An iterative attitude estimation algorithm was proposed to solve multiplicative stochastic matrix in satellite attitude determination system.Based on the principle of linear minimum-variance and projection formula

the attitude iterative filter algorithm was deduced.By linearizing and iterating two times respectively for state equation and measure equation

the algorithm can reduce the influence of linearization error to the attitude determination precision.The algorithm enlarges the application range of EKF in the state estimation of nonlinear systems with multiplicative noise.Simulation results indicate that the proposed algorithm provides effective performance in the presence of multiplicative stochastic matrix.