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.

扩展卡尔曼滤波器（EKF）和互补滤波器（CF）是惯性和磁测量单元中两种最常用的姿态确定算法。已知分别由EKF和CF提供的后姿态估计之间的唯一区别是分配给用于姿态更新的创新的增益矩阵（GM）。通过数学推导得出结论，可以将EKF的GM简化为CF之一，这意味着CF是EKF的近似值。进行了蒙特卡洛模拟，以验证这些简化对EKF性能的影响。主要发现是，在低采样率的情况下，EKF比CF更稳定，因此CF必须更多地依靠陀螺仪的测量来确定姿态，以提高其稳定性。