Orientation sensing apparatus and a method for determining an orientation

An orientation sensing apparatus includes a rotatable first member, an orientation sensor device fixed with the first member for generating orientation data relating to an orientation sensor device orientation, and a rotation sensor device for generating rotation data relating to rotation of the first member. A method for determining an orientation includes assembling a set of sensor data including the orientation data and rotation data and processing the set of sensor data to generate a set of corrected orientation data. The set of corrected orientation data includes the orientation data which has been corrected using the rotation data to reduce the effects of rotation of the first member and misalignment of the gravity sensor device. One or more sets of corrected orientation data may be processed to determine an inclination orientation of the first member or a toolface orientation of a second member which is connected with the first member.