On Covariance Switch-Based Invariant Extended Kalman Filter for Multi-Source Fusion

The good estimation consistency of Invariant Extended Kalman Filter (InEKF) is mainly attributed to its excellent trajectory-independent property. However, when the InEKF is applied to multi-source inertial-based navigation that coexists left-invariant and right-invariant observations, the observation matrix would be unavoidably trajectory-dependent and might lead to the degradation of estimation performance. This paper for the first time performs theoretical analyses on the covariance switch between the left error and the right error in multi-source inertial-based navigation. Furthermore, detailed realizations of the covariance switch-based InEKF are formulated in this work, which are lacked in previous works. Numerical simulations and experiments demonstrate that the covariance switch significantly reduces the attitude errors during the transient phase in contrast with the original method using the incompatible error definition.