Bayesian adaptive robust adjustment of multivariate geodetic measurement processeswith data gaps and nonstationary colored noise

具有数据间隙和非平稳有色噪声的多元大地测量过程的贝叶斯自适应鲁棒调整

• 批准号: 386369985
• 负责人: Dr.-Ing. Hamza Alkhatib
• 金额: --
• 依托单位: Lehrstuhl für Theoretische Geodäsie
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2018
• 资助国家: 德国
• 起止时间: 2017-12-31 至 2022-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/386369985?language=en
• 关键词: Bayesian; adaptive; robust; adjustment; multivariate

Modern geodetic sensors often produce multiple spatial time series which contain huge numbers of measurements, numerous outliers as well as data gaps, and random errors that are characterized by considerable auto- andcross-correlations (i.e., colored noise). In view of these adversities, which cannot be resolved by current geodetic data analysis tools in their entirety, we intend to develop both classical and Bayesian statistics in connection with adjustment procedures that allow for a robust and efficient estimation of parametric models from such spatio-temporal measurement series. To facilitate simultaneous robustness and statistical as well as computational efficiency, we employ on the one hand the principle of expectation maximization (EM). This enables an imputation of the data gaps and concurrently an adaptive estimation of the parameters of the functional model, of the coefficients of a vector autoregressive moving-average (VARMA) colored noise model, and of the shape parameters of the underlying error distribution. The latter is defined by a multivariate, scaled (Student) t-distribution and involves a data-adaptable degree of freedom and scale factor. By estimating these quantities, the shape and in particular the tail characteristics of the probability densityfunction is adapted to the actual error and outlier characteristics present in the data. In a subsequent work step, we will also allow for dynamic changes of the parameters of the functional and of the noise model. Finally, we investigate Bayesian procedures based on Mean-Field Variational Bayes and Markov Chain Monte Carlo (MCMC) techniques, which allow for the incorporation of prior information regarding the parameters of the functional model, of the VARMA model and of the underlying t-distribution into the adaptive robust adjustment. Since the adjustment yields detailed probabilistic information regarding all of the unknown model parameters, we will for instance also be able to rigorously test hypotheses about the assumed error distribution, about suspected auto-/cross-correlation patterns, and about the time-variability of such patterns. We apply the static version of the general observation model and estimation procedure to adjustment problems based on geodetic data sets stemming from geo-referencing of static multi-sensor systems. Their referencing sensors can be 3D positioning sensors, like GNSS equipment or tacheometer. The dynamic version is applied to loading test data stemming from an arch bridge. Due to the anticipated high level of flexibility and efficiency of the methods, we expect them to be applicable also to other types of geodetic sensor data, as obtained e.g. in satellite geodesy.

现代大地测量传感器通常会产生多个空间时间序列，其中包含大量测量值、大量异常值以及数据间隙以及以相当大的自相关和互相关（即有色噪声）为特征的随机误差。鉴于当前的大地测量数据分析工具无法完全解决这些逆境，我们打算开发与调整程序相关的经典统计和贝叶斯统计，以便从此类时空参数模型中进行稳健且有效的估计测量系列。为了同时提高鲁棒性和统计以及计算效率，我们一方面采用期望最大化（EM）原则。这使得能够对数据间隙进行插补，同时对函数模型的参数、向量自回归移动平均（VARMA）有色噪声模型的系数以及基础误差分布的形状参数进行自适应估计。后者由多元缩放（学生）t 分布定义，并涉及数据适应性自由度和比例因子。通过估计这些量，概率密度函数的形状（特别是尾部特征）适应数据中存在的实际误差和异常值特征。在后续工作步骤中，我们还将允许函数和噪声模型的参数动态变化。最后，我们研究基于平均场变分贝叶斯和马尔可夫链蒙特卡罗 (MCMC) 技术的贝叶斯过程，该技术允许合并有关函数模型、VARMA 模型和底层 t 分布参数的先验信息进入自适应鲁棒调整。由于调整会产生有关所有未知模型参数的详细概率信息，因此我们还能够严格测试有关假设误差分布、可疑自相关/互相关模式以及此类模型的时间变异性的假设。模式。我们将一般观测模型和估计程序的静态版本应用于基于静态多传感器系统地理参考产生的大地测量数据集的调整问题。它们的参考传感器可以是 3D 定位传感器，例如 GNSS 设备或测距仪。动态版本适用于加载来自拱桥的测试数据。由于这些方法预期具有高水平的灵活性和效率，我们希望它们也适用于其他类型的大地测量传感器数据，例如获得的数据。在卫星大地测量学中。