In this paper, we present a robust multi-state constraint Kalman filter (MSCKF) for visual inertial navigation of mobile robots. We assume the hardware of a mobile robot consists of an inertial measurement unit (IMU) and a monocular camera. The MSCKF is a well-known visual inertial navigation algorithm which performs tightly-coupled fusion between IMU and camera measurements over a sliding window of camera poses, like fixed lag smoother. The conventional MSCKF calculates the residuals as the differences between camera measurements and the re-projected points from the triangulated 3D point, which is calculated by using camera measurements and the pose information over the sliding window. However, the uncertainties of camera poses and image measurements are not considered in this triangulation process. Our algorithm is enforced to estimate robust and precise results by providing a good linearization point related with a feature 3D position based on uncertainty based triangulation, which considers the uncertainties of all sources related with triangulation. The proposed algorithm is validated by the dataset, which is generated known trajectory and features, and real world experimental datasets.
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