The Equivalent Probability Density Error Model To Linear Entity In Vector GIS

In the domain of GIS uncertainty research, positional uncertainty and attribute uncertainty are of the major research objects. Spatial points, line segments, polygons and bodies are of the basic contents to GIS positional uncertainty research, While positional uncertainty research of line segment is also the base for that of polygons and bodies. So, positional uncertainty theory research of linear entity counts for much for GIS positional uncertainty theory research.People have explored in the domain of GIS uncertainty for a long term and obtained a series of theory achievements, accumulated much of experience, but because of the difficulty and complexity of GIS uncertainty theory, together with the localization of the people' s comprehension during various history stage, now there are many theory questions are out of whole perceived and reasonable solved, these questions are mainly embodied as following:I. Error distributing mechanism of linear entity;II. Modeling mechanism and geometric explanation on Error model of linear entity;III. Normal mathematics expression on error model band(body) and its corresponding boundary envelop line (surface);IV. Visualization operation method and application research in two-dimensional field or three-dimensional field on linear entity;V. Scientific indexes for precision evaluation of linear entity.These questions are of the central obstacles which restrict positional uncertainty theory research and practical application. If these questions will not be solved systematically, then the GIS positional uncertainty theory not only can not be put into practice and application, but also can not be put into other complex uncertainty theory research.Thanks to GIS is a kind of compute application subject, while GIS positional uncertainty theory research is based on compute technology, so, in order to take full advantage of the compute technology, considering the discrete attribute of the probability density distributing function of random line segment, in this dissertation, numerical value algorithm is regarded as the main research method. At the same time, based on the research actuality of GIS positional uncertainty theory and some of the basic subjects, such as probability theory, (spatial)statistics, fuzzy mathematics, matrix theory, random process, spatial analytic geometry and tridimensional geometry, and so on, the GIS positional uncertainty theory of linear entity has been tidied systematically and researched deeply, and then a set of rigorous and integrated GIS positional uncertainty theory and operation ways of linear entity are brought forward, some cases study and conclusions analysis are provided, the latest research achievements and the correlative conclusions of GIS positional uncertainty theory are also expressed by means of visualization technology to the greatest extent.The major research contents can be generalized as following:Chapter one , introduction. In this chapter, GIS uncertainty is introduced from the world uncertainty, some of the correlative concepts are expounded, the research actuality of GISuncertainty theory is discussed, and the research contents of this dissertation are put forward.Chapter two, research retrospection on GIS positional uncertainty of linear entity.In this chapter, the research course of linear entity positional uncertainty theory and the evolvement history of error model modeling mechanism in GIS uncertainty theory are together discussed, the advancements and illogicalities of each kind of error model are researched, and the corresponding theoretical deficiencies are pointed out based on error distribution, modeling mechanism, geometric explanation, scale of error model , etc. Base on which , the detailed research contents and objects are brought forward lastly.Chapter three, research on plane similitude conversion modeling technology in the quality control for GIS digital dada.The technologies of gross error detection, criterion for model reliability, model optimization and precision examination for the conversion data during the similitude conversion modeling course of GIS digital dada are researched thoroughly, and then a set ofsystematical and rigorous theory and operation method on plane similitude conversion------information diffusion estimation model on plane similitude conversion is brought forward. Based on the information diffusion estimation model, some of systematic errors and gross errors which are produced from coordinates conversion or drawings transmutation will be eliminated to great extent.Chapter four, research on "The Equivalent Probability Density Error Model" of 2-dimensional random line segmentChapter four and the following chapter five are of the most importance of the dissertation.The simplification expression of 2-dimensional random point probability density distribution function has been deeply researched, some of the properties and correlative conclusions are deduced or proved, based on which, the theoretical foundation has been established for the research of error model and the following concepts of "figure gene" and "standard error ellipse expansion or shrink coefficient".Based on continuous viewpoint and random process, the expression and the random model of probability density distribution function of random linear segment are researched, the spatial figure characteristics of 2-dimensional random point probability density distribution function is discussed, the common grounds between the research of 2-dimensional random linear segment and the research of 2-dimensional random point are pointed out, and the information matrix of arbitrary points on the linear segment has been deduced too, based on which, the error models are classified and the theoretical deficiencies on the modeling mechanism of the accepted errormodel band-"g-band" are also indicated, and then the concepts of "The equivalentprobability density error model"(marked as 'TEPDEM" in brief) and "The standard error ellipse expansion or shrink coefficient "( marked as "SEEC" in brief) are brought forward, 'TEPDEM" mechanism and its corresponding calculation formulae are narrated and educed.Based on the numerical value algorithm and the modeling mechanism, mathematical expressions and visualization operation methods of 'TEPDEM" and its corresponding boundary envelop are deeply researched, and the probability calculation method on randomlinear segment drops in its corresponding "TEPDEM" is presented, based on which, the error model scale has been ascertained successfully.Lastly, the area calculation method on 'TEPDEM" of linear segment is deduced, from which the precision description index to positional uncertainty of 2-dimensional linear entity ------the average band width to 'TEPDEM" has been ascertained.Chapter five, research on 2- dimensional ecumenic curves "TEPDEM"Based on the research actuality and some of the theoretical deficiencies of positional uncertainty theory of ecumenic curves, the modeling mechanism to "TEPDEM" of 2-dimensional anomalous curves has been deeply studied.Based on the spline method and the numerical value algorithm, the ascertainment approaches of cubic spline fitting curve, the discrete points count on the fitting curve which can ensure GIS research precision, the information matrix of arbitrary points on fitting curve, and "TEPDEM" of the fitting curve, etc .are all solved. In addition, the ascertainment theory on the boundary envelop of "TEPDEM" has been researched too, and so a kind of new method for the coordinates calculation of error model boundary envelop is brought forward.The probability calculation method on fitting curve drops in the corresponding 'TEPDEM" is educed, and some of the cases on the modeling theory, visualization operation and probability calculation of 'TEPDEM" of fitting curve are presented.Lastly, the orientation precision description index on 'TEPDEM" of fitting curve is also educed.Chapter six, research on 3- dimensional linear segment "TEPDEM"The research actuality on positional uncertainty theory of spatial linear segment has been studied, and the illogicality on its modeling mechanism is also pointed out In order to take advantage of the modeling mechanism of "TEPDEM", considering the precision property of spatial coordinates , the reason why to select the plane x-O-y as projection plane is then discussed, so, a "flat roof" for following research is built successfully.The information matrix of arbitrary point on the projection linear segment to 3-dimensional linear segment in the plane x-o-y has been deduced. Based on "TEPDEM", the concepts of "figure gene" and "scale gene" of "TEPDEM" are brought forward. Based on the probability confident level of the projection line segment drops in the corresponding "TEPDEM", the ascertainment method of "scale gene" has been studied, and then according to the "figure gene" and "scale gene", the figure and the scale of "TEPDEM" of 3- dimensional linear segment are solved successfully.The information matrix of arbitrary point on spatial linear segment is researched, based on which, the standard error ellipsoid parameters to arbitrary point on spatial linear segment (the axis length of the standard error ellipsoid and its corresponding spatial azimuth) are then deduced, and according to the spatial coordinates, "figure gene" , "scale gene" and its corresponding standard error ellipsoid parameters of the arbitrary point on the spatial linear segment, the analytic expression of the spatial error ellipsoid which can be used to describe the positional uncertainty of the arbitrary point on the spatial linear segment has been educed too.Lastly, the envelop surface ascertainment theory and the orientation precision description index on "TEPDEM" of the spatial random linear segment are also deeply researched.Chapter seven, research on 3- dimensional ecumenic curves 'TEPDEM"The spatial curve fitting model------Bezier curve has been introduced and studied, and thedeficiency of Bezier curve when it is used for positional uncertainty research is pointed out The reasons why we utilize the spline method are discussed, the spatial fitting curves function expression based on the spline method is constructed, the properties of "continuous, quadratic differential and passing through all characteristic points" to the constructed function are ensured, a foundation for positional uncertainty research of spatial anomalous curves is built.Based on the complex Simpson formula and 0.1 times subject map precision, the partition points numbers m(i) between both of the arbitrary adjacent characteristic points of spatial fitting curve has been educed by means of iteration algorithm , so the precision guarantee and theoretical support for how to take advantage of numerical value algorithm to research positional uncertainty of the spatial fitting curve are now provided.Based on random process , the information matrix of arbitrary point on the projection curve of 3- dimensional fitting curve in the plane x-O-y is educed. Based on 'TEPDEM" of the projection curve in the plane x-O-y, the "figure gene" and "scale gene" of the spatial fitting curve positional uncertainty error model body are ascertained. And based on the probability confident level of the projection curve drops in the corresponding 'TEPDEM", the ascertainment method of "scale gene" is presented . According to the "figure gene" and "scale gene" , the figure and the scale of "TEPDEM" of 3- dimensional anomalous curve are solved successfully.The information matrix of arbitrary point on spatial fitting curve is researched, based on which, the standard error ellipsoid parameters to the arbitrary point on spatial fitting curve are then educed, and according to the spatial coordinates, together with "figure gene" , "scale gene" and its corresponding standard error ellipsoid parameters of the arbitrary point on the spatial fitting curve, the analytic expression of the spatial error ellipsoid which can be used to describe the positional uncertainty of the arbitrary point on the spatial anomalous curve is educed .based on which, the modeling mechanism of spatial anomalous curve "TEPDEM" is now solved successfully.Lastly, the envelop surface ascertainment theory and the orientation precision description index on 'TEPDEM" of spatial anomalous curve are researched deeply.All in all , based on numerical value algorithm and the modeling mechanism of "TEPDEM", the positional uncertainty theory of linear entity in vector GIS is tidied systematically and researched deeply ,and the central contributions and innovations about this dissertation are summarized as following:The modeling technology of plane similitude conversion is researched with creativity based on fuzzy information optimizing theory , and a set of systematical and rigorous theory and operation method on the technologies of gross error detection, judgement criterion formodel reliability, model optimization and precision evaluation for the conversion data during the similitude conversion modeling course of GIS digital dada are presented, based on which, the systematic errors and the gross errors in digital data which are produced from the course of coordinates conversion or drawings transmutation will be eliminated to great extent.The modeling mechanism of "TEPDEM" is researched deeply------the concepts of"standard error ellipse expansion or shrink coefficient" , "figure gene" , "scale gene", together with their corresponding calculation formulae and operation methods are presented based on the modeling mechanism of "TEPDEM". The probability calculation method on linear entity (planar linear entity or projection of spatial linear entity) falls in its corresponding 'TEPDEM" is also deeply researched , and the conclusion of "The probability on linear entity falls in its corresponding 'TEPDEM" is relational with the coordinates precision of linear entity characteristic points" is proved theoretically . Based on probability theory , the figure and the scale of "TEPDEM" of linear entity are solved successfully, and which established the theoretical basis for production and practical applications of positional uncertainty theory in vector GIS.Based on numerical value algorithm and "TEPDEM", a set of rigorous theory and scientific method on error model boundary envelop line (or surface) are researched and presented.Considering the discrete attribute of the spatial probability density distributing function of linear entity, numerical value algorithm is systematically adopted for the theory research of linear entity positional uncertainty in vector GIS------In order to take full advantage of the computer visualization technology, the visualization operation ways and means on error model and its corresponding boundary envelop of linear entity are put in practice by discrete approaches , based on which ,the modeling mechanism of error model is clear discovered , the research thoughts on GIS uncertainty theory are then suddenly enlightened.Whereas the practical requirements about production and application , the orientation precision description indexes to "TEPDEM" of linear entity are also deeply researched, and then the concepts of " The average band width of error model band " and " The average cross section area of error model body " are presented.In conclusion, based on numerical value algorithm and the modeling mechanism of error model, the positional uncertainty theory of linear entity in GIS has been tidied systematically and researched deeply, a brand-new approach on the theory research of vector GIS positional uncertainty is inaugurated, and the theory and method which can be used for reference are also provided, at the same time, the theory basis for GIS positional uncertainty research has been tamped to great extent.