# Distributed Orbit Determination for Global Navigation Satellite System with Inter-Satellite Link
## 7 Conclusions  
The fundamental theory of satellite orbit determination for autonomous navigation is introduced. Four algorithms for autonomous navigation with onboard data processing, i.e., whole-constellation centralized extended Kalman filter (WCCEKF), iterative cascade extended Kalman filter (ICEKF), increased measurement covariance extended Kalman filter (IMCEKF), and balanced extended Kalman filter (BEKF), are illustrated. The WCCEFK technique processes the measurement data for orbit determination by a main satellite while the other three algorithms distribute the computation on every satellite in the constellation. The simulation results show that the method WCCEKF has the optimal orbit determination accuracy among the four methods but demands the largest computation loads. Similar computation amounts are observed in the three distributed algorithms. Compared to the ICEKF technique, covariance matrices of the other satellites are absorbed into the measurement  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Methods** & **Computation Amount (FLOPS: Floating-Point Operations Per Second)** \\ \hline WCCEKF & \(4N_{I}^{2}(N_{I}^{2}-1)+(N_{I_{W}}-1)N_{I_{W}}(N_{I_{W}}+1)/6+(2N_{I}^{2}+7N_ {I_{W}}+1)\times m\) \\ ICEKF or IMCEKF & \(4N_{I}^{2}(N_{I}^{2}-1)+(N_{I}-1)N_{I}(N_{I}+1)/6+(2N_{I}^{2}+7N_{I}+1)\times( m/n)\) \\ BEKF & \(4N_{I}^{2}(N_{I}^{2}-1)+(N_{I}-1)N_{I}(N_{I}+1)/6+(2N_{I}^{2}+7N_{I}+1)\times( m/2n)\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Computation amounts, unit: FLOPS (floating-point operations per second).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Algorithm** & **Description** & **Computation Amount** & **Orbital Accuracy** \\ \hline WCCEKF & Whole-constellation centralized EKF & Maximum & Best \\ ICEKF & Iterative cascade EKF & Minimum & Normal \\ IMCEKF & Increased measurement covariance EKF & Minimum & Normal \\ BEKF & Balanced EKF & Minimum & Better \\ \hline \hline \end{tabular}
\end{table}
Table 2: Comparisons of performances.  
Figure 6: Computation amounts.  
covariance matrix in the method of IMCEKF. As a result, a smaller orbit error is observed in the IMCEKF algorithm than in the ICEKF. Since the BEKF method estimates the state vectors of the satellites on both ends of the ISL in a balanced mean and increases their accuracy simultaneously, this method yields the best results among the three distributed estimation algorithms. The BEKF can be considered as an appropriate distributed data processing algorithm for a GNSS.  
[PERSON] conceived the idea with [PERSON]; [PERSON], [PERSON], and [PERSON] verified the feasibility of the proposed method and implemented different algorithms in the simulations; [PERSON] and [PERSON] analyzed the simulation results; [PERSON] and [PERSON] wrote the first version of the manuscript.  
This research is supported by the Key Projects of Chinese National Natural Science Foundation (grant number 41830110) and the Fundamental Research Funds for the Central Universities of China (grant number 2018 BQ7414).  
We would like to thank the anonymous reviewers and members of the editorial team for their comments and contributions.  
The authors declare no conflict of interest.