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

2026-03-24

AI Summary

This study addresses the fundamental limitation in distributed localization where the fusion center receives only rate–distortion-optimally compressed observations from multiple sensors, which can severely degrade positioning accuracy. Under line-of-sight propagation and Gaussian wideband waveform assumptions, the authors derive a frequency-domain Cramér–Rao lower bound that reveals how conventional rate–distortion compression may discard spectral components critical for localization, resulting in substantial information loss. To mitigate this, the work advocates for localization-aware compression and demonstrates that a simple band-selection strategy can improve localization accuracy by several orders of magnitude over traditional rate–distortion approaches at the same bitrate. The theoretical analysis leverages a Gaussian rate–distortion test channel and Whittle’s spectral Fisher information framework, yielding closed-form solutions in a two-band, two-level special case.

Technology Category

• Intelligent Robots: Localization, Mapping, and Navigation
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Distributed Search

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization

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 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.

Problem

• distributed localization
• rate-distortion compression
• accuracy limits
• Cramér-Rao bound
• sensing and communication

Innovation

• rate-distortion optimization
• distributed localization
• Cramér-Rao lower bound
• spectral Fisher information
• localization-aware compression