Gu Zhiyong, Lai Jiancheng, Wang Chunyong, Yan Wei, Ji Yunjing, Li Zhenhua
Appl Opt. 2018 Dec 1;57(34):9951-9957. doi: 10.1364/AO.57.009951.
The waveform fitting technique has been a prevailing method for accurate extraction of a range of objects from an observed signal. Exploration of range precision then became a significant research topic to evaluate the performance of the technique with the corruption of noise. In this paper, we derive an analytical solution of the maximum likelihood estimation for the Gaussian model as the probability density function (PDF) of the range estimator. The variance of the linear version of the PDF is consistent with the Cramer-Rao bound (CRB). Thus, the variance of the PDF is regarded as the theoretical range precision (TRP) compared with the CRB. The verification results show the TRP can perfectly describe the variance of the simulation data while the CRB provides a lower bound. At a higher signal-to-noise ratio (SNR), both the TRP and CRB have the ability to provide an accurate description of the range precision. At a lower SNR, the TRP still performs well while the CRB is too loose to bound the variance on the unbiased estimation.
波形拟合技术一直是从观测信号中精确提取一系列目标的常用方法。随着噪声干扰的出现，对距离精度的探索成为评估该技术性能的一个重要研究课题。在本文中，我们推导了高斯模型作为距离估计器概率密度函数（PDF）的最大似然估计的解析解。PDF线性版本的方差与克拉美罗界（CRB）一致。因此，与CRB相比，PDF的方差被视为理论距离精度（TRP）。验证结果表明，TRP能够完美地描述模拟数据的方差，而CRB提供了一个下限。在较高的信噪比（SNR）下，TRP和CRB都能够准确描述距离精度。在较低的SNR下，TRP仍然表现良好，而CRB过于宽松，无法界定无偏估计的方差。
