Outlier-robust Schmidt-Kalman filter using variational inference

The Schmidt-Kalman filter (SKF) achieves filtering consistency in the presence of biases in system dynamic and measurement models through accounting for their impacts when updating the state estimate and covariance. However, the performance of the SKF may break down when the measurements are subject to non-Gaussian and heavy-tail noise. To address this, we impose the Wishart prior distribution on the precision matrix of measurement noise, such that the measurement likelihood now has heavier tails than the Gaussian distribution to deal with the potential occurrence of outliers. Variational inference is invoked to establish analytically tractable methods for computing the posterior of the system state, system biases, and the measurement noise precision matrix. The principle of the SKF considers the effect of system biases but does not actively estimate them when two variants of outlier-robust SKFs are incorporated. We evaluate their performance in terms of estimation accuracy and filtering consistency using simulations and real-world data. Promising results are obtained.