I was reading recently about the near-loss of the Solar and Heliospheric Observatory (SOHO) spacecraft back in 1998, in this Wikipedia article. This article mentions that
Only one gyro remained operational after this recovery, and on December 21 that gyro failed. Attitude control was accomplished with manual thruster firings that consumed 7 kg of fuel weekly, while ESA developed a new gyroless operations mode that was successfully implemented on February 1, 1999.
What is this gyroless operations mode? What does it depend on to determine the spacecraft's attitude? Are there other spacecraft that use it?