Adaptive invariant Kalman filtering for attitude estimation on SO (3) thorough feedback calibration of prior error covariance

For invariant attitude dynamics evolving on matrix Lie groups, by proposing the stochastic feedback–based covariance calibration scheme, an adaptive invariant Kalman filter (AIKF) is elaborated to deal with the attitude estimation problems corrupted by unknown or inaccurate process noise statistics. The invariant Kalman filter (IKF) takes into account the geometry property of attitude dynamics and can boost the estimation performance; however, IKF requires accurate knowledge of the noise statistics and an incorrect noise parameter is prone to deteriorating the precision of final estimates. To eliminate this impact, instead of using the original covariance propagation step of IKF, the prior error covariance of the proposed AIKF is online calibrated based on the posterior information of the feedback stochastic sequence. As the main advantage, the statistics parameter of system process noise is no longer required in the proposed AIKF and the negative influence by unknown/incorrect noise parameters can be reduced significantly. The mathematical foundation for the new adaption scheme of AIKF is also presented. The AIKF's advantage in filtering adaptability and simplicity is further demonstrated by numerical simulations.