The Models And Experiments For Positional Uncertainties Of Spatial Data In GIS

Based on the review of the recent developments concerning the uncertainty of the spatial data in GIS, this paper studies the models of the positional uncertainty of the foundational feature in GIS, and the digital experiment for investigating the errors of curves is carried out. The main resultsare as follow:(1) The personal viewpoints on the concepts about the uncertainties in GIS are declared.(2) An useful property of the error ellipse is revealed and proved: 'The random point withtwo-dimensional normal distribution falls on one side of the tangent line of the error ellipse with a constant probability, and this probability is independent of the tangent point'.(3) The confidence regions of points, lines and polygons are established respectively. The relations between the regions established and their confidence levels are discussed analytically by using the probability theory.(4) The Monte Carlo method is applied to the study of the positional uncertainties. The general procedure of simulating the confidence level is provided and the confidence levels of the different regions are simulated. Numerical example shows that the actual confidence level of a point depends chiefly on the covariance matrix of the field survey random vector and the shape of the confidence regions, and the confidence level of a line is almost independent of the length of the line.(5) An error model named the stochastic error process of curves is proposed to describe the errors of curves. In terms of the stochastic process, five characteristics concerning the local error of curves, namely, mean error function, accurate function, absolute error function, standard error belt and the correlation function of errors are put forwarded. And the total error of a curve can be expressed by a mean square integral of the stochastic error process. The probabilistic meanings and geometric meanings of the characteristics mentioned above are also discussed.(6) A scan digitizing test is designed in order to check the efficiency of the model proposed. In the test, two pieces of curves are digitized for more than 100 times and lots of data concerningthe errors of curves are obtained. The impacts of the speed of digitization, person, the density of digitization, the scale of the screen, the number of control points and the pretreatment of the image are also investigated in the test.(7) The formulae for computing the sample functions of the stochastic error process are given and 100 sample functions are derived from the digitizing test. The cause and the impact of system errors are analyzed. The error distributions of points and its statistical correlation are discussed. The error characteristics of curves are estimated and shown in manner of graph based on the sample functions. The result of the test shows that the system error in digitized map data isn't negligible, and the errors of points on curves are chiefly dependent on the curvature and the concavity of the curves. Finally, a comparison is made to illustrate the impacts of factors mentioned above.