Nested Gaussian filters for recursive Bayesian inference and nonlinear tracking in state space models

TL;DR

This paper presents a nested Gaussian filtering approach for efficient recursive Bayesian inference and nonlinear tracking in state-space models, reducing computational costs and improving performance in high-dimensional problems.

Contribution

It introduces a Gaussian approximation within the nested hybrid filtering framework, enhancing efficiency for high-dimensional state and parameter estimation.

Findings

Reduced computational cost compared to Monte Carlo methods

Effective tracking in high-dimensional state spaces

Improved parameter estimation in Lorenz 63 model

Abstract

We introduce a new sequential methodology to calibrate the fixed parameters and track the stochastic dynamical variables of a state-space system. The proposed method is based on the nested hybrid filtering (NHF) framework of [1], that combines two layers of filters, one inside the other, to compute the joint posterior probability distribution of the static parameters and the state variables. In particular, we explore the use of deterministic sampling techniques for Gaussian approximation in the first layer of the algorithm, instead of the Monte Carlo methods employed in the original procedure. The resulting scheme reduces the computational cost and so makes the algorithms potentially better-suited for high-dimensional state and parameter spaces. We describe a specific instance of the new method and then study its performance and efficiency of the resulting algorithms for a stochastic Lorenz 63 model with uncertain parameters.