On the performance of particle filters with adaptive number of particles

Understand

We investigate the performance of a class of particle filters (PFs) that can automatically tune their computational complexity by evaluating online certain predictive statistics which are invariant for a broad class of state-space models.

• To be specific, we propose a family of block-adaptive PFs based on the methodology of Elvira et al (2017).
• In this class of algorithms, the number of Monte Carlo samples (known as particles) is adjusted periodically, and we prove that the theoretical error bounds of the PF actually adapt to the updates in the number of particles.
• The evaluation of the predictive statistics that lies at the core of the methodology is done by generating fictitious observations, i.e., particles in the observation space.