Student-t Process Quadratures for Filtering of Non-Linear Systems with Heavy-Tailed Noise
This addresses filtering in nonlinear systems with heavy-tailed noise, which is an incremental improvement for applications like signal processing or robotics.
The paper tackled the problem of designing a moment transformation for Student-t distributed random variables to account for integration error in nonlinear filtering, and it showed that the proposed method outperforms state-of-the-art moment transforms in numerical examples.
The aim of this article is to design a moment transformation for Student- t distributed random variables, which is able to account for the error in the numerically computed mean. We employ Student-t process quadrature, an instance of Bayesian quadrature, which allows us to treat the integral itself as a random variable whose variance provides information about the incurred integration error. Advantage of the Student- t process quadrature over the traditional Gaussian process quadrature, is that the integral variance depends also on the function values, allowing for a more robust modelling of the integration error. The moment transform is applied in nonlinear sigma-point filtering and evaluated on two numerical examples, where it is shown to outperform the state-of-the-art moment transforms.