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

We present an efficient numerical implementation of the $\delta$-Generalized Labeled Multi-Bernoulli 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 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.