Auxiliary particle filtering: recent developments

1. Auxiliary particle filtering:recent developments Nick Whiteley and Adam M. Johansen Summarized by Eun-Sol Kim

2. Background-SSMs(State Space Models) x1 f x2 … xn g y1 y2 … yn

3. Background-Particle Filtering • The integrals required for a Bayesian recursive filter cannot solved analytically *Prediction step *Update step • So, we represent the posterior probabilities by a set of randomly chosen weighted samples

4. Background- Sequential Importance Resampling

5. Weaknesses of SIR • If there is an outlier, SIR is not robust. • If the observation density is tailed distribution, SIR is not robust From Filtering via Simulation: Auxiliary Particle Filters (1999, M.K.Pitt& N. Shephard)

6. Main idea of APF • Auxiliary variable(particle index): k

7. Algorithm for APF

8. Generic approaches choosing predictive likelihood • Using the approximations of the transition densities and update densities • The multivariate t distribution (centered at the mode) • In the multimodal case, a mixture of multivariate t distributions.

9. Experiment • Compare the performance of the PF and APF for an angular time series model • Hidden states

10. Experimental results (1/2)

11. Experimental results (2/2)