Time delay estimation via cross-correlation in the presence of large estimation errors
Time delay estimation via cross-correlation in the presence of large estimation errors
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DOI：
10.1109/tassp.1982.1163992
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发表时间：
1982-12
期刊：
影响因子：
--
通讯作者：
J. Ianniello
中科院分区：
文献类型：
--
作者：
J. Ianniello
在两个传感器接收到的公共随机信号的到达时间差的估计，其中每个传感器也接收不相关的噪声，被检查小的和大的估计误差。它示出，作为后集成的信噪比降低，相关器表现出阈值效应，也就是说，一个大的错误（异常估计）的概率迅速增加。近似的理论结果异常的概率，并进行了实验验证。对于门控模式和非门控模式两者检查时延估计的方差，在门控模式中，对应于最接近真实时延的相关峰值的时延被用作时延的估计，在非门控模式中，对应于相关器延迟时间的整个范围上的最大峰值的时延被用作估计。基于小误差分析，将两种模式的观测方差与理论方差进行比较。对于门控模式，可以从线性标准可靠地预测信噪比，低于该信噪比时，观察到的方差开始与小误差理论显著不同。然而，它示出的非门控模式的预期方差可以离开小误差理论在一个更高的信噪比比门控模式，因此，由于异常的方差可以是最重要的因素，在确定该区域的小误差分析的适用性。
The estimate of the difference in time of arrival of a common random signal received at two sensors, each of which also receives uncorrelated noise, is examined for both small and large estimation errors. It is shown that as the post-integration signal-to-noise ratio decreases, the correlator exhibits a thresholding effect; that is, the probability of a large error (an anomalous estimate) increases rapidly. Approximate theoretical results for the probability of an anomaly are presented and are verified experimentally. The variance of the time delay estimate is examined for both a gated mode, in which the time delay corresponding to the correlation peak closest to the true time delay is used as the estimate of time delay, and an ungated mode, in which the time delay corresponding to the largest peak over the full range of the correlator delay times is used as the estimate. The observed variance for both modes is compared with the theoretical variance based on a small error analysis. For the gated modes, the signal-to-noise ratio below which the observed variance begins to differ significantly from the small error theory can be reliably predicted from a linearity criterion. It is shown, however, that the expected variance for the ungated mode can depart from the small error theory at a higher signal-to-noise ratio than for the gated modes; thus the variance due to anomalies can be the most important factor in determining the region of applicability of the small error analysis.