The block-diagonal least squares method, which theoretically has specific requirements for the observation data and the spatial distribution of its precision, plays an important role in ultra-high degree gravity field...The block-diagonal least squares method, which theoretically has specific requirements for the observation data and the spatial distribution of its precision, plays an important role in ultra-high degree gravity field determination. On the basis of block-diagonal least squares method, three data processing strategies are employed to determine the gravity field models using three kinds of simulated global grid data with different noise spatial distri- bution in this paper. The numerical results show that when we employed the weight matrix corresponding to the noise of the observation data, the model computed by the least squares using the full normal matrix has much higher precision than the one estimated only using the block part of the normal matrix. The model computed by the block-diagonal least squares method without the weight matrix has slightly lower precision than the model computed using the rigorous least squares with the weight matrix. The result offers valuable reference to the using of block-diagonal least squares method in ultra-high gravity model determination.展开更多
This paper studies large-scale multi-input multi-output(MIMO)orthogonal frequency division multiplexing(OFDM)communications in a broadband frequency-selective channel,where a massive MIMO base station(BS)communicates ...This paper studies large-scale multi-input multi-output(MIMO)orthogonal frequency division multiplexing(OFDM)communications in a broadband frequency-selective channel,where a massive MIMO base station(BS)communicates with multiple users equipped with multi-antenna.We develop a hybrid precoding design to maximize the weighted sum-rate(WSR)of the users by optimizing the digital and the analog precoders alternately.For the digital part,we employ block-diagonalization to eliminate inter-user interference and apply water-filling power allocation to maximize the WSR.For the analog part,the optimization of the PSN is formulated as an unconstrained problem,which can be efficiently solved by a gradient descent method.Numerical results show that the proposed block-diagonal hybrid precoding algorithm can outperform the existing works.展开更多
A new method of predicting chaotic time series is presented based on a local Lyapunov exponent, by quantitatively measuring the exponential rate of separation or attraction of two infinitely close trajectories in stat...A new method of predicting chaotic time series is presented based on a local Lyapunov exponent, by quantitatively measuring the exponential rate of separation or attraction of two infinitely close trajectories in state space. After recon- structing state space from one-dimensional chaotic time series, neighboring multiple-state vectors of the predicting point are selected to deduce the prediction formula by using the definition of the locaI Lyapunov exponent. Numerical simulations are carded out to test its effectiveness and verify its higher precision over two older methods. The effects of the number of referential state vectors and added noise on forecasting accuracy are also studied numerically.展开更多
This paper focuses on estimating a new high-resolution Earth’s gravity field model named SGG-UGM-2 from satellite gravimetry,satellite altimetry,and Earth Gravitational Model 2008(EGM2008)-derived gravity data based ...This paper focuses on estimating a new high-resolution Earth’s gravity field model named SGG-UGM-2 from satellite gravimetry,satellite altimetry,and Earth Gravitational Model 2008(EGM2008)-derived gravity data based on the theory of the ellipsoidal harmonic analysis and coefficient transformation(EHA-CT).We first derive the related formulas of the EHA-CT method,which is used for computing the spherical harmonic coefficients from grid area-mean and point gravity anomalies on the ellipsoid.The derived formulas are successfully evaluated based on numerical experiments.Then,based on the derived least-squares formulas of the EHA-CT method,we develop the new model SGG-UGM-2 up to degree 2190 and order 2159 by combining the observations of the Gravity Field and Steady-State Ocean Circulation Explorer(GOCE),the normal equation of the Gravity Recovery and Climate Experiment(GRACE),marine gravity data derived from satellite altimetry data,and EGM2008-derived continental gravity data.The coefficients of degrees 251–2159 are estimated by solving the block-diagonal form normal equations of surface gravity anomalies(including the marine gravity data).The coefficients of degrees 2–250 are determined by combining the normal equations of satellite observations and surface gravity anomalies.The variance component estimation technique is used to estimate the relative weights of different observations.Finally,global positioning system(GPS)/leveling data in the mainland of China and the United States are used to validate SGG-UGM-2 together with other models,such as European improved gravity model of the earth by new techniques(EIGEN)-6C4,GECO,EGM2008,and SGG-UGM-1(the predecessor of SGG-UGM-2).Compared to other models,the model SGG-UGM-2 shows a promising performance in the GPS/leveling validation.All GOCE-related models have similar performances both in the mainland of China and the United States,and better performances than that of EGM2008 in the mainland of China.Due to the contribution of GRACE data and the new marine gravity anomalies,SGG-UGM-2 is slightly better than SGG-UGM-1 both in the mainland of China and the United States.展开更多
基金supported by the National Natural Science Foundation of China for Distinguished Young Scholars (41404028)
文摘The block-diagonal least squares method, which theoretically has specific requirements for the observation data and the spatial distribution of its precision, plays an important role in ultra-high degree gravity field determination. On the basis of block-diagonal least squares method, three data processing strategies are employed to determine the gravity field models using three kinds of simulated global grid data with different noise spatial distri- bution in this paper. The numerical results show that when we employed the weight matrix corresponding to the noise of the observation data, the model computed by the least squares using the full normal matrix has much higher precision than the one estimated only using the block part of the normal matrix. The model computed by the block-diagonal least squares method without the weight matrix has slightly lower precision than the model computed using the rigorous least squares with the weight matrix. The result offers valuable reference to the using of block-diagonal least squares method in ultra-high gravity model determination.
基金supported by National Natural Science Foundation of China(No.61771005)
文摘This paper studies large-scale multi-input multi-output(MIMO)orthogonal frequency division multiplexing(OFDM)communications in a broadband frequency-selective channel,where a massive MIMO base station(BS)communicates with multiple users equipped with multi-antenna.We develop a hybrid precoding design to maximize the weighted sum-rate(WSR)of the users by optimizing the digital and the analog precoders alternately.For the digital part,we employ block-diagonalization to eliminate inter-user interference and apply water-filling power allocation to maximize the WSR.For the analog part,the optimization of the PSN is formulated as an unconstrained problem,which can be efficiently solved by a gradient descent method.Numerical results show that the proposed block-diagonal hybrid precoding algorithm can outperform the existing works.
基金Project supported by the National Natural Science Foundation of China (Grant No. 61201452)
文摘A new method of predicting chaotic time series is presented based on a local Lyapunov exponent, by quantitatively measuring the exponential rate of separation or attraction of two infinitely close trajectories in state space. After recon- structing state space from one-dimensional chaotic time series, neighboring multiple-state vectors of the predicting point are selected to deduce the prediction formula by using the definition of the locaI Lyapunov exponent. Numerical simulations are carded out to test its effectiveness and verify its higher precision over two older methods. The effects of the number of referential state vectors and added noise on forecasting accuracy are also studied numerically.
基金We appreciate the help from Torsten Mayer-Gürr and Andreas Kvas for providing us the NEQ system of the ITSG-Grace2018 model.This research was financially supported by the National Natural Science Foundation of China(41574019 and 41774020)the German Academic Exchange Service(DAAD)Thematic Network Project(57421148)+2 种基金the Major Project of High-Resolution Earth Observation System,and Science Fund for Creative Research Groups of the National Natural Science Foundation of China(41721003)the Fundamental Research Funds for the Central Universities(N170103009)We also thank the editor and the anonymous reviewers for their constructive remarks that helped us to improve the quality of the manuscript.
文摘This paper focuses on estimating a new high-resolution Earth’s gravity field model named SGG-UGM-2 from satellite gravimetry,satellite altimetry,and Earth Gravitational Model 2008(EGM2008)-derived gravity data based on the theory of the ellipsoidal harmonic analysis and coefficient transformation(EHA-CT).We first derive the related formulas of the EHA-CT method,which is used for computing the spherical harmonic coefficients from grid area-mean and point gravity anomalies on the ellipsoid.The derived formulas are successfully evaluated based on numerical experiments.Then,based on the derived least-squares formulas of the EHA-CT method,we develop the new model SGG-UGM-2 up to degree 2190 and order 2159 by combining the observations of the Gravity Field and Steady-State Ocean Circulation Explorer(GOCE),the normal equation of the Gravity Recovery and Climate Experiment(GRACE),marine gravity data derived from satellite altimetry data,and EGM2008-derived continental gravity data.The coefficients of degrees 251–2159 are estimated by solving the block-diagonal form normal equations of surface gravity anomalies(including the marine gravity data).The coefficients of degrees 2–250 are determined by combining the normal equations of satellite observations and surface gravity anomalies.The variance component estimation technique is used to estimate the relative weights of different observations.Finally,global positioning system(GPS)/leveling data in the mainland of China and the United States are used to validate SGG-UGM-2 together with other models,such as European improved gravity model of the earth by new techniques(EIGEN)-6C4,GECO,EGM2008,and SGG-UGM-1(the predecessor of SGG-UGM-2).Compared to other models,the model SGG-UGM-2 shows a promising performance in the GPS/leveling validation.All GOCE-related models have similar performances both in the mainland of China and the United States,and better performances than that of EGM2008 in the mainland of China.Due to the contribution of GRACE data and the new marine gravity anomalies,SGG-UGM-2 is slightly better than SGG-UGM-1 both in the mainland of China and the United States.
