Developed and investigated Mathematical and algorithmic support for basic modes of operation of strapdown inertial navigation system (SINS) and the control system motion in the areas of manned flight of small-sized spacecraft was developed and investigated. To improve the accuracy of SINS algorithms for complex information processing with astro sensor were developed. The results (methods, models, software and algorithmic support) can be used when designing strapdown systems of orientation and navigation of the new generation for smallsized spacecraft, as well as for development of new and modernization of the existing software of SINS small-sized spacecraft.