Multiple sigma-point Kalman smoothers for high-dimensional state-space models

Abstract

This article presents a new multiple state-partitioning solution to the Bayesian smoothing problem in nonlinear high-dimensional Gaussian systems. The key idea is to partition the original state into several low-dimensional subspaces, and apply an individual smoother to each of them. The main goal is to reduce the state dimension each filter has to explore, to reduce the curse of dimensionality and eventual loss of accuracy. We provide the theoretical multiple smoothing formulation and a new nested sigma-point approximation to the resulting smoothing solution. The performance of the new approach is shown for the 40-dimensional Lorenz model.