针对直达（LOS）与非直达（NLOS）环境中的定位问题，提出了一种波形已知条件下的单阵地多目标直接定位（DPD）算法。该算法针对发射时间已知和未知两种情况，利用多径信号到达角度与时延关于障碍物（或反射体）、观测站与目标位置参数的数学关系，建立了三维目标位置的最大似然（ML）函数，无需估计测量参数，避免了传统两步定位方法所需的非直达径识别与数据关联。为了克服多目标定位中的高维非线性优化问题，该算法利用独立波形信息将多目标定位解耦为对各个目标单独求解。通过对目标函数有效近似，算法在发射时间已知和未知两种情况下均仅需三维网格搜索，比相应的两步定位方法具有更低的计算量。此外，基于多径定位场景，推导了发射时间已知和未知两种情况下的位置估计克拉美罗界（CRB）。仿真结果表明：算法的定位性能能够逼近相应的克拉美罗界，比传统两步定位方法和子空间直接定位算法具有更高的定位精度。
To realize localization in mixed Line-of-Sight and Non-Line-of-Sight (LOS/NLOS) environments with high precision, this paper proposes a Direct Position Determination (DPD) algorithm for multiple targets with known signal waveforms received by an antenna array. By relating the arrival angle and arrival time of the multipath signal to the positions of the obstacles (reflectors), receivers and targets, we derive the Maximum Likelihood (ML)-based functions in terms of 3D target positions in both cases of known and unknown transmitting times. The proposed algorithm can skip the estimation of intermediate parameters, thus solving the problems of NLOS identification and data association inherent in traditional two-step localization methods. To avoid multi-dimensional nonlinear optimization which is frequently encountered in localization of multiple targets, the proposed algorithm decouples the locations of multiple targets into several location problems of each target by exploiting information of uncorrelated known waveforms. By making the approximation of the objective function, only a 3D grid search is required in both cases of known and unknown transmitting times. Therefore, our algorithm is computationally more attractive compared with two-step localization methods. Additionally, we derive the compact Cramér-Rao Bound (CRB) expressions for target positions based on the multipath model when the transmitting times are known or unknown. Simulation results demonstrate that the performance of the proposed algorithm can reach the associated CRB, and is superior to traditional two-step localization methods and existing subspace-based DPD algorithms.
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