Privacy-Preserving Decentralized Cooperative Localization with Range-Only Measurements: A Convex Optimization Based Approach
2026-06-29 • Robotics
Robotics
AI summaryⓘ
The authors address the problem of robots working together to find their locations without sharing exact positions, which is important for privacy. They created a new method that uses math optimization to keep measurements within strict error limits, avoiding noisy or complex privacy methods. Their system only shares abstract information instead of direct location data, allowing robots to agree on positions securely. Simulations show their approach is more accurate and scalable than previous methods while protecting privacy.
Cooperative localizationRange-based measurementsPrivacy-preservingSemi-Definite Programming (SDP)Maximum-Volume Inscribed Ellipsoid (MVE)Linear Matrix Inequalities (LMIs)Decentralized algorithmsConvex optimizationMulti-robot systemsMonte Carlo simulations
Authors
Nitesh Kumar, Reyshwanth Ganeshan, Sixu Li, Sivakumar Rathinam, Swaroop Darbha
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.