Control-enabled Observability and Sensitivity Functions in Visual-Inertial Odometry

Visual-inertial odometry (VIO) is an important component in autonomous navigation of Unmanned Aerial Vehicles (UAVs) in GPS-denied or degraded environments. VIO is a nonlinear estimation problem where control inputs, such as acceleration and angular velocity, have significant impact on the estimation performance. In this paper, we examine the effects of controls on the VIO problem. We first propose a sensitivity function that characterizes the relationship between the errors in the control inputs and the state estimation performance. This function depends on the control inputs, which is unique for nonlinear systems since for linear systems, state observability properties are independent of control inputs. We next derive analytical expressions of the sensitivity functions for various VIO scenarios relevant to UAV motions. Using Monte-Carlo simulations, we validate the derived sensitivity functions. We also show an interesting fact that deceleration along the velocity direction yields better estimation performance than acceleration with the same magnitude.