座標轉換方法、極座標的計算方法及加速度感測系統

This coordinate system transformation algorithm is applied on an accelerometer. It transforms the acceleration vector provided from accelerometer in a rectangular coordinate system to an independent coordinate system to retrieve the inclination information of the object. This algorithm is first to rotate the acceleration vector around 1st-axis and have its projected vector on the plane constructed from the other two axes aligned to the 2nd-axis. After that, rotate the acceleration vector on the 1st-2nd-axes plane, have it aligned on the 2nd-axis and calculate the rotation angle to get the 1st desired angle between the original acceleration vector and 1st-axis of the independent coordinate system. Based on the same concept of vector rotations, the angles between the horizontal plane, which is perpendicular to the acceleration vector, and the 2nd-axis and 3rd-axis can be calculated respectively. This algorithm can be applied on some clinical applications to detect if the patients or elderly people are trying to get out of bed. It can be also applied on the clinical evaluation of the patient's capability of dynamic posture control.