Particle filter with a proposal distribution generated by the ensemble transform Kalman filter

The particle filter (PF) provides an approximation of a non-Gaussian probability density function (PDF) of the system state on the basis of the importance sampling/resampling approach. However, the PF usually requires a prohibitively large ensemble size to achieve a good estimation. Accordingly, the PF tends to require huge computational cost. One way to reduce the computational cost is to use the proposal PDF similar to the posterior PDF. In order to obtain a good proposal PDF, we consider to use the ensemble transform Kalman filter (ETKF), which is one of ensemble square root filters. If we obtain a proposal PDF by using the ETKF, we can efficiently generate a large number of samples from the proposal PDF. We then perform the importance sampling/resampling to represent the posterior PDF. The weight in the importance sampling/resampling procedure can be efficiently calculated for each of the samples due to some favorable properties of the ETKF. As the ETKF is derived under the assumption of a linear Gaussian observation model, it does not necessarily provide a good estimate in the case with non-linear or non-Gaussian observation. However, by introducing the importance sampling/resampling procedure as done in the normal PF, we can take into consideration a non-linear or non-Gaussian property of the observation. In this paper, we explain about the algorithm in which the proposal PDF is obtained using the ETKF. We also compare it with other algorithms which combines ensemble Kalman filters with the PF.