The answer here describes the attitude determination goals of the future russian crew module federatsiya. The idea is to use two different GPS receivers at the end of the spacecraft, when the spacecraft is rotating(almost tumbling) and looses its absolute attitude reference, this method will be able to give attitude within certain time using signal delays of the GPS. Ideally, one would require 3 GPS antennas for solution for 3 axis. But this assumes the spacecraft is tumbling, therefore if given sufficient time one can probably converge to proper attitude using some algorithm. Also, as mentioned in the paper provided in the above link, the soyuz MS does use gyro in loop for the attitude determination using GPS. However, the federatsiya's one of the failure modes assumes gyro has failed and can get attitude without gyro too. Obviously this must have time penalty
ISS uses same technique, I think as Technology Demonstrator as mentioned in this link