Case II: Dim Object Tracking

Three sensor networks, i.e., GTO, SSO, and GBS, are tested by tracking 100 dim GEO objects for three days. Only the analytical R´enyi divergence is employed in this test case to

determine the sensor control vector. Theoretically, both the R´enyi divergence and the Cauchy- Schwarz divergence can produce similar results.

0 10 20 30 40 50 60 70 Time (hour) 0 5 10 15 20 25 Position error (km) GBS GTO SSO

(a) Average position errors

0 10 20 30 40 50 60 70 Time (hour) 0 10 20 30 40 50 60 70 80 90 100 110

Number of objects detected

GBS GTO SSO

(b) Number of targets detected

Figure 5.5.8: Position accuracy and cardinality estimation results

Fig. 5.5.8a shows the averaged position errors of the 100 dim GEO space objects. The velocity results are again omitted because the trends are similar to the position error. As shown in the figure, the GTO sensor network reduces the position error to around 5 km after 20 hours of tracking and the errors are maintained around 5 km for the rest of the simulation. However, the position errors of the other two sensor networks fail to converge, and the SSO provides the worst accuracy in state estimation.

Fig. 5.5.8b shows the number of dim objects detected by the three methods. The result of the GBS is surprisingly better than SSO. Compared with GBS, SSO has a larger relative distance to most GEO objects because the orbital plane of the SSO is nearly vertical to the equator and most objects in GEO have low inclinations. The final results illustrate that both GBS and SSO can only detect a small portion of the 100 tested objects due to the low brightness. The GTO approach can detect 95 out of 100 objects, and the other five undetected objects all have RCS values lower than 0.03. The GTO sensor network is generally effective for tracking dim GEO object and substantially increases the range of detectable object sizes as compared to other networks, though there is still a lower limit depending on sensor constraints.

0 10 20 30 40 50 60 70 Time (hour) 0 1000 2000 3000 4000 5000 6000 7000 Number of measurements GBS GTO SSO

(a) Number of measurements

0 10 20 30 40 50 60 70 Time (hour) 0 10 20 30 40 50 60

Number of visible objects

GBS GTO SSO

(b) Number of visible objects

Figure 5.5.9: Number of measurements and visible objects

It is observed from the figure that only the GTO sensor network can steadily produce measure- ments over the entire simulation, while GBS and SSO are often unable to produce any new measurements. Fig. 5.5.9b shows the number of objects visible to each sensor network. There are around 20 to 40 objects visible to the GTO sensor network at most epochs. On the contrary, the other two sensor networks can only provide access to a few targets due to the larger relative distance between the GEO targets and sensors. As discussed previously, the GTO sensors are able to approach the GEO belt, and therefore have more opportunity to detect the dim GEO object than the SSO and GBS sensor networks. The significant difference further demonstrates the better performance of the GTO sensor network for dim GEO object detection.

5.6

Summary

This chapter investigates the use of space-based multi-sensor networks for multi-target es- timation of GEO space objects. Two SBS sensor networks (three GTO and three SSO) and two hybrid sensor networks (GBS-GTO and GBS-SSO) are presented and tested. The analytical formulation of R´enyi divergence for two LMB densities is derived to measure the information gain, and a simplified reward function of multi-sensor tasking is defined as the sum of infor- mation divergences of each sensor node to improve the efficiency of large-scale GEO object tracking. Two numerical simulations including 905 GEO objects and 100 dim GEO objects

are designed for validation. Results indicate that the SBS and hybrid sensor networks outper- form the GBS approach in terms of orbital state estimation, the number of targets detected and the number of measurements collected. The derived R´enyi divergence provides similar sensor tasking performance compared to the Cauchy-Schwarz divergence with a better computational performance. In addition, the GTO sensor network significantly outperforms other sensor net- works for tracking dim GEO object because of its better viewing geometry for GEO objects.

Recommendations

6.1

Summary and Conclusions

This dissertation was aimed to develop novel methods of tracklet association and RFS- based statistical multi-target tracking and multi-sensor tasking to improve the capability and capacity of the current space object cataloguing. The major difficulties and challenges of these techniques were first investigated. To achieve accurate catalogue maintenance, two improved tracklet association methods were proposed for efficient and effective processing of increasing numbers of uncorrelated tracklets. The performance of these new methods was studied using real measurements. A comprehensive comparison of four recently-developed labelled RFS fil- ters was carried out to assess their performance for different space object tracking tasks. This thesis then explored the use of the BVP tracklet association method for the initialisation of the LMB filter to achieve a more efficient initialisation process for new space object tracking. A rigorous comparison between the BVP and the traditional CAR and PAR birth models was conducted using objects from different orbital domains. Finally, to allocate sensor resources to make better use of limited information, the analytical formulation for the R´enyi divergence of LMB RFSs was derived and formulated as an objective function to address the multi-sensor tasking problem. The proposed method allocates a set of space-based and ground-based sensor networks for GEO object tracking, and their performances were studied using different scenar-

ios of space object tracking.

For the tracklet association problem, a new algorithm called the improved IVP method was proposed, which determines the association by optimising a new loss function defined in the non-singular canonical space. Simulations were carried out using real optical data from various orbital regions. The results indicated that the improved IVP method achieves better association performance compared with the IVP and BVP methods for the tested real data, and it provides the most efficient computational performance because the measurement noise cali- bration process does not need to be considered. However, the improved IVP method yields low true negative rate for the association of tracklets in the same constellation. As an effective solu- tion, a common ellipse algorithm was proposed to distinguish false associations by determining if a best fitting common ellipse to all hypothetical ellipses of the constellation tracklets can be found. Results indicated a significant improvement in the true negative rate of the association results.

For the multiple space object tracking problem, the multi-target Bayesian recursion ap- proach based on the labelled RFS theory was validated as a viable solution through various simulated scenarios. The LMB filter is suited for optical SSA sensors because the small sen- sor FOV yields a natural grouping and gating that reduces the computational complexity. The comparison results of four labelled RFS filters indicated that the LMB filter is a viable solu- tion for tracking space objects because it can achieve good performance for both accuracy and efficiency.

For the multi-target tracking of new space objects, the BVP optimisation method was for- mulated as a new birth model for the initialisation of the LMB filter for recursive filtering and estimation. The major advantage this new birth model has over the previously developed CAR/PAR birth model is that the initial target state is approximated by a single Gaussian com- ponent, while a large number of GM components are generally produced by the CAR/PAR method. As a result, the BVP birth model can result in significant improvement of the compu- tational demand for the filtering process. The proposed method was tested by tracking multiple

GEO and GTO objects in various scenarios. Results validated that the BVP-LMB filter provides similar accuracy of state and cardinality estimation compared to the CAR/PAR-LMB filter, and it achieves superior results of computational efficiency in all test cases.

For the multi-sensor tasking problem, the analytical formulation of the R´enyi divergence for LMB RFSs was derived and formulated as the reward function for this problem. The pro- posed multi-sensor tasking method is implemented using several space-based and ground-based sensor networks to monitor GEO. Results indicated that the R´enyi divergence is highly effec- tively in reducing estimation errors for a large population of space objects, and it is more com- putationally efficient than the Cauchy-Schwarz divergence for δ-GLMB RFSs. In addition, the GTO sensor network was validated as a viable solution for tracking dim objects in GEO due to its better viewing geometry for the GEO domain.

The work in this thesis has demonstrated that the proposed new methods are able to pro- vide improved performance in terms of accuracy, effectiveness, and/or efficiency compared to the state-of-the-art methods. These are beneficial for robust SOC maintenance as well as the expansion of the capacity of the current SOC for accommodating more uncorrelated and undis- covered space objects.