Discrete-time sequential Monte Carlo methods for filtering and optimization.

Professor Joaquin Miguez (Universidad Carlos III de Madrid)

The course ran in the Autumn term 2013. 
The lectures started on Wednesday, 2nd October.
Room 140 9am-10am followed by tutorials and computing sessions in Room 410 from 10am-11am.

---

1. Filtering for state-space models.
(1 lecture on 02/10 + 1 lab session on 09/10)

• Introduction and background: state-space models, Kalman filtering and its variations.
• Other non-SMC filters.
• Practical work: implementation of an extended Kalman filter for target tracking.

---

2. Particle filtering.
(2 lectures on 16/10 and 23/10 + 1 lab session on 30/10)

• Bootstrap filter.
• Sequential importance sampling.
• Asymptotic convergence.
• Extensions: auxiliary PF, Rao-Blackwellized PF, Gaussian-sum PF, density assisted PF.
• Practical work: implementation of standard, auxiliary and Rao-Blawellized particle filters for a target tracking problem.

---

3. Parallelization of particle filters.
(1 lecture on 06/11 + 1 lab session on 13/11)

• Distributed/parallel particle filtering.
• Distributed resampling with non-proportional allocation.
• Local selection methods.
• Practical work: comparison of centralized vs. parallelized PFs.

---

4. Estimation of the filter density.
(1 lecture on 20/11 + 1 lab session on 27/11)

• Problem statement.
• Kernel density estimation.
• Convergence of the density estimator.
• MAP estimators.
• Approximation of functionals.
• Practical work: implementation of various MAP estimators using the approximate filter density. 

---

5. SMC methods for optimization.
(1 lecture on 06/12 + 1 lab session on 11/12)

• Objective functions and a posteriori densities.
• Particle MAP estimation / optimization algorithms.
• Asymptotic convergence.
• Practical work: solving a multidimensional optimization problem by way of a particle filter.