Projected Feedback Particle Filtering for Chaotic Dynamical Systems Using Lyapunov Vectors
Yujing Zhou, Ryne Beeson · 2024
Particle flow methods are effective in resolving the particle degeneracy issue in the standard particle filtering algorithm. However, flow methods have their own difficulties, such as the necessity to solve a Poisson equation in the feedback particle filtering (FPF) method. This is computationally heavy, and we observe a numerical sensitivity and singularity issue dependent on parameter selection when applying to chaotic dynamical systems with limited particle size and coarse integration step size. In this paper, we address the numerical singularity issue by flowing particles in the unstable subspace (UAS), and we name the novel method the projected FPF. It brings the local dynamical information into the assimilation step by using the finite-time Lyapunov exponents and vectors to project observations and particle states to the UAS, where the error diverges. The projected FPF is tested against the Lorenz 1963 model – a nonlinear, low-dimensional, chaotic dynamical system.