An explicit variance reduction expression for the Rao-Blackwellised particle filter, Report no. LiTH-ISY-R-2979

Particle lters (PFs) have shown to be very potent tools for state estimation in nonlinear and/or non-Gaussian state-space models. For certain models, containing a conditionally tractable substructure (typically conditionally linear Gaussian or with nite support), it is possible to exploit this structure in order to obtain more accurate estimates. This has become known as Rao-Blackwellised particle ltering (RBPF). However, since the RBPF is typically more computationally demanding than the standard PF per particle, it is not always bene cial to resort to Rao-Blackwellisation. For the same computational e ort, a standard PF with an increased number of particles, which would also increase the accuracy, could be used instead. In this paper, we have analysed the asymptotic variance of the RBPF and provide an explicit expression for the obtained variance reduction. This expression could be used to make an e cient discrimination of when to apply Rao-Blackwellisation, and when not to.