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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 PREFACE 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 not mention 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 The contents of the research - Research overview of geodetic network construction work in Vietnam - 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 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 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 Defensed points - 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 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 The structure and content of the dissertation The structure of the dissertation consists of three parts: Introduction: Introduce the urgency, purpose, object and scope of the research, offer defensed points and new points The content is presented in 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 Chapter 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), 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 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 OPTIMAL DESIGN OF FREE COMBINED GPS – TERRITORIAL NETWORKS 2.1 General optimal problem The most general optimal problem could be represented as follows [4]: f(X) X Rn g i (X) 0, i 1,2, ,m h j (X) , 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) is constrained inequality h j (X) is constrained inequality 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 fTij Q xxfij (2.10) ij in which: fij is coefficient vector of weighting function of edge azimuth Sij fij (a ij bij a ij d Root mean square error of mutual points bij )T (2.11) mTH Qxx Qyy ij (2.12) mxij Qxx ; m yij Qyy (2.13) in which: Qxx Qxi xi Qxi xi 2Qxi xj (2.14) Qyy Qyi yi Qyi yi 2Qyi y j (2.15) e.Ellipse error of point position E F Q xx Q yy p Qxx Q yy p 2 P (Qxx Q yy )2 4Qxy in which: tg(2. ) 2.Q xy Q xx Q yy (2.16) (2.17) (2.18) (2.19) f.Ellipse mutual error of point position 2 F 2 E2 Q Q xx Q yy (Q xx Q yy )2 4Q 2 xy (2.20) xx Q yy (Q xx Q yy )2 4Q 2xy (2.21) tg(2. ) in which: 2.Q xy Q xx Qyy (2.22) Qxx Qxi xi 2Qx x Qx jx j (2.23) Qyy Qyi yi 2Qy y Qy jy j (2.24) Qxy Qxi yi 2Qx y Qx jy j (2.25) i j i j i j 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 Evaluate the reliability of the adjustment results according to the distribution χ (χ r, 1-α / ≤ V T PV≤ χ 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 17 Figure 3.2 Block diagram of option 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 points to determine coordinates, 21 measuring angles, measurement edges and baselines Figure 3.1: Adjustment deviations of free combined GPS – territorial networks (21 measuring angles, measurement edges and 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, edges and 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 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 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 stable points including: A , B, C and D with angles The requirement is to design the network from the initial points, eliminating measurements related to 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 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: options may occur in order of priority from low to high accuracy, in which network option had18 measurements (added 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 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 13 Pass Pass 8 Pass Pass 36 Optim 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 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” 24 Table 4.3: Comparison of the optimal surveying network Numbe Numb Target r of Option er of functio baselin angles n es 162 89 120 74 Optim 120 55 Pass al design options for Bac Ninh Constrained conditions Accura Reliabili cy ty Pass Pass Pass Pass Pass Pass Effecti ve (%) 26 4.2.1.3 Comments The experimental results show that, the optimal design method of free combined GPS – territorial networks according to redundancy levels in combination with electronic computers helped the designer easily see the weakness of the network in order to have plans to complement reasonable number of measurement values while ensuring the accuracy and reliability of the geodetic networks 4.2.2 Experiment in processing, analyzing free combined GPS – territorial networks 4.2.2.1 Detect rough errors Free combined GPS – territorial networks (Measurements were 21 angles and 13 baselines) Figure 4.2: Detecting rough errors of free combined GPS – territorial networks 25 Comment Results of experimental calculations for the types of free combined GPS – territorial networks shows that robust estimation method with the selection of extended Huber weight function gave faster results and accurate determination of measurement containing rough errors Therefore, it is highly effective for large free combined GPS – territorial networks, specifically, the ability to detect rough errors (T) in terms of the limit m (mean square error of measurements) as follows: a) Free combined GPS – territorial networks (21 angles, 13 baselines) had measurements with rough errors accounting for about 13% of the redundancy as followings: - T ( (3m; 5m], the algorithm detected about 60% - T ( [6m; 10m), the algorithm detected about 83% - T ≥ 10m, the algorithm detected most measurements containing rough errors b) Free combined GPS – territorial networks (21 measurements, 13 edges and 13 baselines) with measurements containing rough errors accounting for about 12% of redundancy, the detection of rough errors as follows: - T (3m; 5m), the algorithm detected about 83% - T ≥ 5m, the algorithm detected most measurements containing rough errors c GPS – territorial transfer network (8 angels, edges, baselines): - T [6m; 7m), the algorithm detected measurement containing rough errors - T ≥ 7m, the algorithm detected measurements containing rough errors 4.2.2.2 Analyze free combined GPS – territorial networks Compare results after adjustment by adjustment method with "clean" measurement compared to standard model 26 Table 4.10: The coordinate deviation of the adjustment method with the "clean" measurement value compared to the standard model N (1) Free combined GPS – territorial type (2) G-GPS (21 angles, baselines) G-GPS (21 angles, 13baseline) GS-GPS (21 angles, edges, and 13 baseline) GS-GPS (21 corners, 13 edges, and 13 baselines) Adjustment with "clean" measurements Measurements containing rough error Rate of measurements containing rough error (m) (m) (m) (m) (3) (4) (5) (6) 0.002 0.017 0.004 0.015 (7) (8) 10% 0.0 0.0 0.0 0.0 0.002 0.002 0.002 0.003 0.0 0.0 0.0 0.0 0.001 0.002 0.002 0.001 8.5% 10.6% 12.7% ten% 0.0 0.004 0.0 0.008 12.5% 0.0 0.001 0.0 0.002 11.6% 0.0 0.001 0.0 0.002 13.3% The values in columns (3), (4), (5) and (6) are the maximum and minimum coordinate deviations of the adjustment method with the "clean" measurement compared to the standard model Analyze robust estimation results Figure 4.5: Correction deviations of the free combined GPS – territorial networks (21 angles, 13 baselines) 27 Figure 4.6: Correction deviation of transfer network (8 angles, edges, baselines) Comment: From experimental calculation results for some types of free combined GPS – territorial networks, the following comments are given - Using robust estimation method combined with analysis chart of measurement results after adjustment of large free combined GPS – territorial networks for intuitive and reliable results - For large geodetic networks with reasonable redundancy value (r ≥ 0.5t) of free-ground mesh-GPS mixtures, the application of a solid estimation method with the selection of Huber weight function extended to detect and eliminates rough errors for reliable results - For large geodetic network with reasonable redundancy values (r ≥ 0.5t) of free combined GPS – territorial networks, if the number of measurements containing rough error of less than 10% of the total redundancy value and rough error value does not exceed 10m (10 times the square error of the measurement), then results of robust estimation method with extended Huber weight function are relatively affected by the rough errors 28 CONCLUSIONS AND RECOMMENDATIONS Conclusion From the theoretical studies, surveys and analysis of the experimental results of the optimal design method and the adjustment of free combined GPS – territorial networks, some conclusions could be drawn: Researched to apply suitable optimal design problem for free combined GPS – territorial networks The dissertation proposed the optimal design of free combined GPS – territorial networks according to the redundancy of measurement quantity with high efficiency The dissertation researched and applied the problem of solving and analyzing free combined GPS – territorial networks by robust estimation method even in case the measurement value contains rough errors with reliable results The retrieval algorithm has a clear advantage in the optimal design of free combined GPS – territorial networks, as it is very effective when adding new measurement quantities Triangular-edge triangular ground network and transfer network combined GPS measurement not only increase accuracy but also the ability to detect rough errors Recommendations: Apply variance-covariance estimation method to estimate variance of measurements of free combined GPS – territorial networks, which helps to determine the exact weight of the measured values Apply the free adjustment method to process the data of free combined GPS – territorial networks to avoid the effect of the original data error of free GPS – territorial networks LIST OF AUTHOR’S PUBLISHED SCIENTIFIC WORKS RELATED TO CONTENTS OF THE DISSERTATION A Scientific projects: Luu Anh Tuan (author, 2014)“Researching adjustment of free combined BPS - territorial networks in combination with Robust estimator in the conditions of Vietnam” a scientific project at grassroot level, code T15-29 B Articles: Vietnamese Luu Anh Tuan (2014), “Adjustment of combined GPS - territorial networks with regressive formula”, Natural Resources and Environment Magazine, Ministry of Natural Resources and Environment, volume (189)/4-2014 Luu Anh Tuan (2014), “Researching the dependence of GPS values to adjustment results in solving the free combined GPS territorial networks”, Natural Resources and Environment Magazine, Ministry of Natural Resources and Environment, volume 9(191)/5-2014 Luu Anh Tuan (2014), “Adjustment of free combined GPS territorial networks in combination with Robust algorithm”, Natural Resources and Environment Magazine, Ministry of Natural Resources and Environment, volume 11(193)/6-2014 Luu Anh Tuan (2014), “Optimal design of free combined GPS territorial networks using regressive formula”, Natural Resources and Environment Magazine, Ministry of Natural Resources and Environment, volume 16(198)/8-2014 Luu Anh Tuan ( 2014), “Researching Robust Kalman Filtering application in geometric adjustment”, the 21st Science Conference, Hanoi University of Mining and Geology, 11/2014 Luu Anh Tuan (2015), “Researching model of adjustment of free combined GPS - territorial networks in combination with Robust algorithm in conditions of Vietnam”, Natural Resources and Environment Magazine, Ministry of Natural Resources and Environment, volume 21(227)/11-2015 Luu Anh Tuan, Truong Quang Hieu (2015), “Student distribution law and its applicability in statistical test”, Natural Resources and Environment Magazine, Ministry of Natural Resources and Environment, volume 22(228)/11-2015 Luu Anh Tuan (2016), “Optimal design of geometric network based on GPS baselines and Robustness analysis”, Natural Resources and Environment Magazine, Ministry of Natural Resources and Environment, volume 19(219)/10-2016 Luu Anh Tuan (2016), “Applying Robustness method in analyzing combined GPS- territorial networks”, Natural Resources and Environment Magazine, Ministry of Natural Resources and Environment, volume 19(249)/10-2016 10 Luu Anh Tuan (2018), “Chosing weighting function of stable estimation in geometric networks”, Natural Resources and Environment Magazine, Ministry of Natural Resources and Environment, volume 12(290)/6-2018 11 Luu Anh Tuan (2018), “Comparing repeated weighting methods in geometric networks”, Natural Resources and Environment Magazine, Ministry of Natural Resources and Environment, volume 12(290)/6-2018 12 Hoang Ngoc Ha, Luu Anh Tuan (2019), “ Application of Robust adjustment and analysis of GPS - territorial and aerial networks”, Measuring and mapping science review, No 39/3-2019 English LUU Anh Tuan, TRUONG Quang Hieu (2014), “Reliability evaluation of Geodetic Horizontal control networks in Tunnel execution”, Proceedings of the 3rd international conference on Advances in Mining and Tunneling 21-22 October 2014, Vung Tau, Viet Nam Anh Tuan Luu (2016), “Application of correlation robust estimation in the adjustment of geodetic network”, GMMT2016 International symposium on Geo-Spatial and Mobile mapping technologies and summer school for Mobile mapping technology Anh Tuan Luu, Ngoc Giang Le (2016), “Application of weighting robust estimation in geodetic networks”, GMMT2016 International symposium on Geo-Spatial and Mobile mapping technologies and summer school for Mobile mapping technology Ngoc Giang Le, Anh Tuan Luu, Minh Hung Trương, Quang Hieu Trương (2016),“Strict adjustment of traverse without measuring angle of connection”, GMMT2016 - International symposium on Geo-Spatial and Mobile mapping technologies and summer school for Mobile mapping technology ... standard model N (1) Free combined GPS – territorial type (2) G -GPS (21 angles, baselines) G -GPS (21 angles, 13baseline) GS -GPS (21 angles, edges, and 13 baseline) GS -GPS (21 corners, 13 edges, and... combined GPS - territorial networks in conditions of Vietnam - Research to computer programming, serving optimal design and data processing Research Methods - Search methods: Search, collect documents... combined GPS - territorial networks for some large geodesic networks in Vietnam The contents of the research - Research overview of geodetic network construction work in Vietnam 2 - Research
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Xem thêm: 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 , 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