Observability Analysis and Navigation Filter Optimization of High-Orbit Satellite Navigation System Based on GNSS
Abstract
:1. Introduction
- (1)
- We propose a new method for calculating the observable degree of a high-orbit satellite navigation system based on GNSS, which can simultaneously give the relative observability of each state component at each moment and the overall observability of the system;
- (2)
- We design an adaptive optimization method of navigation filter based on this observable degree, which maps the observable degree of the state component to a feedback weighting factor to improve the performance of the navigation filter;
- (3)
- Based on the GNSS navigation system, we combine the proposed observability calculation method as an adjustment factor of the adaptive filter for filter optimization. Numerical simulation shows that the method effectively improves the navigation filter accuracy of the navigation systems of the high-orbit satellite based on GNSS.
2. Navigation Model Based on GNSS
2.1. State Equation of the Navigation System
2.2. Measure Equation of the Navigation System
2.3. Model Linearization
3. Observability of the Navigation System
3.1. Observability Qualitative Analysis
3.2. Observable Degree Analysis
4. Optimized Filter Algorithm for Navigation System Based on the Observable Degree
Algorithm 1 Adaptive Extend Kalman Filter |
1: Input: Optimal estimation of and covariance matrix in moment |
2: Output: Optimal estimation of and covariance matrix in moment k |
Step 1: Calculate the state transition , measurement matrix and state covariance matrix by Equations (19)–(23) |
Step 2: Repeat Step 1 and calculate the state transition matrix and measurement matrix at moment , written as . |
Step 3: Use the in Step 1 and Step 2 then calculate the by Equation (18). |
Step 4: Define a mapping function based on the criterion in Section 3 then calculate the by Equation (25). |
Step 5: Calculate the new filter gain matrix by Equation (24). |
Step 6: Calculate and and output them. |
5. Simulation Analysis
5.1. Simulation Conditions
5.2. Simulation Results and Analysis
6. Conclusions
Author Contributions
Funding
Conflicts of Interest
Abbreviations
GNSS | Global Navigation Satellite System |
EKF | Extend Kalman filter |
AKF | adaptive Kalman filter |
IGSO | inclined geo-synchronization orbit |
UTC | Universal Time |
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Xiao, Y.; Zhou, X.; Wang, J.; He, Z.; Zhou, H. Observability Analysis and Navigation Filter Optimization of High-Orbit Satellite Navigation System Based on GNSS. Appl. Sci. 2020, 10, 7513. https://doi.org/10.3390/app10217513
Xiao Y, Zhou X, Wang J, He Z, Zhou H. Observability Analysis and Navigation Filter Optimization of High-Orbit Satellite Navigation System Based on GNSS. Applied Sciences. 2020; 10(21):7513. https://doi.org/10.3390/app10217513
Chicago/Turabian StyleXiao, Yaqi, Xuanying Zhou, Jiongqi Wang, Zhangming He, and Haiyin Zhou. 2020. "Observability Analysis and Navigation Filter Optimization of High-Orbit Satellite Navigation System Based on GNSS" Applied Sciences 10, no. 21: 7513. https://doi.org/10.3390/app10217513
APA StyleXiao, Y., Zhou, X., Wang, J., He, Z., & Zhou, H. (2020). Observability Analysis and Navigation Filter Optimization of High-Orbit Satellite Navigation System Based on GNSS. Applied Sciences, 10(21), 7513. https://doi.org/10.3390/app10217513