Error-State Kalman Filter based Visual-Inertial Odometry Using Orientation Measurement on Unit Quaternion Group

The inaccessibility of data from standard sensor suites on closed-platform unmanned aerial vehicles (UAVs) has been a hindrance to developing a compatible visual-inertial odometry (VIO). Despite the advance of recent VIO research, these works often emphasize fusing detailed sensor models with available sensor data at relatively high frequencies. To address this issue, in this paper, we derive an innovation signal for an orientation measurement model on the unit quaternion group ${\mathbb{S}^3}$ based on the error-state Kalman filter (ESKF) framework. Leveraging the error-state formulation, the innovation signal directly exploits the geometric error representation on ${\mathbb{S}^3}$ instead of treating unit quaternions as ℝ<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> vectors. Flight experiments on a small commercial UAV (Fig. 1) have been carried out to compare the performance of the proposed ESKF with quaternion measurements on ${\mathbb{S}^3}$ (ESKF-Q) against the original ESKF framework. Experimental results demonstrate that while both representations of unit quaternion measurements in ESKF framework improve orientation estimates with unperturbed orientation measurement model, only the proposed ESKF-Q exhibits convergent state estimates in the presence of uncertainties in the orientation measurement model.