Iterative Semidefinite Relaxation for Geolocation of Uncooperative Radars Using Doppler Frequency Measurements

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.