本文選題：點位測量隨機誤差 + 二維空間分布模型　； 參考：《中國科學(xué)院大學(xué)(中國科學(xué)院東北地理與農(nóng)業(yè)生態(tài)研究所)》2017年博士論文

【摘要】：GIS產(chǎn)品質(zhì)量是用戶最關(guān)心的問題之一,也是商業(yè)利潤得到保證的前提,空間數(shù)據(jù)位置不確定性研究正是針對該問題提出的。矢量空間數(shù)據(jù)包括空間點元、線元和面元,其中點元構(gòu)成線元,線元構(gòu)成面元。因此,點元位置不確定性是空間數(shù)據(jù)位置不確定性研究的基礎(chǔ)。該研究已形成了較為完整的理論體系,但還未應(yīng)用于實踐,其根本原因在于難以建立現(xiàn)實可用的點元誤差分布模型。因此,建立實際的點元誤差分布模型是位置不確定性理論應(yīng)用于實踐的第一步。關(guān)于點元誤差分布模型的研究主要集中在數(shù)字化對點誤差方面,而隨著現(xiàn)代測繪技術(shù)的迅猛發(fā)展,實地測量數(shù)據(jù)成為GIS空間數(shù)據(jù)的重要來源之一。因此,實地點位測量誤差分布模型的建立對于GIS空間數(shù)據(jù)位置不確定性研究具有越來越重要的意義�，F(xiàn)今測量學(xué)領(lǐng)域仍然采用傳統(tǒng)的“點位中誤差”對實地點位測量數(shù)據(jù)進(jìn)行質(zhì)量描述。然而“點位中誤差”作為一維精度指標(biāo)難以完整描述點位誤差二維分布模式,即無法準(zhǔn)確反映測定點位的空間位置不確定性。因此,對點位實地測量隨機誤差的二維分布模型進(jìn)行深入研究具有一定的理論和實際應(yīng)用價值。本文應(yīng)用現(xiàn)今常用的點位實地測量方法進(jìn)行大量實驗,結(jié)合概率論與數(shù)理統(tǒng)計知識和經(jīng)典測量平差的相關(guān)理論,建立不同測繪技術(shù)下點位實地測量隨機誤差的二維分布模型,并研究其變化規(guī)律,得出如下結(jié)論:1、揭示點位實地測量隨機誤差服從二維正態(tài)分布應(yīng)用數(shù)學(xué)方法對實地點位測量數(shù)據(jù)進(jìn)行檢驗,得出GPS RTK和經(jīng)典實地點位測量隨機誤差均服從二維正態(tài)分布。2、構(gòu)建點位實地測量隨機誤差平面分布描述指標(biāo)體系在點位實地測量隨機誤差服從二維正態(tài)分布的基礎(chǔ)上,計算誤差橢圓的幾何參量,依此構(gòu)建點位測量隨機誤差平面分布量化指標(biāo)體系:誤差分布方向、誤差分布大小與誤差分布形態(tài)。3、探究GPS RTK點位測量隨機誤差平面分布指標(biāo)的時間變化規(guī)律得出GPS RTK測點隨機誤差分布指標(biāo)隨地方恒星時呈現(xiàn)二次項傅里葉函數(shù)變化規(guī)律,并且分布指標(biāo)時間變化趨勢之間具有一定相關(guān)性。4、提出GPS單點定位系統(tǒng)誤差的數(shù)學(xué)改正模型發(fā)現(xiàn)GPS單點定位誤差隨地方恒星時呈現(xiàn)規(guī)律變化,依此建立GPS單點定位系統(tǒng)誤差數(shù)學(xué)改正模型,經(jīng)模型改正后定位精度得到較大提高。本研究建立了點位實地測量隨機誤差二維空間分布模型,為實地測繪產(chǎn)品的空間位置不確定性理論研究及實際應(yīng)用提供堅實的科學(xué)依據(jù)。
[Abstract]:The quality of GIS products is one of the most concerned issues for users, and it is also a prerequisite for the guarantee of commercial profits. The research on location uncertainty of spatial data is aimed at this problem. Vector spatial data includes spatial point element, line element and surface element, where point element constitutes line element and line element constitutes plane element. Therefore, point element location uncertainty is the basis of spatial data location uncertainty research. The research has formed a relatively complete theoretical system, but it has not been applied in practice, the fundamental reason is that it is difficult to establish the practical usable point error distribution model. Therefore, it is the first step of the application of position uncertainty theory to establish the actual point error distribution model. The research of point element error distribution model is mainly focused on digital point error. With the rapid development of modern surveying and mapping technology, field measurement data become one of the important sources of GIS spatial data. Therefore, it is more and more important to establish the error distribution model for GIS spatial data location uncertainty. In the field of surveying, the traditional "point error" is still used to describe the quality of the field data. However, as a one-dimensional precision index, the "point center error" can hardly describe the two-dimensional distribution model of the point position error, that is, it can not accurately reflect the uncertainty of the spatial position of the measured point. Therefore, it is of great theoretical and practical value to study the two-dimensional distribution model of random errors in spot measurement. In this paper, a large number of experiments are carried out by using the commonly used spot field measurement methods, combining with the knowledge of probability theory and mathematical statistics and the relevant theories of classical measurement adjustment, a two-dimensional distribution model of random error of spot field measurement under different surveying and mapping techniques is established. By studying its changing law, the following conclusion is drawn: 1. It reveals that random errors of spot field measurement can be checked by mathematical method from two-dimensional normal distribution. It is concluded that the random errors of both GPS RTK and classical spot measurements are based on the two-dimensional normal distribution, and the system of describing the plane distribution of random errors of the spot field measurement is constructed on the basis of the two-dimensional normal distribution of the random errors of the spot field measurements. The geometric parameters of error ellipse are calculated, and the quantization index system of random error plane distribution of point position measurement is constructed according to this system: the direction of error distribution, The size of error distribution and the shape of error distribution. 3. The temporal variation rule of random error plane distribution index of GPS RTK spot measurement is studied. The random error distribution index of GPS RTK measurement point presents quadratic Fourier function variation law with local star time. There is a certain correlation between the time variation trend of the distribution index. 4. The mathematical correction model of the GPS single point positioning system error is proposed. It is found that the GPS single point positioning error varies with the local star time. According to this model, the error correction model of GPS single point positioning system is established, and the positioning accuracy is greatly improved after the model correction. In this study, a two-dimensional spatial distribution model of random errors in spot survey is established, which provides a solid scientific basis for the theoretical research and practical application of spatial position uncertainty of field surveying and mapping products.
【學(xué)位授予單位】：中國科學(xué)院大學(xué)(中國科學(xué)院東北地理與農(nóng)業(yè)生態(tài)研究所)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2017
【分類號】：P228.4;P208

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