Wireless sensor network(WSN)positioning has a good effect on indoor positioning,so it has received extensive attention in the field of positioning.Non-line-of sight(NLOS)is a primary challenge in indoor complex enviro...Wireless sensor network(WSN)positioning has a good effect on indoor positioning,so it has received extensive attention in the field of positioning.Non-line-of sight(NLOS)is a primary challenge in indoor complex environment.In this paper,a robust localization algorithm based on Gaussian mixture model and fitting polynomial is proposed to solve the problem of NLOS error.Firstly,fitting polynomials are used to predict the measured values.The residuals of predicted and measured values are clustered by Gaussian mixture model(GMM).The LOS probability and NLOS probability are calculated according to the clustering centers.The measured values are filtered by Kalman filter(KF),variable parameter unscented Kalman filter(VPUKF)and variable parameter particle filter(VPPF)in turn.The distance value processed by KF and VPUKF and the distance value processed by KF,VPUKF and VPPF are combined according to probability.Finally,the maximum likelihood method is used to calculate the position coordinate estimation.Through simulation comparison,the proposed algorithm has better positioning accuracy than several comparison algorithms in this paper.And it shows strong robustness in strong NLOS environment.展开更多
To improve the prediction accuracy of chaotic time series, a new methodformed on the basis of local polynomial prediction is proposed. The multivariate phase spacereconstruction theory is utilized to reconstruct the p...To improve the prediction accuracy of chaotic time series, a new methodformed on the basis of local polynomial prediction is proposed. The multivariate phase spacereconstruction theory is utilized to reconstruct the phase space firstly, and on its basis, apolynomial function is applied to construct the prediction model, then the parameters of the modelaccording to the data matrix built with the embedding dimensions are estimated and a one-stepprediction value is calculated. An estimate and one-step prediction value is calculated. Finally,the mean squared root statistics are used to estimate the prediction effect. The simulation resultsobtained by the Lorenz system and the prediction results of the Shanghai composite index show thatthe local polynomial prediction errors of the multivariate chaotic time series are small and itsprediction accuracy is much higher than that of the univariate chaotic time series.展开更多
In this paper, we propose a new method that combines chaotic series phase space reconstruction and local polynomial estimation to solve the problem of suppressing strong chaotic noise. First, chaotic noise time series...In this paper, we propose a new method that combines chaotic series phase space reconstruction and local polynomial estimation to solve the problem of suppressing strong chaotic noise. First, chaotic noise time series are reconstructed to obtain multivariate time series according to Takens delay embedding theorem. Then the chaotic noise is estimated accurately using local polynomial estimation method. After chaotic noise is separated from observation signal, we can get the estimation of the useful signal. This local polynomial estimation method can combine the advantages of local and global law. Finally, it makes the estimation more exactly and we can calculate the formula of mean square error theoretically. The simulation results show that the method is effective for the suppression of strong chaotic noise when the signal to interference ratio is low.展开更多
In this study, a multivariate local quadratic polynomial regression(MLQPR) method is proposed to design a model for the sludge volume index(SVI). In MLQPR, a quadratic polynomial regression function is established to ...In this study, a multivariate local quadratic polynomial regression(MLQPR) method is proposed to design a model for the sludge volume index(SVI). In MLQPR, a quadratic polynomial regression function is established to describe the relationship between SVI and the relative variables, and the important terms of the quadratic polynomial regression function are determined by the significant test of the corresponding coefficients. Moreover, a local estimation method is introduced to adjust the weights of the quadratic polynomial regression function to improve the model accuracy. Finally, the proposed method is applied to predict the SVI values in a real wastewater treatment process(WWTP). The experimental results demonstrate that the proposed MLQPR method has faster testing speed and more accurate results than some existing methods.展开更多
The extended Kantorovich method is employed to study the local stress concentrations at the vicinity of free edges in symmetrically layered composite laminates subjected to uniaxial tensile load upon polynomial stress...The extended Kantorovich method is employed to study the local stress concentrations at the vicinity of free edges in symmetrically layered composite laminates subjected to uniaxial tensile load upon polynomial stress functions. The stress fields are initially assumed by means of the Lekhnitskii stress functions under the plane strain state. Applying the principle of complementary virtual work,the coupled ordinary differential equations are obtained in which the solutions can be obtained by solving a generalized eigenvalue problem. Then an iterative procedure is established to achieve convergent stress distributions. It should be noted that the stress function based extended Kantorovich method can satisfy both the traction-free and free edge stress boundary conditions during the iterative processes. The stress components near the free edges and in the interior regions are calculated and compared with those obtained results by finite element method（FEM）. The convergent stresses have good agreements with those results obtained by three dimensional（3D） FEM. For generality, various layup configurations are considered for the numerical analysis. The results show that the proposed polynomial stress function based extended Kantorovich method is accurate and efficient in predicting the local stresses in composite laminates and computationally much more efficient than the 3D FEM.展开更多
In this paper, we try to find numerical solution of y'(x)= p(x)y(x)+g(x)+λ∫ba K(x, t)y(t)dt, y(a)=α. a≤x≤b, a≤t≤b or y'(x)= p(x)y(x)+g(x)+λ∫xa K(x, t)y(t)dt, y(a)=α. a≤x≤b, a≤t≤b by using Local p...In this paper, we try to find numerical solution of y'(x)= p(x)y(x)+g(x)+λ∫ba K(x, t)y(t)dt, y(a)=α. a≤x≤b, a≤t≤b or y'(x)= p(x)y(x)+g(x)+λ∫xa K(x, t)y(t)dt, y(a)=α. a≤x≤b, a≤t≤b by using Local polynomial regression (LPR) method. The numerical solution shows that this method is powerful in solving integro-differential equations. The method will be tested on three model problems in order to demonstrate its usefulness and accuracy.展开更多
Under the condition that the total distribution function is continuous and bounded on （ -∞,∞ ）, we constructed estimations for distribution and hazard functions with local polynomial method, and obtained the rate ...Under the condition that the total distribution function is continuous and bounded on （ -∞,∞ ）, we constructed estimations for distribution and hazard functions with local polynomial method, and obtained the rate of strong convergence of the estimations.展开更多
In this paper, auxiliary information is used to determine an estimator of finite population total using nonparametric regression under stratified random sampling. To achieve this, a model-based approach is adopted by ...In this paper, auxiliary information is used to determine an estimator of finite population total using nonparametric regression under stratified random sampling. To achieve this, a model-based approach is adopted by making use of the local polynomial regression estimation to predict the nonsampled values of the survey variable y. The performance of the proposed estimator is investigated against some design-based and model-based regression estimators. The simulation experiments show that the resulting estimator exhibits good properties. Generally, good confidence intervals are seen for the nonparametric regression estimators, and use of the proposed estimator leads to relatively smaller values of RE compared to other estimators.展开更多
Approximation of finite population totals in the presence of auxiliary information is considered. A polynomial based on Lagrange polynomial is proposed. Like the local polynomial regression, Horvitz Thompson and ratio...Approximation of finite population totals in the presence of auxiliary information is considered. A polynomial based on Lagrange polynomial is proposed. Like the local polynomial regression, Horvitz Thompson and ratio estimators, this approximation technique is based on annual population total in order to fit in the best approximating polynomial within a given period of time (years) in this study. This proposed technique has shown to be unbiased under a linear polynomial. The use of real data indicated that the polynomial is efficient and can approximate properly even when the data is unevenly spaced.展开更多
In this research article,we construct a family of derivative free simultaneous numerical schemes to approximate all real zero of non-linear polynomial equation.We make a comparative analysis of the newly constructed n...In this research article,we construct a family of derivative free simultaneous numerical schemes to approximate all real zero of non-linear polynomial equation.We make a comparative analysis of the newly constructed numerical schemes with a well-known existing simultaneous method for determining all the distinct real zeros of polynomial equations using computer algebra system Mat Lab.Lower bound of convergence of simultaneous schemes is calculated using Mathematica.Global convergence property of the numerical schemes is presented by taking random starting initial approximation and their convergence history are graphically presented.Some real life engineering applications along with some higher degree polynomials are considered as numerical test problems to show performance and efficiency of the derivative free family of numerical methods with comparison of an existing method of same order in literature.Local computational order of convergence,CPU time,graph of computational order of convergence and residual error graphs elaborate efficiency,robustness and authentication of the suggested family of numerical methods in its domain.展开更多
Based on the idea of local polynomial double-smoother, we propose an estimator of a conditional cumulative distribution function with dependent and left-truncated data. It is assumed that the observations form a stati...Based on the idea of local polynomial double-smoother, we propose an estimator of a conditional cumulative distribution function with dependent and left-truncated data. It is assumed that the observations form a stationary a-mixing sequence. Asymptotic normality of the estimator is established. The finite sample behavior of the estimator is investigated via simulations.展开更多
Most of the near-field source localization methods are developed with the approximated signal model,because the phases of the received near-field signal are highly non-linear.Nevertheless,the approximated signal model...Most of the near-field source localization methods are developed with the approximated signal model,because the phases of the received near-field signal are highly non-linear.Nevertheless,the approximated signal model based methods suffer from model mismatch and performance degradation while the exact signal model based estimation methods usually involve parameter searching or multiple decomposition procedures.In this paper,a search-free near-field source localization method is proposed with the exact signal model.Firstly,the approximative estimates of the direction of arrival(DOA)and range are obtained by using the approximated signal model based method through parameter separation and polynomial rooting operations.Then,the approximative estimates are corrected with the exact signal model according to the exact expressions of phase difference in near-field observations.The proposed method avoids spectral searching and parameter pairing and has enhanced estimation performance.Numerical simulations are provided to demonstrate the effectiveness of the proposed method.展开更多
基金supported by the National Natural Science Foundation of China under Grant No.62273083 and No.61973069Natural Science Foundation of Hebei Province under Grant No.F2020501012。
文摘Wireless sensor network(WSN)positioning has a good effect on indoor positioning,so it has received extensive attention in the field of positioning.Non-line-of sight(NLOS)is a primary challenge in indoor complex environment.In this paper,a robust localization algorithm based on Gaussian mixture model and fitting polynomial is proposed to solve the problem of NLOS error.Firstly,fitting polynomials are used to predict the measured values.The residuals of predicted and measured values are clustered by Gaussian mixture model(GMM).The LOS probability and NLOS probability are calculated according to the clustering centers.The measured values are filtered by Kalman filter(KF),variable parameter unscented Kalman filter(VPUKF)and variable parameter particle filter(VPPF)in turn.The distance value processed by KF and VPUKF and the distance value processed by KF,VPUKF and VPPF are combined according to probability.Finally,the maximum likelihood method is used to calculate the position coordinate estimation.Through simulation comparison,the proposed algorithm has better positioning accuracy than several comparison algorithms in this paper.And it shows strong robustness in strong NLOS environment.
文摘To improve the prediction accuracy of chaotic time series, a new methodformed on the basis of local polynomial prediction is proposed. The multivariate phase spacereconstruction theory is utilized to reconstruct the phase space firstly, and on its basis, apolynomial function is applied to construct the prediction model, then the parameters of the modelaccording to the data matrix built with the embedding dimensions are estimated and a one-stepprediction value is calculated. An estimate and one-step prediction value is calculated. Finally,the mean squared root statistics are used to estimate the prediction effect. The simulation resultsobtained by the Lorenz system and the prediction results of the Shanghai composite index show thatthe local polynomial prediction errors of the multivariate chaotic time series are small and itsprediction accuracy is much higher than that of the univariate chaotic time series.
基金supported by the Natural Science Foundation of Chongqing Science & Technology Commission,China (Grant No.CSTC2010BB2310)the Chongqing Municipal Education Commission Foundation,China (Grant Nos.KJ080614,KJ100810,and KJ100818)
文摘In this paper, we propose a new method that combines chaotic series phase space reconstruction and local polynomial estimation to solve the problem of suppressing strong chaotic noise. First, chaotic noise time series are reconstructed to obtain multivariate time series according to Takens delay embedding theorem. Then the chaotic noise is estimated accurately using local polynomial estimation method. After chaotic noise is separated from observation signal, we can get the estimation of the useful signal. This local polynomial estimation method can combine the advantages of local and global law. Finally, it makes the estimation more exactly and we can calculate the formula of mean square error theoretically. The simulation results show that the method is effective for the suppression of strong chaotic noise when the signal to interference ratio is low.
文摘In this study, a multivariate local quadratic polynomial regression(MLQPR) method is proposed to design a model for the sludge volume index(SVI). In MLQPR, a quadratic polynomial regression function is established to describe the relationship between SVI and the relative variables, and the important terms of the quadratic polynomial regression function are determined by the significant test of the corresponding coefficients. Moreover, a local estimation method is introduced to adjust the weights of the quadratic polynomial regression function to improve the model accuracy. Finally, the proposed method is applied to predict the SVI values in a real wastewater treatment process(WWTP). The experimental results demonstrate that the proposed MLQPR method has faster testing speed and more accurate results than some existing methods.
基金supported by the National Natural Science Foundation of China (Grants 11372145, 11372146, and 11272161)the State Key Laboratory of Mechanics and Control of Mechanical Structures (Nanjing University of Aeronautics and astronautics) (Grant MCMS-0516Y01)+1 种基金Zhejiang Provincial Top Key Discipline of Mechanics Open Foundation (Grant xklx1601)the K. C. Wong Magna Fund through Ningbo University
文摘The extended Kantorovich method is employed to study the local stress concentrations at the vicinity of free edges in symmetrically layered composite laminates subjected to uniaxial tensile load upon polynomial stress functions. The stress fields are initially assumed by means of the Lekhnitskii stress functions under the plane strain state. Applying the principle of complementary virtual work,the coupled ordinary differential equations are obtained in which the solutions can be obtained by solving a generalized eigenvalue problem. Then an iterative procedure is established to achieve convergent stress distributions. It should be noted that the stress function based extended Kantorovich method can satisfy both the traction-free and free edge stress boundary conditions during the iterative processes. The stress components near the free edges and in the interior regions are calculated and compared with those obtained results by finite element method（FEM）. The convergent stresses have good agreements with those results obtained by three dimensional（3D） FEM. For generality, various layup configurations are considered for the numerical analysis. The results show that the proposed polynomial stress function based extended Kantorovich method is accurate and efficient in predicting the local stresses in composite laminates and computationally much more efficient than the 3D FEM.
文摘In this paper, we try to find numerical solution of y'(x)= p(x)y(x)+g(x)+λ∫ba K(x, t)y(t)dt, y(a)=α. a≤x≤b, a≤t≤b or y'(x)= p(x)y(x)+g(x)+λ∫xa K(x, t)y(t)dt, y(a)=α. a≤x≤b, a≤t≤b by using Local polynomial regression (LPR) method. The numerical solution shows that this method is powerful in solving integro-differential equations. The method will be tested on three model problems in order to demonstrate its usefulness and accuracy.
文摘Under the condition that the total distribution function is continuous and bounded on （ -∞,∞ ）, we constructed estimations for distribution and hazard functions with local polynomial method, and obtained the rate of strong convergence of the estimations.
文摘In this paper, auxiliary information is used to determine an estimator of finite population total using nonparametric regression under stratified random sampling. To achieve this, a model-based approach is adopted by making use of the local polynomial regression estimation to predict the nonsampled values of the survey variable y. The performance of the proposed estimator is investigated against some design-based and model-based regression estimators. The simulation experiments show that the resulting estimator exhibits good properties. Generally, good confidence intervals are seen for the nonparametric regression estimators, and use of the proposed estimator leads to relatively smaller values of RE compared to other estimators.
文摘Approximation of finite population totals in the presence of auxiliary information is considered. A polynomial based on Lagrange polynomial is proposed. Like the local polynomial regression, Horvitz Thompson and ratio estimators, this approximation technique is based on annual population total in order to fit in the best approximating polynomial within a given period of time (years) in this study. This proposed technique has shown to be unbiased under a linear polynomial. The use of real data indicated that the polynomial is efficient and can approximate properly even when the data is unevenly spaced.
文摘In this research article,we construct a family of derivative free simultaneous numerical schemes to approximate all real zero of non-linear polynomial equation.We make a comparative analysis of the newly constructed numerical schemes with a well-known existing simultaneous method for determining all the distinct real zeros of polynomial equations using computer algebra system Mat Lab.Lower bound of convergence of simultaneous schemes is calculated using Mathematica.Global convergence property of the numerical schemes is presented by taking random starting initial approximation and their convergence history are graphically presented.Some real life engineering applications along with some higher degree polynomials are considered as numerical test problems to show performance and efficiency of the derivative free family of numerical methods with comparison of an existing method of same order in literature.Local computational order of convergence,CPU time,graph of computational order of convergence and residual error graphs elaborate efficiency,robustness and authentication of the suggested family of numerical methods in its domain.
基金supported by National Natural Science Foundation of China(No.11301084)Natural Science Foundation of Fujian Province(No.2014J01010)
文摘Based on the idea of local polynomial double-smoother, we propose an estimator of a conditional cumulative distribution function with dependent and left-truncated data. It is assumed that the observations form a stationary a-mixing sequence. Asymptotic normality of the estimator is established. The finite sample behavior of the estimator is investigated via simulations.
基金supported by the Key Laboratory of Dynamic Cognitive System of Electromagnetic Spectrum Space(KF20202109)the National Natural Science Foundation of China(82004259)the Young Talent Training Project of Guangzhou University of Chinese Medicine(QNYC20190110).
文摘Most of the near-field source localization methods are developed with the approximated signal model,because the phases of the received near-field signal are highly non-linear.Nevertheless,the approximated signal model based methods suffer from model mismatch and performance degradation while the exact signal model based estimation methods usually involve parameter searching or multiple decomposition procedures.In this paper,a search-free near-field source localization method is proposed with the exact signal model.Firstly,the approximative estimates of the direction of arrival(DOA)and range are obtained by using the approximated signal model based method through parameter separation and polynomial rooting operations.Then,the approximative estimates are corrected with the exact signal model according to the exact expressions of phase difference in near-field observations.The proposed method avoids spectral searching and parameter pairing and has enhanced estimation performance.Numerical simulations are provided to demonstrate the effectiveness of the proposed method.
