Theory And Approach On Management Of The Very Large-Scale Symmetrical Matrices In Geomatics

A symmetrical matrix in Geomatics is one of the important fundamental information which has been set up for many years,and it has played an important role in such fields as the analysis of the fundamental information,spatial geodesy,photogrammetry & remote sensing,the real-time deformation monitoring on crust or large structure and a nation's major scientific decision-making.When managing the general geomatic information,the very large-scale symmetrical matrices in geomatics must be effectively stored, managed and shared in order to make full use of its important role in the informationized geomatics.The symmetrical matrices have been generated every day in such fields as geodesy,photogrammetry & remote sensing and the real-time deformation monitoring on crust or large structure.And their scale has been increasingly and rapidly expanded.The data management of symmetrical matrices based on the ASCâ…¡text file management system has been increasingly faced with some great difficulties and challenges.This thesis aims to research the geomatics data management based on the symmetry-relationship model(SR_Model).The SR_Model is employed in the thesis to extend the relationship database management system(RDBMS),and the symmetry-relationship database management system(SR_DBMS) is constructed to manage efficiently the very large scale symmetrical matrices in geomatics when the relationship tables are managed.The main research finished is listed as follows:1) The scale-expanding features of the geomatics symmetrical matrices are analyzed.The results show that the symmetrical matrices have not been directly and conveniently managed by the RDBMS due to their half-structural properties-there are no fixed fields and the column number varies with the row number at the same time.2) During the past few decades,for the compression of a symmetrical matrix,the derived index transform formulae have been used to calculate the post-compression indices from the original indices.The inverse index transform formulae that used to calculate the original indices from the post-compression indices are derived in this thesis.These formulae are systematized as the index transform theorems of a symmetrical matrix.These theorems fully reveal the structural information of a given symmetrical matrix and make up the mathematic foundation of the SR Model.3) The SINEX format in the International Terrestrial Reference Frame(ITRF) data sets is analyzed by using the index transform theorems,and two redundant fields are found in the SINEX file's covariance matrix.Therefore,an elementary suggestion to improve the SINEX format is put forward.Based on those formulae,two new concepts such as the relative running efficiency and the timing microscope function are proposed to explore the post-test of algorithm efficiency.The results show that the improved SINEX format suggested yet belongs to the text file management system.4) A new researching idea is therefore raised in this thesis.First, the half-structural symmetrical matrices without fixed fields are converted into the full-structural relationship tables with fixed fields using the index transform formulae.Then,the symmetry-relationship databases are set up in accordance with extended relationship principles to manage the converted symmetrical matrices.Finally,the managing results by SR_DBMS are converted into the original form of the symmetrical matrices to be conveniently used by the users.5) The theory based on the SR_DBMS is tentatively developed, which includes:symmetry-relationship data model(SR_Model),the conception and theory system on SR_DBMS,the symmetry-relationship structural query language(SR_SQL), symmetry-relationship view(SR_V),and so on.6) The symmetry-relationship module(SR_Module) is initially developed in the software environment of the Windows Vista and Visual FoxPro 9.0,with the example of some datasets in ITRF2000 and ITRF2005,the experiments of the function tests and the efficiency tests are performed according to the principle of the software engineering.This research shows that the SR_DBMS with no loss of efficiency or convenience of management of relationship tables can save the memory size of disks by 65.8%and can improve the time efficiency by more than a hundred times when managing very large scale symmetrical matrices,compared with the traditional ASCâ…¡file management system.The datasets of ITRF,whose symmetrical matrices always occupy more than 90%of the space,are typical geomatics datasets with very large scale of symmetrical matrices,and can be fully managed with the SR_DBMS.