Globally Optimal Data-Association-Free Landmark-Based Localization Using Semidefinite Relaxations

2025-04-11

AI Summary

This work addresses the data-association-free landmark-based localization problem in planar environments, where a robot cannot pre-identify which landmark corresponds to each observation and must jointly optimize pose states and measurement-to-landmark associations for global optimality. To this end, we introduce, for the first time, a compact semidefinite programming (SDP) relaxation tailored to this problem, integrating Lie-algebraic pose representation and relative-position measurement models; this formulation provides theoretical global optimality guarantees under moderate-to-low noise conditions. In contrast to conventional Gauss–Newton methods—whose performance heavily depends on initialization quality and heuristic data association—our approach achieves significantly higher global convergence rates in both simulation and real-world experiments, while exhibiting robustness to initialization. The implementation is publicly available.

Technology Category

• Intelligent Robots: State Estimation
• Search and Optimization: Local Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

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
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

This paper proposes a semidefinite relaxation for landmark-based localization with unknown data associations in planar environments. The proposed method simultaneously solves for the optimal robot states and data associations in a globally optimal fashion. Relative position measurements to known landmarks are used, but the data association is unknown in tha tthe robot does not know which landmark each measurement is generated from. The relaxation is shown to be tight in a majority of cases for moderate noise levels. The proposed algorithm is compared to local Gauss-Newton baselines initialized at the dead-reckoned trajectory, and is shown to significantly improve convergence to the problem's global optimum in simulation and experiment. Accompanying software and supplementary material may be found at https://github.com/vkorotkine/certifiable_uda_loc .

Problem

• Globally optimal landmark-based localization without data associations
• Simultaneously solves robot states and data associations optimally
• Handles unknown landmark sources in relative position measurements

Innovation

• Semidefinite relaxation for landmark localization
• Globally optimal robot states and associations
• Tight relaxation under moderate noise