scholarly journals TMF: A GNSS Tropospheric Mapping Function for the Asymmetrical Neutral Atmosphere

2021 ◽  
Vol 13 (13) ◽  
pp. 2568
Author(s):  
Di Zhang ◽  
Jiming Guo ◽  
Tianye Fang ◽  
Na Wei ◽  
Wensheng Mei ◽  
...  
Keyword(s):  
Large Scale ◽  
Least Squares Method ◽  
Computational Cost ◽  
Elevation Angle ◽  
Mapping Function ◽  
Nonlinear Least Squares ◽  
Least Square ◽  
Neutral Atmosphere ◽  
Medium Range Weather Forecast ◽  
Mapping Functions

Tropospheric mapping function plays a vital role in the high precision Global Navigation Satellites Systems (GNSS) data processing for positioning. However, most mapping functions are derived under the assumption that atmospheric refractivity is spherically symmetric. In this paper, the pressure, temperature, and humidity fields of ERA5 data with the highest spatio-temporal resolution available from the European Centre for Medium-range Weather Forecast (ECMWF) were utilized to compute ray-traced delays by the software WHURT. Results reveal the universal asymmetry of the hydrostatic and wet tropospheric delays. To accurately represent these highly variable delays, a new mapping function that depends on elevation and azimuth angles—Tilting Mapping Function (TMF)—was applied. The basic idea is to assume an angle between the tropospheric zenith direction and the geometric zenith direction. Ray-traced delays served as the reference values. TMF coefficients were fitted by Levenberg–Marquardt nonlinear least-squares method. Comparisons demonstrate that the TMF can improve the MF-derived slant delay’s accuracy by 73%, 54% and 29% at the 5° elevation angle, against mapping functions based on the VMF3 concept, without, with a total and separate estimation of gradients, respectively. If all coefficients of a symmetric mapping function are determined together with gradients by a least-square fit at sufficient elevation angles, the accuracy is only 6% lower than TMF. By adopting the b and c coefficients of VMF3, TMF can keep its high accuracy with less computational cost, which could be meaningful for large-scale computing.

scholarly journals Evaluation of Symmetric Neutral-Atmosphere Mapping Functions Using Ray-Tracing Through Radiosonde Observations

2013 ◽  
Vol 48 (4) ◽  
pp. 171-189
Author(s):  
A.H. Souri ◽  
M.A. Sharifi
Keyword(s):  
Ray Tracing ◽  
Elevation Angle ◽  
Mapping Function ◽  
Ground Truth ◽  
Ease Of Use ◽  
Tropospheric Delay ◽  
Neutral Atmosphere ◽  
Mapping Functions ◽  
Climatic Regions ◽  
Online Mapping

Abstract The aim of this paper is to compare the validity of six recent symmetric mapping functions. The mapping function models the elevation angle dependence of the tropospheric delay. Niell Mapping Function (NMF), Vienna Mapping Function (VMF1), University of New Brunswick- VMF1 (UNB-VMF1) mapping functions, Global Mapping Function (GMF) and Global Pressure and Temperature (GPT2)/GMF are evaluated by using ray tracing through 25 radiosonde stations covering different climatic regions in one year. The ray-traced measurements are regarded as “ground truth”. The ray-tracing approach is performed for diverse elevation angle starting at 5° to 15°. The results for both hydrostatic and non-hydrostatic components of mapping functions support the efficiency of online-mapping functions. The latitudinal dependence of standard deviation for 5° is also demonstrated. Although all the tested mapping functions can provide satisfactory results when used for elevation angles above 15°, for high precision geodetic measurements, it is highly recommended that the online-mapping functions (UNBs and VMF1) be used.The results suggest that UNB models, like VMF have strengths and weaknesses and do not stand out as being consistently better or worse than the VMF1. The GPT2/GMF provided better accuracy than GMF and NMF. Since all of them do not require site specific data; therefore GPT2/GMF can be useful as regards its ease of use.

scholarly journals Symmetric Neutral-Atmosphere Mapping Functions: A Review of the State-Of-The-Art

2013 ◽  
Vol 48 (4) ◽  
pp. 159-170 ◽  
Author(s):  
M.A. Sharifi ◽  
A.H. Souri
Keyword(s):  
State Of The Art ◽  
Elevation Angle ◽  
Mapping Function ◽  
Temporal Variations ◽  
Neutral Atmosphere ◽  
Radio Waves ◽  
Mapping Functions ◽  
Long Baseline ◽  
Global Mapping ◽  
Spatio Temporal

ABSTRACT The aim of this paper is to review of six recent symmetric mapping functions. The mapping function can be largely used for GPS meteorological measurements, InSAR atmospheric corrections and precise measurements of very long baseline interferometry (VLBI). These spacebased techniques use radio signal that propagate through the Earth's atmosphere. The electrically-neutral region, predominantly the troposphere, affects the speed and direction of travel of radio waves leading to existence of excess path. The mapping function models the elevation angle dependence of the delay. Within the past decade, significant improvements have been achieved in order to use of Numerical Weather Models (NWM) for geodetic positioning. Ray-tracing algorithms have been performed through refractivity shells retrieved from NWMs in order to relate zenith delays to slant delays. Therefore, there seems to be a real need for deep review of recent developments in the mapping function domain. This paper proposes a comprehensive review of the symmetric mapping functions state of the art, their spatio-temporal variations and used NWM and generic models. Niell Mapping Function (NMF), Vienna Mapping Function (VMF1), University of New Brunswick-VMF1 (UNB-VMF1) mapping functions, Global Mapping Function (GMF) and Global Pressure and Temperature (GPT2)/GMF are reviewed in this paper.

scholarly journals Extended Local Analysis of Inexact Gauss-Newton-like Method for Least Square Problems using Restricted Convergence Domains

2016 ◽  
Vol 54 (1) ◽  
pp. 17-33
Author(s):  
Ioannis K. Argyros ◽  
Santhosh George
Keyword(s):  
Convergence Analysis ◽  
Computational Cost ◽  
Nonlinear Least Squares ◽  
Least Square ◽  
Error Tolerance ◽  
Local Analysis ◽  
Large Radius ◽  
Special Cases ◽  
Local Convergence Analysis ◽  
Least Square Problems

Abstract We present a local convergence analysis of inexact Gauss-Newton-like method (IGNLM) for solving nonlinear least-squares problems in a Euclidean space setting. The convergence analysis is based on our new idea of restricted convergence domains. Using this idea, we obtain a more precise information on the location of the iterates than in earlier studies leading to smaller majorizing functions. This way, our approach has the following advantages and under the same computational cost as in earlier studies: A large radius of convergence and more precise estimates on the distances involved to obtain a desired error tolerance. That is, we have a larger choice of initial points and fewer iterations are also needed to achieve the error tolerance. Special cases and numerical examples are also presented to show these advantages.

scholarly journals Sensitivity of GNSS tropospheric gradients to processing options

2019 ◽  
Vol 37 (3) ◽  
pp. 429-446 ◽  
Author(s):  
Michal Kačmařík ◽  
Jan Douša ◽  
Florian Zus ◽  
Pavel Václavovic ◽  
Kyriakos Balidakis ◽  
...  
Keyword(s):  
Real Time ◽  
Elevation Angle ◽  
Mapping Function ◽  
Global Navigation Satellite Systems ◽  
Gradient Estimates ◽  
Post Processing ◽  
Data Set ◽  
Mapping Functions ◽  
Gradient Mapping

Abstract. An analysis of processing settings impacts on estimated tropospheric gradients is presented. The study is based on the benchmark data set collected within the COST GNSS4SWEC action with observations from 430 Global Navigation Satellite Systems (GNSS) reference stations in central Europe for May and June 2013. Tropospheric gradients were estimated in eight different variants of GNSS data processing using precise point positioning (PPP) with the G-Nut/Tefnut software. The impacts of the gradient mapping function, elevation cut-off angle, GNSS constellation, observation elevation-dependent weighting and real-time versus post-processing mode were assessed by comparing the variants by each to other and by evaluating them with respect to tropospheric gradients derived from two numerical weather models (NWMs). Tropospheric gradients estimated in post-processing GNSS solutions using final products were in good agreement with NWM outputs. The quality of high-resolution gradients estimated in (near-)real-time PPP analysis still remains a challenging task due to the quality of the real-time orbit and clock corrections. Comparisons of GNSS and NWM gradients suggest the 3∘ elevation angle cut-off and GPS+GLONASS constellation for obtaining optimal gradient estimates provided precise models for antenna-phase centre offsets and variations, and tropospheric mapping functions are applied for low-elevation observations. Finally, systematic errors can affect the gradient components solely due to the use of different gradient mapping functions, and still depending on observation elevation-dependent weighting. A latitudinal tilting of the troposphere in a global scale causes a systematic difference of up to 0.3 mm in the north-gradient component, while large local gradients, usually pointing in a direction of increasing humidity, can cause differences of up to 1.0 mm (or even more in extreme cases) in any component depending on the actual direction of the gradient. Although the Bar-Sever gradient mapping function provided slightly better results in some aspects, it is not possible to give any strong recommendation on the gradient mapping function selection.

scholarly journals Multiple Linear Analysis Methods for the Quantification of Irreversibly Binding Radiotracers

2008 ◽  
Vol 28 (12) ◽  
pp. 1965-1977 ◽  
Author(s):  
Su Jin Kim ◽  
Jae Sung Lee ◽  
Yu Kyeong Kim ◽  
James Frost ◽  
Gary Wand ◽  
...  
Keyword(s):  
Statistical Power ◽  
Least Squares Method ◽  
Multiple Linear Regression Model ◽  
Nonlinear Least Squares ◽  
Compartment Model ◽  
Linear Analysis ◽  
Graphical Analysis ◽  
Least Square ◽  
Positron Emission ◽  
Nonlinear Least Squares Method

Gjedde—Patlak graphical analysis (GPGA) has commonly been used to quantify the net accumulations (Kin) of radioligands that bind or are taken up irreversibly. We suggest an alternative approach (MLAIR: multiple linear analysis for irreversible radiotracers) for the quantification of these types of tracers. Two multiple linear regression model equations were derived from differential equations of the two-tissue compartment model with irreversible binding. Multiple linear analysis for irreversible radiotracer 1 has a desirable feature for ordinary least square estimations because only the dependent variable CT( t) is noisy. Multiple linear analysis for irreversible radiotracer 2 provides Kin from direct estimates of the coefficients of independent variables without the mediation of a division operation. During computer simulations, MLAIR1 provided less biased Kin estimates than the other linear methods, but showed a high uncertainty level for noisy data, whereas MLAIR2 increased the robustness of estimation in terms of variability, but at the expense of increased bias. For real [11C]MeNTI positron emission tomography data, both methods showed good correlations, with parameters estimated using the standard nonlinear least squares method. Multiple linear analysis for irreversible radiotracer 2 parametric images showed remarkable image quality as compared with GPGA images. It also showed markedly improved statistical power for voxelwise comparisons than GPGA. The two MLAIR approaches examined were found to have several advantages over the conventional GPGA method.

Fast sparse image reconstruction method in through-the-wall radars using limited memory Broyden–Fletcher–Goldfarb–Shanno algorithm

2021 ◽  
pp. 1-11
Author(s):  
Candida Mwisomba ◽  
Abdi T. Abdalla ◽  
Idrissa Amour ◽  
Florian Mkemwa ◽  
Baraka Maiseli
Keyword(s):  
Image Reconstruction ◽  
Large Scale ◽  
Optimization Problems ◽  
Classical Method ◽  
Computational Cost ◽  
Least Square ◽  
Computational Time ◽  
Reconstruction Method ◽  
Nonlinear Methods ◽  
Limited Memory

Abstract Compressed sensing allows recovery of image signals using a portion of data – a technique that has drastically revolutionized the field of through-the-wall radar imaging (TWRI). This technique can be accomplished through nonlinear methods, including convex programming and greedy iterative algorithms. However, such (nonlinear) methods increase the computational cost at the sensing and reconstruction stages, thus limiting the application of TWRI in delicate practical tasks (e.g. military operations and rescue missions) that demand fast response times. Motivated by this limitation, the current work introduces the use of a numerical optimization algorithm, called Limited Memory Broyden–Fletcher–Goldfarb–Shanno (LBFGS), to the TWRI framework to lower image reconstruction time. LBFGS, a well-known Quasi-Newton algorithm, has traditionally been applied to solve large scale optimization problems. Despite its potential applications, this algorithm has not been extensively applied in TWRI. Therefore, guided by LBFGS and using the Euclidean norm, we employed the regularized least square method to solve the cost function of the TWRI problem. Simulation results show that our method reduces the computational time by 87% relative to the classical method, even under situations of increased number of targets or large data volume. Moreover, the results show that the proposed method remains robust when applied to noisy environment.

scholarly journals Determining Robust Reaction Kinetics from Limited Data

2021 ◽  
Author(s):  
Gizem Ozbuyukkaya ◽  
Robert Parker ◽  
Goetz Veser
Keyword(s):  
Parameter Estimation ◽  
Kinetic Parameter ◽  
Cross Validation ◽  
Computational Cost ◽  
Synthetic Data ◽  
Nonlinear Least Squares ◽  
Least Square ◽  
Data Sets ◽  
Limited Data ◽  
Kinetic Parameter Estimation

Accurate chemical kinetics are essential for reactor design and operation. However, despite recent advances in “big data” approaches, availability of kinetic data is often limited in industrial practice. Herein, we present a comparative proof-of-concept study for kinetic parameter estimation from limited data. Cross-validation (CV) is implemented to nonlinear least-squares (LS) fitting and evaluated against Markov chain Monte Carlo (MCMC) and genetic algorithm (GA) routines using synthetic data generated from a simple model reaction. As expected, conventional LS is fastest but least accurate in predicting true kinetics. MCMC and GA are effective for larger data sets but tend to overfit to noise for limited data. Cross-validation least-square (LS-CV) strongly outperforms these methods at much reduced computational cost, especially for significant noise. Our findings suggest that implementation of cross-validation with conventional regression provides an efficient approach to kinetic parameter estimation with high accuracy, robustness against noise, and only minimal increase in complexity.

scholarly journals Assessment of the Accuracy of the Saastamoinen Model and VMF1/VMF3 Mapping Functions with Respect to Ray-Tracing from Radiosonde Data in the Framework of GNSS Meteorology

2020 ◽  
Vol 12 (20) ◽  
pp. 3337
Author(s):  
Peng Feng ◽  
Fei Li ◽  
Jianguo Yan ◽  
Fangzhao Zhang ◽  
Jean-Pierre Barriot
Keyword(s):  
Ray Tracing ◽  
Elevation Angle ◽  
Mapping Function ◽  
Satellite System ◽  
Radiosonde Data ◽  
Mapping Functions ◽  
Gnss Meteorology ◽  
Rms Error ◽  
Zenith Hydrostatic Delay ◽  
Global Navigation Satellite

In this paper, we assess, in the framework of Global Navigation Satellite System (GNSS) meteorology, the accuracy of GNSS propagation delays corresponding to the Saastamoinen zenith hydrostatic delay (ZHD) model and the Vienna Mapping function VMF1/VMF3 (hydrostatic and wet), with reference to radiosonde ray-tracing delays over a three-year period on 28 globally distributed sites. The results show that the Saastamoinen ZHD estimates have a mean root mean square (RMS) error of 1.7 mm with respect to the radiosonde. We also detected some seasonal signatures in these Saastamoinen ZHD estimates. This indicates that the Saastamoinen model, based on the hydrostatic assumption and the ground pressure, is insufficient to capture the full variability of the ZHD estimates over time with the accuracy needed for GNSS meteorology. Furthermore, we found that VMF3 slant hydrostatic delay (SHD) estimates outperform the corresponding VMF1 SHD estimates (equivalent SHD RMS error of 4.8 mm for VMF3 versus 7.1 mm for VMF1 at 5° elevation angle), with respect to the radiosonde SHD estimates. Unexpectedly, the situation is opposite for the VMF3 slant wet delay (SWD) estimates compared to VMF1 SWD estimates (equivalent SWD RMS error of 11.4 mm for VMF3 versus 7.0 mm for VMF1 at 5° elevation angle). Our general conclusion is that the joint approach using ZHD models and mapping functions must be revisited, at least in the framework of GNSS meteorology.

scholarly journals Renormalization group theory of molecular dynamics

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Daiji Ichishima ◽  
Yuya Matsumura
Keyword(s):  
Molecular Dynamics ◽  
Renormalization Group ◽  
Critical Exponent ◽  
Computational Efficiency ◽  
Large Scale ◽  
Dissipative Particle Dynamics ◽  
Computational Cost ◽  
Coarse Graining ◽  
Spatial Dimension ◽  
Deborah Number

AbstractLarge scale computation by molecular dynamics (MD) method is often challenging or even impractical due to its computational cost, in spite of its wide applications in a variety of fields. Although the recent advancement in parallel computing and introduction of coarse-graining methods have enabled large scale calculations, macroscopic analyses are still not realizable. Here, we present renormalized molecular dynamics (RMD), a renormalization group of MD in thermal equilibrium derived by using the Migdal–Kadanoff approximation. The RMD method improves the computational efficiency drastically while retaining the advantage of MD. The computational efficiency is improved by a factor of $$2^{n(D+1)}$$ 2 n ( D + 1 ) over conventional MD where D is the spatial dimension and n is the number of applied renormalization transforms. We verify RMD by conducting two simulations; melting of an aluminum slab and collision of aluminum spheres. Both problems show that the expectation values of physical quantities are in good agreement after the renormalization, whereas the consumption time is reduced as expected. To observe behavior of RMD near the critical point, the critical exponent of the Lennard-Jones potential is extracted by calculating specific heat on the mesoscale. The critical exponent is obtained as $$\nu =0.63\pm 0.01$$ ν = 0.63 ± 0.01 . In addition, the renormalization group of dissipative particle dynamics (DPD) is derived. Renormalized DPD is equivalent to RMD in isothermal systems under the condition such that Deborah number $$De\ll 1$$ D e ≪ 1 .

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