Adaptive POD-Galerkin Technique for Reservoir Simulation and Optimization     

Voloskov  Dmitry  Pissarenko  Dimitri 《Mathematical Geosciences》2021,53(8):1951-1975

Mathematical Geosciences - This paper introduces a novel method using an adaptive functional basis for reduced order models based on proper orthogonal decomposition (POD). The method is intended to...  相似文献   

Extreme value theory-based integrity monitoring of global navigation satellite systems     

Dimitri Panagiotakopoulos  Arnab Majumdar  Washington Yotto Ochieng 《GPS Solutions》2014,18(1):133-145

Measurements consistency-based Receiver Autonomous Integrity Monitoring (RAIM) is the main technique for monitoring the integrity of global satellite navigation systems at the user-level. Existing RAIM algorithms utilize two tests, in the position domain a test for RAIM availability and in the measurement domain a test for failure detection. These tests involve the computation of three parameters: test statistic, decision threshold, and protection level. The test statistic is based on the actual measurements in the form of the sum of the squared errors (SSE). The decision threshold is chosen on the basis of the statistical characteristics of the SSE including the assumption that the errors are normally distributed. However, in practice residual, error distributions exhibit heavier tails than predicted by the Gaussian model. Therefore, this paper challenges the normality assumption of the residual navigation errors in three ways. First, real data are used to assess its impact on the traditional RAIM algorithm. Second, extreme value theory is applied to the tails, and the generalized extreme value (GEV) distribution is derived to capture residual navigation errors. Third, the performance of the traditional RAIM approach is compared with that employing the GEV distribution. The results demonstrate that the GEV model is a more accurate representation of the distribution of residual navigation errors than the conventional Gaussian model and should be used in the development of integrity monitoring algorithms.  相似文献