In this article, we consider the problem of estimating the location and velocity of a moving source using a distributed passive radar sensor network. We first derive the maximum likelihood estimator (MLE) using direct sensor observations, when the source signal is unknown and modeled as a deterministic process. Since the MLE obtains the source location and velocity estimates through a search process over the parameter space and is quite computationally intensive, we also developed an efficient algorithm to solve the problem using a two-step approach. The first step finds the time difference of arrival (TDOA) and frequency difference of arrival (FDOA) estimates for each sensor with respect to a reference sensor by using a two-dimensional fast Fourier transform and interpolation, while the second step employs an iterative reweighted least square (IRLS) approach with a varying weighting matrix to determine the source location and velocity. To benchmark the performance of the proposed methods, a constrained Cramér–Rao bound (CRB) for the considered source localization problem is derived. Numerical results show that the IRLS approach has a lower signal-to-noise ratio threshold phenomenon compared with several recent TDOA/FDOA-based methods, especially when the source is considerably farther away from some sensors than others, creating a larger disparity in the quality of sensors observations.

中文翻译：

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分布式传感器的最大似然和基于IRLS的移动源定位

在本文中，我们考虑使用分布式无源雷达传感器网络估算移动源的位置和速度的问题。当源信号未知并且被建模为确定性过程时，我们首先使用直接传感器观察来推导最大似然估计器（MLE）。由于MLE通过在参数空间上的搜索过程获取源位置和速度估计值，并且计算量很大，因此我们还开发了一种有效的算法来使用两步法解决该问题。第一步，通过使用二维快速傅里叶变换和插值，找到每个传感器相对于参考传感器的到达时间差（TDOA）和到达频率差（FDOA）估算值，而第二步则采用具有可变权重矩阵的迭代最小加权平方（IRLS）方法来确定源位置和速度。为了对所提出方法的性能进行基准测试，导出了考虑的源定位问题的约束Cramér-Rao界（CRB）。数值结果表明，与几种最近的基于TDOA / FDOA的方法相比，IRLS方法具有更低的信噪比阈值现象，尤其是当光源与某些传感器的距离远得多时，在质量上存在更大的差异传感器的观察结果。推导了考虑的源定位问题的约束克拉美-饶界（CRB）。数值结果表明，与几种最近的基于TDOA / FDOA的方法相比，IRLS方法具有更低的信噪比阈值现象，尤其是当光源与某些传感器的距离远得多时，在质量上存在更大的差异传感器的观察结果。推导了考虑的源定位问题的约束克拉美-饶界（CRB）。数值结果表明，与几种最近的基于TDOA / FDOA的方法相比，IRLS方法具有更低的信噪比阈值现象，尤其是当光源与某些传感器的距离远得多时，在质量上存在更大的差异传感器的观察结果。