A current trend in activity recognition is to use just one easily carried accelerometer, either integrated into a mobile phone, carried in a pocket, or attached to an animal's collar. The main disadvantage of this approach is that the orientation of the accelerometer is generally unknown. Therefore, one cannot separate body-related accelerations from the gravitational acceleration or determine the real directions of the observed accelerations accurately. As a solution, we introduce a new technique where jerk (changes of accelerations) is analyzed instead of the original acceleration signal. The total jerk magnitude is completely orientation-independent and it reflects only body-related accelerations. If the direction of the gravitation can be approximated even loosely, then the jerk signal can be further enriched with valuable information on jerk angles (direction changes). According to our experiments this kind of jerk-filtered signal produces robust features and can improve the recognition accuracy remarkably.