Mobile robot control is a classic problem in the robotic community. It is particularly true in the agricultural field where repetitive tasks can be handled using AGV. In this paper, we address the problem of combine harvester control using a single CP-DGPS receiver, without any attitude measurement unit. A non linear, velocity independent control law has been designed. It relies upon the kinematic model of the combine harvester. Two approaches aimed at estimating the heading of the farm vehicle have been investigated. One uses GPS velocity measurements: the kinematic model of the harvester imposes that its linear velocity is directed along the vehicle axle. So the heading of the vehicle can be roughly estimated from raw velocity measurements. The other relies upon a Kalman state reconstructor and produces an indirect measurement of the heading. The reconstructor has been designed thanks to the kinematic model of the harvester, and taking into account for the sensor noise. The control law has been implemented on a combine harvester. Experiments have been carried out using both kinds of heading estimations on an almost flat ground. The standard deviation from the mean of the lateral position is about three centimeters, and the bias smaller than five centimeters. Both methods are compared an some conclusions are drawn.