In order to improve the accuracy of free flight conflict detection and reduce the false alarm rate, an improved flight conflict detection algorithm is proposed based on Gauss-Hermite particle filter（GHPF）. The algor...In order to improve the accuracy of free flight conflict detection and reduce the false alarm rate, an improved flight conflict detection algorithm is proposed based on Gauss-Hermite particle filter（GHPF）. The algorithm improves the traditional flight conflict detection method in two aspects：（i） New observation data are integrated into system state transition probability, and Gauss-Hermite Filter（GHF） is used for generating the importance density function.（ii） GHPF is used for flight trajectory prediction and flight conflict probability calculation. The experimental results show that the accuracy of conflict detection and tracing with GHPF is better than that with standard particle filter. The detected conflict probability is more precise with GHPF, and GHPF is suitable for early free flight conflict detection.展开更多
This paper investigates the downlink capacity distribution and the outage probability of the interested area of maximum ratio transmission-selection combining(MRT-SC) scheme in the distributed antenna system(DAS).Comp...This paper investigates the downlink capacity distribution and the outage probability of the interested area of maximum ratio transmission-selection combining(MRT-SC) scheme in the distributed antenna system(DAS).Composite fading channels are assumed,which include path loss,lognormal shadowing and multi-path Rayleigh fading.Analytical approximations of the capacity's cumulative distribution function(CDF),the outage capacity,the mean capacity,and the outage probability of the interested area are derived by means of moment generation function(MGF) and Gauss-Hermite series expansion based approaches.The influence of antenna number,path loss exponent,and shadowing standard deviation on the capacity distribution are investigated.The simulation results agree with the analytical approximations well,and thus the analytical approximations are able to substitute the time-intensive Monte Carlo simulation for further investigation.展开更多
A sparse-grid method for solving multi-dimensional backward stochastic differential equations （BSDEs） based on a multi-step time discretization scheme [31] is presented. In the multi-dimensional spatial domain, i.e....A sparse-grid method for solving multi-dimensional backward stochastic differential equations （BSDEs） based on a multi-step time discretization scheme [31] is presented. In the multi-dimensional spatial domain, i.e. the Brownian space, the conditional mathe- matical expectations derived from the original equation are approximated using sparse-grid Gauss-Hermite quadrature rule and （adaptive） hierarchical sparse-grid interpolation. Error estimates are proved for the proposed fully-discrete scheme for multi-dimensional BSDEs with certain types of simplified generator functions. Finally, several numerical examples are provided to illustrate the accuracy and efficiency of our scheme.展开更多
基金Supported by the Joint Project of National Natural Science Foundation of ChinaCivil Aviation Administration of China(U1333116)
文摘In order to improve the accuracy of free flight conflict detection and reduce the false alarm rate, an improved flight conflict detection algorithm is proposed based on Gauss-Hermite particle filter（GHPF）. The algorithm improves the traditional flight conflict detection method in two aspects：（i） New observation data are integrated into system state transition probability, and Gauss-Hermite Filter（GHF） is used for generating the importance density function.（ii） GHPF is used for flight trajectory prediction and flight conflict probability calculation. The experimental results show that the accuracy of conflict detection and tracing with GHPF is better than that with standard particle filter. The detected conflict probability is more precise with GHPF, and GHPF is suitable for early free flight conflict detection.
文摘This paper investigates the downlink capacity distribution and the outage probability of the interested area of maximum ratio transmission-selection combining(MRT-SC) scheme in the distributed antenna system(DAS).Composite fading channels are assumed,which include path loss,lognormal shadowing and multi-path Rayleigh fading.Analytical approximations of the capacity's cumulative distribution function(CDF),the outage capacity,the mean capacity,and the outage probability of the interested area are derived by means of moment generation function(MGF) and Gauss-Hermite series expansion based approaches.The influence of antenna number,path loss exponent,and shadowing standard deviation on the capacity distribution are investigated.The simulation results agree with the analytical approximations well,and thus the analytical approximations are able to substitute the time-intensive Monte Carlo simulation for further investigation.
基金Acknowledgments. The first author was supported by the US Air Force Office of Scientific Research under grant FA9550-11-1-0149. The first author was also supported by the Advanced Simulation Computing Research （ASCR）, Department of Energy, through the Householder Fellowship at ORNL. The ORNL is operated by UT-Battelle, LLC, for the United States Depart-ment of Energy under Contract DE-AC05-00OR22725. The second author was supported by the US Air Force Office of Scientific Research under grant FA9550-11-1-0149. The third author was supported by the Natural Science Foundation of China under grant 11171189. The third author was also supported by the Natural Science Foundation of China under grant 91130003. The thrid author was also supported by Shandong Province Natural Science Foundation under grant ZR2001AZ002.
文摘A sparse-grid method for solving multi-dimensional backward stochastic differential equations （BSDEs） based on a multi-step time discretization scheme [31] is presented. In the multi-dimensional spatial domain, i.e. the Brownian space, the conditional mathe- matical expectations derived from the original equation are approximated using sparse-grid Gauss-Hermite quadrature rule and （adaptive） hierarchical sparse-grid interpolation. Error estimates are proved for the proposed fully-discrete scheme for multi-dimensional BSDEs with certain types of simplified generator functions. Finally, several numerical examples are provided to illustrate the accuracy and efficiency of our scheme.
