  Gibbs sampling is one of the most popular Markov chain Monte Carlo algorithms
because of its simplicity, scalability, and wide applicability within many
fields of statistics, science, and engineering. In the labeled random finite
sets literature, Gibbs sampling procedures have recently been applied to
efficiently truncate the single-sensor and multi-sensor $\delta$-generalized
labeled multi-Bernoulli posterior density as well as the multi-sensor adaptive
labeled multi-Bernoulli birth distribution. However, only a limited discussion
has been provided regarding key Gibbs sampler architecture details including
the Markov chain Monte Carlo sample generation technique and early termination
criteria. This paper begins with a brief background on Markov chain Monte Carlo
methods and a review of the Gibbs sampler implementations proposed for labeled
random finite sets filters. Next, we propose a short chain, multi-simulation
sample generation technique that is well suited for these applications and
enables a parallel processing implementation. Additionally, we present two
heuristic early termination criteria that achieve similar sampling performance
with substantially fewer Markov chain observations. Finally, the benefits of
the proposed Gibbs samplers are demonstrated via two Monte Carlo simulations.
