Observability analysis of inertial navigation errors from optical flow subspace constraint

• Observability analysis of the time-varying dynamics yields geometric insights about the unobservable subspace.
• Camera and IMU jointly rotating in distinct piece-wise constant attitude segments during a straight path yield observable IMU errors.
• The analysis shows the effect of lateral maneuvers on the observability of misalignment, and velocity error along and orthogonal to the ground velocity.
• Monte Carlo simulation indicates the fusion of inertial and optical flow data mitigates the position error growth relative to just unaided inertial navigation during GPS outage.

Fusion of inertial and vision sensors is an effective aid to inertial navigation systems (INS) during GPS outage. Optical flow-aided inertial navigation circumvents feature tracking, landmark mapping, and state vector augmentation typical of simultaneous localization and mapping (SLAM). This paper focuses on the observability analysis of INS errors from implicit measurements of the optical flow subspace constraint, and derives how observable and unobservable directions are affected by the motion of a camera rigidly coupled to an inertial measurement unit (IMU). Straight motion and piecewise constant (PWC) attitude segments yield the random constant IMU errors observable. The unobservable directions are the three-dimensional (3D) position error, the velocity error along the ground velocity, and the combination of angular misalignment about the local vertical and the velocity error along the horizontal direction orthogonal to the ground velocity. The velocity error along the ground velocity becomes observable with horizontal maneuvering. A Monte Carlo simulation validates the observability analysis, and reveals the feasibility of IMU calibration and the mitigation of navigation error growth with the aid of the optical flow subspace constraint compared with the unaided INS.