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TDOA based direct positioning maximum likelihood estimator and the cramer-rao bound

机译：基于TDOA的直接定位最大似然估计器和Cramer-Rao界

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摘要

The maximum likelihood estimator (MLE) and its performance for the localization of a stationary emitter using a network of spatially separated passive stationary sensors is presented. The conventional approach for localization using multiple sensors is to first estimate the time differences of arrival (TDOAs) independently between pairs of sensors and then find the location of the emitter using the intersection point of the hyperbolas defined by these TDOAs. It has recently been shown that this two-step approach is suboptimal and an alternate direct position determination (DPD) approach has been proposed. In the work presented here we take the DPD approach to derive the MLE and show that the MLE outperforms the conventional two-step approach.We analyze the two commonly occurring cases of signal waveform unknown and signal waveform known with unknown transmission time. This paper covers a wide variety of transmitted signals such as narrowband or wideband, lowpass or bandpass, etc. Sampling of the received signals has a quantization-like effect on the location estimate and so a continuous time model is used instead.We derive the Fisher information matrix (FIM) and show that the proposed MLE attains the Cramer-Rao lower bound (CRLB) for high signal-to-noise ratios (SNRs).
机译：提出了最大似然估计器（MLE）及其使用空间分离的无源静止传感器网络对静止发射器进行定位的性能。使用多个传感器进行定位的常规方法是，首先独立估计成对传感器之间的到达时间差（TDOA），然后使用由这些TDOA定义的双曲线的交点找到发射器的位置。最近已经显示出，这种两步方法是次优的，并且已经提出了一种替代的直接位置确定（DPD）方法。在本文介绍的工作中，我们采用DPD方法推导了MLE，并表明MLE优于传统的两步法。我们分析了信号波形未知和传输时间未知的两种常见情况。本文涵盖各种传输信号，例如窄带或宽带，低通或带通等。接收信号的采样对位置估计具有类似量化的影响，因此使用连续时间模型代替。信息矩阵（FIM），并表明针对高信噪比（SNR），拟议的MLE达到了Cramer-Rao下界（CRLB）。

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