The non-linearity problem of aircraft system could not be overcome by using the MEMS sensor only.In order to improve the accuracy of aerial vehicle attitude,an aircraft attitude estimation of the MEMS sensor based on ...The non-linearity problem of aircraft system could not be overcome by using the MEMS sensor only.In order to improve the accuracy of aerial vehicle attitude,an aircraft attitude estimation of the MEMS sensor based on modified particle filter is proposed.The aircraft attitude is optimized by the conjugate gradient method,and the drift error of gyroscope is reduced.Moreover,the particle weight is updated by the observed value to obtain an optimized state estimate.Finally,the conjugate gradient method and the modified particle filter are weightily combined to determine the optimal weighting factor.The attitude estimation is carried out with STM32 and MEMS sensor as the core to design system.The experimental results show that the static and dynamic attitude estimation performances of the aircraft are improved.The performances are well,the attitude data is relatively stable,and the tracking characteristics are better.Moreover,it has better robustness and stability.展开更多
In order to estimate the systematic error in the processof maneuvering target adaptive tracking, a new method is proposed.The proposed method is a linear tracking scheme basedon a modified input estimation approach. A...In order to estimate the systematic error in the processof maneuvering target adaptive tracking, a new method is proposed.The proposed method is a linear tracking scheme basedon a modified input estimation approach. A special augmentationin the state space model is considered, in which both the systematicerror and the unknown input vector are attached to thestate vector. Then, an augmented state model and a measurementmodel are established in the case of systematic error, andthe corresponding filter formulas are also given. In the proposedscheme, the original state, the acceleration and the systematicerror vector can be estimated simultaneously. This method can notonly solve the maneuvering target adaptive tracking problem in thecase of systematic error, but also give the system error value inreal time. Simulation results show that the proposed tracking algorithmoperates in both the non-maneuvering and the maneuveringmodes, and the original state, the acceleration and the systematicerror vector can be estimated simultaneously.展开更多
Introducing frequency agility into a distributed multipleinput multiple-output(MIMO)radar can significantly enhance its anti-jamming ability.However,it would cause the sidelobe pedestal problem in multi-target paramet...Introducing frequency agility into a distributed multipleinput multiple-output(MIMO)radar can significantly enhance its anti-jamming ability.However,it would cause the sidelobe pedestal problem in multi-target parameter estimation.Sparse recovery is an effective way to address this problem,but it cannot be directly utilized for multi-target parameter estimation in frequency-agile distributed MIMO radars due to spatial diversity.In this paper,we propose an algorithm for multi-target parameter estimation according to the signal model of frequency-agile distributed MIMO radars,by modifying the orthogonal matching pursuit(OMP)algorithm.The effectiveness of the proposed method is then verified by simulation results.展开更多
There are two attitude estimation algorithms based on the different representations of attitude errors when modified Rodrigues parameters are applied to attitude estimation. The first is multiplicative error attitude ...There are two attitude estimation algorithms based on the different representations of attitude errors when modified Rodrigues parameters are applied to attitude estimation. The first is multiplicative error attitude estimator （MEAE）, whose attitude error is expressed by the modified Rodrigues parameters representing the rotation from the estimated to the true attitude. The second is subtractive error attitude estimator （SEAE）, whose attitude error is expressed by the arithmetic difference between the true and the estimated attitudes. It is proved that the two algorithms are equivalent in the case of small attitude errors. It is possible to describe rotation without encountering singularity by switching between the modified Rodrigues parameters and their shadow parameters. The attitude parameter switching does not bring disturbance to MEAE, but it does to SEAE. This article introduces a modification to eliminate the disturbance on SEAE, and simulation results demonstrate the efficacy of the presented algorithm.展开更多
A modified unscented particle filtering scheme for nonlinear tracking is proposed, in view of the potential drawbacks （such as, particle impoverishment and numerical sensitivity in calculating the prior） of the conv...A modified unscented particle filtering scheme for nonlinear tracking is proposed, in view of the potential drawbacks （such as, particle impoverishment and numerical sensitivity in calculating the prior） of the conventional unscented particle filter （UPF） confronted in practice. Specifically, a different derivation of the importance weight is presented in detail. The proposed method can avoid the calculation of the prior and reduce the effects of the impoverishment problem caused by sampling from the proposal distribution, Simulations have been performed using two illustrative examples and results have been provided to demonstrate the validity of the modified UPF as well as its improved performance over the conventional one.展开更多
In this paper,we consider a Cauchy problem of the time fractional diffusion equation(TFDE)in x∈[0,L].This problem is ubiquitous in science and engineering applications.The illposedness of the Cauchy problem is explai...In this paper,we consider a Cauchy problem of the time fractional diffusion equation(TFDE)in x∈[0,L].This problem is ubiquitous in science and engineering applications.The illposedness of the Cauchy problem is explained by its solution in frequency domain.Furthermore,the problem is formulated into a minimization problem with a modified Tikhonov regularization method.The gradient of the regularization functional based on an adjoint problem is deduced and the standard conjugate gradient method is presented for solving the minimization problem.The error estimates for the regularized solutions are obtained under Hp norm priori bound assumptions.Finally,numerical examples illustrate the effectiveness of the proposed method.展开更多
In this paper we discuss the convergence of a modified Newton’s method presented by A. Ostrowski [1] and J.F. Traub [2], which has quadratic convergence order but reduces one evaluation of the derivative at every two...In this paper we discuss the convergence of a modified Newton’s method presented by A. Ostrowski [1] and J.F. Traub [2], which has quadratic convergence order but reduces one evaluation of the derivative at every two steps compared with Newton’s method. A convergence theorem is established by using a weak condition a≤3-2(2<sup>1/2</sup>) and a sharp error estimate is given about the iterative sequence.展开更多
In this paper, we consider the initial boudary value problem for modified Zakharov system in 3 dimensions with small initial condition. By using the continuity lemma and the linear interpolation theory, together with ...In this paper, we consider the initial boudary value problem for modified Zakharov system in 3 dimensions with small initial condition. By using the continuity lemma and the linear interpolation theory, together with the properties of Sobolev spaces and the Galerkin method, we obtain the existence and uniqueness of the global solution.展开更多
A Fourier spectral method for the generalized Korteweg-de Vries equation with periodic boundary conditions is analyzed, and a corresponding optimal error estimate in L^2-norm is obtained. It improves the result presen...A Fourier spectral method for the generalized Korteweg-de Vries equation with periodic boundary conditions is analyzed, and a corresponding optimal error estimate in L^2-norm is obtained. It improves the result presented by Maday and Quarteroni. A modified Fourier pseudospectral method is also presented, with the same convergence properties as the Fourier spectral method.展开更多
This paper proposes a novel method for estimating the sparse inverse covariance matrixfor longitudinal data with informative dropouts. Based on the modified Cholesky decomposition,the sparse inverse covariance matrix ...This paper proposes a novel method for estimating the sparse inverse covariance matrixfor longitudinal data with informative dropouts. Based on the modified Cholesky decomposition,the sparse inverse covariance matrix is modelled by the autoregressive regression model,which guarantees the positive definiteness of the covariance matrix. To account for the informativedropouts, we then propose a penalized estimating equation method using the inverse probabilityweighting approach. The informative dropout propensity parameters are estimated by the generalizedmethod of moments. The asymptotic properties are investigated for the resulting estimators.Finally, we illustrate the effectiveness and feasibility of the proposed method through Monte Carlosimulations and a practical application.展开更多
In this paper,we propose a new extension of the traditional Rayleigh distribution called the modified Kies Rayleigh distribution.The new distribution contains one scale and one shape parameter and its hazard rate func...In this paper,we propose a new extension of the traditional Rayleigh distribution called the modified Kies Rayleigh distribution.The new distribution contains one scale and one shape parameter and its hazard rate function can be increasing and bathtub-shaped.Some mathematical properties of the new distribution are derived including quantiles and moments.The parameters of modified Kies Rayleigh distribution are estimated based on progressively Type-II censored data.For this purpose,we consider two estimation methods,namely maximum likelihood and maximum product of spacing estimation methods.To compare the efficiency of the proposed estimators,a simulation study is carried out.To show the applicability of the new model as well as the estimation methods,one real data for failure times of software is analyzed.Based on the empirical parts,we can conclude that the proposed model can be considered as a good model in the field of life testing and reliability analysis compared with other competing models.展开更多
In this paper maximum ranked set sampling procedure with unequal samples (MRSSU) is proposed. Maximum likelihood estimator and modified maximum likelihood estimator are obtained and their properties are studied under ...In this paper maximum ranked set sampling procedure with unequal samples (MRSSU) is proposed. Maximum likelihood estimator and modified maximum likelihood estimator are obtained and their properties are studied under exponential distribution. These methods are studied under both perfect and imperfect ranking (with errors in ranking). These estimators are then compared with estimators based on simple random sampling (SRS) and ranked set sampling (RSS) procedures. It is shown that relative efficiencies of the estimators based on MRSSU are better than those of the estimator based on SRS. Simulation results show that efficiency of proposed estimator is better than estimator based on RSS under ranking error.展开更多
In this paper,we discuss the conforming finite element method for a modified interior transmission eigenvalues problem.We present a complete theoretical analysis for the method,including the a priori and a posteriori ...In this paper,we discuss the conforming finite element method for a modified interior transmission eigenvalues problem.We present a complete theoretical analysis for the method,including the a priori and a posteriori error estimates.The theoretical analysis is conducted under the assumption of low regularity on the solution.We prove the reliability and efficiency of the a posteriori error estimators for eigenfunctions up to higher order terms,and we also analyze the reliability of estimators for eigenvalues.Finally,we report numerical experiments to show that our posteriori error estimator is effective and the approximations can reach the optimal convergence order.The numerical results also indicate that the conforming finite element eigenvalues approximate the exact ones from below,and there exists a monotonic relationship between the conforming finite element eigenvalues and the refractive index through numerical experiments.展开更多
In this paper,we derive a residual based a posteriori error estimator for a modified weak Galerkin formulation of second order elliptic problems.We prove that the error estimator used for interior penalty discontinuou...In this paper,we derive a residual based a posteriori error estimator for a modified weak Galerkin formulation of second order elliptic problems.We prove that the error estimator used for interior penalty discontinuous Galerkin methods still gives both upper and lower bounds for the modified weak Galerkin method,though they have essentially different bilinear forms.More precisely,we prove its reliability and efficiency for the actual error measured in the standard DG norm.We further provide an improved a priori error estimate under minimal regularity assumptions on the exact solution.Numerical results are presented to verify the theoretical analysis.展开更多
In this study we have proposed a modified ratio type estimator for population variance of the study variable y under simple random sampling without replacement making use of coefficient of kurtosis and median of an au...In this study we have proposed a modified ratio type estimator for population variance of the study variable y under simple random sampling without replacement making use of coefficient of kurtosis and median of an auxiliary variable x. The estimator’s properties have been derived up to first order of Taylor’s series expansion. The efficiency conditions derived theoretically under which the proposed estimator performs better than existing estimators. Empirical studies have been done using real populations to demonstrate the performance of the developed estimator in comparison with the existing estimators. The proposed estimator as illustrated by the empirical studies performs better than the existing estimators under some specified conditions i.e. it has the smallest Mean Squared Error and the highest Percentage Relative Efficiency. The developed estimator therefore is suitable to be applied to situations in which the variable of interest has a positive correlation with the auxiliary variable.展开更多
In this paper,we propose a new biased estimator namely modified almost unbiased Liu estimator by combining almost unbiased Liu estimator(AULE)andridge estimator(RE)in a linear regression model when multicollinearity p...In this paper,we propose a new biased estimator namely modified almost unbiased Liu estimator by combining almost unbiased Liu estimator(AULE)andridge estimator(RE)in a linear regression model when multicollinearity presents amongthe independent variables.Necessary and sufficient conditions for the proposed estimator over the ordinary least square estimator,RE,AULE and Liu estimator(LE)in the mean squared error matrix sense are derived,and the optimal biasing parameters are obtained.To illustrate the theoretical findings,a Monte Carlo simulation study is carried out and a numerical example is used.展开更多
In this article,we propose a new biased estimator,namely stochastic restricted modified almost unbiased Liu estimator by combining modified almost unbiased Liu estimator(MAULE)and mixed estimator(ME)when the stochasti...In this article,we propose a new biased estimator,namely stochastic restricted modified almost unbiased Liu estimator by combining modified almost unbiased Liu estimator(MAULE)and mixed estimator(ME)when the stochastic restrictions are available and the multicollinearity presents.The conditions of supe-riority of the proposed estimator over the ordinary least square estimator,ME,ridge estimator,Liu estimator,almost unbiased Liu estimator,stochastic restricted Liu esti-mator and MAULE in the mean squared error matrix sense are obtained.Finally,a numerical example and a Monte Carlo simulation are given to illustrate the theoretical findings.展开更多
基金National Natural Science Foundation of China(No.61261029)
文摘The non-linearity problem of aircraft system could not be overcome by using the MEMS sensor only.In order to improve the accuracy of aerial vehicle attitude,an aircraft attitude estimation of the MEMS sensor based on modified particle filter is proposed.The aircraft attitude is optimized by the conjugate gradient method,and the drift error of gyroscope is reduced.Moreover,the particle weight is updated by the observed value to obtain an optimized state estimate.Finally,the conjugate gradient method and the modified particle filter are weightily combined to determine the optimal weighting factor.The attitude estimation is carried out with STM32 and MEMS sensor as the core to design system.The experimental results show that the static and dynamic attitude estimation performances of the aircraft are improved.The performances are well,the attitude data is relatively stable,and the tracking characteristics are better.Moreover,it has better robustness and stability.
基金supported by the National Natural Science Foundation of China(91538201)
文摘In order to estimate the systematic error in the processof maneuvering target adaptive tracking, a new method is proposed.The proposed method is a linear tracking scheme basedon a modified input estimation approach. A special augmentationin the state space model is considered, in which both the systematicerror and the unknown input vector are attached to thestate vector. Then, an augmented state model and a measurementmodel are established in the case of systematic error, andthe corresponding filter formulas are also given. In the proposedscheme, the original state, the acceleration and the systematicerror vector can be estimated simultaneously. This method can notonly solve the maneuvering target adaptive tracking problem in thecase of systematic error, but also give the system error value inreal time. Simulation results show that the proposed tracking algorithmoperates in both the non-maneuvering and the maneuveringmodes, and the original state, the acceleration and the systematicerror vector can be estimated simultaneously.
文摘Introducing frequency agility into a distributed multipleinput multiple-output(MIMO)radar can significantly enhance its anti-jamming ability.However,it would cause the sidelobe pedestal problem in multi-target parameter estimation.Sparse recovery is an effective way to address this problem,but it cannot be directly utilized for multi-target parameter estimation in frequency-agile distributed MIMO radars due to spatial diversity.In this paper,we propose an algorithm for multi-target parameter estimation according to the signal model of frequency-agile distributed MIMO radars,by modifying the orthogonal matching pursuit(OMP)algorithm.The effectiveness of the proposed method is then verified by simulation results.
基金National Natural Science Foundation of China (10572114)
文摘There are two attitude estimation algorithms based on the different representations of attitude errors when modified Rodrigues parameters are applied to attitude estimation. The first is multiplicative error attitude estimator （MEAE）, whose attitude error is expressed by the modified Rodrigues parameters representing the rotation from the estimated to the true attitude. The second is subtractive error attitude estimator （SEAE）, whose attitude error is expressed by the arithmetic difference between the true and the estimated attitudes. It is proved that the two algorithms are equivalent in the case of small attitude errors. It is possible to describe rotation without encountering singularity by switching between the modified Rodrigues parameters and their shadow parameters. The attitude parameter switching does not bring disturbance to MEAE, but it does to SEAE. This article introduces a modification to eliminate the disturbance on SEAE, and simulation results demonstrate the efficacy of the presented algorithm.
文摘A modified unscented particle filtering scheme for nonlinear tracking is proposed, in view of the potential drawbacks （such as, particle impoverishment and numerical sensitivity in calculating the prior） of the conventional unscented particle filter （UPF） confronted in practice. Specifically, a different derivation of the importance weight is presented in detail. The proposed method can avoid the calculation of the prior and reduce the effects of the impoverishment problem caused by sampling from the proposal distribution, Simulations have been performed using two illustrative examples and results have been provided to demonstrate the validity of the modified UPF as well as its improved performance over the conventional one.
基金Supported by the National Natural Science Foundation of China(Grant No.11471253 and No.11571311)
文摘In this paper,we consider a Cauchy problem of the time fractional diffusion equation(TFDE)in x∈[0,L].This problem is ubiquitous in science and engineering applications.The illposedness of the Cauchy problem is explained by its solution in frequency domain.Furthermore,the problem is formulated into a minimization problem with a modified Tikhonov regularization method.The gradient of the regularization functional based on an adjoint problem is deduced and the standard conjugate gradient method is presented for solving the minimization problem.The error estimates for the regularized solutions are obtained under Hp norm priori bound assumptions.Finally,numerical examples illustrate the effectiveness of the proposed method.
基金Jointly supported by China Major Key Project for Basic Researcher and Provincial Natrural Science Foundation.
文摘In this paper we discuss the convergence of a modified Newton’s method presented by A. Ostrowski [1] and J.F. Traub [2], which has quadratic convergence order but reduces one evaluation of the derivative at every two steps compared with Newton’s method. A convergence theorem is established by using a weak condition a≤3-2(2<sup>1/2</sup>) and a sharp error estimate is given about the iterative sequence.
文摘In this paper, we consider the initial boudary value problem for modified Zakharov system in 3 dimensions with small initial condition. By using the continuity lemma and the linear interpolation theory, together with the properties of Sobolev spaces and the Galerkin method, we obtain the existence and uniqueness of the global solution.
基金Project supported by the National Natural Science Foundation of China (No. 60874039)Shanghai Leading Academic Discipline Project (No. J50101)
文摘A Fourier spectral method for the generalized Korteweg-de Vries equation with periodic boundary conditions is analyzed, and a corresponding optimal error estimate in L^2-norm is obtained. It improves the result presented by Maday and Quarteroni. A modified Fourier pseudospectral method is also presented, with the same convergence properties as the Fourier spectral method.
基金supported by the National Natural Science Foundation of China(Grant No.12171450).
文摘This paper proposes a novel method for estimating the sparse inverse covariance matrixfor longitudinal data with informative dropouts. Based on the modified Cholesky decomposition,the sparse inverse covariance matrix is modelled by the autoregressive regression model,which guarantees the positive definiteness of the covariance matrix. To account for the informativedropouts, we then propose a penalized estimating equation method using the inverse probabilityweighting approach. The informative dropout propensity parameters are estimated by the generalizedmethod of moments. The asymptotic properties are investigated for the resulting estimators.Finally, we illustrate the effectiveness and feasibility of the proposed method through Monte Carlosimulations and a practical application.
基金the Deanship Scientific Research(DSR)King Abdulaziz University,Jeddah under Grant No.(G:337-130-1441).
文摘In this paper,we propose a new extension of the traditional Rayleigh distribution called the modified Kies Rayleigh distribution.The new distribution contains one scale and one shape parameter and its hazard rate function can be increasing and bathtub-shaped.Some mathematical properties of the new distribution are derived including quantiles and moments.The parameters of modified Kies Rayleigh distribution are estimated based on progressively Type-II censored data.For this purpose,we consider two estimation methods,namely maximum likelihood and maximum product of spacing estimation methods.To compare the efficiency of the proposed estimators,a simulation study is carried out.To show the applicability of the new model as well as the estimation methods,one real data for failure times of software is analyzed.Based on the empirical parts,we can conclude that the proposed model can be considered as a good model in the field of life testing and reliability analysis compared with other competing models.
文摘In this paper maximum ranked set sampling procedure with unequal samples (MRSSU) is proposed. Maximum likelihood estimator and modified maximum likelihood estimator are obtained and their properties are studied under exponential distribution. These methods are studied under both perfect and imperfect ranking (with errors in ranking). These estimators are then compared with estimators based on simple random sampling (SRS) and ranked set sampling (RSS) procedures. It is shown that relative efficiencies of the estimators based on MRSSU are better than those of the estimator based on SRS. Simulation results show that efficiency of proposed estimator is better than estimator based on RSS under ranking error.
基金supported by the National Natural Science Foundation of China(Nos.12261024,11561014)Science and Technology Planning Project of Guizhou Province(Guizhou Kehe fundamental research-ZK[2022]No.324).
文摘In this paper,we discuss the conforming finite element method for a modified interior transmission eigenvalues problem.We present a complete theoretical analysis for the method,including the a priori and a posteriori error estimates.The theoretical analysis is conducted under the assumption of low regularity on the solution.We prove the reliability and efficiency of the a posteriori error estimators for eigenfunctions up to higher order terms,and we also analyze the reliability of estimators for eigenvalues.Finally,we report numerical experiments to show that our posteriori error estimator is effective and the approximations can reach the optimal convergence order.The numerical results also indicate that the conforming finite element eigenvalues approximate the exact ones from below,and there exists a monotonic relationship between the conforming finite element eigenvalues and the refractive index through numerical experiments.
基金The first author was supported by Guangdong Basic and Applied Basic Research Foundation(Grant Nos.2018A030307024 and 2020A1515011032)by National Natural Science Foundation of China(Grant No.11526097)+2 种基金The second author was supported by National Natural Science Foundation of China(Grant Nos.11871272 and 11871281)The third author was supported by National Natural Science Foundation of China(Grant No.11701197)The fourth author was supported by Guangdong Basic and Applied Basic Research Foundation(Grant No.2018A0303100016).
文摘In this paper,we derive a residual based a posteriori error estimator for a modified weak Galerkin formulation of second order elliptic problems.We prove that the error estimator used for interior penalty discontinuous Galerkin methods still gives both upper and lower bounds for the modified weak Galerkin method,though they have essentially different bilinear forms.More precisely,we prove its reliability and efficiency for the actual error measured in the standard DG norm.We further provide an improved a priori error estimate under minimal regularity assumptions on the exact solution.Numerical results are presented to verify the theoretical analysis.
文摘In this study we have proposed a modified ratio type estimator for population variance of the study variable y under simple random sampling without replacement making use of coefficient of kurtosis and median of an auxiliary variable x. The estimator’s properties have been derived up to first order of Taylor’s series expansion. The efficiency conditions derived theoretically under which the proposed estimator performs better than existing estimators. Empirical studies have been done using real populations to demonstrate the performance of the developed estimator in comparison with the existing estimators. The proposed estimator as illustrated by the empirical studies performs better than the existing estimators under some specified conditions i.e. it has the smallest Mean Squared Error and the highest Percentage Relative Efficiency. The developed estimator therefore is suitable to be applied to situations in which the variable of interest has a positive correlation with the auxiliary variable.
文摘In this paper,we propose a new biased estimator namely modified almost unbiased Liu estimator by combining almost unbiased Liu estimator(AULE)andridge estimator(RE)in a linear regression model when multicollinearity presents amongthe independent variables.Necessary and sufficient conditions for the proposed estimator over the ordinary least square estimator,RE,AULE and Liu estimator(LE)in the mean squared error matrix sense are derived,and the optimal biasing parameters are obtained.To illustrate the theoretical findings,a Monte Carlo simulation study is carried out and a numerical example is used.
文摘In this article,we propose a new biased estimator,namely stochastic restricted modified almost unbiased Liu estimator by combining modified almost unbiased Liu estimator(MAULE)and mixed estimator(ME)when the stochastic restrictions are available and the multicollinearity presents.The conditions of supe-riority of the proposed estimator over the ordinary least square estimator,ME,ridge estimator,Liu estimator,almost unbiased Liu estimator,stochastic restricted Liu esti-mator and MAULE in the mean squared error matrix sense are obtained.Finally,a numerical example and a Monte Carlo simulation are given to illustrate the theoretical findings.
