Conditional equivalence between Extended Kalman filter and complementary filter for two-vector gyro-aided attitude determination

Extended Kalman Filter (EKF) and Complementary Filter (CF) are the two most commonly-used attitude determination algorithms in inertial and magnetic measurement units. It is known that the only difference between the a posterior attitude estimates provided by EKF and CF respectively is the gain matrix (GM) assigned to innovation for attitude update. Through mathematical derivation, it is concluded that the GM of EKF can be simplified to the one of CF, which means that CF is an approximation to EKF. Monte Carlo simulations were done to validate what influence of these simplifications is put on the performance of EKF. The main finding is EKF is more stable than CF in condition of low sampling rate, and hence CF must rely more on the measurements of gyroscope for attitude determination to improve its stability.

Automated summary

Extended Kalman Filter (EKF) and Complementary Filter (CF) are commonly used attitude determination algorithms, with the main difference being the gain matrix used for attitude update. Mathematical derivation shows that CF is an approximation to EKF, and in low sampling rate conditions, EKF is more stable than CF.