Particle-based, online estimation of tangent filters with application to parameter estimation in nonlinear state-space models

TL;DR

This paper introduces a particle-based online algorithm for estimating tangent filters in hidden Markov models, enabling efficient recursive maximum likelihood parameter estimation with proven convergence properties.

Contribution

It presents a novel, computationally efficient particle-based method for online tangent filter estimation with theoretical convergence guarantees.

Findings

Algorithm has linear complexity and limited memory use.

Proven convergence including a central limit theorem.

Demonstrated effectiveness in a simulation study.

Abstract

This paper presents a novel algorithm for efficient online estimation of the filter derivatives in general hidden Markov models. The algorithm, which has a linear computational complexity and very limited memory requirements, is furnished with a number of convergence results, including a central limit theorem with an asymptotic variance that can be shown to be uniformly bounded in time. Using the proposed filter derivative estimator we design a recursive maximum likelihood algorithm updating the parameters according the gradient of the one-step predictor log-likelihood. The efficiency of this online parameter estimation scheme is illustrated in a simulation study.