We derive fundamental accuracy limits for distributed localization when a fusion center has access only to independently rate-distortion (RD)-optimally compressed versions of multi-sensor observations, under a line-of-sight propagation model with a Gaussian wideband waveform. Using the Gaussian RD test-channel model together with a Whittle spectral Fisher-information characterization, we obtain an explicit frequency-domain Cramér-Rao lower bound. A two-band, two-level specialization yields closed-form expressions and reveals a rate-induced regime change: RD-optimal compression under a squared-error distortion measure can eliminate localization-informative spectral content. A simple band-selective scheme can outperform RD compression by orders of magnitude at the same rate, motivating localization-aware compression for networked sensing and integrated sensing and communication systems.

翻译：我们推导了分布式定位的基本精度极限，其中融合中心仅能访问多传感器观测的独立速率-失真（RD）最优压缩版本，传播模型采用具有高斯宽带波形的视距传播模型。利用高斯RD测试信道模型结合Whittle谱Fisher信息表征，我们得到了显式的频率域Cramér-Rao下界。一个双频带、双电平的特例给出了闭式表达式，并揭示了一种速率诱导的相变现象：在平方误差失真测度下的RD最优压缩可能消除包含定位信息的频谱内容。一种简单的频带选择方案在相同速率下可将RD压缩的性能提升数个数量级，这激发了面向网络化感知与集成感知通信系统的定位感知压缩需求。