Transport Map Coupling Filter for State-Parameter Estimation
Jan Grashorn, Matteo Broggi, Ludovic Chamoin, Michael Beer
TL;DR
The paper tackles state- and parameter-estimation in nonlinear stochastic systems where Gaussian assumptions may fail. It introduces a transport-map coupling filter that represents the joint state–measurement distribution via invertible maps to a standard normal reference, enabling straightforward conditioning on measurements through map inversion. Maps are constructed in a Knothe–Rosenblatt form and trained by minimizing a KL divergence, with extensions to joint state-parameter estimation achieved through a normalization step to address scale differences and optional likelihood oversampling to boost robustness. The approach is demonstrated on a Duffing oscillator with non-Gaussian noise, showing that the method yields reduced posterior variance and reliable convergence, validating the practical potential for real-time, non-Gaussian filtering in engineering 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.