Direction cosine matrix estimation with an inertial measurement unit

Estimating attitude using an inexpensive MEMS inertial measurement unit has many applications in smart phones, wearable sensors, rehabilitation medicine and robots. Traditional approaches to attitude estimation from the aerospace world focus on the use of either Euler angles or quaternions. These approaches suffer from disadvantages including singularities and nonlinear models. This paper proposes a method to estimate the direction cosine matrix (DCM) which encapsulates attitude information, instead of Euler angles or quaternions. The DCM does not suffer from singularities and also has linear dynamics. A rigorous DCM estimation algorithm, that incorporates automatic magnetometer bias calibration and satisfaction of an inherent orthonormal property of the DCM, is developed. The validity of the developed algorithm is demonstrated through experimental results with estimation of attitude on a 5-DOF robot. The estimation results are compared with values computed from encoders on the robot as well as with results from previously published algorithms.