Abstract
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-based multimodel 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-basedmultimodel approach when the existence probability of the outliers is uncertain.
Highlights
As a classical state estimation method, Kalman filter [1] has been thoroughly applied in a variety of applications such as positioning, navigation, brain imaging, and traffic control, together with its numerous nonlinear or off-line extensions [2,3,4,5,6]
These estimators assume that the model parameters and the noise statistics are exactly known, which is too perfect for most real applications and usually cannot be satisfied, resulting in reduced accuracy of the state estimation
There is lack of works targeting on the flexibility of the robustness, i.e. most current available filters are only suitable for the non-Gaussian noise with fixed or specific degree of non-Gaussianity, e.g. heavytailedness
Summary
As a classical state estimation method, Kalman filter [1] has been thoroughly applied in a variety of applications such as positioning, navigation, brain imaging, and traffic control, together with its numerous nonlinear or off-line extensions [2,3,4,5,6]. There is lack of works targeting on the flexibility of the robustness, i.e. most current available filters are only suitable for the non-Gaussian noise with fixed or specific degree of non-Gaussianity, e.g. heavytailedness These estimators are vulnerable to the outliers with an uncertain or time-variant existence probability in the system and measurement processes. An adaptive approach to changeable noise covariances has been developed in [9] and approaches using parameters learning have been proposed in [10,11,12] for the non-Gaussian noises, these works do not take into account the uncertain degree of heavy-tailedness, which makes the robustness of these filters lack of flexibility. We demonstrate that the proposed fusion strategy offers better model fusion for state estimation in the presence of non-Gaussian noises with uncertain degree of heavy-tailedness.
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