimation is often
used in geodesics, based on the estimation theory M proposed by
Huber in 1964. However, the classic Huber, Danish, Tukey, IGG or L
1 weighting methods currently in common use are only applied in the
case of independent and effective measurements for geodetic
networks with the same measurements as angular networks, edge
networks, or angle-to-edge networks that have measurements with
fewer rough errors. Therefore, the above methods are not suitable for
geodetic networks with many types of measurements taking into
account the correlation between measurements.
3.2 Proposing the use of robust estimation function for

free combined GPS- territorial networks
Free combined GPS- territorial network is a type of
networks with different types of measurements such as angular
measurements, edge measurements and GPS. In addition, GPS
measurements are correlated with each other. On the other hand, the
correlation among baselines increases the effect of the rough error
measurement value on other measurements as well as its hiding.
Therefore, when searching for rough errors, it is impossible to
consider measurements to be independent. Within scope of this
dissertation, it only mentions correlation between the components of
the baselines without considering the correlation among the
baselines.
To solve the above problem, extended Huber weight function
for the free combined GPS – territorial networks were proposed.
The extended Huber weight function (HB-HL) have the following
form [6], [14]:
wi 1
vi c
wi
w ii
w ii

c
; vi
vi

vi

; pi

pi w i ;

vi

(3.32)

w jj 1;
c
vi

; vi

c

vi

vi
vi
vi

;w jj

c
vj

; vj

vj
vj

; pij

pij w ij ;

vi

c; v j
c; v j

c;
c;


15
Where c is a constant and is chosen c = 1.5,
following formula:
vi

0

Qvv

P

(Qvv )ii
1

is determined by the
(3.33)

AQx AT

(3.34)
3.3 Procedure of robust estimation for free combined GPS –
territorial networks in plane perpendicular coordinates
1. Select the unknown, the selected unknown is the correction number
of the approximate coordinates of the points to be determined in the
networks.
2. Approximate coordinates calculation: Assume the coordinates of a
point and the measurements in the approximate coordinate networks
of X (0) points in the networks.
3. Establish a
numerical equation system for correcting
measurement values
4. Establish a standard equation system
5. Prepare and solve extended standard equation system
6. Use the extended Huber weight function in robust estimation
a. Process data according to robust estimation
From V, calculate w 1 according to (3.32) for measurement
values satisfying conditions vi
measurements is p (1)

c , the new weight of independent

p1w1 and the new weight of dependent

(1)
11

(1)

(1)
(1)
(1)
measurements p
, p 22
. Solve
p11w11
p22 w (1)
p12 w12
22 , p12
the standard equation system, the second estimated value of the
unknown X is found the correction number V has the form:

X (1)
1
V

R (1) AT P (1) L
1
AX
L

Similar to the case of V, from V
respective
measurements

(1)

, calculate weights for the

p(2)

p1w 2

(2)
(2)
(2)
(2)
(1) (2)
and p11
, p 22
, continue to
p11(1) w11
p22
w 22 , p12(2) p12(1) w12
solve the standard equation system, apply the same alternative


16
calculation, until the deviation of the solution of two consecutive times
must match the required error limit, then stop calculating.
The final result of the unknown
and the correction number V is

X (k)

V

k

k

R( k ) AT P L
k
AX
L

7 .Evaluate the reliability of the adjustment results according to the
distribution χ 2 (χ 2 r, 1-α / 2 ≤ V T PV≤ χ 2 r, α / 2), analyze the results after
adjustment.
3.4 Process of methods for processing and analyzing free combined
GPS – territorial networks with rough errors.

Block diagram of option 1


17
Figure 3.2. Block diagram of option 1
Start

Enter data
Territorial
measurements
transferred to plane

GPS values
Adjustment of GPS network

Calculate transfer
Calculate

Calculate transfer
Calculate

GPS values in plane
perpendicular system

Calculate matrix of
variance

Estimated variance of
measurements
Adjustment according to
SBPNN method

Robust estimation

Yes

Test tough
errors
No

Adjustment
results

Start


18

3.4.1 Robust estimation method (method 1)
Step 1: Adjustments of GPS network in geocentric space
perpendicular coordinate system (GPS μ = 1), C X, Y, Z. are gained.
Step 2: Calculate the coordinate conversion (X, Y, Z), the
covariance matrix from geocentric space perpendicular coordinate
system into the plane perpendicular coordinate system (x, y) and
convert the baselines into coordinate degrees ∆x, ∆y.
Step 3: Estimate the variance of the measurements in the plane
perpendicular coordinate system.
Step 4: Robust estimation of free combined GPS – territorial
networks
3.4.2 Adjustment method with "clean" measurement values
(method 2)
Step 1: Adjustments of GPS network in geocentric space
perpendicular coordinate system (GPS μ = 1), C X, Y, Z. are gained
Step 2: Calculate the coordinates conversion (X, Y, Z), the
covariance matrix from the geocentric space perpendicular coordinate
system into the plane perpendicular coordinate system (x, y) and
convert the baselines into coordinate degrees ∆x, ∆y.
Step 3: Estimate the variance of the measurements in the plane
perpendicular coordinate system.
Step 4: Robust estimation of free combined GPS – territorial
networks, rough errors are detected.
Step 5: Create a "clean" measurement and adjustment of free
combined GPS – territorial networks with the least square method.
3.4.3 Examine the accuracy of some robust estimation methods
Experiment of free combined GPS – territorial networks
includes: Geodetic network has 6 points to determine coordinates, 21
measuring angles, 7 measurement edges and 6 baselines.
Figure 3.1: Adjustment deviations of free combined GPS –

territorial networks (21 measuring angles, 7 measurement edges
and 6 baselines)


19

3.4.4 .Comment on the accuracy of some robust estimation methods
From the results of empirical calculations and graphs (3.1), it
is shown that: The robust estimation method using the extended
Huber weight function gave the best results for the survey methods,
namely: rough errors give in the model were detected with accurate
position, the determined values of rough (experimental adjustment
deviation) were close to the rough error values put into the
experiment. For example, free combined GPS – territorial networks
(21 measurements, 7 edges and 6 baselines), the number of
measurements with detected rough error was 5, the corresponding


20
rough error value was defined as 3600.51”, 3598.31”, 993.86mm,
999.38mm, 998.53mm. In particular, the Danish, Tukey, Huber, and
L1 methods had rough error values which were not close to the
experimental values.
Chapter 4
EXPERIMENT OF OPTIMAL DESIGN AND DATA
PROCESSING OF FREE COMBINED GPS – TERRITORIAL
NETWORKS
4.1. Building the program
4.1.2. Block diagram and modules of the program:
The modules of the program are based on the optimal

design algorithm and the robust estimation process of free combined
GPS – territorial networks.
4.1.2.1. File module
The basic function of the file module is to manage files such
as copying, moving, opening, deleting, searching, etc.
4.1.2.2.Module for editing and processing GPS data
This module has the function of reading the result information
(*.txt) or (*.html) after processing GPS measurements (processing
edge - Baselines) and editing according to the specified file formats.
GPS network adjustment and variance estimation of GPS
measurements so that after adjustment μGPS = 1, calculate the
coordinate conversion, covariance matrix from the WGS-84 system
to the perpendicular coordinate system.

Figure 4.1: Window image of GPS data processing module interface
4.1.2.3. Optimal design module


21

Figure 4.2: Window image of optimal design module interface
The function of this module is to optimize the design of free
combined GPS – territorial networks and input data that can be read
from the file or imported directly from the program's window. The
data file structure has the following form:
4.1.2.4. Data processing module
This module allows adjustment of the free combined GPS –
territorial networks according to the principle of least squares or
processing geodetic data containing rough errors according to Robust
estimation algorithm. The input data of the program can be read from

the data file or imported directly from the program's window.

Figure 4.3: Window image of data processing module interface
4.2 Experimental calculations
4.2.1. Optimal design of free combined GPS – territorial networks
based on redundancy
4.2.1. Lang Son experimental geodetic network
Assuming the initial territorial network had 6 points to be
determined (A, B, C, D, II, III) with 21 angular measurements,
however, after being used, two points II and III were displaced or


22
damaged and could not be used again. Therefore, the network had
only 4 stable points including: A , B, C and D with 8 angles. The
requirement is to design the network from the initial 6 points,
eliminating measurements related to 2 points II and III, taking
advantage of ground measurements and adding GPS measurements.
Thus, the problem became the optimal design of free combined GPS
– territorial networks with 8 angular measurements and 26 possible
GPS measurements, so that only GPS measurement were being
dealt with. To solve the above problem, the process is to calculate
redundancy of GPS measurements, arrange baselines according to
low to high redundancy levels, use the retrieval algorithm to
supplement the baselines in the sorted order in order that the
number of measurements fell within the constrained conditions.
Experimental results showed that: 5 options may occur in order of
priority from low to high accuracy, in which network option had18
measurements (added 5 baselines: AB, BD, BC , III II, A II),
network accuracy achieved m P = 8.8mm, m S / S = 1/112431, mα =

1.62''. On the other hand, the measured value could be 34, the
designed measurement value was 18, so it satisfied the constrained
conditions of measurements (15≤ ∑yi ≤20). Therefore, an additional
measure of 5 baselines was optimal.
Table 4.1: Comparison of optimal design options for Lang Son
surveying network
Constrained
Effecti
Numbe
Numb
Target
conditions
ve
r of
Option er of
functio
(%)
baselin
Accura Reliabili
angles
n
es
cy
ty
1
8
13
Pass
Pass
2

8
8
Pass
Pass
36
Optim
8
5
Pass
Pass
Pass
al

4.2.1.2. Experimental geodetic network in Bac Ninh province
Assuming the initial experimental network had 36 points to be
determined with 162 measurement angles. Because the three points


23
GB - 09, GB - 25 and GB - 31 were damaged, the network had only
stable 33 points with 120 corners. The requirement is to design a
network consisting of 36 initial points, eliminating measurements
related to 3 points GB - 09, GB - 25 and GB - 31, taking advantage of
existing ground measurements and adding GPS measurement values
so that the network measuring cost was the lowest while satisfying
the required accuracy of the cadastral network (mP ≤ 5cm, mS/S ≤
1/50,000, absolute value of error squares of lateral azimuth less than
400m after adjustment (m P ≤ 1.2cm), absolute value of lateral
squared error of 400m after adjustment (mα ≤ 5'') and reliability of
network.

Experimenting with two groups of GPS measuring quantities
with different levels of redundancy, the following results were
obtained: In order to achieve the accuracy required by the norm, if
using the group of GPS measurements with low redundancy level, it
needed only additional measurement of 55 baselines, network
accuracy reached: mP = 11.5mm, mS/S = 1/52193, mα = 2.93”, while
using measurements with high level of redundancy, measurement of
74 baseline must be added, network accuracy reached: mP = 18.2mm,
mS/S = 1/49171, mα = 2.55”.