Measurement model and observability analysis for optical flow-aided inertial navigation

We introduce a navigation filter fused with information of visual optical flow and data collected from an inertial measurement unit during GPS signal degradation. Under the assumption that the tracked feature points are located on a level plane, the feature depth can be explicitly expressed and an exact measurement model was derived. Moreover, an error model analysis for a block-matching-based optical flow algorithm has been investigated. The measurement error follows a Gaussian distribution, which is a prerequisite for leveraging the error-state Kalman filter. Subsequently, a local observability analysis of the proposed filter was performed yielding the expression of three unobservable directions. We emphasize the ability of the proposed filter to estimate the aircraft's state, especially for accurate altitude estimation, without any help of prior knowledge or extra sensors. Finally, an extensive Monte Carlo analysis was used to verify the findings in the observability results showing that all states can be estimated except the absolute horizontal positions and rotation around the gravity vector. The effectiveness of the proposed filter is demonstrated through experimental hardware used to acquire outdoor flight test data.