A Novel Federated Structure of Invariant EKF Using Left-/Right-Invariant Observations

In this article, we propose a novel federated structure of the invariant extended Kalman filter (IEKF) using the left- and right-invariant observations. A proper invariant error should be chosen to exploit the trajectory-independent property of the IEKF. For the left- and right-invariant observations, the left-IEKF (LIEKF) and the right-IEKF (RIEKF) are designed, respectively. However, in applications, both left- and right-invariant observations are often used together while using multiple aiding sensors to improve estimation performance. If either the LIEKF or RIEKF is selected and implemented as a centralized filter, the measurement matrix contains current state estimates in mismatched observation-related terms. As a result, as the state estimation error increases, the calculation of the Kalman gain is affected, and the filter cannot properly correct the error. For such situations, we propose a federated structure that updates the left- and right-invariant observations separately in the allocated subfilters. In the subfilter assigned with left-invariant observations, the error is corrected using the LIEKF, and in the subfilter assigned with right-invariant observations, the error is corrected using the RIEKF. Since each subfilter uses trajectory-independent Kalman gain, it is expected to improve the estimation performance compared to the centralized structure. The performance of the proposed method is evaluated and compared to the centralized LIEKF and RIEKF through Monte-Carlo simulations for an inertial navigation example. Also, the proposed method is validated by a publicly available dataset of a ground vehicle equipped with a global positioning system (GPS) and wheel encoders.