Nonstationary stochastic processes in least squares collocation --- NonStopLSC

最小二乘搭配中的非平稳随机过程---NonStopLSC

• 批准号: 435703911
• 负责人: Professor Dr. Wolf-Dieter Schuh
• 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: 2019
• 资助国家: 德国
• 起止时间: 2018-12-31 至 2022-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/435703911?language=en
• 关键词: Nonstationary; stochastic; processes; least; squares

Through inverse modeling and adjustment techniques, the geodesists try to derive mathematical models from their measurements to get a better understanding of the processes in the system Earth. Sophisticated deterministic and stochastic models are developed to achieve the best possible reflection of reality and the remaining uncertainty. While deterministic modeling has been improved by much effort, there are still serious weaknesses in the applied stochastic models and representations. Especially in the collocation approach a remove-restore technique is often used to, on the one hand side, guarantee stationarity and, on the other side, get better access to the different frequency contents, which is often hidden in the empirical covariance sequence. Within this project, the representation of stochastic signals with autoregressive processes is proposed which are able to describe the complete frequency spectrum. It shall be highlighted that this is not only the case for stationary processes, but also for time-variable signals. But in theory, this process representation is restricted to equispaced infinite measurement series. Therefore, both representations - the covariance and the process representation - have their pros and cons. A framework for the fusion of the pros is proposed here. The main focus of this proposal is a further development of stochastic model representations, which can reflect the full signal content and have the capability to switch from the usual assumption of time-stationary to time-variable stochastic models. We want to build up and extent a methodical framework to connect the filter and the covariance approach represented by autoregressive processes and least squares collocation. We do this in a strictly formalized way using the 'Magic Square' mechanism which opens the possibility to switch between these two approaches. The proposed extension from the time-discrete processes to stochastic ordinary differential equations opens the way to derive continuous covariance functions from discrete covariance sequences. As a result a family of covariance functions will be established, which will be able to describe the entire signal content as well as the time-variability of stochastic processes.To study this methodical framework with real applications we will refine the analysis of real measurement series from geodetic data sets (from dedicated geodetic satellite missions GOCE, GRACE, GRACE/GRACE-FO and GRAV-D airborne gravity data) especially with respect to their time-variable stochastic signal characteristics.

通过逆建模和调整技术，测地线学家试图从他们的测量中推导出数学模型，以更好地理解地球系统中的过程。复杂的确定性和随机模型被开发出来，以尽可能地反映现实和剩余的不确定性。虽然确定性建模已经得到了很大的改进，但在应用的随机模型和表示中仍然存在严重的弱点。特别是在配置方法中，经常使用去除-恢复技术，一方面保证平稳性，另一方面可以更好地访问隐藏在经验协方差序列中的不同频率内容。在这个项目中，提出了具有自回归过程的随机信号的表示，它能够描述整个频谱。应该强调的是，这不仅适用于平稳过程，也适用于时变信号。但在理论上，这种过程表示仅限于等距无限测量序列。因此，协方差表示和过程表示都有各自的优点和缺点。这里提出了一个融合优点的框架。该建议的主要重点是进一步发展随机模型表示，它可以反映完整的信号内容，并且能够从通常的时间平稳假设切换到时变随机模型。我们想要建立并扩展一个系统的框架来连接滤波器和由自回归过程和最小二乘配置表示的协方差方法。我们使用“魔方”机制以一种严格形式化的方式做到这一点，该机制打开了在这两种方法之间切换的可能性。将时间离散过程推广到随机常微分方程，开辟了从离散协方差序列导出连续协方差函数的途径。因此，将建立一组协方差函数，它将能够描述整个信号内容以及随机过程的时变性。为了在实际应用中研究这一方法框架，我们将细化对大地测量数据集（来自专用大地测量卫星任务GOCE、GRACE、GRACE/GRACE- fo和gravd航空重力数据）的实际测量序列的分析，特别是对其时变随机信号特征的分析。