  Particle filtering is a powerful approximation method that applies to state
estimation in nonlinear and non-Gaussian dynamical state-space models.
Unfortunately, the approximation error depends exponentially on the system
dimension. This means that an incredibly large number of particles may be
needed to appropriately control the error in very large scale filtering
problems. The computational burden required is often prohibitive in practice.
Rebeschini and Van Handel (2013) analyse a new approach for particle filtering
in large-scale dynamic random fields. Through a suitable localisation operation
they reduce the dependence of the error to the size of local sets, each of
which may be considerably smaller than the dimension of the original system.
The drawback is that this localisation operation introduces a bias. In this
work, we propose a modified version of Rebeschini and Van Handel's blocked
particle filter. We introduce a new degree of freedom allowing us to reduce the
bias. We do this by enlarging the space during the update phase and thus
reducing the amount of dependent information thrown away due to localisation.
By designing an appropriate tradeoff between the various tuning parameters it
is possible to reduce the total error bound via allowing a temporary
enlargement of the update operator without really increasing the overall
computational burden.
