Uncertainties in Galilean Spacetime

State estimation plays an important role in various types of systems, such as moving object tracking in the field of robotics and autonomous driving. The correct and accurate representation of the state has a huge impact on the estimation results in terms of accuracy and reliability. An elegant way for the encapsulation of the Euclidean state vector is the use of Lie groups, which allows appropriate handling of the associated uncertainties. Although better results are obtained compared to working in the Euclidean space, the commonly used representations such as the special Euclidean group exclude one important part: uncertainty in time. In this paper, we investigate this aspect and look at the problem of state estimation of moving objects from a different perspective. We propose the Galilei group as an elegant way of state representation and analyze the effect of uncertainties of the separate parameters on an object’s state represented as an event in spacetime. To show the practical applicability, we derive the necessary equations for the integration of our novel representation into an extended Kalman filter to serve as the basis of an object tracking scenario.