In bearings-only target motion analysis (TMA), the observer is often required to outmaneuver the target. However, under specific conditions, an observer moving with constant velocity is sufficient to compute the state of a target that changes its course. A maximum likelihood estimator (MLE) has been developed for this problem in the literature. Unfortunately, the MLE is not only computationally expensive but also prone to divergence problems when poorly initialised. To overcome these shortcomings, this paper proposes a novel quadratically constrained weighted instrumental variable (QC-WIV) estimator. Being a closed-form algorithm, the proposed QC-WIV is inherently more stable than the MLE while at the same time being computationally much more efficient. Moreover, it is shown analytically to be asymptotically unbiased. Numerical simulation studies are presented to corroborate the performance advantage of the proposed QC-WIV, where it is observed to be asymptotically efficient as well. In addition, the QC-WIV performance is on par with the MLE in small noise scenarios for both cases of known and unknown maneuver time. More importantly, the QC-WIV is observed to produce stable estimation performance in large noise levels at which the MLE suffers from divergence.

中文翻译：

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从非机动平台进行仅轴承机动目标运动分析的代数闭式解决方案

在仅轴承目标运动分析 (TMA) 中，观察者通常需要以机动性战胜目标。然而，在特定条件下，以恒定速度移动的观察者足以计算改变其航向的目标的状态。文献中已经针对这个问题开发了最大似然估计器 (MLE)。不幸的是，MLE 不仅在计算上很昂贵，而且在初始化不当时也容易出现发散问题。为了克服这些缺点，本文提出了一种新的二次约束加权工具变量 (QC-WIV) 估计器。作为一种封闭形式的算法，所提出的 QC-WIV 本质上比 MLE 更稳定，同时计算效率更高。此外，分析表明它是渐近无偏的。提出了数值模拟研究以证实所提出的 QC-WIV 的性能优势，其中观察到它也是渐近有效的。此外，对于已知和未知机动时间的情况，QC-WIV 性能在小噪声场景中与 MLE 相当。更重要的是，观察到 QC-WIV 在 MLE 遭受发散的大噪声水平下产生稳定的估计性能。