Privacy-Preserving Decentralized Cooperative Localization with Range-Only Measurements: A Convex Optimization Based Approach

2026-06-28

AI Summary

This work addresses the privacy risks inherent in multi-robot cooperative localization in GPS-denied environments, where sharing explicit position information may lead to sensitive data leakage. The authors propose a decentralized cooperative localization framework that leverages semidefinite programming (SDP) to compute the maximum-volume inscribed ellipsoid (MVE), achieving global spatial consistency across the network by exchanging only dual variables—without transmitting explicit positional coordinates. Departing from conventional privacy-preserving strategies such as noise injection or encryption, the method establishes a privacy mechanism grounded in a bounded noise model and introduces intersection plane constraints derived from landmark measurements, combined with a local linear matrix inequality (LMI) decomposition technique. Extensive 3D Monte Carlo simulations demonstrate that the proposed approach not only preserves privacy but also achieves higher localization accuracy than existing SDP-based methods, while exhibiting strong scalability and suitability for parallel computation.

Abstract

Cooperative localization using range-based measurements is critical for multi-robot systems operating in GPS-denied and unstructured environments. However, traditional cooperative approaches require sharing explicit spatial coordinates across the network, presenting a severe security vulnerability in privacy-sensitive missions. While recent literature has explored privacy-preserving alternatives, these methods typically rely on accuracy-degrading noise injection or computationally prohibitive cryptographic protocols. To overcome these limitations, we propose a novel, natively privacy-preserving Decentralized Cooperative Localization (DCL) framework based on convex optimization. Discarding probabilistic noise models, we assume strictly bounded measurement noise and formulate the localization problem via Semi-Definite Programming (SDP) to compute a Maximum-Volume Inscribed Ellipsoid (MVE). Our approach introduces novel intersection-plane constraints derived from landmark measurements to significantly tighten individual spatial bounds. To incorporate inter-robot range measurements securely, we uniquely decompose coupling constraints into localized Linear Matrix Inequalities (LMIs). Agents achieve fleet-wide spatial consensus by iteratively exchanging only abstract dual variables, completely avoiding the transmission of explicit primal position estimates. Extensive 3D Monte Carlo simulations demonstrate that our DCL framework outperforms existing SDP-based localization method in accuracy, while guaranteeing operational privacy and maintaining highly scalable, parallelizable computation.

Problem

• cooperative localization
• privacy-preserving
• range-only measurements
• multi-robot systems
• GPS-denied environments

Innovation

• privacy-preserving
• decentralized cooperative localization
• convex optimization
• semi-definite programming
• linear matrix inequalities