Taylor Moment Expansion for Continuous-Discrete Gaussian Filtering and Smoothing
This addresses a problem in signal processing and control for applications like robotics or finance, offering a novel method for a known bottleneck in non-linear filtering.
The paper tackled non-linear Gaussian filtering and smoothing in continuous-discrete state-space models by proposing a Taylor moment expansion (TME) method, which approximates SDE moments with a temporal Taylor expansion and demonstrated significant outperformance over state-of-the-art methods in estimation accuracy and numerical stability in numerical experiments.
The paper is concerned with non-linear Gaussian filtering and smoothing in continuous-discrete state-space models, where the dynamic model is formulated as an Itô stochastic differential equation (SDE), and the measurements are obtained at discrete time instants. We propose novel Taylor moment expansion (TME) Gaussian filter and smoother which approximate the moments of the SDE with a temporal Taylor expansion. Differently from classical linearisation or Itô--Taylor approaches, the Taylor expansion is formed for the moment functions directly and in time variable, not by using a Taylor expansion on the non-linear functions in the model. We analyse the theoretical properties, including the positive definiteness of the covariance estimate and stability of the TME Gaussian filter and smoother. By numerical experiments, we demonstrate that the proposed TME Gaussian filter and smoother significantly outperform the state-of-the-art methods in terms of estimation accuracy and numerical stability.