This paper discusses the course keeping control problem for a small autonomous boat using low cost sensors. Comparing with full scale ships, a small boat is more sensitive to the environmental disturbances because of its small size and low inertia. The sensors available in the boat are a low cost GPS and a rate gyro while the commonly used compass in ship control is absent. The combined effect from disturbance, poor accuracy and significant delay in GPS measurement makes it a challenging task to achieve good performance. In this paper, we propose a simple dynamic model for the boat's horizontal motion. The model is based on the Nomoto's model and can be seen as an extension to it. The model describes the dynamics between rudder deflection and the boat's velocity vector angle while Nomoto's model reveals that between rudder deflection and the boat's yaw angle. With the proposed model there is no need for a yaw sensor for control if the boat's moving direction can be measured. GPS is a convenient device for that job. Based on the derived model, we apply mixed H₂/H_∞ control method to design the controller. It can guarantee the robust stability, and as the same time it can optimize the performance in the sense of H₂ norm. The experimental data show that the proposed approach is proved to be effective and useful.