Labeled Random Finite Sets and the Bayes Multi-Target Tracking Filter

An analytic solution to the multi-target Bayes recursion known as the delta-Generalized Labeled Multi-Bernoulli (delta-GLMB) filter has been recently proposed by Vo andVo in [Labeled Random Finite Sets and Multi-Object Conjugate Priors, IEEE Trans. Signal Process., vol. 61, no. 13, pp. 3460-3475, 2014]. As a sequel to that paper, the present paper details efficient implementations of the delta-GLMB multi-target tracking filter. Each iteration of this filter involves an update operation and a prediction operation, both of which result in weighted sums of multi-target exponentials with intractably large number of terms. To truncate these sums, the ranked assignment and K-th shortest path algorithms are used in the update and prediction, respectively, to determine the most significant terms without exhaustively computing all of the terms. In addition, using tools derived from the same framework, such as probability hypothesis density filtering, we present inexpensive (relative to the delta-GLMB filter) look-ahead strategies to reduce the number of computations. Characterization of the L-1-error in the multi-target density arising from the truncation is presented.