A flexible robust student’s t-based multimodel approach with maximum Versoria criterion

The performance of the state estimation for Gaussian state space models can be degraded if the models are affected by the non-Gaussian process and measurement noises with uncertain degree of non-Gaussianity. In this paper, we propose a flexible robust Student's t multi-model approach. More specifically, the degrees of freedom parameter from the Student's t distribution is assumed unknown and modelled by a Markov chain of state values. In order to capture more information of the Student's t distributions propagated through multiple models, we establish a model-based Versoria cost function in the form of a weighted mixture rather than the original form, and maximize the function to interact and fuse the multiple models. Simulated results prove the flexibility of the robustness of the proposed Student's t multi-model approach when the existence probability of the outliers is uncertain

Student-t process quadratures for filtering of non-linear systems with heavy-tailed noise

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.Peer reviewe