Based on Fermat’s principle, two-point ray tracing method was studied in three-dimensional structure. By means of first order Taylor’s incomplete series expansion (i.e. no expansion to the length of the ray), a symm...Based on Fermat’s principle, two-point ray tracing method was studied in three-dimensional structure. By means of first order Taylor’s incomplete series expansion (i.e. no expansion to the length of the ray), a symmetry block tridiagonal matrix equation set was deduced. Further, the positive definiteness of coefficient matrix was discussed, and the positive definiteness was accurately proved in a mathematical way. It assured that the algorithm was well-posed. Associated with iterative method, the solution to ray tracing can be got through step-by-step linearized iteration of the nonlinear problem. An algorithm of the whole path iterative ray tracing method in three-dimensional velocity structure was obtained. This method shows a clear and simple as well as explicit computation formula, which makes ray tracing computation easily applicable in practice. The correction vector is obtained through finding the solution to the positive definite block tridiagonal equation set, which ensures the method is robust convergence. This study offers a new kind of feasible and efficient ray tracing method for three dimensional seismic migration and tomography. Meanwhile, it also provides the prerequisite guarantee to design a fast algorithm.展开更多
The paper proposes an economical and fast algorithm for deriving trajectories from sporadic tracking points collected in location-based services (LBS). Although many traffic studies or applications can benefit from th...The paper proposes an economical and fast algorithm for deriving trajectories from sporadic tracking points collected in location-based services (LBS). Although many traffic studies or applications can benefit from the derived trajectories, the sporadic tracking points are always implicitly overlooked by most of existing map-matching algorithms. The algorithm proposed in this paper finds network paths or trajectories traveled by vehicles through augmenting GPS data with odometer data. An odometer can provide data of traveled distance which are compared with the lengths of candidate network paths in order to find the most approximate network path approaching the trajectory of a vehicle. Tracking points are classified into anchor points and non-anchor points. The former are used to divide trajectories, and the latter screen candidate network paths. An elliptic selection zone and a reduction process are applied to the selection of possible road segments composing candidate network paths. A brute-force searching algorithm is developed to find candidate network paths and calculate their lengths. A two-step screening process is designed to select the final result from candidate network paths. Finally, a series of experiments are conducted to validate the proposed algorithm.展开更多
基金Project(40674071) supported by the National Natural Science Foundation of Chinaproject(KFAS2002-2003) supported by Korea Foundation for Advanced Studies
文摘Based on Fermat’s principle, two-point ray tracing method was studied in three-dimensional structure. By means of first order Taylor’s incomplete series expansion (i.e. no expansion to the length of the ray), a symmetry block tridiagonal matrix equation set was deduced. Further, the positive definiteness of coefficient matrix was discussed, and the positive definiteness was accurately proved in a mathematical way. It assured that the algorithm was well-posed. Associated with iterative method, the solution to ray tracing can be got through step-by-step linearized iteration of the nonlinear problem. An algorithm of the whole path iterative ray tracing method in three-dimensional velocity structure was obtained. This method shows a clear and simple as well as explicit computation formula, which makes ray tracing computation easily applicable in practice. The correction vector is obtained through finding the solution to the positive definite block tridiagonal equation set, which ensures the method is robust convergence. This study offers a new kind of feasible and efficient ray tracing method for three dimensional seismic migration and tomography. Meanwhile, it also provides the prerequisite guarantee to design a fast algorithm.
基金Supported by the National Natural Science Foundation of China (No40701142)the Scientific Research Starting Foundation for Returned Overseas Chinese Scholars, Ministry of Education, China
文摘The paper proposes an economical and fast algorithm for deriving trajectories from sporadic tracking points collected in location-based services (LBS). Although many traffic studies or applications can benefit from the derived trajectories, the sporadic tracking points are always implicitly overlooked by most of existing map-matching algorithms. The algorithm proposed in this paper finds network paths or trajectories traveled by vehicles through augmenting GPS data with odometer data. An odometer can provide data of traveled distance which are compared with the lengths of candidate network paths in order to find the most approximate network path approaching the trajectory of a vehicle. Tracking points are classified into anchor points and non-anchor points. The former are used to divide trajectories, and the latter screen candidate network paths. An elliptic selection zone and a reduction process are applied to the selection of possible road segments composing candidate network paths. A brute-force searching algorithm is developed to find candidate network paths and calculate their lengths. A two-step screening process is designed to select the final result from candidate network paths. Finally, a series of experiments are conducted to validate the proposed algorithm.
