## 3 Distributed Cubature Kalman Filter
### Distributed Cubature Kalman Filter
## 6 Conclusions

In this paper, we investigated the distributed Bayesian filter and proposed a distributed cubature Kalman filter. In order to solve the problems of weak observability and time-varying communication topology, we introduced Kullback-Leibler (K-L) divergence to measure the difference of local estimates, and the consensus estimate is achieved under the K-L average of local estimates. The simulation results indicate that, for the distributed space object tracking problem, the proposed DCKF has better results than DEKF and DCIF. Moreover, the proposed algorithm does not rely on the same measurement mapping of each sensor and can successfully track a space object for the time-varying communication topology and weak observability of some sensors. This work was partially supported by the National Natural Science Foundations of China 61403399. [PERSON], [PERSON], [PERSON], [PERSON] and [PERSON] contributed to the idea. [PERSON] developed the algorithm, and [PERSON] and [PERSON] collected the data and performed the simulations. [PERSON], [PERSON] and [PERSON] analyzed the experimental results and wrote this paper [PERSON] and [PERSON] supervised the study and reviewed this paper. All authors have read and approved the final manuscript. The authors declare no conflict of interest. ## References

* (1) [PERSON]; [PERSON]; [PERSON] Applying aerospace technologies to current issues using systems engineering: 3 rd aess chapter summit. _IEEE Aerosp. Electron. Syst. Mag._**2013**, _28_, 34-41. * (2) [PERSON]; [PERSON] An overview of space situational awareness. In Proceedings of the 2013 16 th IEEE International Conference on Information Fusion (FUSION), Istanbul, Turkey, 9-12 July 2013; pp. 1029-1036. * (3) [PERSON]; [PERSON]; [PERSON] Global space situational awareness sensors. In Proceedings of the 2010 Advanced Maui Optical and Space Surveillance Conference, Maui, HI, USA, 14-17 September 2010. * (4) [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] Space-based wireless sensor networks: Design issues. In Proceedings of the 2010 IEEE Aerospace Conference, Big Sky, MT, USA, 6-13 March 2010, pp. 1-14. * (5) [PERSON]; [PERSON]; [PERSON]; [PERSON] Spacecraft tracking using sampled-data Kalman filters. _IEEE Control Syst._**2008**, _28_, doi:10.1109/MCS.2008.923231. * (6) [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] Comparison of three approximate kinematic models for space object tracking. In Proceedings of the 2013 16 th International Conference on IEEE Information Fusion (FUSION), Istanbul, Turkey, 9-12 July 2013; pp. 1005-1012. * (7) [PERSON]; [PERSON] _Optimal Filtering_; Prentice-Hall: Upper Saddle River, NJ, USA, 1979; pp. 62-77. * (8) [PERSON]; [PERSON]; [PERSON]; [PERSON] Stochastic stability of the discrete-time extended Kalman filter. _IEEE Trans. Autom. Control_**1999**, _44_, 714-728. * (9) [PERSON]; [PERSON] [PERSON]; [PERSON] Extended Kalman filter tuning in sensorless PMSM drives. _IEEE Trans. Ind. Appl._**2003**, _39_, 1741-1747. * [PERSON] et al. (2001) [PERSON]; [PERSON]; [PERSON] Improving the singular evolutive extended Kalman filter for strongly nonlinear models for use in ocean data assimilation. _Inverse Probl._**2001**, _17_, 1535. * [PERSON] et al. (2000) [PERSON]; [PERSON]; [PERSON] A new method for the nonlinear transformation of means and covariances in filters and estimators. _IEEE Trans. Autom. Control_**2000**, _45_, 477-482. * [PERSON] et al. (2017) [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] Adaptive Unscented Kalman Filter for Target Tracking in the Presence of Nonlinear Systems Involving Model Mismatches. _Remote Sens._**2017**, \(9\), 657. * [PERSON] and [PERSON] (2009) [PERSON]; [PERSON] [PERSON] Cubature kalman filters. _IEEE Trans. Autom. Control_**2009**, _54_, 1254-1269. * [PERSON] et al. (2010) [PERSON]; [PERSON]; [PERSON] Cubature Kalman filtering for continuous-discrete systems: theory and simulations. _IEEE Trans. Signal Process._**2010**, _58_, 4977-4993.