"These objects show physics we don't understand" said the cat to the laser pointer. Seriously though I think we'll find that the super acrobatic lights (the only exciting part of this) are being produced by powerful transmitters owned by the military, and they're showing up during training because that's exactly when the transmitters are pointed near our planes, because the transmitters are built to detect planes and that's how you test them. Most likely the military is aware of this, but the real good plane detection stuff is super secret, and it's a lot easier to keep a new sensor/transmitter secret than a new plane. Sucks they're not allowed to tell their pilots but it makes sense.

I dunno what do you think? Seems like the most parsimonious explanation to me.