A Bias-Reduced Nonlinear WLS Method for TDOA/FDOA-Based Source Localization
A Bias-Reduced Nonlinear WLS Method for TDOA/FDOA-Based Source Localization
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基于 TDOA/FDOA 的源定位的偏差减少非线性 WLS 方法
DOI：
10.1109/tvt.2015.2508501
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发表时间：
2016-10-01
影响因子：
6.8
通讯作者：
Ansari, Nirwan
中科院分区：
文献类型：
--
作者：
Wang, Gang;Cai, Shu;Ansari, Nirwan
我们解决的源定位问题，同时使用到达时间差（TDOA）和到达频率差（FDOA）的测量。我们分两步解决这个问题，在每一步中，我们制定了一个非线性加权最小二乘（WLS）问题，其次是偏见减少计划。在第一步中，我们制定了一个非线性WLS问题，仅使用TDOA测量，并推导出WLS解决方案的偏差，然后使用它来开发一个无偏的WLS解决方案，通过从WLS解决方案减去偏差。在第二步中，我们制定了另一个非线性WLS问题相结合的结果，在第一步和FDOA测量。为了避免局部收敛的潜在风险，该WLS问题被降低到一个近似WLS问题，对于它的全局最优解可以获得。还推导出WLS解的偏差，然后从WLS解中减去偏差以减小偏差。仿真结果表明，该方法不仅降低了误差，而且达到了Cramér-Rao下界精度。
We address the source localization problem by using both time-difference-of-arrival (TDOA) and frequency-difference-of-arrival (FDOA) measurements. We solve this problem in two steps, and in each step, we formulate a nonlinear weighted least squares (WLS) problem followed by a bias reduction scheme. In the first step, we formulate a nonlinear WLS problem using TDOA measurements only and derive the bias of the WLS solution, which is then used to develop an unbiased WLS solution by subtracting the bias from the WLS solution. In the second step, we formulate another nonlinear WLS problem by combining the results in the first step and the FDOA measurements. To avoid the potential risk of local convergence, this WLS problem is reduced to an approximate WLS problem, for which the globally optimal solution can be obtained. The bias of the WLS solution is also derived and then subtracted from the WLS solution to reduce the bias. Simulation results show that the bias of the proposed method is reduced and that the Cramér-Rao lower bound accuracy is also achieved.