时间序列异常值探测的Bayes方法及其在GNSS动态数据处理中的应用

Processing outliers is one of the core contents of GNSS dynamic data processing and quality control system and is also an important premise for obtaining high precision, robustness and reliable results of navigation and position. This project proposes a thorough new approach, Bayesian method, for detecting outliers in time series based on modern statistical theory and technology. Firstly, from the point of Bayesian hypothesis testing theory, a set of Bayesian methods for time series outlier detection, type distinction and abnormal magnitude estimation and correction are proposed based on the posterior probabilities of different types of classification variables. Secondly, starting from analyzing masking causes and manifestations of outlier patches detection, an adaptive Gibbs sampling algorithm is designed to correctly calculate the posterior probabilities of classification variables, so as to prevent the occurrence of masking phenomena effectively. Finally, a Bayesian method for abnormal magnitude estimation and calculation is proposed in the respective of Bayesian point estimation based on the idea of mean shift model. The research of Bayesian methods for time series outlier detection will proposes rigorous scientific theories and effective technical means for resolving the problems in GNSS dynamic processing data and quality control system better, such as the problems of outlier detection in satellite clock errors, cycle slips detection and so on. Furthermore, the research will promote the development of the modern theories about survey error and dynamic data processing.

异常值处理是GNSS动态测量数据处理与质量控制体系中的核心内容之一，也是获得高精度、稳健、可靠的导航定位结果的重要前提。 本项目运用现代Bayes统计理论和技术，研究、提出时间序列异常值探测的Bayes方法。首先，从Bayes假设检验的角度，基于不同类型的识别变量后验概率，提出一套对时间序列异常值进行定位、类型区分和定值修复的Bayes方法；其次，从分析成片异常值探测中隐差现象产生的原因和表现形式入手，设计一种自适应Gibbs抽样算法，用于正确计算识别变量后验概率值，以有效防止隐差现象的发生；最后，从Bayes点估计的角度,基于均值漂移模型的思想，提出异常扰动参数的Bayes估计方法和计算方法。 时间序列异常值探测的Bayes方法的研究，将为卫星钟差异常值的处理、周跳的探测和修复等问题的更好解决，提供严密的科学理论和行之有效的技术手段，促进现代测量误差理论与动态数据处理方法的发展。

异常值处理是 GNSS 动态测量数据处理与质量控制体系中的核心内容。本项目紧紧围绕GNSS动态测量数据处理的实际，运用现代Bayes统计理论和方法，全面、深入地研究了时间序列中异常值的探测问题。首先，从 Bayes 假设检验的角度，提出了基于不同类型识别变量的AR模型异常值探测的Bayes方法和ARMA模型异常值探测的Bayes方法。其次，针对成片异常值探测中出现的隐差效应和异常值对模型拟合的不良影响，提出了AR模型中成片AO类异常值探测的抗掩盖和淹没型Bayes方法和ARMA模型稳健拟合与异常值同时探测的Bayes方法。最后，将新理论和新方法应用于卫星多故障探测和识别、BDS星地时间同步钟差异常值处理和钟差预报等GNSS动态数据处理与质量控制中，为获得高精度、稳健、可靠的GNSS导航定位结果，提供了严密的科学理论和行之有效的技术手段。本项目的研究思路和成果对GNSS时间序列异常值的处理将提供重要的参考，同时对动态测量数据处理与质量控制的进一步丰富和发展将起到积极的促进作用。