Application of a Randomized-Finite Set Statistics Technique (R-FISST) to Space Situational Awareness

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Abstract

This paper presents a novel approach to keeping the Random Finite Set (RFS) based Bayesian recursions tractable. We propose a randomized scheme using a Markov Chain Monte Carlo (MCMC) based technique and finite set statistics (FISST), termed Randomized FISST (R-FISST). This technique samples highly probable association hypotheses and uses them to approximate the posterior RFS based multi-object probability density function (pdf). It samples hypotheses without enforcing a heuristic number of samples so the number of samples is able to adjust naturally to the ambiguity of the data association problem (DAP). This provides the technique with a level of robustness to false associations. This is illustrated using two space situational awareness (SSA) examples. In the first example we compare the R-FISST technique to the Global Nearest Neighbor (GNN) technique. GNN represents the extreme case where the tracking problem is kept tractable, but the approximation of the multi-object pdf lacks association diversity, which leads to divergence in cardinality. The second example shows the scalability of the R-FISST technique by demonstrating its performance on collisional cascading, i.e., a cascading space object fragmentation event.

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Abbreviations

t :

Time

X :

The set of objects

n :

The cardinality of the object set

Z :

The set of observations

m :

The cardinality of observation set

$$q^{(n)}$$ :

A particular hypothesis consisting of n objects

$$\omega ^{q^{(n)}}_{t}$$ :

Weight of a hypothesis containing n objects at time step t

$$\nu$$ :

All possible permutations on the numbers 1 to n

$$\nu _i$$ :

The ith element of the permutation

$$\sigma ^{(n)}$$ :

An n object data association hypothesis

$$\sigma ^b_n$$ :

A birth hypothesis consisting of n birth objects

V :

Sensor volume

$$P_d$$ :

Probability of detection

$$P_s$$ :

Probability of survival

$$\lambda _C, \lambda _B$$ :

Average clutter/birth arrival rate

References

1. Bar-Shalom, Y., Fortmann, T.: Tracking and Data Association. Academic Press, San Diego (1988)

2. Bergman, N., Doucet, A.: Markov chain Monte Carlo data association for target tracking. In: Proc. ICASSP (2000)

3. Blackman, S.: Multiple hypothesis tracking for multiple target tracking. IEEE Trans. Aerosp. Electron. Syst. 19, 5–19 (2004)

4. Chakravorty, S., Faber, W.R., Hussein, I.I., Mishra, U.R.: A belief space perspective of RFS based multi-target tracking and its relationship to MHT

5. Cong, S., et al.: Markov chain Monte Carlo approach for association probability evaluation. Proc. IEEE 151, 185–193 (2004)

6. Faber, W., Chakravorty, S., Hussein, I.: A randomized sampling based approach to multi-object tracking. In: Proceedings of the 18th International Conference on Information Fusion, pp. 1307–1314. IEEE, Piscataway, NJ (2015)

7. Faber, W., Chakravorty, S., Hussein, I.: A randomized sampling based approach to multi-object tracking with comparison to HOMHT. Adv. Astronaut. Sci. 156, 1307 (2015)

8. Faber, W., Chakravorty, S., Hussein, I.: R-FISST and the data association problem with applications to space situational awareness. In: Proceedings of the AIAA/AAS Astrodynamics Specialist Conference. Long Beach, CA (2016)

9. Faber, W., Zaidi, W., Hussein, I., Roscoe, C.W.T., Wilkins, M.P., Paul W., Schumacher, J.: Application of multi-hypothesis sequential Monte Carlo for breakup analysis. In: Proceedings of the AAS/AIAA Astrodynamics Specialist Conference, Stevenson, WA, Paper AAS 17-579 (2017)

10. Fortmann, T., Bar-Shalom, Y., Scheffe, M.: Sonar tracking of multiple targets using joint probabilistic data association. IEEE J. Ocean. Eng. 8, 173–184 (1983)

11. Hoang, H., Vo, B.T., Vo, B.N.: A fast implementation of the generalized multi Bernoulli filter with joint prediction and update. In: International Conference on Information Fusion (2015)

12. Johnson, N.L., Krisko, P.H., Lieu, J.C., Am-Meador, P.D.: NASA’s new breakup model of evolve 4.0. Adv. Space Res. 28, 1377–1384 (2001)

13. Kelecy, T., Shoemaker, M., Jah, M.: Application of the constrained admissible region multiple hypothesis filter to initial orbit determination of a break-up. In: Proceedings of the 6th European Conference on Space Debris, Darmstadt, Germany (2013)

14. Mahler, R.P.S.: Statistical Multisource-Multitarget Information Fusion. Artec House, New York (2007)

15. Munkres, J.: Algorithms for the assignment and transportation problems. J. Soc. Ind. Appl. Math. 5(1), 32–38 (1957)

16. Oh, S., Russell, S., Sastry, S.: Markov chain Monte Carlo data association for mutli-target tracking. IEEE Trans. Autom. Control 54(3), 481–497 (2009)

17. Pasula, H., et al.: Tracking many objects with many sensors. In: Proc. IJCAI (1999)

18. Reid, D.: An algorithm for tracking multiple targets. IEEE Trans. Autom. Control 24(6), 843–854 (1979)

19. Resident space object catalog https://www.space-track.org/. Web (2017)

20. Schuhmacher, D., Vo, B.T., Vo, B.N.: A consistent metric for performance evaluation of multi-object filters. IEEE Trans. Signal Process. 56(8), 3447–3457 (2008)

21. Stauch, J., Bessell, T., Rutten, M., Baldwin, J., Jah, M., Hill, K.: Joint probabilistic data association and smoothing applied to multiple space object tracking. J. Guid. Control. Dyn. 41(1), 19–33 (2018)

22. Vo, B.T., et al.: An analytic implementation of the cardinalized probability hypothesis density filter. IEEE Trans. Signal Process. 55, 3553–3567 (2007)

23. Vo, B.N., et al.: Labeled random finite sets and multi-object conjugate priors. IEEE Trans. Signal Process. 61, 3460–3475 (2013)

24. Vo, B.N., et al.: Labeled random finite sets and the Bayes multi-target tracking filter. IEEE Trans. Signal Process. 62, 6554–6567 (2014)

Acknowledgements

This work was funded by AFOSR Grant Number: FA9550-13-1-0074 under the Dynamic Data Driven Application Systems (DDDAS) program.

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Correspondence to S. Chakravorty.

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Faber, W.R., Mishra, U.R., Chakravorty, S. et al. Application of a Randomized-Finite Set Statistics Technique (R-FISST) to Space Situational Awareness. J Astronaut Sci 69, 1149–1178 (2022). https://doi.org/10.1007/s40295-022-00331-1