  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 covariance
intersection and it approximates the multi-sensor, multi-object Bayes filter's
posterior distribution using the geometric mean of each sensor's
measurement-updated distribution. This filter can be used for distributed
fusion 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, which we adapt to account for
object existence. 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 filter, which has linear
complexity in the number of sensors. We evaluate both filters' performances on
simulated data and the results indicate that the filters are accurate.
