A GPU-based ray tracing approach for the prediction of multireflections on measurement objects and the a priori estimation of low-reflection measurement poses

Abstract. In Global Navigation Satellite System (GNSS) tomography, precise information about the tropospheric water vapor distribution is derived from integral measurements like ground-based GNSS slant wet delays (SWDs). Therefore, the functional relation between observations and unknowns, i.e., the signal paths through the atmosphere, have to be accurately known for each station–satellite pair involved. For GNSS signals observed above a 15∘ elevation angle, the signal path is well approximated by a straight line. However, since electromagnetic waves are prone to atmospheric bending effects, this assumption is not sufficient anymore for lower elevation angles. Thus, in the following, a mixed 2-D piecewise linear ray-tracing approach is introduced and possible error sources in the reconstruction of the bended signal paths are analyzed in more detail. Especially if low elevation observations are considered, unmodeled bending effects can introduce a systematic error of up to 10–20 ppm, on average 1–2 ppm, into the tomography solution. Thereby, not only the ray-tracing method but also the quality of the a priori field can have a significant impact on the reconstructed signal paths, if not reduced by iterative processing. In order to keep the processing time within acceptable limits, a bending model is applied for the upper part of the neutral atmosphere. It helps to reduce the number of processing steps by up to 85 % without significant degradation in accuracy. Therefore, the developed mixed ray-tracing approach allows not only for the correct treatment of low elevation observations but is also fast and applicable for near-real-time applications.

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Towards an expert system for a priori estimation of reconfiguration latency in dynamically reconfigurable logic

Field-Programmable Logic and Applications - Lecture Notes in Computer Science ◽

10.1007/3-540-63465-7_223 ◽

1997 ◽

pp. 183-192 ◽

Cited By ~ 7

Author(s):

Patrick Lysaght

Keyword(s):

Expert System ◽

A Priori ◽

Reconfigurable Logic ◽

Dynamically Reconfigurable ◽

A Priori Estimation

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A priori estimation of the systematic error of consistently derived theories for thin structures

International Journal of Solids and Structures ◽

10.1016/j.ijsolstr.2019.10.010 ◽

2020 ◽

Vol 190 ◽

pp. 1-21 ◽

Cited By ~ 1

Author(s):

Patrick Schneider ◽

Reinhold Kienzler

Keyword(s):

Systematic Error ◽

A Priori ◽

Thin Structures ◽

A Priori Estimation

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A priori estimation of sequencing effort in complex microbial metatranscriptomes

Ecology and Evolution ◽

10.1002/ece3.6941 ◽

2020 ◽

Vol 10 (23) ◽

pp. 13382-13394 ◽

Cited By ~ 1

Author(s):

Toni Monleon‐Getino ◽

Jorge Frias‐Lopez

Keyword(s):

A Priori ◽

A Priori Estimation

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Bifurcation Behaviors of Steady-State Solution to a Discrete General Brusselator Model

Discrete Dynamics in Nature and Society ◽

10.1155/2020/5417218 ◽

2020 ◽

Vol 2020 ◽

pp. 1-14

Author(s):

Ruyun Ma ◽

Zhongzi Zhao

Keyword(s):

A Priori ◽

Global Bifurcation ◽

Small Neighborhood ◽

Steady State Solution ◽

Solution Curve ◽

Bifurcation Theorem ◽

Brusselator Model ◽

Constant Solution ◽

A Priori Estimation ◽

Increasing Function

We study the local and global bifurcation of nonnegative nonconstant solutions of a discrete general Brusselator model. We generalize the linear u in the standard Brusselator model to the nonlinear fu. Assume that f∈C0,∞,0,∞ is a strictly increasing function, and f′f−1a∈0,∞. Taking b as the bifurcation parameter, we obtain that the solution set of the problem constitutes a constant solution curve and a nonconstant solution curve in a small neighborhood of the bifurcation point b0j,f−1a,ab/f−1a2. Moreover, via the Rabinowitz bifurcation theorem, we obtain the global structure of the set of nonconstant solutions under the condition that fs/s2 is nonincreasing in 0,∞. In this process, we also make a priori estimation for the nonnegative nonconstant solutions of the problem.

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A priori estimation of memory effects in reduced-order models of nonlinear systems using the Mori–Zwanzig formalism

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2017.0385 ◽

2017 ◽

Vol 473 (2205) ◽

pp. 20170385 ◽

Cited By ~ 16

Author(s):

Ayoub Gouasmi ◽

Eric J. Parish ◽

Karthik Duraisamy

Keyword(s):

Evolution Equations ◽

Nonlinear Dynamical Systems ◽

A Priori ◽

Time History ◽

Original System ◽

Memory Kernel ◽

Nonlinear Dynamical ◽

History Of ◽

Consistent Basis ◽

A Priori Estimation

Reduced models of nonlinear dynamical systems require closure, or the modelling of the unresolved modes. The Mori–Zwanzig procedure can be used to derive formally closed evolution equations for the resolved physics. In these equations, the unclosed terms are recast as a memory integral involving the time history of the resolved variables. While this procedure does not reduce the complexity of the original system, these equations can serve as a mathematically consistent basis to develop closures based on memory approximations. In this scenario, knowledge of the memory kernel is paramount in assessing the validity of a memory approximation. Unravelling the memory kernel requires solving the orthogonal dynamics, which is a high-dimensional partial differential equation that is intractable, in general. A method to estimate the memory kernel a priori , using full-order solution snapshots, is proposed. The key idea is to solve a pseudo orthogonal dynamics equation, which has a convenient Liouville form, instead. This ersatz arises from the assumption that the semi-group of the orthogonal dynamics is a composition operator for one observable. The method is exact for linear systems. Numerical results on the Burgers and Kuramoto–Sivashinsky equations demonstrate that the proposed technique can provide valuable information about the memory kernel.

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