Kalman filtering is widely used in satellite attitude determination because of its good performance.The classical EKF algorithm represents the estimated error vector in the estimated attitude coordinate system

because there is no consideration to estimate the deviation between the attitude coordinate system and the true attitude coordinate system

which leads to decrease of attitude estimation precision.To solve this problem

Andrle M S introduces error consistent represent method through geometric transformation

and on this basis

he proposes GEKF algorithm attitude error quaternion and gyro drift increment through geometric transformation of consistency representation

solve the problem that estimate error vector representation is not consistent.The principle of error consistency representation is introduced

and apply GEKF algorithm to gyro model with constant drift and time drift.Simulation experiments show that the GEKF algorithm is more accurate than MEKF on gyro drift estimation

and filtering precision is improved significantly.