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 𝛼 𝑡 =( 𝑥 𝑡 , 𝑣𝑥 𝑡 , 𝑧 𝑡 , 𝑣𝑧 𝑡 )′

10. Experimental results (1/2)

11. Experimental results (2/2)