Observability Analysis and Navigation Filter Optimization of High-Orbit Satellite Navigation System Based on GNSS  
[PERSON]  
1 College of Liberal Arts and Science, National University of Defense Technology, Changsha 410073, China; [EMAIL_ADDRESS] (Y.X. ); [EMAIL_ADDRESS] (X.Z. ); [EMAIL_ADDRESS] (J.W. ); [EMAIL_ADDRESS] (Z.H.) [PERSON]  
1 College of Liberal Arts and Science, National University of Defense Technology, Changsha 410073, China; [EMAIL_ADDRESS] (Y.X. ); [EMAIL_ADDRESS] (X.Z. ); [EMAIL_ADDRESS] (J.W. ); [EMAIL_ADDRESS] (Z.H.) [PERSON]  
1 College of Liberal Arts and Science, National University of Defense Technology, Changsha 410073, China; [EMAIL_ADDRESS] (Y.X. ); [EMAIL_ADDRESS] (X.Z. ); [EMAIL_ADDRESS] (J.W. ); [EMAIL_ADDRESS] (Z.H.) [PERSON]  
1 College of Liberal Arts and Science, National University of Defense Technology, Changsha 410073, China; [EMAIL_ADDRESS] (Y.X. ); [EMAIL_ADDRESS] (X.Z. observability. For the navigation system of high-orbit satellites based on GNSS, the geometrical observability refers to that the line of sight of the high-orbit satellite to the navigation constellation is visible, the physical observability refers to that the effective observation data of the high-orbit satellite measurement equipment on the GNSS navigation satellite can be obtained and the engineering observability refers to that after obtaining effective observation data, the value of the user's state variables that meet the engineering accuracy requirements can be estimated. These three levels of observability are names as 'visibility', 'testability', and 'availability'. Among them, the 'availability' in this article refers to the observability in the control field. It is the basis for judging the performance of the navigation system and the reflection of the ability of the control system to determine the state variables at the initial moment [12]. In addition, good observability is the guarantee for the state filter convergence of the navigation system of high-orbit satellite [13; 14]. Therefore, research on the observability of the navigation system is an important link in the design of the navigation system and the optimization of the navigation filter algorithm and has important theoretical and practical significance. Since the navigation system of high-orbit satellites based on GNSS is a nonlinear system, there are currently two main methods to analyze the observability for the nonlinear system: one is to transfer the nonlinear system into a linear system by linearizing the nonlinear system and then distinguish the observability by using the Grammar matrix of the linear system [15; 16]. The second method analyzes the observability of the navigation system through the observability discriminant matrix which can be computed through the Lie derivative in the differential manifold [17; 18]. However, the calculation complexity of the second method is high and its operating efficiency may also be reduced when the system equation is complex. The observability can only qualitatively judge whether the navigation system is observable. To quantify the observability of the system and its state components, the observable degree needs to be applied [19]. The analysis method of the observable degree has not been clearly defined. [PERSON] [20] firstly proposed the method in 1983 which uses the eigenvalues and eigenvectors of the estimated error covariance matrix to describe the observability of the system state. However, the method can only work after the filter, and the system observability cannot be given in real-time. Reference [21] proposed a method to analyze the observable degree of the system through the singular value of the observable matrix. The method can judge the observability of the system before filter and is a pre-analysis method. However, this method can only give the overall observability of the system and cannot obtain the observability for each state component of the system.