Post date: Jun 01, 2017 3:17:25 PM
In a nutshell, a particle filter aims to estimate the posterior using a surrogate , i.e. the importance density, that is easier to sample. The estimation is carried out in a sequential manner (i.e. sequential importance sampling) by assuming Markovian (last state only) dependence, and is given by the following two equations:
(support-point update)
(weight update)
for each element index
in the state space. The notations are the latent state and noisy observation at time .
For more details, see the tutorial on the particle filter in [1]. Its counterpart, i.e. the Extended Kalman Filter (EKF), is also discussed in [1].
[1] Arulampalam, M. S., Maskell, S., Gordon, N., & Clapp, T. (2002). A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking. IEEE Transactions on signal processing, 50(2), 174-188.