IEEE Transactions on Automatic Control, Vol.53, No.8, 1864-1875, 2008
On an optical inertial navigation system - Part II
In Part I, we developed the optical transfer function of the lens-fiber system for quasi-monochromatic, incoherent excitation, and studied the properties of the kernel function. We also studied the cross-talk between the fibers of the lens-fiber system for a worker bee and an artificial eye, and showed that it is not significant. This allows us in this paper, to consider a mathematical idealization of a corneal surface as a continuum of lens-fiber systems. We consider this surface to be a regular immersion of class r >= 2 that is the image in R-3 of a simply connected, open set in R-2. We study the change in the power propagated in the fiber due to virtual motions of the corneal surface and show that for motion along the axis, the power propagated is invariant. Finally, we show that the ego-motion estimation problem is well-posed for sufficiently rich quasi-monochromatic, incoherent excitation on an allowable, regular corneal surface, and further show that the solution does not depend on the parameterization of the surfaces or the parameters of the aircraft (such as mass and inertia matrix) on which the ONS is mounted.