Spline-Based Initialization of Monocular Visual–Inertial State Estimators at High Altitude

Due to the lack of direct distance measurements, robust and accurate state estimation at high altitude but GPS-denied environments is a challenging task. A possible solution is monocular visual-inertial estimators, in which visual and inertial measurements are properly fused to recover the metric estimates. However, these estimators suffer from initialization under poor numerical conditioning or even degeneration, due to difficulties in retrieving observations of visual features with sufficient parallax, and the excessive period of inertial measurement integration. In this letter, we introduce the joint formulation into the spline-based high altitude estimator initialization method for monocular visual-inertial navigation system, in which the fitting of the spline and the alignment of visual measurements and inertial measurements are jointly optimized to recover metric estimates. The method ensures that sufficient excitation is contained in the inertial measurements when initialized, which eliminates the numerical issues. Compared with the work of Liu and Shen, the joint formulation makes our initialization method insensitive to the choice of spline parameters. Thus, the adaptivity to various environments and motions is obtained, as well as higher accuracy. The method is applicable for both loosely coupled and tightly coupled visual-inertial estimators. Extensive experiments are conducted to validate our approach.