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