However, the bus vibration signals collected are dependent on the smartphone own coordinate system; the signals will vary with the posture change of the smartphone, and the drift of bus acceleration signals is introduced in the inertial coordinate system in which the actual situation of the bus vibration is showed.

The inertial coordinate system in which the bus vibration comfort will be calculated can be regarded as an intermediate status between the smartphone and the world coordinate system, while its origin is identical with the origin of the smartphone's coordinate system and its axes are paralleling to the axes of the world coordinate system.

Therefore, the acceleration signals need to be transformed from smartphone coordinate system to inertial coordinate system.

According to this theory, the triaxial acceleration is regarded as a vector, whose three direction cosines are the cosines of three angles between the vector and the three axes, and then the coordinate transformation from the smartphone's coordinate system to the inertial coordinate system will be realized.

are used to denote triaxial accelerations in inertial coordinate system, because the acceleration vector A is unique, so they satisfy