National Digital Switching System Engineering and Technology Research Center, Zhengzhou 450002, China.
Sensors (Basel). 2018 Nov 26;18(12):4139. doi: 10.3390/s18124139.
This study discusses the localization problem based on time delay and Doppler shift for a far-field scenario. The conventional location methods employ two steps that first extract intermediate parameters from the received signals and then determine the source position from the measured parameters. As opposed to the traditional two-step methods, the direct position determination (DPD) methods accomplish the localization in a single step without computing intermediate parameters. However, the DPD cost function often remains non-convex, thereby it will cost a high amount of computational resources to find the estimated position through traversal search. Weiss proposed a DPD estimator to mitigate the computational complexity via eigenvalue decomposition. Unfortunately, when the computational resources are rather limited, Weiss's method fails to satisfy the timeliness. To solve this problem, this paper develops a DPD estimator using expectation maximization (EM) algorithm based on time delay and Doppler shift. The proposed method starts from choosing the transmitter-receiver range vector as the hidden variable. Then, the cost function is separated and simplified via the hidden variable, accomplishing the transformation from the high dimensional nonlinear search problem into a few one dimensional search subproblems. Finally, the expressions of EM repetition are obtained through Laplace approximation. In addition, we derive the Cramér⁻Rao bound to evaluate the best localization performance in this paper. Simulation results confirm that, on the basis of guaranteeing high accuracy, the proposed algorithm makes a good compromise in localization performance and computational complexity.
本研究讨论了远场场景下基于时滞和多普勒频移的定位问题。传统的定位方法采用两步法，首先从接收到的信号中提取中间参数，然后从测量参数中确定源的位置。与传统的两步法不同，直接位置确定（DPD）方法在单个步骤中完成定位，而无需计算中间参数。然而，DPD 代价函数通常仍然是非凸的，因此通过遍历搜索找到估计位置将花费大量的计算资源。Weiss 通过特征值分解提出了一种 DPD 估计器来降低计算复杂度。不幸的是，当计算资源非常有限时，Weiss 的方法无法满足实时性要求。为了解决这个问题，本文提出了一种基于时滞和多普勒频移的使用期望最大化（EM）算法的 DPD 估计器。该方法从选择发射机-接收机距离矢量作为隐变量开始。然后，通过隐变量对代价函数进行分离和简化，将高维非线性搜索问题转化为几个一维搜索子问题。最后，通过拉普拉斯近似得到 EM 重复的表达式。此外，我们还推导出了克拉美-罗界，以评估本文中最佳的定位性能。仿真结果证实，在保证高精度的基础上，该算法在定位性能和计算复杂度方面取得了很好的折衷。
