In view of the unsatisfactory time - consuming performance of linear equation solution in the existing least squares ellipse fitting algorithm implemented on field programmable gate array( FPGA) platform ,the Cholesky decomposition algorithm was used to solve the linear equation ,and an iterative adaptive square root solution structure based on Coordinate Rotation Digital Computer ( CORDIC) algorithm was proposed by using unidirectional rotation ,merging iteration ,and adaptive adjustable iteration times to solve the square root operation in Cholesky decomposition. The experimental results show that the improved square root algorithm has a good effect on shortening the output latency of Cholesky decomposition ,and Cholesky decomposition achieves 63. 26% improvement over the existing LDLT decom- position algorithm on FPGA platform. Under the condition that the absolute error of ellipse fitting algorithm is less than 0. 1pixel ,the computer speed can be improves by more than 1 000 times based on FPGA ,so it is suitable for applica- tions with high real-time requirements.