Probing robustness of nonlinear filter stability numerically using Sinkhorn divergence

TL;DR

This paper uses the Sinkhorn algorithm to numerically demonstrate exponential stability of particle and ensemble Kalman filters for deterministic systems, linking stability to convergence via Wasserstein distance.

Contribution

It introduces a numerical approach to assess nonlinear filter stability using Sinkhorn divergence, connecting stability with filter bias and RMSE.

Findings

Exponential stability of particle and ensemble Kalman filters demonstrated.

Wasserstein distance correlates with filter bias and RMSE.

Numerical relation established between filter stability and convergence.

Abstract

Using the recently developed Sinkhorn algorithm for approximating the Wasserstein distance between probability distributions represented by Monte Carlo samples, we demonstrate exponential filter stability of two commonly used nonlinear filtering algorithms, namely, the particle filter and the ensemble Kalman filter, for deterministic dynamical systems. We also establish numerically a relation between filter stability and filter convergence by showing that the Wasserstein distance between filters with two different initial conditions is proportional to the bias or the RMSE of the filter.