Learning nonlinear state-space models using smooth particle-filter-based likelihood approximations
For practitioners estimating parameters in nonlinear state-space models, this method reduces the noise and computational cost of particle-filter-based likelihood optimization.
This paper addresses the challenge of noisy likelihood estimates in particle-filter-based maximum likelihood estimation for nonlinear state-space models. It proposes iteratively re-evaluating the likelihood approximation from a single particle filter run across different parameter values, enabling deterministic local optimization and yielding accurate parameter estimates.
When classical particle filtering algorithms are used for maximum likelihood parameter estimation in nonlinear state-space models, a key challenge is that estimates of the likelihood function and its derivatives are inherently noisy. The key idea in this paper is to run a particle filter based on a current parameter estimate, but then use the output from this particle filter to re-evaluate the likelihood function approximation also for other parameter values. This results in a (local) deterministic approximation of the likelihood and any standard optimization routine can be applied to find the maximum of this local approximation. By iterating this procedure we eventually arrive at a final parameter estimate.