A method of attitude estimation with a low-cost, strap-on MEMS sensor was proposed in the article. The method relies on dynamic gyroscope bias change estimation and updates during detected stops of the robot. The algorithm has been tested in laboratory with iRobot Roomba robot and should be improved to be useful in an industrial environment. The measurement of attitude of a mobile platform is necessary for correct navigation, especially in autonomous vehicles, which use dead reckoning between position updates from external sources. Since the system is intended to operate indoors, in industrial halls and shops, it cannot avail of GPS and Earth magnetic field sensors because of anomalies, which are common inside the steel constructions. Therefore, the accuracy of the gyroscope-based attitude estimation is significant. The proposed method aims to address the common problem of gyroscope bias drift, by dynamic update of sensor bias and simultaneous use of all gyroscope axes, to improve the quality of the measurements. A popular 3-axial gyroscope and 3-axial accelerometer sensors were used during the test runs. Obtained results suggest that it is possible to improve short-term accuracy of inertial dead reckoning, to get a system that could be of practical use in industrial AGV systems or intelligent vehicles.