Contemporary information mini-satellites have general mass up to 500 kg and are placed onto the orbit altitudes from 500 up to 1500 km. For such spacecraft some principle problems on precise attitude determination and in-flight calibration are considered and elaborated methods are presented for their solving. Original multiple discrete algorithms for filtering, integration and calibration of a strapped-down inertial navigation system for precise determining the spacecraft attitude, are presented. This system contains electrostatic micro-accelerometer, an inertial measurement unit based on the gyro sensors, an astronomical system based on star trackers, multi-head Sun sensor and magnetic sensor, the that are fixed to the spacecraft body.