基于拉盖尔模型的超声信号渡越时间测量性能分析

摘要

传统窄带模型仅能通过数值计算统计出超声信号渡越时间的测量性能.针对这一问题,提出基于拉盖尔模型计算理论克拉下限的方法.研究了拉盖尔函数及其时间导数的性质,得到时间导数内积矩阵,并将其应用到费舍尔矩阵中,能够快速精确计算克拉下限.对混合指数模型仿真表明,在高斯白噪声背景下,渡越时间方差与理论克拉下限具有良好的一致性；受窄带噪声和反射等因素影响,实测数据的渡越时间方差与理论克拉下限存在较大偏差.%The performance of ToF (Time of Flight) measurement for ultrasonic wave can be obtained only by numeric calculation in traditional narrow band model.To this problem,a method based on Laguerre model is proposed for CRLB (Cramer-Rao Lower Bound) calculation.The characteristics of Lagueree function and its time derivative were studied,and the time derivative inner matrix was derived,which was applied in Fisher matrix,then the CRLB can be calculated fast and accurately.The simulation on hybrid exponential model polluted by Gaussian white noise testified the well coherence between the variance of ToF and the theoretic CRLB obtained with Laguerre model.The variance of ToF obtained by real data has great difference with the theoretic bound for the impact of narrow band noise and reverberant interference.