Chinese scientists invent the navigation and positioning system based on commercial communications satellites and develop them successfully into China Area Positioning System (CAPS). In principle, this system is diffe...Chinese scientists invent the navigation and positioning system based on commercial communications satellites and develop them successfully into China Area Positioning System (CAPS). In principle, this system is different from the GPS broadcasting satellite navigation class, where the propagation epoch of original navigation signals for pseudo-range measurement is from a ground master control station rather than from satellite transponders. This paper addresses the establishment of the three observation equation models for the navigation and positioning system based on communications satellites, and expresses them identically to operator equations and optimized models. Furthermore, both algorithms of the linear solution for the observable characteristic equation and the least-squares solution for the condition number more than 4 are discussed, with several methods for the exact solution, such as improving the behavior of coefficient matrices, right estimation for the weighted right hand side and selection of iteration forms of solutions, and the influence of the condition number on improving navigation and positioning accuracy is also analyzed carefully. Hopefully, all the works would be contributive to further development of the navigation and positioning system based on communications satellites, and be potentially valuable to other satellite navigation and positioning systems.展开更多
Panel count data occur in many clinical and observational studies and in some situations the observation process is informative. In this article, we propose a new joint model for the analysis of panel count data with ...Panel count data occur in many clinical and observational studies and in some situations the observation process is informative. In this article, we propose a new joint model for the analysis of panel count data with time-dependent covariates and possibly in the presence of informative observation process via two latent variables. For the inference on the proposed model, a class of estimating equations is developed and the resulting estimators are shown to be consistent and asymptotically normal. In addition, a lack-of-fit test is provided for assessing the adequacy of the model. The finite-sample behavior of the proposed methods is examined through Monte Carlo simulation studies which suggest that the proposed approach works well for practical situations. Also an illustrative example is provided.展开更多
基金Supported by the National Basic Research and Development Program of China (Grant No. 2007CB815500)
文摘Chinese scientists invent the navigation and positioning system based on commercial communications satellites and develop them successfully into China Area Positioning System (CAPS). In principle, this system is different from the GPS broadcasting satellite navigation class, where the propagation epoch of original navigation signals for pseudo-range measurement is from a ground master control station rather than from satellite transponders. This paper addresses the establishment of the three observation equation models for the navigation and positioning system based on communications satellites, and expresses them identically to operator equations and optimized models. Furthermore, both algorithms of the linear solution for the observable characteristic equation and the least-squares solution for the condition number more than 4 are discussed, with several methods for the exact solution, such as improving the behavior of coefficient matrices, right estimation for the weighted right hand side and selection of iteration forms of solutions, and the influence of the condition number on improving navigation and positioning accuracy is also analyzed carefully. Hopefully, all the works would be contributive to further development of the navigation and positioning system based on communications satellites, and be potentially valuable to other satellite navigation and positioning systems.
基金partially supported by National Natural Science Foundation of China(11671267)Scientific Research Level Improvement Quota Project of Capital University of Economics and Business and Scientific Research Foundation for Young Teachers of Capital University of Economics and Business(00591654490336)+6 种基金partially supported by the National Natural Science Foundation of China(Nos.11301212,11401146)partially supported by the National Natural Science Foundation of China Grants(No.11231010,11171330 and 11021161)Key Laboratory of RCSDS,CAS(No.2008DP173182)partly supported by National Natural Science Foundation of China(11271155)Specialized Research Fund for the Doctoral Program of Higher Education(20110061110003)Scientific Research Fund of Jilin University(201100011)Jilin Province Natural Science Foundation(20101596)
文摘Panel count data occur in many clinical and observational studies and in some situations the observation process is informative. In this article, we propose a new joint model for the analysis of panel count data with time-dependent covariates and possibly in the presence of informative observation process via two latent variables. For the inference on the proposed model, a class of estimating equations is developed and the resulting estimators are shown to be consistent and asymptotically normal. In addition, a lack-of-fit test is provided for assessing the adequacy of the model. The finite-sample behavior of the proposed methods is examined through Monte Carlo simulation studies which suggest that the proposed approach works well for practical situations. Also an illustrative example is provided.
