  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.
