  The Poisson multi-Bernoulli mixture (PMBM) is a multi-object conjugate prior
for the closed-form Bayes random finite sets filter. The extended object PMBM
filter provides a closed-form solution for multiple extended object filtering
with standard models. This paper considers computationally lighter alternatives
to the extended object PMBM filter by propagating a Poisson multi-Bernoulli
(PMB) density through the filtering recursion. A new local hypothesis
representation is presented where each measurement creates a new Bernoulli
component. This facilitates the developments of methods for efficiently
approximating the PMBM posterior density after the update step as a PMB. Based
on the new hypothesis representation, two approximation methods are presented:
one is based on the track-oriented multi-Bernoulli (MB) approximation, and the
other is based on the variational MB approximation via Kullback-Leibler
divergence minimisation. The performance of the proposed PMB filters with gamma
Gaussian inverse-Wishart implementations are evaluated in a simulation study.
