We present an efficient numerical implementation of the $\delta$-GeneralizedLabeled Multi-Bernoulli multi-target tracking filter. Each iteration of thisfilter involves an update operation and a prediction operation, both of whichresult in weighted sums of multi-target exponentials with intractably largenumber of terms. To truncate these sums, the ranked assignment and K-thshortest path algorithms are used in the update and prediction, respectively,to determine the most significant terms without exhaustively computing all ofthe terms. In addition, using tools derived from the same framework, such asprobability hypothesis density filtering, we present inexpensive look-aheadstrategies to reduce the number of computations. Characterization of the$L_{1}$-error in the multi-target density arising from the truncation ispresented.
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