Differential equation dynamical system based assessment model in GNSS interoperability  

作　　者：HAN Tao LU XiaoChun WANG Xue RAO YongNan ZOU DeCai YANG JianFei WU YangYang 

机构地区：[1]National Time Service Center,Xi'an 710600,China [2]Key Laboratory of Precision Navigation and Timing Technology,Chinese Academy of Sciences,Xi'an 710600,China [3]Graduate University of the Chinese Academy of Sciences,Beijing 100049,China [4]Department of Economics and Management,Northwestern University,Xi'an 710127,China

出　　处：《Science China(Physics,Mechanics & Astronomy)》2011年第6期996-1003,共8页中国科学：物理学、力学、天文学（英文版）

基　　金：supported by the National Natural Science Foundation of China (Grant Nos.11073022 and 71072160);the National Basic Research Program of China (Grant No.2007CB815502);the Western Light (Grant No.Y001YR4701)

摘　　要：With the development of Global Navigation Satellite System (GNSS),the idea of GNSS interoperability is born and has become the focus of study in the field of satellite navigation.The popularity for GNSS to augment the interoperability with the existing ones necessitates the study of the assessment algorithm of this idea.In this paper,an assessment algorithm for interoperability comprehensive benefits based on the differential equation dynamical system is discussed.There are two important aspects in GNSS that interoperability will affect:one is the performance advancement;the other one is the cost of adopting interoperability.While researching the complex relationship between the performance and cost,we found this relationship is similar as what between prey and predator in biomathematics,so the Lotka-Volterra model used to depict the prey-predator relationship is a felicitous tool.After building a differential dynamical model,we analyze the existence and stability of the positive equilibrium in the model.Then a Cost-Effective Function of GNSS is constructed based on the positive equilibrium,which is employed to assess the interoperability,qualitatively and quantitatively.Finally,the paper demonstrates the significance of the model and its application by citing a numerical example.With the development of Global Navigation Satellite System （GNSS）,the idea of GNSS interoperability is born and has become the focus of study in the field of satellite navigation.The popularity for GNSS to augment the interoperability with the existing ones necessitates the study of the assessment algorithm of this idea.In this paper,an assessment algorithm for interoperability comprehensive benefits based on the differential equation dynamical system is discussed.There are two important aspects in GNSS that interoperability will affect：one is the performance advancement;the other one is the cost of adopting interoperability.While researching the complex relationship between the performance and cost,we found this relationship is similar as what between prey and predator in biomathematics,so the Lotka-Volterra model used to depict the prey-predator relationship is a felicitous tool.After building a differential dynamical model,we analyze the existence and stability of the positive equilibrium in the model.Then a Cost-Effective Function of GNSS is constructed based on the positive equilibrium,which is employed to assess the interoperability,qualitatively and quantitatively.Finally,the paper demonstrates the significance of the model and its application by citing a numerical example.

关 键 词：INTEROPERABILITY assessment model differential dynamical system GNSS STABILITY 

分 类 号：Q141[生物学—生态学] TN967.1[生物学—普通生物学]