A Linear Kalman Filter for MARG Orientation Estimation Using the Algebraic Quaternion Algorithm

Real-time orientation estimation using low-cost inertial sensors is essential for all the applications where size and power consumption are critical constraints. Such applications include robotics, human motion analysis, and mobile devices. This paper presents a linear Kalman filter for magnetic angular rate and gravity sensors that processes angular rate, acceleration, and magnetic field data to obtain an estimation of the orientation in quaternion representation. Acceleration and magnetic field observations are preprocessed through a novel external algorithm, which computes the quaternion orientation as the composition of two algebraic quaternions. The decoupled nature of the two quaternions makes the roll and pitch components of the orientation immune to magnetic disturbances. The external algorithm reduces the complexity of the filter, making the measurement equations linear. Real-time implementation and the test results of the Kalman filter are presented and compared against a typical quaternion-based extended Kalman filter and a constant gain filter based on the gradient-descent algorithm.