A Simplified Extended Kalman Filter Used for Magnetic and Inertial Measurement Units

As a sensor unit, a magnetic and inertial measurement unit (MIMU) is mainly composed of a tri-axis gyroscope, a tri-axis accelerometer and a tri-axis magnetometer. The Extended Kalman Filter (EKF) is the currently preferred algorithm used to fuse the outputs of the MIMU sensor in order to determine the attitude of the MIMU's carrier platform. One of the main problems of the EKF is its high computational cost, which is largely due to solving the matrix inversion in the Kalman gain. This article simplifies the Kalman gain by ensuring it does not contain any matrices that would require an inversion operation. This is achieved by simplifying the linearized measurement matrix (the Jacobian matrix) through orthogonalizing the observation and reference vectors. The inversion of the matrix contained in the Kalman gain can then be mathematically derived and the derived matrix can eventually replace the matrix inversion, in order to avoid the inversion operation when the EKF is executed. The simplified EKF is compared to the traditional EKF experimentally and the results show that the simplified method has similar accuracy to the traditional method, but with a faster execution time.