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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

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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

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