Eckhardt Tobias, Gerberding Oliver
Institut für Experimentalphysik, Universität Hamburg, 22761, Hamburg, Germany.
Sci Rep. 2024 Sep 23;14(1):21988. doi: 10.1038/s41598-024-70392-9.
Compact laser interferometers with large dynamic range are one of the core emerging tools to improve low frequency performance in gravitational wave detectors by providing local displacement sensing with sub 1 precision. Strong sinusoidal frequency modulations are used in such laser interferometers to create heterodyne-like photodetector signals from which the phase and other parameters, such as the absolute distance, can be extracted. The nested sinusoidal function in such signals is a challenge for the real-time parameter estimation in low-noise applications. In this article, we present an algorithm to calculate exact signal parameters in a non-iterative way from such interferometric signals. The algorithm makes use of a recurrence relation between Bessel functions to enable a direct extraction of modulation parameters from the signal. Additionally, the algorithm is capable of dealing with high phase dynamics where the Doppler-shift of the signal becomes relevant and can limit the range and precision of the parameter estimation, if not accounted for. Simulations show that the algorithm is computationally efficient, can be well parallelised and the phase estimation is close to optimal precision given by the Cramer-Rao lower bound of the signal parameters.
具有大动态范围的紧凑型激光干涉仪是通过提供精度低于1的局部位移传感来提高引力波探测器低频性能的核心新兴工具之一。这种激光干涉仪中使用强正弦频率调制来产生类似外差的光电探测器信号，从中可以提取相位和其他参数，如绝对距离。此类信号中的嵌套正弦函数对低噪声应用中的实时参数估计构成挑战。在本文中，我们提出了一种算法，以非迭代方式从此类干涉信号中计算精确的信号参数。该算法利用贝塞尔函数之间的递推关系，能够直接从信号中提取调制参数。此外，该算法能够处理高相位动态，其中信号的多普勒频移变得相关，如果不加以考虑，可能会限制参数估计的范围和精度。仿真表明，该算法计算效率高，可以很好地并行化，并且相位估计接近信号参数的克拉美罗下界给出的最佳精度。
