Transport Map Coupling Filter for State-Parameter Estimation

TL;DR

This paper introduces a transport map coupling filter that improves state-parameter estimation in non-linear, non-Gaussian stochastic systems by approximating arbitrary transition densities using transport maps.

Contribution

It presents a novel filtering approach based on transport maps that can handle arbitrary transition densities, enhancing accuracy over traditional filters.

Findings

Effective in non-Gaussian noise scenarios

Handles arbitrary transition densities

Improves estimation accuracy in non-linear systems

Abstract

Many dynamical systems are subjected to stochastic influences, such as random excitations, noise, and unmodeled behavior. Tracking the system's state and parameters based on a physical model is a common task for which filtering algorithms, such as Kalman filters and their non-linear extensions, are typically used. However, many of these filters use assumptions on the transition probabilities or the covariance model, which can lead to inaccuracies in non-linear systems. We will show the application of a stochastic coupling filter that can approximate arbitrary transition densities under non-Gaussian noise. The filter is based on transport maps, which couple the approximation densities to a user-chosen reference density, allowing for straightforward sampling and evaluation of probabilities.