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A Quaternion Based Error State Kalman Filter for Attitude Estimation Using Low-cost MEMS MARG Sensors

Low-cost MEMS MARG sensors have been widely applied for attitude estimation, and the error state Kalman filter (ESKF) is an essential data fusion technology. To eliminate the confusions regarding problems like error state selection and filter modeling, this paper presents detailed derivations and concise final formulations of two different ESKFs based on the left- and right-multiplied error quaternion, respectively. Unit quaternion is used for attitude representation, and the error states consist of the attitude errors represented as a small rotation vector and the gyro bias variations. We found that two previous derived formulations for design matrix in the literature are equivalent. The proposed algorithms are implemented and compared with conventional methods using a set of experimental data, the results show that although both the dynamic matrix and design matrix of the attitude error related states distinguish from each other, the attitude estimation results of two filters are completely identical, and the performance of ESKF is better than that of the conventional methods.