The focus of this work is the implementation of Gaussian process regression for continuity of measurement for small uncrewed aircraft systems (sUAS). This method supplies a continuous estimate with uncertainty of the three-dimensional wind vector along a predicted flight trajectory. The Gaussian process is implemented with GPyTorch, which is derived from the popular machine learning Python library, PyTorch.

Wind observations come from the TORUS-LItE dataset collected with the RAAVEN platform. An onboard five-hole probe measures the air-relative velocity vector, from which the wind can be calculated using the GPS velocity. This absolute wind from the multi-hole probe is treated as the ground truth during validation.

Several Gaussian processes are compared with different input and output parameterizations. The inputs include normalized latitude, longitude, altitude, time, autopilot eastward wind, and autopilot northward wind. The kernel used is the squared-exponential radial basis function with separate length-scales for each input dimension. The outputs are the three-dimensional wind vector. A batch independent approach is compared to a multi-task Gaussian process that uses correlated outputs with a learned inter-task (output) covariance matrix. Hyperparameters are learned by minimizing the negative marginal log-likelihood for 50 training epochs using the Adam optimizer.

Each flight is subdivided into a series of rolling windows, and predictions over a 30 second horizon are generated with the previous 30 seconds of data used for inference. Predictive uncertainty is derived from the posterior multivariate normal distribution. The root-mean-square error is calculated for 1, 5, 10, and 30 second forecasts.

A second sUAS flight track is introduced to test whether temporally and spatially coincident observations from a nearby sUAS can improve local predictions. The supplemental RAAVEN aircraft is separated from the primary RAAVEN by approximately 100 m in altitude, and the supplementary RAAVEN's multi-hole probe wind components are added to the Gaussian process input vector.

Results show that predictions up to 5 seconds have low error throughout all the flights. Adding a second sUAS shows promising results for spatially coincident observations but provides little value from temporally coincident observations. The uncertainty in the predictions is quantified and compared over various short term time horizons.