Stability of Non-linear Filter for Deterministic Dynamics

Abstract

This papers shows that nonlinear filter in the case of deterministic dynamics is stable with respect to the initial conditions under the conditions that observations are sufficiently rich, both in the context of continuous and discrete time filters. Earlier works on the stability of the nonlinear filters are in the context of stochastic dynamics and assume conditions like compact state space or time independent observation model, whereas we prove filter stability for deterministic dynamics with more general assumptions on the state space and observation process. We give several examples of systems that satisfy these assumptions. We also show that the asymptotic structure of the filtering distribution is related to the dynamical properties of the signal.

24 pages, 1 figure. In V4, typos are corrected and few proofs are modified

References in corpus (4)

• On the Stability of Kalman-Bucy Diffusion Processes
• Degenerate Kalman filter error covariances and their convergence onto the unstable subspace
• Observability and nonlinear filtering
• Asymptotic Properties of Linear Filter for Noise Free Dynamical System

Cited by in corpus (1)

• Probing robustness of nonlinear filter stability numerically using Sinkhorn divergence