  In this paper, we propose two efficient, approximate formulations of the
multi-sensor labelled multi-Bernoulli (LMB) filter, which both allow the
sensors' measurement updates to be computed in parallel. Our first filter is
based on the direct mathematical manipulation of the multi-sensor, multi-object
Bayes filter's posterior distribution. Unfortunately, it requires the division
of probability distributions and its extension beyond linear Gaussian
applications is not obvious. Our second filter is based on geometric average
fusion and it approximates the multi-sensor, multi-object Bayes filter's
posterior distribution using the geometric average of each sensor's
measurement-updated distribution. This filter can be used under non-linear
conditions; however, it is not as accurate as our first filter. In both cases,
we approximate the LMB filter's measurement update using an existing loopy
belief propagation algorithm. Both filters have a constant complexity in the
number of sensors, and linear complexity in both number of measurements and
objects. This is an improvement on an iterated-corrector LMB (IC-LMB) filter,
which has linear complexity in the number of sensors. The proposed filters are
of interest when tracking many objects using several sensors, where filter
run-time is more important than filter accuracy. We evaluate both filters'
performances on simulated data and the results indicate that the filters' loss
of accuracy compared to the IC-LMB filter is not significant.
