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Nonlinear systems of affine control inputs overarch many sensor fusioninstances. Analyzing whether a state variable in such a nonlinear system can beestimated (i.e., observability) informs better estimator design. Among theresearch on local observability of nonlinear systems, approaches based ondifferential geometry have attracted much attention for the solid theoreticfoundation and suitability to automated deduction. Such approaches usually workwith a system model of unconstrained control inputs and assume that the controlinputs and observation outputs are timestamped by the same clock. To ourknowledge, it has not been shown how to conduct the observability analysis withadditional constraints enforced on the system's observations or control inputs.To this end, we propose procedures to convert a system model of affine controlinputs with linear constraints into a constraint-free standard model which isapt to be analyzed by the classic observability analysis procedure. Then, thewhole analysis procedure is illustrated by applying to the well-studied visualinertial odometry (VIO) system which estimates the camera-IMU relative pose andtime offset. The findings about unobservable variables under degenerate motionconcur with those obtained with linearized VIO systems in other studies,whereas the findings about observability of time offset extend those inprevious studies. These findings are further validated by simulation.

NOCT: Nonlinear Observability with Constraints and Time Offset