Entropy Of Surveying Data Error Distribution And Application

Abstract:Under a certain condition, the surveying error distribution of surveying data acquired must be obvious. The characteristics investigation of surveying error distribution is a prerequisite for error analysis and data processing. The surveying data is toward massive, dynamic and multi-resource error. It is limited for the classical error theory to process present type of surveying data. The main limitations summarized as follow:①the limitation of uncertainty expressed by error,②the uniquity of error representation means,③the entanglement of error classification,④the complexityof error synthesis. In view of the existing problems in the data processing, surveying uncertainty is used to measure data uncertainty and assess data quality in the field of GIS and measurement.The uncertainty of surveying data is actually a kind of generalized error. From the perspective of information theory, data acquisition, error processing and the quality evaluation of surveying data is a process of information transmission. Because information entropy is used to measure the uncertainty of random variables, it can be used to study data uncertainty. Entropy is one of the distribution digital characteristics, expressed by the form of probability distribution and the range of probability distribution. Study on the measurement data error distribution entropy is the basis of expanding the entropy theory cited in the field of surveying and data processing, is a prerequisite for investigating data uncertainty based on entropy, and is an effective way to expand the generalized error theory. The research of surveying data error distribution entropy has been achieved some results in the past half century, but there are still some problems as follows:1) The entropy can reflect surveying data uncertainty under a certain observation conditions, but how to estimate different distribution entropy, and how to get the mechanism of error entropy et al issues is lack of investigation systematically.2) Contaminated distribution once promoted the development of surveying data processing theory, and the probability density function 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 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.