Implementation of High Efficiency Non-Linear Least Squares in FPGA Devices for Digital Spectroscopy

In measurement tasks, such as the determination of the arrival time of events, several methods based on least squares routines have been demonstrated. But often the high potential of digital least squares methods in high-resolution spectroscopy cannot be fully exploited in practical due to expensive calculation burden or to weaknesses that arise in the convergence process, especially in real-time applications and in spatial computing FPGA device implementation. The paper presents an implementation into a Xilinx Virtex-5 SX50-SG-1 FPGA device of the Levenberg-Marquardt algorithm that is one of the most efficient methods to solve non-linear least squares problems.