Robust Linearly Constrained Invariant Filtering for a Class of Mismatched Nonlinear Systems

Standard state estimation techniques require a perfect knowledge of the system’s model, that is, process and measurement equations, inputs and the corresponding noise statistics. In practice this assumption does not hold and therefore robust filtering methods must be accounted for. A new approach to tackle a potential model mismatch via linear constraints within the Kalman filter, and its extended version (EKF), has been recently shown to be a very promising solution. This letter further explores robust linearly constrained filtering in the context of the Invariant EKF (InEKF). With respect to the EKF, the InEKF is a recent filtering technique which has been shown to better handle the particular structure of a class of problems through the use of Lie groups. In this contribution, a new robust linearly constrained InEKF is introduced, together with particular parametric mismatched models and mitigation strategies through linear constraints. Numerical results for an illustrative navigation example are provided to show the performance improvement and support the discussion.