Could it have been a canard design? Piaggio has a twin, and there was the Beechcraft "Starship" which has since been withdrawn from the market. These rwo are twin engine pushers, but turbine powered rather than piston. You could have been hearing the prop noise of course.

Single engined canards are all ( so far as I know ) Burt Rutan designs - Vari-Eze, Long-Eze, and so forth. All are pusher designs, piston engined.

If any of these were far enough away and at the right angle they might well have looked a bit l.ike an F-15.

Bill.