We consider the interior inverse scattering problem for recovering the shape of a penetrable partially coated cavity with external obstacles from the knowledge of measured scattered waves due to point sources.In the f...We consider the interior inverse scattering problem for recovering the shape of a penetrable partially coated cavity with external obstacles from the knowledge of measured scattered waves due to point sources.In the first part,we obtain the well-posedness of the direct scattering problem by the variational method.In the second part,we establish the mathematical basis of the linear sampling method to recover both the shape of the cavity,and the shape of the external obstacle,however the exterior transmission eigenvalue problem also plays a key role in the discussion of this paper.展开更多
In this paper, we consider the inverse scattering by chiral obstacle in electromagnetic fields, and prove that the linear sampling method is also effective to determine the support of a chiral obstacle from the noisy ...In this paper, we consider the inverse scattering by chiral obstacle in electromagnetic fields, and prove that the linear sampling method is also effective to determine the support of a chiral obstacle from the noisy far field data.展开更多
In this paper,we consider the time-harmonic electromagnetic scattering by a perfect conductor in a homogeneous chiral environment.For three-dimensional cylindrical structures,it can be simplified as a two–dimensional...In this paper,we consider the time-harmonic electromagnetic scattering by a perfect conductor in a homogeneous chiral environment.For three-dimensional cylindrical structures,it can be simplified as a two–dimensional model problem,which can be modeled by two scalar Helmholtz equations via coupled boundary conditions.The boundary integral equation method is used to prove the unique existence of the weak solution to this problem.Then we apply the linear sampling method to recover the scatterer from one of the far field pattern of wave fields.Some numerical examples are shown to verify the correctness and effectiveness of the proposed method.展开更多
Some difficulties are pointed out in the methods for identification of obstacles based on the numerical verification of tile inclusion of a function in the range of an operator. Numerical examples are given to illustr...Some difficulties are pointed out in the methods for identification of obstacles based on the numerical verification of tile inclusion of a function in the range of an operator. Numerical examples are given to illustrate theoretical conclusions. Alternative methods of identification of obstacles are mentioned： the Support Function Method （SFM） and the Modified Rayleigh Conjecture （MRC） method.展开更多
Uniform linear array(ULA)radars are widely used in the collision-avoidance radar systems of small unmanned aerial vehicles(UAVs).In practice,a ULA's multi-target direction of arrival(DOA)estimation performance suf...Uniform linear array(ULA)radars are widely used in the collision-avoidance radar systems of small unmanned aerial vehicles(UAVs).In practice,a ULA's multi-target direction of arrival(DOA)estimation performance suffers from significant performance degradation owing to the limited number of physical elements.To improve the underdetermined DOA estimation performance of a ULA radar mounted on a small UAV platform,we propose a nonuniform linear motion sampling underdetermined DOA estimation method.Using the motion of the UAV platform,the echo signal is sampled at different positions.Then,according to the concept of difference co-array,a virtual ULA with multiple array elements and a large aperture is synthesized to increase the degrees of freedom(DOFs).Through position analysis of the original and motion arrays,we propose a nonuniform linear motion sampling method based on ULA for determining the optimal DOFs.Under the condition of no increase in the aperture of the physical array,the proposed method obtains a high DOF with fewer sampling runs and greatly improves the underdetermined DOA estimation performance of ULA.The results of numerical simulations conducted herein verify the superior performance of the proposed method.展开更多
This paper uses a grouping-adjusting procedure to the data from a median linear regression model, and estimtes the regression coefficients by the method of weighted least squares. This method simplifies computation an...This paper uses a grouping-adjusting procedure to the data from a median linear regression model, and estimtes the regression coefficients by the method of weighted least squares. This method simplifies computation and in the meantime, preserves the same asymptotic normal distribution for the estimator, as in the ordinary minimum L_1-norm estimates.展开更多
This paper is concerned with the stability analysis and stabilization of networked discrete-time and sampled-data linear systems with random packet losses. Asymptotic stability, mean-square stability, and stochastic s...This paper is concerned with the stability analysis and stabilization of networked discrete-time and sampled-data linear systems with random packet losses. Asymptotic stability, mean-square stability, and stochastic stability are considered. For networked discrete-time linear systems, the packet loss period is assumed to be a finite-state Markov chain. We establish that the mean-square stability of a related discrete-time system which evolves in random time implies the mean-square stability of the system in deterministic time by using the equivalence of stability properties of Markovian jump linear systems in random time. We also establish the equivalence of asymptotic stability for the systems in deterministic discrete time and in random time. For networked sampled-data systems, a binary Markov chain is used to characterize the packet loss phenomenon of the network. In this case, the packet loss period between two transmission instants is driven by an identically independently distributed sequence assuming any positive values. Two approaches, namely the Markov jump linear system approach and randomly sampled system approach, are introduced. Based on the stability results derived, we present methods for stabilization of networked sampled-data systems in terms of matrix inequalities. Numerical examples are given to illustrate the design methods of stabilizing controllers.展开更多
Optical two-way time-frequency transfer(O-TWTFT),utilizing optical frequency comb carriers and linear optical sampling,effectively enables space-to-ground optical frequency standard comparisons.Previously reported det...Optical two-way time-frequency transfer(O-TWTFT),utilizing optical frequency comb carriers and linear optical sampling,effectively enables space-to-ground optical frequency standard comparisons.Previously reported detection sensitivities of O-TWTFTs were typically in the nanoWatt level,necessitating high-power optical frequency combs to compensate for significant losses in high-orbit satellite-to-ground passes.Such hardware-based solutions,while effective,tend to be costly.This paper presents a novel data post-processing algorithm to enhance sensitivity.Unlike previous timing methods,which depend solely on optical phase data and discard intensity information—resulting in elevated errors,especially under low-reception power,our approach employs complex least squares(CLS)estimation in the complex frequency domain.By preserving all intermediate data and avoiding noise from phase unwrapping,it achieves superior sensitivity and accuracy.Experiments over a 113-kilometer free-space link validate the algorithm's robustness,delivering a detection sensitivity of0.1 nanoWatts—over tenfold better than prior techniques—despite a 100-decibel link loss,comparable to Earth-Moon optical links.展开更多
In this paper,a hybrid approach which combines linear sampling method and the Bayesian method is proposed to simultaneously reconstruct multiple obsta-cles.The number of obstacles and the approximate geometric informa...In this paper,a hybrid approach which combines linear sampling method and the Bayesian method is proposed to simultaneously reconstruct multiple obsta-cles.The number of obstacles and the approximate geometric information arefirst qualitatively obtained by the linear sampling method.Based on the reconstructions of the linear sampling method,the Bayesian method is employed to obtain more refined details of the obstacles.The well-posedness of the posterior distribution is proved by using the Hellinger metric.The Markov Chain Monte Carlo algorithm is proposed to explore the posterior density with the initial guesses provided by the linear sampling method.Numerical experiments are provided to testify the effectiveness and efficiency of the proposed method.展开更多
In this paper, we are concerned with the inverse transmission eigenvalue problem to recover the shape as well as the constant refractive index of a penetrable medium scatterer. The linear sampling method is employed t...In this paper, we are concerned with the inverse transmission eigenvalue problem to recover the shape as well as the constant refractive index of a penetrable medium scatterer. The linear sampling method is employed to determine the transmission eigenvalues within a certain wavenumber interval based on far-field measurements. Based on a prior information given by the linear sampling method, the neural network approach is proposed for the reconstruction of the unknown scatterer. We divide the wavenumber intervals into several subintervals, ensuring that each transmission eigenvalue is located in its corresponding subinterval. In each such subinterval, the wavenumber that yields the maximum value of the indicator functional will be included in the input set during the generation of the training data. This technique for data generation effectively ensures the consistent dimensions of model input. The refractive index and shape are taken as the output of the network. Due to the fact that transmission eigenvalues considered in our method are relatively small,certain super-resolution effects can also be generated. Numerical experiments are presented to verify the effectiveness and promising features of the proposed method in two and three dimensions.展开更多
基金supported by the Natural Science Foundation of Xinjiang Uygur Autonomous Region of China(2019D01A05)supported by the NSFC(11571132)。
文摘We consider the interior inverse scattering problem for recovering the shape of a penetrable partially coated cavity with external obstacles from the knowledge of measured scattered waves due to point sources.In the first part,we obtain the well-posedness of the direct scattering problem by the variational method.In the second part,we establish the mathematical basis of the linear sampling method to recover both the shape of the cavity,and the shape of the external obstacle,however the exterior transmission eigenvalue problem also plays a key role in the discussion of this paper.
文摘In this paper, we consider the inverse scattering by chiral obstacle in electromagnetic fields, and prove that the linear sampling method is also effective to determine the support of a chiral obstacle from the noisy far field data.
基金Supported in part by the Research Project on Teaching Reform in Ordinary Higher Education Institutions in Hunan Province(No.HNJG-20231470)。
文摘In this paper,we consider the time-harmonic electromagnetic scattering by a perfect conductor in a homogeneous chiral environment.For three-dimensional cylindrical structures,it can be simplified as a two–dimensional model problem,which can be modeled by two scalar Helmholtz equations via coupled boundary conditions.The boundary integral equation method is used to prove the unique existence of the weak solution to this problem.Then we apply the linear sampling method to recover the scatterer from one of the far field pattern of wave fields.Some numerical examples are shown to verify the correctness and effectiveness of the proposed method.
文摘Some difficulties are pointed out in the methods for identification of obstacles based on the numerical verification of tile inclusion of a function in the range of an operator. Numerical examples are given to illustrate theoretical conclusions. Alternative methods of identification of obstacles are mentioned： the Support Function Method （SFM） and the Modified Rayleigh Conjecture （MRC） method.
基金National Natural Science Foundation of China(61973037)National 173 Program Project(2019-JCJQ-ZD-324)。
文摘Uniform linear array(ULA)radars are widely used in the collision-avoidance radar systems of small unmanned aerial vehicles(UAVs).In practice,a ULA's multi-target direction of arrival(DOA)estimation performance suffers from significant performance degradation owing to the limited number of physical elements.To improve the underdetermined DOA estimation performance of a ULA radar mounted on a small UAV platform,we propose a nonuniform linear motion sampling underdetermined DOA estimation method.Using the motion of the UAV platform,the echo signal is sampled at different positions.Then,according to the concept of difference co-array,a virtual ULA with multiple array elements and a large aperture is synthesized to increase the degrees of freedom(DOFs).Through position analysis of the original and motion arrays,we propose a nonuniform linear motion sampling method based on ULA for determining the optimal DOFs.Under the condition of no increase in the aperture of the physical array,the proposed method obtains a high DOF with fewer sampling runs and greatly improves the underdetermined DOA estimation performance of ULA.The results of numerical simulations conducted herein verify the superior performance of the proposed method.
基金Research supported By AFOSC, USA, under Contract F49620-85-0008oy NNSFC of China.
文摘This paper uses a grouping-adjusting procedure to the data from a median linear regression model, and estimtes the regression coefficients by the method of weighted least squares. This method simplifies computation and in the meantime, preserves the same asymptotic normal distribution for the estimator, as in the ordinary minimum L_1-norm estimates.
基金Supported by Agency for Science, Technology and Research (Grant No. SERC 052 101 0037)the National Natural Science Foundation of China(Grant No. 60828006)NSFC-Guangdong Joint Foundation (Grant No. U0735003)
文摘This paper is concerned with the stability analysis and stabilization of networked discrete-time and sampled-data linear systems with random packet losses. Asymptotic stability, mean-square stability, and stochastic stability are considered. For networked discrete-time linear systems, the packet loss period is assumed to be a finite-state Markov chain. We establish that the mean-square stability of a related discrete-time system which evolves in random time implies the mean-square stability of the system in deterministic time by using the equivalence of stability properties of Markovian jump linear systems in random time. We also establish the equivalence of asymptotic stability for the systems in deterministic discrete time and in random time. For networked sampled-data systems, a binary Markov chain is used to characterize the packet loss phenomenon of the network. In this case, the packet loss period between two transmission instants is driven by an identically independently distributed sequence assuming any positive values. Two approaches, namely the Markov jump linear system approach and randomly sampled system approach, are introduced. Based on the stability results derived, we present methods for stabilization of networked sampled-data systems in terms of matrix inequalities. Numerical examples are given to illustrate the design methods of stabilizing controllers.
基金supported by the National Key Research and Development Programme of China(Grant Nos.2020YFC2200103 and 2020YFA0309800)the National Natural Science Foundation of China(Grant No.T2125010)+4 种基金Strategic Priority Research Programme of Chinese Academy of Sciences(Grant No.XDB35030000)Anhui Initiative in Quantum Information Technologies(Grant No.AHY010100)Key R&D Plan of Shandong Province(Grant No.2021ZDPT01)Shanghai Municipal Science and Technology Major Project(Grant No.2019SHZDZX01)Innovation Programme for Quantum Science and Technology(Grant Nos.2021ZD0300100,2021ZD0300300,and2021ZD0300903)。
文摘Optical two-way time-frequency transfer(O-TWTFT),utilizing optical frequency comb carriers and linear optical sampling,effectively enables space-to-ground optical frequency standard comparisons.Previously reported detection sensitivities of O-TWTFTs were typically in the nanoWatt level,necessitating high-power optical frequency combs to compensate for significant losses in high-orbit satellite-to-ground passes.Such hardware-based solutions,while effective,tend to be costly.This paper presents a novel data post-processing algorithm to enhance sensitivity.Unlike previous timing methods,which depend solely on optical phase data and discard intensity information—resulting in elevated errors,especially under low-reception power,our approach employs complex least squares(CLS)estimation in the complex frequency domain.By preserving all intermediate data and avoiding noise from phase unwrapping,it achieves superior sensitivity and accuracy.Experiments over a 113-kilometer free-space link validate the algorithm's robustness,delivering a detection sensitivity of0.1 nanoWatts—over tenfold better than prior techniques—despite a 100-decibel link loss,comparable to Earth-Moon optical links.
基金supported by the Jilin Sci-Tech fund under JJKH20210797KJsupported by a startup grant from City University of Hong Kong and Hong Kong RGC General Research Funds(projects 12301218,12302919 and 12301420).
文摘In this paper,a hybrid approach which combines linear sampling method and the Bayesian method is proposed to simultaneously reconstruct multiple obsta-cles.The number of obstacles and the approximate geometric information arefirst qualitatively obtained by the linear sampling method.Based on the reconstructions of the linear sampling method,the Bayesian method is employed to obtain more refined details of the obstacles.The well-posedness of the posterior distribution is proved by using the Hellinger metric.The Markov Chain Monte Carlo algorithm is proposed to explore the posterior density with the initial guesses provided by the linear sampling method.Numerical experiments are provided to testify the effectiveness and efficiency of the proposed method.
基金supported by the Jilin Natural Science Foundation,China(No.20220101040JC)the National Natural Science Foundation of China(No.12271207)+2 种基金supported by the Hong Kong RGC General Research Funds(projects 11311122,12301420 and 11300821)the NSFC/RGC Joint Research Fund(project N-CityU 101/21)the France-Hong Kong ANR/RGC Joint Research Grant,A_CityU203/19.
文摘In this paper, we are concerned with the inverse transmission eigenvalue problem to recover the shape as well as the constant refractive index of a penetrable medium scatterer. The linear sampling method is employed to determine the transmission eigenvalues within a certain wavenumber interval based on far-field measurements. Based on a prior information given by the linear sampling method, the neural network approach is proposed for the reconstruction of the unknown scatterer. We divide the wavenumber intervals into several subintervals, ensuring that each transmission eigenvalue is located in its corresponding subinterval. In each such subinterval, the wavenumber that yields the maximum value of the indicator functional will be included in the input set during the generation of the training data. This technique for data generation effectively ensures the consistent dimensions of model input. The refractive index and shape are taken as the output of the network. Due to the fact that transmission eigenvalues considered in our method are relatively small,certain super-resolution effects can also be generated. Numerical experiments are presented to verify the effectiveness and promising features of the proposed method in two and three dimensions.
