This paper presents high-accuracy algorithms for localization of a small autonomous underwater vehicle by comparing geophysical property maps (computer models) to local measurements obtained from vehicle-mounted sensors and an initial position fix. In this paper, we present methods for micro-navigation, which refers to fine-scale, quantitative position determination, that attempt a direct solution for position from a minimal set of measurements, using techniques from computational geometry. Each absolute or differential sensor measurement defines one or more contour lines on the stored geophysical maps along which the vehicle may be located. The contours are found from efficient and robust computation of the real solutions of non-linear interval polynomial systems of equations. A technique for such solutions based on convex hull properties, Bernstein subdivision and interval arithmetic is described in the paper.