We derive here an approach to the nonlinear control of a particular autonomous underwater vehicle architecture. This approach is based on state-variable feedback and estimation in the nonlinear setting but uses many techniques from Linear Quadratic Gaussian methods which are capable of preserving the design aspects of the formulation. The specific task that we consider is the tracking of an unknown ocean floor using current altitude measurements. By guarding the linear aspects as long as possible, we are able to formulate this problem as one of classical disturbance rejection in which {\em a priori} information about the ocean floor may be easily included. The migration from linear to nonlinear control is then performed so as to preserve as many linear design features as is possible