In this article, we propose a novel method utilizing iterative semidefinite relaxation for geolocation of stationary uncooperative radars. In our scenario, the geolocation is to be performed in a receiver located on a moving platform. The proposed method uses frequency measurements that are Doppler-shifted due to the platform motion. First, constructed nonconvex maximum likelihood cost function for position estimation is relaxed to a convex optimization problem by applying linearization to range variables. Then, at each iteration of the method, carrier frequency and position of the radar are estimated jointly. Conducted experiments show that a few iterations are enough for convergence to accurate estimates. The proposed method is computationally less expensive compared to traditional techniques, which require extensive grid search procedures in either position or carrier frequency parameter space. In the experiments, the performance of the proposed method is compared to the state-of-the-art techniques and the Cramer–Rao lower bound (CRLB). It is observed that the proposed method attains the CRLB at low noise levels while still providing accurate solutions at high noise cases. Furthermore, it is also seen that platform-radar geometry has an impact on the proposed method's performance. If the radar lies in the convex hull of the receiver path, the proposed method performs significantly better due to improvement in the linearization of range values.

中文翻译：

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多普勒频率测量法对不合作雷达的地理位置进行迭代半定松弛

在本文中，我们提出了一种使用迭代半定松弛的方法对固定式不合作雷达进行地理定位的方法。在我们的方案中，地理定位将在位于移动平台上的接收器中执行。所提出的方法使用由于平台运动而多普勒频移的频率测量。首先，通过将线性化应用于范围变量，将构造的用于位置估计的非凸最大似然成本函数放宽为凸优化问题。然后，在该方法的每次迭代中，联合估计雷达的载波频率和位置。进行的实验表明，只需进行几次迭代就可以收敛到准确的估计值。与传统技术相比，该方法在计算上更便宜 这需要在位置或载波频率参数空间中进行大量的网格搜索程序。在实验中，将所提出方法的性能与最新技术和Cramer-Rao下界（CRLB）进行了比较。可以看出，所提出的方法在低噪声水平下可获得CRLB，同时在高噪声情况下仍能提供准确的解决方案。此外，还可以看出，平台雷达的几何形状对所提出的方法的性能有影响。如果雷达位于接收器路径的凸包中，则由于范围值的线性化得到了改善，因此该方法的性能明显更好。将该方法的性能与最新技术和Cramer-Rao下界（CRLB）进行了比较。可以看出，所提出的方法在低噪声水平下可获得CRLB，同时在高噪声情况下仍能提供准确的解决方案。此外，还可以看出，平台雷达的几何形状对所提出的方法的性能有影响。如果雷达位于接收器路径的凸包中，则由于范围值的线性化得到了改善，因此该方法的性能明显更好。将该方法的性能与最新技术和Cramer-Rao下界（CRLB）进行了比较。可以看出，所提出的方法在低噪声水平下可获得CRLB，同时在高噪声情况下仍能提供准确的解决方案。此外，还可以看出，平台雷达的几何形状对所提出的方法的性能有影响。如果雷达位于接收器路径的凸包中，则由于范围值的线性化得到了改善，因此该方法的性能明显更好。