It is well known that a single anchor can be used to determine the position and orientation of an agent communicating with it. However, it is not clear what information about the anchor or the agent is necessary to perform this localization, especially when the agent is in the near-field of the anchor. Hence, in this paper, to investigate the limits of localizing an agent with some uncertainty in the anchor location, we consider a wireless link consisting of source and destination nodes. More specifically, we present a Fisher information theoretical investigation of the possibility of estimating different combinations of the source and destination's position and orientation from the signal received at the destination. To present a comprehensive study, we perform this Fisher information theoretic investigation under both the near and far field propagation models. One of the key insights is that while the source or destination's $3$D orientation can be jointly estimated with the source or destination's $3$D position in the near-field propagation regime, only the source or destination's $2$D orientation can be jointly estimated with the source or destination's $2$D position in the far-field propagation regime. Also, a simulation of the FIM indicates that in the near-field, we can estimate the source's $3$D orientation angles with no beamforming, but in the far-field, we can not estimate the source's $2$D orientation angles when no beamforming is employed.

翻译：众所周知，单锚可用于确定与其通信代理的位置和方向。然而，当代理处于锚点的近场区域时，完成此类定位所需关于锚点或代理的具体信息尚不明确。为此，本文针对锚点位置存在不确定性的代理定位极限问题，建立了包含源节点与目的节点的无线链路模型。具体而言，我们基于Fisher信息理论，系统研究了从接收信号中联合估计源节点与目的节点不同位置-方向参数组合的可行性。为全面分析，分别在近场与远场传播模型下开展Fisher信息理论研究。关键发现之一在于：近场传播场景中，源节点/目的节点的三维方向可与三维位置联合估计；而远场传播场景中，仅能实现源节点/目的节点的二维方向与二维位置联合估计。此外，FIM仿真表明：近场条件下无需波束赋形即可估计源节点的三维方向角，但远场条件下若未采用波束赋形则无法估计源节点的二维方向角。