Student's $t$ Information Filter with Adaptive Degree of Freedom for Multi-Sensor Fusion

Safety-critical applications such as autonomous driving require a high-integrity localization system that bounds the errors of the estimation process. In this paper, the classical Kalman filter used for multi-sensor data fusion, which is unable to consistently bound estimation errors with a low probability risk, is replaced by a Student's
$t$
filter. The degree of freedom of the
$t$
distribution offers a way of shaping the heavy tail of the distribution that makes the estimation process more robust in the presence of non-detectable bias and results in a more consistent confidence interval computation. We make use of the heavy-tailed property of the
$t$
distribution by introducing a novel real-time adaptive computation of the degree of freedom. The filtering process is formalized through an informational form, since this makes it easier to include a fault detection and exclusion step where a bank of filters is generated. The performance of the proposed approach is evaluated through a localization problem using data acquired from an experimental vehicle equipped with multiple sensors: a GNSS receiver, wheel-speed sensors, a yaw rate gyro and a smart camera that can detect several lane markings, together with high-definition maps.