In this article, semidefinite programming (SDP) solutions are proposed for the elliptic localization problem in asynchronous radar networks, where the transmitters are subject to clock offsets. Relaxing the nonconvex problem into different convex forms, we design tight SDP (TSDP) and global SDP (GSDP) solutions for this problem. The TSDP solution includes several SDP cones to solve the problem, and the correlation is not considered. Hence, the TSDP solution performs poorly in the presence of correlated noise. We further put forward the GSDP solution to improve the performance by introducing a new GSDP form, which includes only one SDP cone to handle the correlated noise. We also theoretically prove that the GSDP problem is tight enough so that its performance is able to sufficiently approach the Cramér–Rao lower bound (CRLB) accuracy. The simulated results show that the TSDP solution can provide the comparable performance with the GSDP in the absence of related noise. The performance of the GSDP solution can almost attain the CRLB accuracy using less receivers.

中文翻译：

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异步雷达网络中椭圆定位的半定规划解决方案

在本文中，针对发射机受时钟偏移影响的异步雷达网络中的椭圆定位问题提出了半定规划 (SDP) 解决方案。将非凸问题放松为不同的凸形式，我们为这个问题设计了紧 SDP (TSDP) 和全局 SDP (GSDP) 解决方案。TSDP方案包括几个SDP锥来解决问题，不考虑相关性。因此，TSDP 解决方案在存在相关噪声的情况下表现不佳。我们进一步提出了 GSDP 解决方案，通过引入一种新的 GSDP 形式来提高性能，该形式仅包含一个 SDP 锥体来处理相关噪声。我们还从理论上证明了 GSDP 问题足够严格，以至于其性能能够充分接近 Cramer-Rao 下界 (CRLB) 精度。仿真结果表明，在没有相关噪声的情况下，TSDP 解决方案可以提供与 GSDP 相当的性能。GSDP 解决方案的性能几乎可以使用较少的接收器达到 CRLB 精度。