Two-dimensional Distribution Model For Measured-point Random Error

The data quality of the GIS product is one of the most concerned problems for users,and the premise for ensuring the commercial profit.The uncertainty of the position of spatial point,line and surface segment is the main part of the positional uncertainty of spatial data.The vector spatial data includes point element,line element and surface element.The line element is formed by point element,and surface element is formed by line element.So positional uncertainty of point element is the research foundation for the positional uncertainty of the spatial data.The comparatively complete theoretical system has been established for spatial position uncertainty,but has not yet been applied to practice.The primary cause is lacking practical uncertainty model of point element.So it is the first step for the application of the spatial positional uncertainty theory that establishing practical error distribution model of point element.In recent years,the scan digitization positional errors is the major research contents of the error model for the point element.However,with the rapid development of the surveying and mapping technology,the field digital measurement data becomes the major data source for GIS spatial data.Therefore,the exact description for the positioning error of the field surveying data becomes more and more important.Nowadays,the geodesy field still takes the traditional “mean square error” as the description indicator to describe the quality of the field measured-point.However,the mean square error as a one-dimensional precision indicator is difficult to exactly describe error status of the twodimensional point,and is unable to accurately express spatial position uncertainty of point element.So it is more and more important to study the two-dimensional error model of the measured-point data.Based on the probability and mathematical statistics and classic survey adjustment theory,this paper establishes two-dimensional error model for field measured-point data of different surveying mapping technology through statistical analysis of the measured data,and studies the change rule of the model.The main results are as follows:1?Revealing the field positional random error fits two-dimensional normal distributionApplying mathematical methods to test field point-measured data,the result is that positional random error of GPS RTK and classical field point measurement fit two-dimensional normal distribution.2?Building the indicator system for describing the positioning random error horizontal distribution(PREHD)Based on the field positional random error fitting the two-dimensional normal distribution,the quantitative indicator system of PREHD is constructed by geometric parameters of the normal error ellipse.The specific indicators are as follows: the error distribution orientation,size and shape.3?Exploring the temporal variation rule of the GPS RTK PREHDGPS RTK PREHD indicators present regular change of the two-term Fourier function with sidereal time.And there is correlation between the temporal variation trends of different GPS RTK PREHD indicators.4?Proposing a the mathematical correction model for system error of GPS single-point positioning(SPP)It is revealed that positioning error of GPS SPP presents regular variation along with the local sidereal time.Based on the temporal variation rules,the mathematical correction model is built.The corrected positioning accuracy has been greatly improved.This research establishes the horizontal distribution model of field positioning random error.The results provide solid scientific basis for the spatial positioning uncertainty of the field surveying products,and develop the quantitative description theory of the quality of point-measured data.