expression uncertainty caused the difficulty of its entropy estimation.Contaminated distribution entropy, especially, the contaminated normal distribution entropy estimation,is not solved totally by present research. 3)The P-norm distribution is also an important distribution in the development of surveying data processing theory,its accurate calculation entropy complexity because of its probability density function expression is very complex,and it is not suitable for practical application.P-norm distribution entropy calculation can be effectively reduced the need for further research to solve. 4)Gross error must be existed in surveying data acquisition,the contamination rate display the influence degree of gross error,statistics in the practical application of gross error is often affected by the threshold of interference.Contamination rate estimation based on entropy also need perform more investigations. To solve these problems about surveying data distribution entropy,I carried out some research in this paper and obtained outcome as follows: 1)The theory of surveying data entropy,including the concept of entropy and basic nature,relationship between entropy and error, uncertainty,distribution and weigh et al. 2)The entropy law of surveying data error distribution,including the calculation methods of common distribution,the error entropy and the mechanismof error entropy. 3)Estimation method of the contaminated normal distribution entropy,the models of contaminated normal distribution probability density function was investigated by Kullback-Leibler distance.The probability density function difference of two kinds of model is related to mean shift parameter and the variance inflation factor closely when the main distribution is standard normal distribution and the relationship is nonlinear proportional.It is confirmed that two kinds of general model probability density function can not adapt to estimate contaminated normal distribution entropy and entropy coefficient.An approximate formula is suggested for entropy estimation of contaminated normal IV 万方数据
expression uncertainty caused the difficulty of its entropy estimation．Contaminated distribution entropy, especially, the contaminated normal distribution entropy estimation，is not solved totally by present research． 3)The P—norm distribution is also an important distribution in the development of surveying data processing theory,its accurate calculation entropy complexity because of its probability density function expression is very complex，and it is not suitable for practical application。P-norm distribution entropy calculation can be effectively reduced the need for further research to solve． 4)Gross error must be existed in surveying data acquisition，the contamination rate display the influence degree of gross error,statistics in the practical application of gross error is often affected by the threshold of interference．Contamination rate estimation based on entropy also need perform more investigations． To solve these problems about surveying data distribution entropy,I carried out some research in this paper and obtained outcome as follows： 1)The theory of surveying data entropy,including the concept of entropy and basic nature，relationship between entropy and error, uncertainty,distribution and weigh et a1． 2)The entropy law of surveying data error distribution，including the calculation methods of common distribution，the error entropy and the mechanismoferror entropy． 3)Estimation method of the contaminated normal distribution entropy,the models of contaminated normal distribution probability density function was investigated by Kullback-Leibler distance．The probability density function difference of two kinds of model is related to mean shift parameter and the variance inflation factor closely when the main distribution is standard normal distribution and the relationship is nonlinear proportional．It is confirmed that two kinds of general model probability density function can not adapt to estimate contaminated normal distribution entropy and entropy coefficient．An approximate formula is suggested for entropy estimation of contaminated normal 万方数据
distribution. 4)The P-norm distribution entropy simplified method was investigated. It is considered that the probability density function complexity of P-norm distribution is not conducive to the entropy calculation and practical application.The P-norm distribution entropy can be expressed by combination of simple distribution entropy approximately,simplified the calculation process. 5)The GPS RTK error of observation data is analyzed by using entropy method,and an effective means for surveying data error analysis based on entropy has been constructed. 6)An estimation method of contamination rate based on entropy was proposed.It is useful for gross error statistic to avoid limited error selection.Two models of data main distribution were suggested to investigate contamination rate and the estimation methods of contamination rate based on entropy were given out.A numerical simulation was performed to analyze the influence of entropy truncation error on data contamination rate estimation.It is less influence for entropy truncation error to contamination rate estimation based on entropy. Keywords:entropy,entropy coefficience,uncertainty,contaminated normal distribution,P-norm distribution Classification:528.1 万方数据
distrlbution． 4)The P—norm distribution entropy simplified method was investigated． It is considered that the probability density function complexity of P—norm distribution is not conducive to the entropy calculation and practical application．The P—norm distribution entropy can be expressed by combination of simple distribution entropy approximately,simplified the calculation process． 5)The GPS RTK error of observation data i s analyzed by using entropy method，and an effective means for surveying data error analysis based on entropy has been constructed． 6)An estimation method of contamination rate based on entropy was proposed．It is useful for gross error statistic to avoid limited error selection．Two models of data main distribution were suggested to investigate contamination rate and the estimation methods of contamination rate based on entropy were given out．A numerical simulmion was performed to analyze the influence of entropy truncation error on data contamination rate estimation．It iS 1ess influence for entropy truncation error to contamination rate estimation based on entropV． Keywords：entropy，entropy coefficience，uncertainty，contaminated normal distribution，P—norm distribution Classification：528．1 V 万方数据
目录 第1章绪论 1.1研究背景与意义 1.2国内外相关研究评述… .7 12.1测量数据处理理论的发展.… 7 1.2.2熵的概念与发展 .11 12.3基于熵的测量数据处理研究现状及问题 .13 1.3研究内容、目标及论文组织… 16 1.3.1研究内容 …16 1.3.2研究目标 17 1.3.3论文组织 .18 第2章测量数据误差处理研究中的熵 21 2.1信息熵及其性质 21 2.2测量现象的信息熵… 23 2.3熵与误差的关系… .24 2.4熵与不确定度的关系 .25 2.5熵与分布的关系…。 .26 2.6熵与权的关系 27 2.7本章小结 .29 第3章测量数据误差分布的熵律 .31 31测量数据处理常见分布的熵 .31 3.1.】正态分布的熵… .31 3.1.2均匀分布的熵. .34 3.1.3拉普拉斯分布的熵 36 32熵意义上的测量数据误差… 37 3.2】基于熵的不确定度区间39 3.2.2测量数据误差分布的熵值特性… .40 3.23误差分布概率密度函数求解的最大熵方法 41 3.3误差熵的作用基础.… …42 3.3.1基于熵系数的误差分布分析… 42 3.3.2误差嫡带模型 .42 3.3.3误差熵的截断估计… 43 3.3.4误差熵的合成 …44 万方数据
目录 第1章绪论……………………………………………………………………1 1．1研究背景与意义…………………………………………………………1 1．2国内外相关研究评述……………………………………………………7 1．2．1测量数据处理理论的发展…………………………………………．7 1．2．2熵的概念与发展……………………………………………………1 1 1．2．3基于熵的测量数据处理研究现状及问题…………………………13 l_3研究内容、目标及论文组织…………………………………………．．16 1．3．1研究内容……………………………………………………………16 1．3．2研究目标……………………………………………………………1 7 1．3．3论文组织……………………………………………………………18 第2章测量数据误差处理研究中的熵………………………………………21 2．1信息熵及其性质………………………………………………………．．2l 2．2测量现象的信息熵……………………………………………………一23 2-3熵与误差的关系………………………………………………………．．24 2．4熵与不确定度的关系…………………………………………………．．25 2．5熵与分布的关系………………………………………………………一26 2．6熵与权的关系……………………………………………………………27 2．7本章小结………………………………………………………………．．29 第3章测量数据误差分布的熵律……………………………………………3 1 3．1测量数据处理常见分布的熵…………………………………………．．31 3．1．1正态分布的熵………………………………………………………31 3．1．2均匀分布的熵………………………………………………………34 3．1．3拉普拉斯分布的熵…………………………………………………36 3．2熵意义上的测量数据误差……………………………………………一37 3．2．1基于熵的不确定度区间……………………………………………39 3．2．2测量数据误差分布的熵值特性……………………………………40 3．2．3误差分布概率密度函数求解的最大熵方法………………………41 3．3误差熵的作用基础……………………………………………………．．42 3．3．1基于熵系数的误差分布分析………………………………………42 3．3．2误差熵带模型………………………………………………………42 3．3．3误差熵的截断估计…………………………………………………43 3．3．4误差熵的合成………………………………………………………44 万方数据
3.4本章小结 .44 第4章污染正态分布的熵估算研究 47 4.1污染分布与污染正态分布… 47 4.2污染正态分布的概率密度函数 …48 4.2.1均值漂移模型概率密度函数 …48 4.2.2方差扩大模型概率密度函数 …48 4.2.3分析与讨论… 48 4.3污染正态分布密度函数的差异性 49 4.3.1 Kullback-Leibler距离. .49 4.3.2 Kullback-Leibler距离下的污染正态分布密度函数差异性.49 4.4污染正态分布熵的近似估算.51 4.4.1污染正态分布熵的特性分析… .51 4.4.2基于污染率的污染正态分布熵的近似估算 54 4.4.3算例 .55 4.5本章小结.56 第5章P范分布的熵估算研究. ..57 5.1P-范分布的概率密度函数 57 5.1.1P-范分布概率密度函数的两种表达 57 5.1.2P范分布概率密度不同表达形式的一致性证明 .58 5.2P-范分布熵的严密计算. .59 5.2.1P-范分布熵的严密计算公式推导 .59 5.2.2P-范分布熵的特性分析… .61 5.3P.范分布熵的一种近似估计 .62 5.3.1P-范分布的近似表示. …63 53.2P.范分布熵的近似估计.. .…64 5.3.3数值演算及分析… 64 5.4本章小结 .66 第6章熵在测量数据处理中的应用.… .67 6.1 GPS RTK观测数据误差分布的熵分析 .67 6.1.1 GPS RTK观测数据误差分布研究现状与数据来源.67 6.1.2熵分析方法 .68 6.1.3计算与分析… .69 6.1.4本例结论. 70 6.2基于熵的数据污染率估算研究70 万方数据
3．4本章小结………………………………………………………………一44 第4章污染正态分布的熵估算研究………………………………………．47 4．1污染分布与污染正态分布……………………………………………．．47 4．2污染正态分布的概率密度函数………………………………………一48 4．2．1均值漂移模型概率密度函数………………………………………48 4．2．2方差扩大模型概率密度函数………………………………………48 4．2．3分析与讨论…………………………………………………………48 4．3污染正态分布密度函数的差异性……………………………………．．49 4。3。1 Kullback．Leibler距离………………………………………………．49 4．3．2 Kullback．Leibler距离下的污染正态分布密度函数差异性………49 4．4污染正态分布熵的近似估算…………………………………………一5l 4，4．1污染正态分布熵的特性分析………………………………………51 4．4．2基于污染率的污染正态分布熵的近似估算………………………54 4．4．3算例…………………………………………………………………55 4．5本章小结………………………………………………………………一56 第5章P一范分布的熵估算研究……………………………………………一57 5．1 P．范分布的概率密度函数………………………………………………57 5．1．1 P一范分布概率密度函数的两种表达………………………………．57 5．1．2 P一范分布概率密度不同表达形式的一致性证明…………………．58 5．2 P．范分布熵的严密计算…………………………………………………59 5．2．1 P一范分布熵的严密计算公式推导…………………………………．59 5．2．2 P．范分布熵的特性分析……………………………………………．61 5．3 P．范分布熵的一种近似估计……………………………………………62 5．3．1 P．范分布的近似表示………………………………………………．63 5．3．2 P．范分布熵的近似估计……………………………………………．64 5．3．3数值演算及分析……………………………………………………64 5．4本章小结………………………………………………………………～66 第6章熵在测量数据处理中的应用………………………………………．67 6．1 GPS RTK观测数据误差分布的熵分析………………………………．．67 6．1．1 GPS RTK观测数据误差分布研究现状与数据来源………………67 6．1．2熵分析方法…………………………………………………………68 6．1．3计算与分析…………………………………………………………69 6．1．4本例结论……………………………………………………………70 6．2基于熵的数据污染率估算研究………………………………………．．70 万方数据
6.2.1基于熵的数据污染率估算方法… 71 6.2.2熵计算的截断误差对污染率估算的影响分析.72 6.2.3算例及分析 .73 6.2.4本例结论… .74 6.3本章小结… .75 第7章总结与展望 …77 7.1全文总结 .77 7.2研究展望… .78 参考文献… 81 攻读学位期间主要的研究成果 .91 1.主持和参与的科研与生产服务项目.91 2.在读期间第一作者已发表的论文91 致谢93 通 万方数据
6．2．1基于熵的数据污染率估算方法……………………………………71 6．2．2熵计算的截断误差对污染率估算的影响分析……………………72 6．2．3算例及分析…………………………………………………………73 6．2．4本例结论……………………………………………………………74 6．3本章小结………………………………………………………………．．75 第7章总结与展望…………………………………………………………．77 7．1全文总结………………………………………………………………．．77 7．2研究展望………………………………………………………………．．78 参考文献……，………………………………………………………………．．8l 攻读学位期间主要的研究成果………………………………………………．91 1．主持和参与的科研与生产服务项目………………………………………9l 2．在读期间第一作者已发表的论文………………………………………一91 致谢……………………………………………………………………………93 万方数据