This paper presents a new concept of high-reliability strapdown attitude sensing systems for space vehicles. Each system utilizes a set of redundant two-degree-of-freedom gyros. An optimum system configuration is obtained for maximum system reliability and the best measurement accuracy. Improved accuracy of the final data is obtained by using the least-square data reduction technique. Each system possesses a "sensor performance management" feature which is capable of failure detection, faulty gyro identification, system reconfiguration, and, possibly, sensor recalibration. Improvement in reliability, as compared to other types of strapdown systems, is demonstrated. Details of the development are described in terms of a system containing four gyros.