MEMS gyroscopes can provide useful information for dead-reckoning navigation systems if suitable error compensation algorithm is applied. If there is information from other sources available, usually the Kalman filter is used for this task. This work focuses on improving the performance of the sensor if no other information is available and the integration error should be kept low during periods of still (no movement) operation. A filtering algorithm is proposed to follow bias change during sensor operation to reduce integration error and extend time between successive sensor calibrations. The advantage of the proposed solution is its low computational complexity which allows implementing it directly in the micro-controller of controlling the MEMS gyroscope. An intelligent sensor can be build this way, suitable for use in control systems for mobile platforms. Presented results of a simple experiment show the improvement of the angle estimation. During the 12 hours experiment with a common MEMS sensor and no thermal compensation, the maximum orientation angle error was below 8 degrees.