Recall from Section 9.1 that the sensor outputs are distorted due to calibration issues. In the one-dimensional angular velocity case, there were only two parameters, for scale and offset, which appeared in (9.1). In the 3D setting, this would naturally extend to scale and offset parameters; however, the situation is worse because there may also be errors due to non-orthogonality of the MEMS elements. All of these can be accounted for by parameters arranged in a homogeneous transform matrix:
An additional challenge with MEMS sensors is dealing with other subtle dependencies. For example, the outputs are sensitive to the particular temperature of the MEMS elements. If a VR headset heats up during use, then calibration parameters are needed for every temperature that might arise in practice. Fortunately, IMUs usually contain a temperature sensor that can be used to associate the calibration parameters with the corresponding temperatures. Finally, MEMS elements may be sensitive to forces acting on the circuit board, which could be changed, for example, by a dangling connector. Care must be given to isolate external board forces from the MEMS circuit.
Steven M LaValle 2016-12-31