Robust probabilistic conflict prediction for sense and avoid

Safe integration of Unmanned Aircraft Systems (UAS) into the National Airspace (NAS) will require the development and fielding of a sense-and avoid (SAA) capability to augment the traditional “see-and-avoid” regulations of manned aircraft. In this paper, we focus on the problem of correctly predicting an intruder trajectory. Approaches to intruder prediction are typically grouped into three categories: (i) nominal (deterministic), (ii) worst-case, and (iii) probabilistic. Most prediction algorithms envisioned for SAA fall within the probabilistic category. The benefit of a probabilistic approach is that it provides a mechanism to represent unknown variations in the intruder state at future times while also avoiding the overly conservative assumptions inherent in worst-case prediction. The downside of a probabilistic prediction is that it necessitates the construction of a stochastic model that is both useful for computation and accurately represents the “true” uncertainty in intruder predictions. Markovian structure and time-discretization are very common simplifying assumptions made to satisfy the first goal. Data-driven model tuning is typically used for the latter. However, a model is never exact, and a large quantity of data may be needed to guarantee the approximation accuracy is sufficient. The primary contribution of this paper is to present a fourth option for intruder prediction that we refer to as “robust probabilistic prediction.” It is meant to address the risk of model mismatch associated with traditional probabilistic predictions. Conceptually, the idea is to specify only those features of the stochastic model that can be justified by data or expert judgment, leaving a full stochastic model underspecified. Typically, one needs a full stochastic model to “turn the crank” on risk calculations (e.g., probability of Near Mid-Air Collision). However, in robust probabilistic predictions, risk i- defined as the worst-case risk over a space of stochastic models. This relaxes the need for ensuring that all elements of the model are correct. We show that a computationally efficient semi-definite program (SDP) can be used for performing the optimization over the space of stochastic models. Such an approach greatly reduces the risk of model mismatch as well as reducing the data burden required for model validation.