AI 中文总结
该研究针对两类感知模式，推导了相对论运动下的闭式CRB，揭示了超相对论区感知精度标度律的变化，为相对论感知提供了理论基础。
AI 中文摘要
本研究针对基于设备（DB）感知与无设备（DF）感知场景下的相对论运动下的距离和速度估计问题展开研究。通过推导单向与双向传播所诱导的精确时间标度与时移关系，将两种感知模式统一为仿射信号模型。获得闭式克拉美-罗界（CRB），其为归一化速度、均方根（RMS）带宽及均方根时长的显式函数。该界在低速时回归经典结果，但在超相对论区呈现出截然不同的速度标度特性：对于快速退行运动，距离CRB发散而速度CRB消失；对于快速接近运动，两类CRB均消失。DB与DF模式在两个方向上还呈现出不同的渐近阶，表明相对论运动不仅改变信号模型，还改变决定感知精度的基本标度律。
英文摘要
This letter investigates range and velocity estimation under relativistic motion for device-based (DB) and device-free (DF) sensing. By deriving the exact time-scaling and time-shift relations induced by one-way and two-way propagation, both sensing modes are cast into a unified affine signal model. Closed-form Cramér--Rao bounds (CRBs) are obtained as explicit functions of normalized velocity, root-mean-squared (RMS) bandwidth, and RMS duration. The bounds recover the classical low-speed results but exhibit distinct velocity scaling in the ultrarelativistic regime. For rapidly receding motion, the range CRB diverges while the velocity CRB vanishes. For rapidly approaching motion, both CRBs vanish. The DB and DF modes further exhibit different asymptotic orders in the two directions, showing that relativistic motion changes not only the signal model but also the fundamental scaling laws governing sensing accuracy.
Comments5 pages, 3 figures, submitted to IEEE for possible publication
