  This paper investigates the localization problem of high-speed high-altitude
unmanned aerial vehicle (UAV) with a monocular camera and inertial navigation
system. It proposes a navigation method utilizing the complementarity of vision
and inertial devices to overcome the singularity which arises from the
horizontal flight of UAV. Furthermore, it modifies the mathematical model of
localization problem via separating linear parts from nonlinear parts and
replaces a nonlinear least-squares problem with a linearly equality-constrained
optimization problem. In order to avoid the ill-condition property near the
optimal point of sequential unconstrained minimization techniques(penalty
methods), it constructs a semi-implicit continuous method with a trust-region
technique based on a differential-algebraic dynamical system to solve the
linearly equality-constrained optimization problem. It also analyzes the global
convergence property of the semi-implicit continuous method in an infinity
integrated interval other than the traditional convergence analysis of
numerical methods for ordinary differential equations in a finite integrated
interval. Finally, the promising numerical results are also presented.
