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.

现代的大地测量传感器通常会产生多个空间时间序列，这些时间序列包含大量测量，许多异常值以及数据差距以及以相当大的自动和交叉相关性（即彩色噪声）为特征的随机误差。鉴于这些逆境无法通过当前的大地测量数据分析工具来解决这些逆境，我们打算与调整程序相关的经典和贝叶斯统计数据，从而可以从此类时空测量系列中对参数模型进行强有力，有效地估算。为了促进同时鲁棒性和统计以及计算效率，我们一方面采用了期望最大化原则（EM）。这可以插入数据差距，并同时对功能模型参数的自适应估计，矢量自回归自动移动平均（VARMA）彩色噪声模型的系数以及基础误差分布的形状参数的系数。后者由多元缩放（学生）T分布定义，并涉及数据适应程度的自由度和尺度因子。通过估计这些数量，概率密度函数的形状，尤其是尾巴特征可适应数据中存在的实际误差和异常特征。在随后的工作步骤中，我们还将允许函数和噪声模型参数的动态变化。最后，我们研究了基于平均场变异贝叶斯和马尔可夫链蒙特卡洛（MCMC）技术的贝叶斯程序，这些技术允许将有关功能模型的参数，VARMA模型和基本的T-Dibripution的先验信息合并到Adaptive Robust的调整中。由于调整得出有关所有未知模型参数的详细概率信息，因此，我们还将能够严格测试有关假定误差分布的假设，涉及可疑的自动/交叉相关模式以及此类模式的时间变异性。我们将一般观察模型的静态版本和估算过程应用于基于静态多传感器系统的地理参考的测量数据集的调整问题。他们的引用传感器可以是3D定位传感器，例如GNSS设备或速度计。动态版本应用于加载来自Arch Bridge的测试数据。由于预期的方法的高度灵活性和效率，我们希望它们也适用于其他类型的大地传感器数据，例如在卫星测量中。