On the Suboptimality of Rate--Distortion-Optimal Compression: Fundamental Accuracy Limits for Distributed Localization

TL;DR

This paper establishes fundamental limits on distributed localization accuracy when sensors use rate-distortion optimal compression, revealing that such compression can significantly impair localization performance.

Contribution

It introduces a spectral Fisher-information-based analysis and demonstrates that localization-aware compression schemes can outperform rate-distortion optimal methods.

Findings

RD-optimal compression can eliminate localization-informative spectral content.

A simple band-selective scheme can outperform RD compression at the same rate.

Fundamental accuracy limits are derived for distributed localization under compression.

Abstract

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 Cram\'er-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.