We study robust network localization for realistic mixed line-of-sight and non-line-of-sight (LOS/NLOS) scenarios, where (i) NLOS identification is not performed, (ii) no statistical knowledge of the LOS/NLOS measurement error is available, and (iii) no experimental campaign is affordable. We treat the bias term of each range measurement, both for LOS and NLOS, as an unknown parameter. Based on this, we indicate that the ranging biases possess a sparsity property in LOS-heavy scenarios. To exploit this sparsity, we propose the inclusion of a sparsity-promoting term into the conventional cost functions, giving rise to a generic sparsity-promoting regularized formulation. By bounding the cost function, we further develop an alternative generic bound-constrained regularized formulation. To ensure global optimality, we specify the residual error function in these formulations so that they are conveniently solved via relaxation as two semidefinite programs (SDPs). It is also shown that the two SDPs can be equivalent in the sense that they share the same optimal solution. Compared with the sparsity-promoting regularized SDP, the bound-constrained regularized SDP has the advantage that it allows us to develop one data-driven strategy for selecting an appropriate regularization parameter. Numerical results, based on both synthetic- and experimental data, demonstrate the overall enhanced performance of the devised approach, both in terms of localization accuracy and computational efficiency. The remarkable ability of the proposed data-driven method for parameter selection, at the cost of a slight increase in computational complexity, is also shown.

中文翻译：

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利用测距偏差的稀疏性来缓解 NLOS


我们研究针对现实混合视距和非视距 (LOS/NLOS) 场景的鲁棒网络定位，其中 (i) 不执行 NLOS 识别，(ii) 没有 LOS/NLOS 测量的统计知识存在错误，并且 (iii) 无法承担任何实验性活动。我们将 LOS 和 NLOS 的每个距离测量的偏差项视为未知参数。基于此，我们表明测距偏差在 LOS 严重的情况下具有稀疏性。为了利用这种稀疏性，我们建议将稀疏性促进项纳入传统成本函数中，从而产生通用的稀疏性促进正则化公式。通过限制成本函数，我们进一步开发了一种替代的通用边界约束正则化公式。为了确保全局最优性，我们在这些公式中指定了残差函数，以便它们可以通过松弛作为两个半定程序（SDP）方便地求解。它还表明，两个 SDP 可以等效，因为它们共享相同的最优解。与稀疏性促进正则化 SDP 相比，有界约束正则化 SDP 的优点是它允许我们开发一种数据驱动策略来选择合适的正则化参数。基于合成数据和实验数据的数值结果证明了所设计的方法在定位精度和计算效率方面的整体增强性能。还显示了所提出的数据驱动参数选择方法的卓越能力，但代价是计算复杂性略有增加。