Predicting State Uncertainty for GNSS-based UAV Path Planning using Stochastic Reachability

Akshay Shetty and Grace Xingxin Gao

Abstract: An important component of path planning algorithms is predicting state uncertainty in order to ensure probabilistic collision-free paths. While predicting state uncertainty, path planning algorithms generally assume zero mean Gaussian distributions for motion and measurement error models. However, a zero mean Gaussian assumption is not applicable for Global Navigation Satellite System (GNSS) positioning measurements, which typically contain uncertain biases in urban areas due to multipath and non-line-of-sight (NLOS) effects. In this paper, we propose a method to predict the state uncertainty of a UAV in the presence of uncertain GNSS positioning biases using stochastic reachability analysis. We enclose all possible GNSS positioning error distributions arising due to uncertain biases with a probabilistic zonotope. For the on-board state estimation filter, we choose a Kalman filter (KF) and fix a hypothesis for the GNSS positioning error distribution. We first compute the stochastic set of estimation errors resulting from the above hypothesis. We then compute the stochastic reachable sets for a linear motion model of the UAV with linear state feedback control along the candidate path. Finally, we validate the stochastic reachability analysis by evaluating the predicted state uncertainty along candidate paths in a simulated 3D urban environment.
Published in: Proceedings of the 32nd International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2019)
September 16 - 20, 2019
Hyatt Regency Miami
Miami, Florida
Pages: 131 - 139
Cite this article: Shetty, Akshay, Gao, Grace Xingxin, "Predicting State Uncertainty for GNSS-based UAV Path Planning using Stochastic Reachability," Proceedings of the 32nd International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2019), Miami, Florida, September 2019, pp. 131-139. https://doi.org/10.33012/2019.16896
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