In two-way time-of-arrival (TOA) systems, a user device (UD) obtains its position by round-trip communications to a number of anchor nodes (ANs) at known locations. The objective function of the maximum likelihood (ML) method for two-way TOA localization is nonconvex. Thus, the widely-adopted Gauss-Newton iterative method to solve the ML estimator usually suffers from the local minima problem. In this letter, we convert the original estimator into a convex problem by relaxation, and develop a new semidefinite programming (SDP) based localization method for moving UDs, namely SDP-M. Numerical result demonstrates that compared with the iterative method, which often fall into local minima, the SDP-M always converge to the global optimal solution and significantly reduces the localization error by more than 40%. It also has stable localization accuracy regardless of the UD movement, and outperforms the conventional method for stationary UDs, which has larger error with growing UD velocity.

中文翻译：

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具有运动和时钟漂移的用户设备的半定编程双向TOA本地化

在双向到达时间（TOA）系统中，用户设备（UD）通过与已知位置的多个锚点（AN）的往返通信获得其位置。用于双向TOA定位的最大似然（ML）方法的目标函数是非凸的。因此，广泛采用的高斯-牛顿迭代法来求解ML估计量通常会遇到局部极小值问题。在这封信中，我们通过松弛将原始估计量转化为凸问题，并开发了一种新的基于半定规划（SDP）的移动UD定位方法，即SDP-M。数值结果表明，与经常落入局部极小值的迭代方法相比，SDP-M始终收敛于全局最优解，可将定位误差显着降低40％以上。