This paper presents a deep-pipelined FPGA implementation of real-time ellipse estimation for eye tracking. The system is constructed by the Starburst algorithm on a streamoriented architecture and the RANSAC algorithm without any external memories. In particular, the paper presents comparative results between three different hypothesis generators for the RANSAC algorithm based on Cramer's rule, Gauss-Jordan elimination and LU decomposition. The evaluation results showed that the Gauss-Jordan elimination achieved the highest throughput while the solver with Cramer's rule was the most compact and that our proposed architecture achieved a real-time throughput of 62.5 fps with a single FPGA chip without using any external memories.