The Zenith Hydrostatic Delay(ZHD)is essential for high-precision Global Navigation Satellite System(GNSS)and Very Long Baseline Interferometry(VLBI)data processing.Accurate estimation of ZHD relies on in situ atmosphe...The Zenith Hydrostatic Delay(ZHD)is essential for high-precision Global Navigation Satellite System(GNSS)and Very Long Baseline Interferometry(VLBI)data processing.Accurate estimation of ZHD relies on in situ atmospheric pressure,which is primarily variable in the vertical direction.Current atmospheric pressure is either site-specific or has limited spatial coverage,necessitating vertical corrections for broader applicability.This study introduces a model that uses a Gaussian function for the vertical correction of atmospheric pressure when in situ meteorological observations are unavailable.Validation with the fifth-generation European Centre for Medium-Range Weather Forecasts reanalysis(ERA5)reveals an average Bias and RMS for the new model of 0.31 h Pa and 2.96 h Pa,respectively.This corresponds to improvements of 37.5%and 80.3%in terms of RMS compared to two commonly used models(T0and Tvmodels)that require in situ meteorological observations,respectively.Additional validation with radiosonde data shows an average Bias and RMS of 1.85 h Pa and 4.87 h Pa,corresponding to the improvement of 42.8%and 71.1%in RMS compared with T0and Tv models,respectively.These accuracies are sufficient for calculating ZHD to an accuracy of 1 mm by performing atmospheric pressure vertical correction.The new model can correct atmospheric pressure from meteorological stations or numerical weather forecasts to different heights of the troposphere.展开更多
This paper proposes an optimal midcourse guidance method for dual pulse air-to-air missiles,which is based on the framework of the linear Gauss pseudospectral model predictive control method.Firstly,a multistage optim...This paper proposes an optimal midcourse guidance method for dual pulse air-to-air missiles,which is based on the framework of the linear Gauss pseudospectral model predictive control method.Firstly,a multistage optimal control problem with unspecified terminal time is formulated.Secondly,the control and terminal time update formulas are derived analytically.In contrast to previous work,the derivation process fully considers the Hamiltonian function corresponding to the unspecified terminal time,which is coupled with control,state,and costate.On the assumption of small perturbation,a special algebraic equation is provided to represent the equivalent optimal condition for the terminal time.Also,using Gauss pseudospectral collocation,error propagation dynamical equations involving the first-order correction term of the terminal time are transformed into a set of algebraic equations.Furthermore,analytical modification formulas can be derived by associating those equations and optimal conditions to eliminate terminal error and approach nonlinear optimal control.Even with their mathematical complexity,these formulas produce more accurate control and terminal time corrections and remove reliance on task-related parameters.Finally,several numerical simulations,comparisons with typical methods,and Monte Carlo simulations have been done to verify its optimality,high convergence rate,great stability and robustness.展开更多
In this paper,we study the value distribution properties of the generalized Gauss maps of weakly complete harmonic surfaces immersed in R^(m),which is the case where the generalized Gauss mapΦis ramified over a famil...In this paper,we study the value distribution properties of the generalized Gauss maps of weakly complete harmonic surfaces immersed in R^(m),which is the case where the generalized Gauss mapΦis ramified over a family of hypersurfaces{Q_(j)}_(j=1)^(q)in P^(m-1)(C)located in the N-subgeneral position.In addition,we investigate the Gauss curvature estimate for the K-quasiconformal harmonic surfaces immersed in R^(3)whose Gauss maps are ramified over a family of hypersurfaces located in the N-subgeneral position.展开更多
This paper focuses on Gauss principle of least compulsion for relative motion dynamics and derives differential equations of motion from it. Firstly, starting from the dynamic equation of the relative motion of partic...This paper focuses on Gauss principle of least compulsion for relative motion dynamics and derives differential equations of motion from it. Firstly, starting from the dynamic equation of the relative motion of particles, we give the Gauss principle of relative motion dynamics. By constructing a compulsion function of relative motion, we prove that at any instant, its real motion minimizes the compulsion function under Gaussian variation, compared with the possible motions with the same configuration and velocity but different accelerations. Secondly, the formula of acceleration energy and the formula of compulsion function for relative motion are derived because the carried body is rigid and moving in a plane. Thirdly, the Gauss principle we obtained is expressed as Appell, Lagrange, and Nielsen forms in generalized coordinates. Utilizing Gauss principle, the dynamical equations of relative motion are established. Finally, two relative motion examples also verify the results' correctness.展开更多
In this paper,we compute sub-Riemannian limits of Gaussian curvature associated to two kinds of Schouten-Van Kampen affine connections and the adapted connection for a Euclidean C2-smooth surface in the Heisenberg gro...In this paper,we compute sub-Riemannian limits of Gaussian curvature associated to two kinds of Schouten-Van Kampen affine connections and the adapted connection for a Euclidean C2-smooth surface in the Heisenberg group away from characteristic points and signed geodesic curvature associated to two kinds of Schouten-Van Kampen affine connections and the adapted connection for Euclidean C2-smooth curves on surfaces.We get Gauss-Bonnet theorems associated to two kinds of Schouten-Van Kampen affine connections in the Heisenberg group.展开更多
基金supported by the National Natural Science Foundation of China(42304018)the National Natural Science Foundation of China(42330105,42064002,42074035)+3 种基金the Guangxi Natural Science Foundation of China(Guike AD23026177,2020GXNSFBA297145)the Foundation of Guilin University of Technology(GUTQDJJ6616032)Guangxi Key Laboratory of Spatial Information and Geomatics(21238-21-05)the Innovation Project of Guangxi Graduate Education(YCSW2023341)。
文摘The Zenith Hydrostatic Delay(ZHD)is essential for high-precision Global Navigation Satellite System(GNSS)and Very Long Baseline Interferometry(VLBI)data processing.Accurate estimation of ZHD relies on in situ atmospheric pressure,which is primarily variable in the vertical direction.Current atmospheric pressure is either site-specific or has limited spatial coverage,necessitating vertical corrections for broader applicability.This study introduces a model that uses a Gaussian function for the vertical correction of atmospheric pressure when in situ meteorological observations are unavailable.Validation with the fifth-generation European Centre for Medium-Range Weather Forecasts reanalysis(ERA5)reveals an average Bias and RMS for the new model of 0.31 h Pa and 2.96 h Pa,respectively.This corresponds to improvements of 37.5%and 80.3%in terms of RMS compared to two commonly used models(T0and Tvmodels)that require in situ meteorological observations,respectively.Additional validation with radiosonde data shows an average Bias and RMS of 1.85 h Pa and 4.87 h Pa,corresponding to the improvement of 42.8%and 71.1%in RMS compared with T0and Tv models,respectively.These accuracies are sufficient for calculating ZHD to an accuracy of 1 mm by performing atmospheric pressure vertical correction.The new model can correct atmospheric pressure from meteorological stations or numerical weather forecasts to different heights of the troposphere.
基金supported by the National Natural Science Foundation of China(No.62003019)the Young Talents Support Program of Beihang University,China(No.YWF-21-BJ-J-1180).
文摘This paper proposes an optimal midcourse guidance method for dual pulse air-to-air missiles,which is based on the framework of the linear Gauss pseudospectral model predictive control method.Firstly,a multistage optimal control problem with unspecified terminal time is formulated.Secondly,the control and terminal time update formulas are derived analytically.In contrast to previous work,the derivation process fully considers the Hamiltonian function corresponding to the unspecified terminal time,which is coupled with control,state,and costate.On the assumption of small perturbation,a special algebraic equation is provided to represent the equivalent optimal condition for the terminal time.Also,using Gauss pseudospectral collocation,error propagation dynamical equations involving the first-order correction term of the terminal time are transformed into a set of algebraic equations.Furthermore,analytical modification formulas can be derived by associating those equations and optimal conditions to eliminate terminal error and approach nonlinear optimal control.Even with their mathematical complexity,these formulas produce more accurate control and terminal time corrections and remove reliance on task-related parameters.Finally,several numerical simulations,comparisons with typical methods,and Monte Carlo simulations have been done to verify its optimality,high convergence rate,great stability and robustness.
基金supported by the NFSC(11971182,12271189)the NFS of Fujian Province of China(2019J01066,2021J01304)。
文摘In this paper,we study the value distribution properties of the generalized Gauss maps of weakly complete harmonic surfaces immersed in R^(m),which is the case where the generalized Gauss mapΦis ramified over a family of hypersurfaces{Q_(j)}_(j=1)^(q)in P^(m-1)(C)located in the N-subgeneral position.In addition,we investigate the Gauss curvature estimate for the K-quasiconformal harmonic surfaces immersed in R^(3)whose Gauss maps are ramified over a family of hypersurfaces located in the N-subgeneral position.
基金Supported by the National Natural Science Foundation of China (12272248, 11972241)。
文摘This paper focuses on Gauss principle of least compulsion for relative motion dynamics and derives differential equations of motion from it. Firstly, starting from the dynamic equation of the relative motion of particles, we give the Gauss principle of relative motion dynamics. By constructing a compulsion function of relative motion, we prove that at any instant, its real motion minimizes the compulsion function under Gaussian variation, compared with the possible motions with the same configuration and velocity but different accelerations. Secondly, the formula of acceleration energy and the formula of compulsion function for relative motion are derived because the carried body is rigid and moving in a plane. Thirdly, the Gauss principle we obtained is expressed as Appell, Lagrange, and Nielsen forms in generalized coordinates. Utilizing Gauss principle, the dynamical equations of relative motion are established. Finally, two relative motion examples also verify the results' correctness.
文摘In this paper,we compute sub-Riemannian limits of Gaussian curvature associated to two kinds of Schouten-Van Kampen affine connections and the adapted connection for a Euclidean C2-smooth surface in the Heisenberg group away from characteristic points and signed geodesic curvature associated to two kinds of Schouten-Van Kampen affine connections and the adapted connection for Euclidean C2-smooth curves on surfaces.We get Gauss-Bonnet theorems associated to two kinds of Schouten-Van Kampen affine connections in the Heisenberg group.
