Adaptive approximate filtering of state-space models

Approximate Bayesian computation (ABC) filtration of state-space models replaces popular particle filters in cases where the observation models (i.e. likelihoods) are either computationally too demanding or completely intractable, but it is still possible to simulate from them. These sequential Monte Carlo methods evaluate importance weights based on the distance between the true observation and the simulated pseudoobservations. The paper proposes a new adaptive method consisting of probability kernel-based evaluation of importance weights with online determination of kernel scale. It is shown that the resulting algorithm achieves performance close to particle filters in the case of well-specified models, and outperforms generic particle filters and state-of-art ABC filters under heavy-tailed noise and model misspecification.