  Driven by the filtering challenges in linear systems disturbed by
non-Gaussian heavy-tailed noise, the robust Kalman filters (RKFs) leveraging
diverse heavy-tailed distributions have been introduced. However, the RKFs rely
on precise noise models, and large model errors can degrade their filtering
performance. Also, the posterior approximation by the employed variational
Bayesian (VB) method can further decrease the estimation precision. Here, we
introduce an innovative RKF method, the RKFNet, which combines the
heavy-tailed-distribution-based RKF framework with the deep learning (DL)
technique and eliminates the need for the precise parameters of the
heavy-tailed distributions. To reduce the VB approximation error, the
mixing-parameter-based function and the scale matrix are estimated by the
incorporated neural network structures. Also, the stable training process is
achieved by our proposed unsupervised scheduled sampling (USS) method, where a
loss function based on the Student's t (ST) distribution is utilised to
overcome the disturbance of the noise outliers and the filtering results of the
traditional RKFs are employed as reference sequences. Furthermore, the RKFNet
is evaluated against various RKFs and recurrent neural networks (RNNs) under
three kinds of heavy-tailed measurement noises, and the simulation results
showcase its efficacy in terms of estimation accuracy and efficiency.
