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 -
Trang 1MINISTRY 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
Trang 2The 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
Trang 3PREFACE
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
Trang 4- 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
Trang 5- 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
Trang 6Chapter 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),
Trang 7Schreiber (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
Trang 8use 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]:
g (X) 0, i 1,2, ,m
h (X) 0 , j 1,2, ,l
(2.1)
in which: X is a vector vector space with n Rndimensions
f, gi, hj are continuous real equations of X f(X) is target equation
g (X) 0i is constrained inequality
j
h (X) 0 is constrained inequality
Trang 9Variable X is a set of qualities to be found in the optimal problem, a determined value set is a specific plan, often taking non-minus values of that variable set
2.2 Quality standard of control network
Q is the matrix of converse weight of unknowns
xi and yi of point pi
b Root mean square error of edge length
Qxx is the matrix of converse weight of unknowns
c Root mean square error of edge azimuth
Trang 102.Q tg(2 )
2.Q tg(2 )
Trang 112.2.2 General accuracy
Criteria for assessing optimal design [4]:
a Optimal of A grade:min(S Q )p xx
b Optimal of D grade:min(det Q )xx
c Optimal of E grade:min max Qxx
d Optimal of I grade:
xx xx
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
Trang 12- Constrained conditions are accuracy and reliability of networks
Model of the problem of optimal design for free combined GPS – territorial networks is as follows:
Trang 13Block 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
Initial Initial
Adjust plan
Call adjustment number equation
Calculate matrix Save results of plans
Incorrect
Fail Correct
Pass Choose optimal plan
End
Trang 14Figure 2.1: Block diagram of optimal design of free combined
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
Trang 15with 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
Trang 16The 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]:
v c v
c
v
v c v c v