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Efficient error estimation in quantum key distribution

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Chinese Physics B 2015年第1期24卷 153-156页

作者：李默 Patcharapong Treeviriyanupab 张春梅银振强陈巍韩正甫 Key Laboratory of Quantum Information Chinese Academy of Sciences University of Science and Technology of China Synergetic Innovation Center of Quantum Information & Quantum Physics University of Science and Technology of China Department of Computer Science Faculty of Science and Technology Phranakhon Rajabhat UniversityBangkok Thailand

In a quantum key distribution（QKD） system, the error rate needs to be estimated for determining the joint probability distribution between legitimate parties, and for improving the performance of key reconciliation. We propose an efficient error estimation scheme for QKD, which is called parity comparison method（PCM）. In the proposed method, the parity of a group of sifted keys is practically analysed to estimate the quantum bit error rate instead of using the traditional key sampling. From the simulation results, the proposed method evidently improves the accuracy and decreases revealed information in most realistic application situations.

关键词： error estimation parity comparison quantum key distribution

A simple error estimation method for linear-regression-based thermal sharpening techniques with the consideration of scale difference

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Geo-Spatial Information Science 2014年第1期17卷 54-59页

作者： Xuehong CHEN Wentao LI Jin CHEN Wenfeng ZHAN Yuhan RAO State Key Laboratory of Earth Surface Processes and Resource Ecology Beijing Normal UniversityBeijing 100875China Jiangsu Provincial Key Laboratory of Geographic Information Science and Technology International Institute of Earth System ScienceNanjing UniversityNanjing 210093China

Thermal remote sensing imagery is helpful for land cover classification and related analysis.Unfortunately,the spatial resolution of thermal infrared(TIR)band is generally coarser than that of visual near-infrared band,which limits its more precise applications.Various thermal sharpening(TSP)techniques have been developed for improving the spatial resolution of the imagery of TIR band or land surface temperature(LST).However,there is no research on the theoretical estimation of TSP error till now,which implies that the error in sharpened LST imagery is unknown and the further analysis might be not reliable.In this paper,an error estimation method based on classical linear regression theory for the linear-regression-based TSP techniques was firstly introduced.However,the scale difference between the coarse resolution and fine resolution is not considered in this method.Therefore,we further developed an improved error estimation method with the consideration of the scale difference,which employs a novel term named equivalent random sample size to reflect the scale difference.A simulation study of modified TsHARP(a typical TSP technique)shows that the improved method estimated the TSP error more accurately than classical regression theory.Especially,the phenomena that TSP error increases with the increasing resolution gap between the initial and target resolutions can be successfully predicted by the proposed method.

关键词： thermal sharpening error estimation linear regression equivalent random sample size

An Online Model Correction Method Based on an Inverse Problem:Part I—Model error estimation by Iteration

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Advances in Atmospheric Sciences 2015年第10期32卷 1329-1340页

作者： XUE Haile SHEN Xueshun CHOU Jifan State Key Laboratory of Severe Weather Chinese Academy of Meteorological Sciences School of Atmospheric Sciences Lanzhou University Center for Numerical Prediction China Meteorological Administration

errors inevitably exist in numerical weather prediction （NWP） due to imperfect numeric and physical parameterizations. To eliminate these errors, by considering NWP as an inverse problem, an unknown term in the prediction equations can be estimated inversely by using the past data, which are presumed to represent the imperfection of the NWP model （model error, denoted as ME）. In this first paper of a two-part series, an iteration method for obtaining the MEs in past intervals is presented, and the results from testing its convergence in idealized experiments are reported. Moreover, two batches of iteration tests were applied in the global forecast system of the Global and Regional Assimilation and Prediction System （GRAPES-GFS） for July-August 2009 and January-February 2010. The datasets associated with the initial conditions and sea surface temperature （SST） were both based on NCEP （National Centers for Environmental Prediction） FNL （final） data. The results showed that 6th h forecast errors were reduced to 10% of their original value after a 20-step iteration. Then, off-line forecast error corrections were estimated linearly based on the 2-month mean MEs and compared with forecast errors. The estimated error corrections agreed well with the forecast errors, but the linear growth rate of the estimation was steeper than the forecast error. The advantage of this iteration method is that the MEs can provide the foundation for online correction. A larger proportion of the forecast errors can be expected to be canceled out by properly introducing the model error correction into GRAPES-GFS.

关键词： model error past data inverse problem error estimation model correction GRAPES-GFS

Neural Network-Based GNSS Localization error estimation Method

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Neural Network-Based GNSS Localization Error Estimation Meth...

error estimation OF INTERPOLATION ON PORE STRUCTURE ANALYSIS

第十三届中国卫星导航年会

作者： Xinyi Li Baigen Cai Debiao Lu Jiang Liu School of Electronic and Information Engineering Beijing Engineering Research Center of EMC and GNSS Technology for Rail Transport Frontiers Science Center for Smart High-speed Railway System Beijing Jiaotong University

With the development of the Global Navigation Satellite Systems（GNSS）, GNSS-based localization techniques have become the vital source of location for many fundamental applications. However, GNSS localization performance can be affected by the environment on the propagation trajectory,which leads to varying degrees of accuracy degradation. The GNSS localization errors can vary from centimeters to meters level in different environments, an accurate position error estimation model is of great significance, which provides basic information for error correction. GNSS receivers work obeying the same principle, with differences in location algorithms. In this paper, parameters such as SNR（signal noise ratio）, elevation angle, azimuth, and HDOP are extracted as the observed quantities, and the relationship between the total localization error and the observed quantities is studied using neural networks and localization data in different environmental scenarios. The localization error model is then validated using field collected data, and the mean square error of the loss function and the goodness-of-fit values illustrate that the training effect of the Long short-term memory（LSTM） network is better than that of deep neural network（DNN）, and the generalizability of DNN model parameters is better than that of LSTM, both of which can be used to improve the accuracy of static localization and the smoothness of dynamic localization paths.

关键词： DNN neural networks LSTM neural network GNSS localization error estimation performance evaluation

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Journal of Wuhan University of Technology(Materials Science) 1995年第4期10卷 48-51页

作者：管昌生崔崇陆宇萍 Wuhan Univ of Technology Wuhan China

In this paper we computed the data of pore structure with Lagrange interpolation method, analyzed the convergence of the method and deduced the corresponding error estimation formula.

关键词： pore structure interpolation convergence error estimation

Quick estimation of parameters for the land surface data assimilation system and its influence based on the extended Kalman filter and automatic differentiation

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Science China Earth Sciences 2023年第11期66卷 2546-2562页

作者： Jiaxin TIAN Hui LU Kun YANG Jun QIN Long ZHAO Jianhong ZHOU Yaozhi JIANG Xiaogang MA Department of Earth System Science Ministry of Education Key Laboratory for Earth System ModelingInstitute for Global Change StudiesTsinghua UniversityBeijing 100084China National Tibetan Plateau Data Center Key Laboratory of Tibetan Environmental Changes and Land Surfaces ProcessesInstitute of Tibetan Plateau ResearchChinese Academy of SciencesBeijing 100101China State Key Laboratory of Resources and Environmental Information System Institute of Geographic Sciences and Natural Resources ResearchChinese Academy of SciencesBeijing 100101China Chongqing Jinfo Mountain Karst Ecosystem National Observation and Research Station School of Geographical SciencesSouth-west UniversityChongqing 400715China Tsinghua University(Department of Earth System Science)-Xi’an Institute of Surveying and Mapping Joint Research Center for Next-Generation Smart Mapping Beijing 100084China

Soil moisture plays a crucial role in drought monitoring,flood forecasting,and water resource management.Data assimilation methods can integrate the strengths of land surface models(LSM)and remote sensing data to generate highprecision and spatio-temporally continuous soil moisture products.However,one of the challenges of the land data assimilation system(LDAS)is how to accurately estimate model and observation errors.To address this,we had previously proposed a dualcycle assimilation algorithm that can simultaneously estimate the model and observation errors,LSM parameters,and observation operator parameters.However,this algorithm requires a large ensemble size to guarantee stable parameter estimates,resulting in low efficiency and limiting its large-scale applications.To address this limitation,the authors employed the following approaches:(1)using automatic differentiation to compute the Jacobian matrix of LSM instead of constructing a tangent linear model of LSM,and(2)replacing the ensemble Kalman filter framework with the extended Kalman filter(EKF)framework to improve the efficiency of parameter optimization for the dual-cycle algorithm.The EKF-based dual-cycle algorithm accelerated the parameter estimation efficiency near 60 times during a 90-day time period with a model integration time step of 1 h.To evaluate the dual-cycle LDAS at the regional-scale,it was applied to assimilate the SMAP soil moisture over the Tibetan Plateau,and soil moisture estimates were validated using in situ observations from four different climatic areas.The results showed that the EKF-based dual-cycle LDAS corrected biases in both the model and observations and produced more accurate estimates of soil moisture,land surface temperature,and evapotranspiration than did the open loop with default parameters.Furthermore,the spatial distribution of soil parameters(sand content,clay content,and porosity)obtained from the LDAS was more reasonable than those of default values.The EKF-based dual-cycle algorithm developed in this study is

关键词： Soil moisture Data assimilation Parameter optimization Bias correction error estimation Automatic differentiation

Influence of dissipation on solitary wave solution to generalized Boussinesq equation

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Applied Mathematics and Mechanics(English Edition) 2023年第3期44卷 477-498页

作者： Weiguo ZHANG Siyu HONG Xingqian LING Wenxia LI College of Science University of Shanghai for Science and TechnologyShanghai 200093China

This paper uses the theory of planar dynamic systems and the knowledge of reaction-diffusion equations,and then studies the bounded traveling wave solution of the generalized Boussinesq equation affected by dissipation and the influence of dissipation on solitary waves.The dynamic system corresponding to the traveling wave solution of the equation is qualitatively analyzed in detail.The influence of the dissipation coefficient on the solution behavior of the bounded traveling wave is studied,and the critical values that can describe the magnitude of the dissipation effect are,respectively,found for the two cases of b_30 in the equation.The results show that,when the dissipation effect is significant(i.e.,r is greater than the critical value in a certain situation),the traveling wave solution to the generalized Boussinesq equation appears as a kink-shaped solitary wave solution;when the dissipation effect is small(i.e.,r is smaller than the critical value in a certain situation),the traveling wave solution to the equation appears as the oscillation attenuation solution.By using the hypothesis undetermined method,all possible solitary wave solutions to the equation when there is no dissipation effect(i.e.,r=0)and the partial kink-shaped solitary wave solution when the dissipation effect is significant are obtained;in particular,when the dissipation effect is small,an approximate solution of the oscillation attenuation solution can be achieved.This paper is further based on the idea of the homogenization principles.By establishing an integral equation reflecting the relationship between the approximate solution of the oscillation attenuation solution and the exact solution obtained in the paper,and by investigating the asymptotic behavior of the solution at infinity,the error estimate between the approximate solution of the oscillation attenuation solution and the exact solution is obtained,which is an infinitesimal amount that decays exponentially.The influence of the dissipation coefficient on the ampli

关键词： generalized Boussinesq equation influence of dissipation qualitative analysis solitary wave solution oscillation attenuation solution error estimation

Approximate Analytical Solution of the Generalized Kolmogorov-Petrovsky-Piskunov Equation with Cubic Nonlinearity

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Acta Mathematicae Applicatae Sinica 2023年第2期39卷 424-449页

作者： Wei-guo ZHANG Xie-kui HU Xing-qian LING Wen-xia LI College of Science University of Shanghai for Science and TechnologyShanghai 200093China

In this paper,the approximate analytical oscillatory solutions to the generalized KolmogorovPetrovsky-Piskunov equation(gKPPE for short)are discussed by employing the theory of dynamical system and hypothesis undetermined method.According to the corresponding dynamical system of the bounded traveling wave solutions to the gKPPE,the number and qualitative properties of these bounded solutions are received.Furthermore,pulses(bell-shaped)and waves fronts(kink-shaped)of the gKPPE are given.In particular,two types of approximate analytical oscillatory solutions are constructed.Besides,the error estimations between the approximate analytical oscillatory solutions and the exact solutions of the gKPPE are obtained by the homogeneity principle.Finally,the approximate analytical oscillatory solutions are compared with the numerical solutions,which shows the two types of solutions are similar.

关键词： reaction-diffusion equation approximate analytical solution error estimation dynamical system approach

Existence and numerical approximation of a solution to frictional contact problem for electro-elastic materials

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Applied Mathematics(A Journal of Chinese Universities) 2024年第2期39卷 201-219页

作者： Othman Baiz EL-Hassan Benkhira Rachid Fakhar University Ibn Zohr Lab.ESERFP of OuarzazateMorocco University Moulay Ismail Faculty of SciencesLaboratory MACSESTMBP 3103Toulal-MeknesMorocco University Sultan Moulay Slimane Laboratory LS2MEPolydisciplary Faculty of Khouribga25000 KhouribgaMorocco

In this paper,a frictional contact problem between an electro-elastic body and an electrically conductive foundation is studied.The contact is modeled by normal compliance with finite penetration and a version of Coulomb’s law of dry friction in which the coefficient of friction depends on the slip.In addition,the effects of the electrical conductivity of the foundation are taken into account.This model leads to a coupled system of the quasi-variational inequality of the elliptic type for the displacement and the nonlinear variational equation for the electric potential.The existence of a weak solution is proved by using an abstract result for elliptic variational inequalities and a fixed point argument.Then,a finite element approximation of the problem is presented.Under some regularity conditions,an optimal order error estimate of the approximate solution is derived.Finally,a successive iteration technique is used to solve the problem numerically and a convergence result is established.

关键词： piezoelectric material frictional contact variational Inequality fixed point process finite element method error estimation iteration method