Learning nonlinear state-space models using smooth particle-filter-based likelihood approximations

TL;DR

This paper introduces a novel method for nonlinear state-space model parameter estimation that uses smooth particle-filter-based likelihood approximations to reduce noise and improve optimization accuracy.

Contribution

It proposes a new approach combining particle filtering with deterministic likelihood approximation for more reliable maximum likelihood estimation.

Findings

Reduces noise in likelihood estimates during parameter estimation.

Enables the use of standard optimization routines for nonlinear models.

Provides a more stable and accurate parameter estimation process.

Abstract

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.