Pulse detonation engine contrail.

I was in my hot tub watching a TV show on my Kindle and I heard a popping noise, so I paused the show.  (I had the cover on the hot tub which is normal for me when it is cold, but there was also a very cold wind so I was actually under the cover at the time.)  The sound also kinda sounded like a basketball being dribbled during the second half of the event - which is plausible since I could hear kids in the neighborhood.
I was facing southwest at the time and the only thing unusal I noticed was a doughnuts on a rope contrail at the 2 o'clock position.
I did NOT actually see the plane that made the contrail.
During the last year I have seen this type of contrail over Lamberton 2 to 3 times and 1 or 2 times over Wabasso Minnesota. Always in a west to east / east to westly direction.