Robust extended Kalman filter for attitude estimation with multiplicative noises and unknown external disturbances

This study is concerned with the robust extended Kalman filtering problem for non-linear attitude estimation systems with multiplicative noises and unknown external disturbances. The multiplicative noises are modelled by random variables with bounded variance. The unknown external disturbances are described to lie in bounded set. The objective of the addressed attitude estimation problem is to design a filter such that, in the presence of both the multiplicative noises and unknown external disturbances, an optimised upper bound on the state estimation error variance can be guaranteed. Thus, a robust extended Kalman filter (REKF) is presented for attitude estimation with multiplicative noises and unknown external disturbances. Compared with the traditional extended Kalman filter in attitude estimation, the proposed algorithm takes into consideration the effects of multiplicative noises and unknown external disturbances. Moreover, the stability of the proposed REKF can be proved under certain conditions by utilising the stochastic stability theory. Finally, the simulation results demonstrate the effectiveness of the proposed REKF.