Control-enabled Observability in Visual-Inertial Odometry

Visual-inertial odometry (VIO) is a nonlinear estimation problem where control inputs, such as acceleration and angular velocity, play a significant role in the estimation performance. In this paper, we examine effects of controls on the VIO problem. We first analyze the effects of acceleration and angular velocity inputs on state observability of the VIO problem. Representing the vehicle dynamics and the measurement equation in the line of sight coordinates, we prove observability properties for several VIO scenarios, including constant acceleration with no rotation and biased acceleration measurements. We next consider how the acceleration magnitude impacts the estimation performance. Using a planar example and Monte-Carlo simulations, we demonstrate that the estimation accuracy improves as the acceleration magnitude increases. We also show an interesting fact that deceleration along the velocity direction yields better performance than acceleration with the same magnitude for the same amount of time.