From the abstract of "Do birds sleep in flight?", Niels Rattenborg[1]:-
"The recent miniaturization of EEG recording devices now makes it possible to measure brain activity in flight. Determining if and how birds sleep in flight will contribute to our understanding of a largely unexplored aspect of avian behavior and may also provide insight into the function of sleep."
and in the section entitled "Future Directions":-
"Until recently, EEG recording devices were too large for a bird to carry in flight. However, Vyssotski et al. (2006)[2] recently developed and successfully deployed an EEG and a global positioning system (GPS) logger on pigeons during short, daytime homing flights to their loft."
[0]: http://www.vyssotski.ch/neurologger2.html
[1]: https://www.researchgate.net/publication/7093774_Do_birds_sl...
[2]: https://www.researchgate.net/publication/7529290_Miniature_n...