Under the underdetermined blind sources separation(UBSS) circumstance,it is difficult to estimate the mixing matrix with high-precision because of unknown sparsity of signals.The mixing matrix estimation is proposed b...Under the underdetermined blind sources separation(UBSS) circumstance,it is difficult to estimate the mixing matrix with high-precision because of unknown sparsity of signals.The mixing matrix estimation is proposed based on linear aggregation degree of signal scatter plot without knowing sparsity,and the linear aggregation degree evaluation of observed signals is presented which obeys generalized Gaussian distribution(GGD).Both the GGD shape parameter and the signals' correlation features affect the observation signals sparsity and further affected the directionality of time-frequency scatter plot.So a new mixing matrix estimation method is proposed for different sparsity degrees,which especially focuses on unclear directionality of scatter plot and weak linear aggregation degree.Firstly,the direction of coefficient scatter plot by time-frequency transform is improved and then the single source coefficients in the case of weak linear clustering is processed finally the improved K-means clustering is applied to achieve the estimation of mixing matrix.The proposed algorithm reduces the requirements of signals sparsity and independence,and the mixing matrix can be estimated with high accuracy.The simulation results show the feasibility and effectiveness of the algorithm.展开更多
Estimating the covariance matrix of the received signal is a vital step in array signal processing. The traditional estimation method is completed generally by offline way after receiving the continuous sampling snaps...Estimating the covariance matrix of the received signal is a vital step in array signal processing. The traditional estimation method is completed generally by offline way after receiving the continuous sampling snapshots, which cannot meet requirements of real-time performance. In this paper, the calculation of covariance matrix is divided into four pipeline operations, which are multiplication, accumulation, subtraction and division, respectively.The new method leverages the parallel computing function of field programmable gate array(FPGA) to calculate the covariance matrix adopting a pipeline estimation method at each time when the array receives a new sampling snapshot. Compared with the traditional method, the new method not only improves the real-time performance, but also reduces the error in calculation caused by the rapid direction of arrival(DOA) change of the interested signal when the target is highly maneuverable.展开更多
Covariance matrix plays an important role in risk management, asset pricing, and portfolio allocation. Covariance matrix estimation becomes challenging when the dimensionality is comparable or much larger than the sam...Covariance matrix plays an important role in risk management, asset pricing, and portfolio allocation. Covariance matrix estimation becomes challenging when the dimensionality is comparable or much larger than the sample size. A widely used approach for reducing dimensionality is based on multi-factor models. Although it has been well studied and quite successful in many applications, the quality of the estimated covariance matrix is often degraded due to a nontrivial amount of missing data in the factor matrix for both technical and cost reasons. Since the factor matrix is only approximately low rank or even has full rank, existing matrix completion algorithms are not applicable. We consider a new matrix completion paradigm using the factor models directly and apply the alternating direction method of multipliers for the recovery. Numerical experiments show that the nuclear-norm matrix completion approaches are not suitable but our proposed models and algorithms are promising.展开更多
The rotation matrix estimation problem is a keypoint for mobile robot localization, navigation, and control. Based on the quaternion theory and the epipolar geometry, an extended Kalman filter (EKF) algorithm is propo...The rotation matrix estimation problem is a keypoint for mobile robot localization, navigation, and control. Based on the quaternion theory and the epipolar geometry, an extended Kalman filter (EKF) algorithm is proposed to estimate the rotation matrix by using a single-axis gyroscope and the image points correspondence from a monocular camera. The experimental results show that the precision of mobile robot s yaw angle estimated by the proposed EKF algorithm is much better than the results given by the image-only and gyroscope-only method, which demonstrates that our method is a preferable way to estimate the rotation for the autonomous mobile robot applications.展开更多
In this article,the empirical Bayes（EB）estimators are constructed for the estimable functions of the parameters in partitioned normal linear model.The superiorities of the EB estimators over ordinary least-squares...In this article,the empirical Bayes（EB）estimators are constructed for the estimable functions of the parameters in partitioned normal linear model.The superiorities of the EB estimators over ordinary least-squares（LS）estimator are investigated under mean square error matrix（MSEM）criterion.展开更多
This paper investigates the blind algorithm for channel estimation of Orthogonal Frequency Division Multiplexing-Multiple Input Multiple Output (OFDM-MIMO) wireless communication system using the subspace decompositio...This paper investigates the blind algorithm for channel estimation of Orthogonal Frequency Division Multiplexing-Multiple Input Multiple Output (OFDM-MIMO) wireless communication system using the subspace decomposition of the channel received complex baseband signals and proposes a new two-stage blind algorithm. Exploited the second-order cyclostationarity inherent in OFDM with cyclic prefix and the characteristics of the phased antenna, the practical HIPERLAN/2 standard based OFDM-MIMO simulator is established with the sufficient consideration of statistical correlations between the multiple antenna channels under wireless wideband multipath fading environment, and a new two-stage blind algorithm is formulated using rank reduced subspace channel matrix approximation and adaptive Constant Modulus (CM)criterion. Simulation results confirm the theoretical analysis and illustrate that the proposed algorithm is capable of tracking matrix channel variations with fast convergence rate and improving acceptable overall system performance over various common wireless and mobile communication links.展开更多
The commodity transportation capacity between all origin-destination （ OD ） pairs over the multimodal multi-commodities freight transportation network （MMFTN） is determined. A multi-ob- jectives mathematical model...The commodity transportation capacity between all origin-destination （ OD ） pairs over the multimodal multi-commodities freight transportation network （MMFTN） is determined. A multi-ob- jectives mathematical model is formulated for determining the OD capacity over the MMFTN accord- ing to a transporting capacity matrix that increased from the reference matrixes. The corresponding incremental factor for estimating the capacity matrix is obtained via the maximal likelihood estima- tion method that samples data of differences between the estimated commodity volumes and carrying capacities of the critical links. The proposed formulations are tested by an experimental highway and railroad freight transportation network in an existing literature. The relevant results of OD capacities are displayed and applicability of the algorithm is certified.展开更多
Markowitz Portfolio theory under-estimates the risk associated with the return of a portfolio in case of high dimensional data. El Karoui mathematically proved this in [1] and suggested improved estimators for unbiase...Markowitz Portfolio theory under-estimates the risk associated with the return of a portfolio in case of high dimensional data. El Karoui mathematically proved this in [1] and suggested improved estimators for unbiased estimation of this risk under specific model assumptions. Norm constrained portfolios have recently been studied to keep the effective dimension low. In this paper we consider three sets of high dimensional data, the stock market prices for three countries, namely US, UK and India. We compare the Markowitz efficient frontier to those obtained by unbiasedness corrections and imposing norm-constraints in these real data scenarios. We also study the out-of-sample performance of the different procedures. We find that the 2-norm constrained portfolio has best overall performance.展开更多
A method based on the maximum a posteriori probability （MAP） criterion is proposed to estimate the channel frequency response （CFR） matrix and interference- plus-noise spatial covariance matrix （SCM） for multipl...A method based on the maximum a posteriori probability （MAP） criterion is proposed to estimate the channel frequency response （CFR） matrix and interference- plus-noise spatial covariance matrix （SCM） for multiple input and multiple output orthogonal frequency division multiplexing （MIMO-OFDM） systems. An iterative solution is proposed to solve the MAP-based problem and an interference rejection combining （IRC） receiver is derived to suppress co-channel interference （CCI） based on the estimated CFR and SCM. Furthermore, considering the property of SCM, i. e., Hermitian and semi-definite, two schemes are proposed to improve the accuracy of SCM estimation. The first scheme is proposed to parameterize the SCM via a sum of a series of matrices in the time domain. The second scheme measures the SCM on each subcarrier as a low-rank model while the model order can be chosen through the penalized-likelihood approach. Simulation results are provided to demonstrate the effectiveness of the proposed method.展开更多
This paper develops the theory of the kth power expectile estimation and considers its relevant hypothesis tests for coefficients of linear regression models.We prove that the asymptotic covariance matrix of kth power...This paper develops the theory of the kth power expectile estimation and considers its relevant hypothesis tests for coefficients of linear regression models.We prove that the asymptotic covariance matrix of kth power expectile regression converges to that of quantile regression as k converges to one and hence promise a moment estimator of asymptotic matrix of quantile regression.The kth power expectile regression is then utilized to test for homoskedasticity and conditional symmetry of the data.Detailed comparisons of the local power among the kth power expectile regression tests,the quantile regression test,and the expectile regression test have been provided.When the underlying distribution is not standard normal,results show that the optimal k are often larger than 1 and smaller than 2,which suggests the general kth power expectile regression is necessary.Finally,the methods are illustrated by a real example.展开更多
A Direction Of Arrival(DOA) estimator based on the signal separation principle is introduced, and one of representative multidimensional estimators is established by introducing Matrix Operator projection signal steer...A Direction Of Arrival(DOA) estimator based on the signal separation principle is introduced, and one of representative multidimensional estimators is established by introducing Matrix Operator projection signal steering Vector Excision(MOVE) operation. Thanks to Alternating Separation (AS) technique, the multidimensional problem is transformed into a series of one-dimensional optimal ones. Furthermore, an equivalent simplified implementation of the AS is obtained. Finally the definiteness and uniqueness of the estimator are analyzed.展开更多
It was suggested by Pantanen that the mean squared error may be used to measure the inefficiency of the least squares estimator. Styan[2] and Rao[3] et al. discussed this inefficiency and it's bound later. In this...It was suggested by Pantanen that the mean squared error may be used to measure the inefficiency of the least squares estimator. Styan[2] and Rao[3] et al. discussed this inefficiency and it's bound later. In this paper we propose a new inefficiency of the least squares estimator with the measure of generalized variance and obtain its bound.展开更多
We consider the problem of multi-task regression with time-varying low-rank patterns,where the collected data may be contaminated by heavy-tailed distributions and/or outliers.Our approach is based on a piecewise robu...We consider the problem of multi-task regression with time-varying low-rank patterns,where the collected data may be contaminated by heavy-tailed distributions and/or outliers.Our approach is based on a piecewise robust multi-task learning formulation,in which a robust loss function—not necessarily to be convex,but with a bounded derivative—is used,and each piecewise low-rank pattern is induced by a nuclear norm regularization term.We propose using the composite gradient descent algorithm to obtain stationary points within a data segment and employing the dynamic programming algorithm to determine the optimal segmentation.The theoretical properties of the detected number and time points of pattern shifts are studied under mild conditions.Numerical results confirm the effectiveness of our method.展开更多
Precision matrix estimation is an important problem in statistical data analysis.This paper proposes a sparse precision matrix estimation approach,based on CLIME estimator and an efficient algorithm GISSP that was ori...Precision matrix estimation is an important problem in statistical data analysis.This paper proposes a sparse precision matrix estimation approach,based on CLIME estimator and an efficient algorithm GISSP that was originally proposed for li sparse signal recovery in compressed sensing.The asymptotic convergence rate for sparse precision matrix estimation is analyzed with respect to the new stopping criteria of the proposed GISSP algorithm.Finally,numerical comparison of GISSP with other sparse recovery algorithms,such as ADMM and HTP in three settings of precision matrix estimation is provided and the numerical results show the advantages of the proposed algorithm.展开更多
Constant traffic congestion consumes enormous amounts of energy and causes vastly increased journey times. Therefore, real-time traffic information is of great importance to the public because such information is inva...Constant traffic congestion consumes enormous amounts of energy and causes vastly increased journey times. Therefore, real-time traffic information is of great importance to the public because such information is invaluable to more efficient traffic control and travel planning. To obtain such information in metropolises like Shanghai, however, is very challenging due to the extraordinarily large scale and com- plexity of the underlying road network. In this paper, we pro- pose a novel traffic estimation scheme utilizing surveillance cameras pervasively deployed in cities. With only a limited number of roads with cameras, we adopt a measurement- based traffic matrix （TM） estimation method to infer the traf- fic conditions on those roads with no cameras. Extensively trace-driven simulations as well as field study results show that our scheme can achieve high accuracy with a very limited number of measurements. The accuracy of our measurement- based algorithm outperforms the traditional speed-based and model-based approaches by up to 50%.展开更多
基金Supported by the National Natural Science Foundation of China(No.51204145)Natural Science Foundation of Hebei Province of China(No.2013203300)
文摘Under the underdetermined blind sources separation(UBSS) circumstance,it is difficult to estimate the mixing matrix with high-precision because of unknown sparsity of signals.The mixing matrix estimation is proposed based on linear aggregation degree of signal scatter plot without knowing sparsity,and the linear aggregation degree evaluation of observed signals is presented which obeys generalized Gaussian distribution(GGD).Both the GGD shape parameter and the signals' correlation features affect the observation signals sparsity and further affected the directionality of time-frequency scatter plot.So a new mixing matrix estimation method is proposed for different sparsity degrees,which especially focuses on unclear directionality of scatter plot and weak linear aggregation degree.Firstly,the direction of coefficient scatter plot by time-frequency transform is improved and then the single source coefficients in the case of weak linear clustering is processed finally the improved K-means clustering is applied to achieve the estimation of mixing matrix.The proposed algorithm reduces the requirements of signals sparsity and independence,and the mixing matrix can be estimated with high accuracy.The simulation results show the feasibility and effectiveness of the algorithm.
基金supported by the China Academy of Space Technology(CAST)Innovation Fund (2022LX-312-Y-GZ-15)。
文摘Estimating the covariance matrix of the received signal is a vital step in array signal processing. The traditional estimation method is completed generally by offline way after receiving the continuous sampling snapshots, which cannot meet requirements of real-time performance. In this paper, the calculation of covariance matrix is divided into four pipeline operations, which are multiplication, accumulation, subtraction and division, respectively.The new method leverages the parallel computing function of field programmable gate array(FPGA) to calculate the covariance matrix adopting a pipeline estimation method at each time when the array receives a new sampling snapshot. Compared with the traditional method, the new method not only improves the real-time performance, but also reduces the error in calculation caused by the rapid direction of arrival(DOA) change of the interested signal when the target is highly maneuverable.
基金supported by National Natural Science Foundation of China(Grant Nos.10971122,11101274 and 11322109)Scientific and Technological Projects of Shandong Province(Grant No.2009GG10001012)Excellent Young Scientist Foundation of Shandong Province(Grant No.BS2012SF025)
文摘Covariance matrix plays an important role in risk management, asset pricing, and portfolio allocation. Covariance matrix estimation becomes challenging when the dimensionality is comparable or much larger than the sample size. A widely used approach for reducing dimensionality is based on multi-factor models. Although it has been well studied and quite successful in many applications, the quality of the estimated covariance matrix is often degraded due to a nontrivial amount of missing data in the factor matrix for both technical and cost reasons. Since the factor matrix is only approximately low rank or even has full rank, existing matrix completion algorithms are not applicable. We consider a new matrix completion paradigm using the factor models directly and apply the alternating direction method of multipliers for the recovery. Numerical experiments show that the nuclear-norm matrix completion approaches are not suitable but our proposed models and algorithms are promising.
基金supported by National Natural Science Foundation of China (Nos. 60874010 and 61070048)Innovation Program of Shanghai Municipal Education Commission (No. 11ZZ37)+1 种基金Fundamental Research Funds for the Central Universities (No. 009QJ12)Collaborative Construction Project of Beijing Municipal Commission of Education
文摘The rotation matrix estimation problem is a keypoint for mobile robot localization, navigation, and control. Based on the quaternion theory and the epipolar geometry, an extended Kalman filter (EKF) algorithm is proposed to estimate the rotation matrix by using a single-axis gyroscope and the image points correspondence from a monocular camera. The experimental results show that the precision of mobile robot s yaw angle estimated by the proposed EKF algorithm is much better than the results given by the image-only and gyroscope-only method, which demonstrates that our method is a preferable way to estimate the rotation for the autonomous mobile robot applications.
基金the Knowledge Innovation Program of the Chinese Academy of Sciences(KJCX3-SYW-S02)the Youth Foundation of USTC
文摘In this article,the empirical Bayes（EB）estimators are constructed for the estimable functions of the parameters in partitioned normal linear model.The superiorities of the EB estimators over ordinary least-squares（LS）estimator are investigated under mean square error matrix（MSEM）criterion.
文摘This paper investigates the blind algorithm for channel estimation of Orthogonal Frequency Division Multiplexing-Multiple Input Multiple Output (OFDM-MIMO) wireless communication system using the subspace decomposition of the channel received complex baseband signals and proposes a new two-stage blind algorithm. Exploited the second-order cyclostationarity inherent in OFDM with cyclic prefix and the characteristics of the phased antenna, the practical HIPERLAN/2 standard based OFDM-MIMO simulator is established with the sufficient consideration of statistical correlations between the multiple antenna channels under wireless wideband multipath fading environment, and a new two-stage blind algorithm is formulated using rank reduced subspace channel matrix approximation and adaptive Constant Modulus (CM)criterion. Simulation results confirm the theoretical analysis and illustrate that the proposed algorithm is capable of tracking matrix channel variations with fast convergence rate and improving acceptable overall system performance over various common wireless and mobile communication links.
文摘The commodity transportation capacity between all origin-destination （ OD ） pairs over the multimodal multi-commodities freight transportation network （MMFTN） is determined. A multi-ob- jectives mathematical model is formulated for determining the OD capacity over the MMFTN accord- ing to a transporting capacity matrix that increased from the reference matrixes. The corresponding incremental factor for estimating the capacity matrix is obtained via the maximal likelihood estima- tion method that samples data of differences between the estimated commodity volumes and carrying capacities of the critical links. The proposed formulations are tested by an experimental highway and railroad freight transportation network in an existing literature. The relevant results of OD capacities are displayed and applicability of the algorithm is certified.
文摘Markowitz Portfolio theory under-estimates the risk associated with the return of a portfolio in case of high dimensional data. El Karoui mathematically proved this in [1] and suggested improved estimators for unbiased estimation of this risk under specific model assumptions. Norm constrained portfolios have recently been studied to keep the effective dimension low. In this paper we consider three sets of high dimensional data, the stock market prices for three countries, namely US, UK and India. We compare the Markowitz efficient frontier to those obtained by unbiasedness corrections and imposing norm-constraints in these real data scenarios. We also study the out-of-sample performance of the different procedures. We find that the 2-norm constrained portfolio has best overall performance.
基金The National Natural Science Foundation of China(No.61320106003,61222102)the National High Technology Research and Development Program of China(863 Program)(No.2012AA01A506)
文摘A method based on the maximum a posteriori probability （MAP） criterion is proposed to estimate the channel frequency response （CFR） matrix and interference- plus-noise spatial covariance matrix （SCM） for multiple input and multiple output orthogonal frequency division multiplexing （MIMO-OFDM） systems. An iterative solution is proposed to solve the MAP-based problem and an interference rejection combining （IRC） receiver is derived to suppress co-channel interference （CCI） based on the estimated CFR and SCM. Furthermore, considering the property of SCM, i. e., Hermitian and semi-definite, two schemes are proposed to improve the accuracy of SCM estimation. The first scheme is proposed to parameterize the SCM via a sum of a series of matrices in the time domain. The second scheme measures the SCM on each subcarrier as a low-rank model while the model order can be chosen through the penalized-likelihood approach. Simulation results are provided to demonstrate the effectiveness of the proposed method.
文摘This paper develops the theory of the kth power expectile estimation and considers its relevant hypothesis tests for coefficients of linear regression models.We prove that the asymptotic covariance matrix of kth power expectile regression converges to that of quantile regression as k converges to one and hence promise a moment estimator of asymptotic matrix of quantile regression.The kth power expectile regression is then utilized to test for homoskedasticity and conditional symmetry of the data.Detailed comparisons of the local power among the kth power expectile regression tests,the quantile regression test,and the expectile regression test have been provided.When the underlying distribution is not standard normal,results show that the optimal k are often larger than 1 and smaller than 2,which suggests the general kth power expectile regression is necessary.Finally,the methods are illustrated by a real example.
基金Partially supported by the National Natural Science Foundation of China(No.60372036), Natural Science Foundation of Shaanxi Province (2002F24) and Funds from the Information Industry Ministry of China (2002XK610039)
文摘A Direction Of Arrival(DOA) estimator based on the signal separation principle is introduced, and one of representative multidimensional estimators is established by introducing Matrix Operator projection signal steering Vector Excision(MOVE) operation. Thanks to Alternating Separation (AS) technique, the multidimensional problem is transformed into a series of one-dimensional optimal ones. Furthermore, an equivalent simplified implementation of the AS is obtained. Finally the definiteness and uniqueness of the estimator are analyzed.
文摘It was suggested by Pantanen that the mean squared error may be used to measure the inefficiency of the least squares estimator. Styan[2] and Rao[3] et al. discussed this inefficiency and it's bound later. In this paper we propose a new inefficiency of the least squares estimator with the measure of generalized variance and obtain its bound.
基金supported by the National Key R&D Program of China(Grant Nos.2022YFA1003703,2022YFA 1003800)the National Natural Science Foundation of China(Grant Nos.11925106,12231011,11931001,12226007,12326325)+2 种基金supported by the National Natural Science Foundation of China(Grant No.12301380)supported by the National Key R&D Program of China(Grant Nos.2021YFA1000100,2021YFA1000101,2022YFA1003800)the Natural Science Foundation of Shanghai(Grant No.23ZR1419400)。
文摘We consider the problem of multi-task regression with time-varying low-rank patterns,where the collected data may be contaminated by heavy-tailed distributions and/or outliers.Our approach is based on a piecewise robust multi-task learning formulation,in which a robust loss function—not necessarily to be convex,but with a bounded derivative—is used,and each piecewise low-rank pattern is induced by a nuclear norm regularization term.We propose using the composite gradient descent algorithm to obtain stationary points within a data segment and employing the dynamic programming algorithm to determine the optimal segmentation.The theoretical properties of the detected number and time points of pattern shifts are studied under mild conditions.Numerical results confirm the effectiveness of our method.
基金This work was supported by National key research and development program(No.2017YFB0202902)NSFC(No.11771288,No.12090024).
文摘Precision matrix estimation is an important problem in statistical data analysis.This paper proposes a sparse precision matrix estimation approach,based on CLIME estimator and an efficient algorithm GISSP that was originally proposed for li sparse signal recovery in compressed sensing.The asymptotic convergence rate for sparse precision matrix estimation is analyzed with respect to the new stopping criteria of the proposed GISSP algorithm.Finally,numerical comparison of GISSP with other sparse recovery algorithms,such as ADMM and HTP in three settings of precision matrix estimation is provided and the numerical results show the advantages of the proposed algorithm.
文摘Constant traffic congestion consumes enormous amounts of energy and causes vastly increased journey times. Therefore, real-time traffic information is of great importance to the public because such information is invaluable to more efficient traffic control and travel planning. To obtain such information in metropolises like Shanghai, however, is very challenging due to the extraordinarily large scale and com- plexity of the underlying road network. In this paper, we pro- pose a novel traffic estimation scheme utilizing surveillance cameras pervasively deployed in cities. With only a limited number of roads with cameras, we adopt a measurement- based traffic matrix （TM） estimation method to infer the traf- fic conditions on those roads with no cameras. Extensively trace-driven simulations as well as field study results show that our scheme can achieve high accuracy with a very limited number of measurements. The accuracy of our measurement- based algorithm outperforms the traditional speed-based and model-based approaches by up to 50%.
