Phase Residual Estimations for PCVs of Spaceborne GPS Receiver Antenna and Their Impacts on Precise Orbit Determination of GRACE Satellites

In-flight phase center systematic errors of global positioning system（GPS） receiver antenna are the main restriction for improving the precision of precise orbit determination using dual-frequency GPS.Residual approach is one of the valid methods for in-flight calibration of GPS receiver antenna phase center variations（PCVs） from ground calibration.In this paper,followed by the correction model of spaceborne GPS receiver antenna phase center,ionosphere-free PCVs can be directly estimated by ionosphere-free carrier phase post-fit residuals of reduced dynamic orbit determination.By the data processing of gravity recovery and climate experiment（GRACE） satellites,the following conclusions are drawn.Firstly,the distributions of ionosphere-free carrier phase post-fit residuals from different periods have the similar systematic characteristics.Secondly,simulations show that the influence of phase residual estimations for ionosphere-free PCVs on orbit determination can reach the centimeter level.Finally,it is shown by in-flight data processing that phase residual estimations of current period could not only be used for the calibration for GPS receiver antenna phase center of foretime and current period,but also be used for the forecast of ionosphere-free PCVs in future period,and the accuracy of orbit determination can be well improved.

Asymptotic normality of error density estimator in stationary and explosive autoregressive models

In this paper,we consider the limit distribution of the error density function estima-tor in the rst-order autoregressive models with negatively associated and positively associated random errors.Under mild regularity assumptions,some asymptotic normality results of the residual density estimator are obtained when the autoregressive models are stationary process and explosive process.In order to illustrate these results,some simulations such as con dence intervals and mean integrated square errors are provided in this paper.It shows that the residual density estimator can replace the density\estimator"which contains errors.

RESIDUAL A POSTERIORI ERROR ESTIMATE TWO-GRID METHODS FOR THE STEADY (NAVIER-STOKES) EQUATION WITH STREAM FUNCTION FORM

Residual based on a posteriori error estimates for conforming finite element solutions of incompressible Navier-Stokes equations with stream function form which were computed with seven recently proposed two-level method were derived. The posteriori error estimates contained additional terms in comparison to the error estimates for the solution obtained by the standard finite element method. The importance of these additional terms in the error estimates was investigated by studying their asymptotic behavior. For optimal scaled meshes, these bounds are not of higher order than of convergence of discrete solution.

A computational model of the human glucose-insulin regulatory system

Objective：A computational model of insulin secretion and glucose metabolism for assisting the diagnosis of diabetes mellitus in clinical research is introduced.The proposed method for the estimation of parameters for a system of ordinary differential equations（ODEs）that represent the time course of plasma glucose and insulin concentrations during glucose tolerance test（GTT）in physiological studies is presented.The aim of this study was to explore how to interpret those laboratory glucose and insulin data as well as enhance the Ackerman mathematical model.Methods：Parameters estimation for a system of ODEs was performed by minimizing the sum of squared residuals（SSR）function,which quantifies the difference between theoretical model predictions and GTT＇s experimental observations.Our proposed perturbation search and multiple-shooting methods were applied during the estimating process.Results：Based on the Ackerman＇s published data,we estimated the key parameters by applying R-based iterative computer programs.As a result,the theoretically simulated curves perfectly matched the experimental data points.Our model showed that the estimated parameters,computed frequency and period values,were proven a good indicator of diabetes.Conclusion：The present paper introduces a computational algorithm to biomedical problems,particularly to endocrinology and metabolism fields,which involves two coupled differential equations with four parameters describing the glucose-insulin regulatory system that Ackerman proposed earlier.The enhanced approach may provide clinicians in endocrinology and metabolism field insight into the transition nature of human metabolic mechanism from normal to impaired glucose tolerance.

Efficient Numerical Scheme for the Solution of HIV Infection CD4^(+)T-Cells Using Haar Wavelet Technique

In this paper,Haar collocation algorithmis developed for the solution of first-order ofHIV infection CD4^(+)T-Cells model.In this technique,the derivative in the nonlinear model is approximated by utilizing Haar functions.The value of the unknown function is obtained by the process of integration.Error estimation is also discussed,which aims to reduce the error of numerical solutions.The numerical results show that the method is simply applicable.The results are compared with Runge-Kutta technique,Bessel collocation technique,LADM-Pade and Galerkin technique available in the literature.The results show that the Haar technique is easy,precise and effective.

Enhanced baseline determination for formation flying LEOs by relative corrections of phase center and code residual variations

Formation flying Low Earth Orbiters(LEOs)are important for implementing new and advanced concepts in Earth observation missions.Precise Baseline Determination(PBD)is a prerequisite for LEOs to complete specified mission targets.PBD is usually performed based on space-borne GNSS data,the relative corrections of phase center and code residual variations play crucial roles in achieving the best relative orbit accuracy.Herein,the influences of antenna Relative Phase Centre Variations(RPCVs)and Single-Difference(SD)Melbourne-Wu¨bbena(MW)Combination Residuals Variations(SD MWVs)on PBD are studied.The methods were tested using flight data from Gravity Recovery And Climate Experiment(GRACE)and GRACE Follow-On(GRACE-FO).Results showed that the maximum values for RPCVs and SD MWVs were 14 mm and 0.32 cycles,respectively.Then,the RPCVs correction significantly enhanced the baseline accuracy;the K-Band Ranging(KBR)measurement consistency improved by 30.1%and 37.5%for GRACE and GRACE-FO,respectively.The application of SD MWVs further improved the accuracy and reliability of PBD results.For GRACE,the ambiguities fixing success rate increased from 85.1%to 97.9%and a baseline consistency of 0.57 mm was achieved for the KBR measurements.It was found that the correction of both RPCVs and SD MWVs reduced the carrier phase observation minus computation residuals from double-difference ionosphere-free combination.In addition,in-flight data processing demonstrated that RPCVs and SD MWVs estimations for the current period could be used for the previous and subsequent periods.

CONVERGENCE OF ADAPTIVE EDGE ELEMENT METHODS FOR THE 3D EDDY CURRENTS EQUATIONS

We consider an Adaptive Edge Finite Element Method （AEFEM） for the 3D eddy currents equations with variable coefficients using a residual-type a posteriori error estimator. Both the components of the estimator and certain oscillation terms, due to the occurrence of the variable coefficients, have to be controlled properly within the adaptive loop which is taken care of by appropriate bulk criteria. Convergence of the AEFEM in terms of reductions of the energy norm of the discretization error and of the oscillations is shown. Numerical results are given to illustrate the performance of the AEFEM.

A Review of Unified A Posteriori Finite Element Error Control

This paper aims at a general guideline to obtain a posteriori error estimates for the finite element error control in computational partial differential equations.In the abstract setting of mixed formulations,a generalised formulation of the corresponding residuals is proposed which then allows for the unified estimation of the respective dual norms.Notably,this can be done with an approach which is applicable in the same way to conforming,nonconforming and mixed discretisations.Subsequently,the unified approach is applied to various model problems.In particular,we consider the Laplace,Stokes,Navier-Lamé,and the semi-discrete eddy current equations.