Comparison of Bingham Filter and Extended Kalman Filter in IMU Attitude Estimation

This paper reports the implementation of the Bingham filter (BF), a recently developed stochastic filter on SO(3), in the IMU attitude estimation problem. The BF uses the Bingham distribution, a probability distribution defined on the unit three-sphere, i.e., the space of unit quaternions, to model the attitude of a rigid body, and uses Bayes' formula to update the prediction with new attitude measurements. We compared the BF with the widely used multiplicative extended Kalman filter (MEKF) for accuracy and convergence speed through both the simulated and experimental IMU data. We used the gyroscope and accelerometer signals to estimate the tilt attitude (roll and pitch) with heading angle left uncorrected. We tested two types of measurements: attitude converted from measured acceleration and the measured acceleration itself. Results showed some benefits of BF over MEKF in terms of estimation accuracy and convergence speed from large initial errors. However, the computational cost of BF is also much higher than MEKF. Incidental findings also showed that using the full acceleration measurement improves the accuracy of the MEKF compared to using the attitude measurement converted from acceleration.