On the Consistency of Multi-Robot Cooperative Localization: A Transformation-Based Approach

Abstract

This letter investigates the inconsistency problem caused by the mismatch of observability properties commonly found in multi-robot cooperative localization (CL) and simultaneous localization and mapping (SLAM). To address this issue, we propose a transformation-based approach that introduces a linear time-varying transformation to ensure the transformed system possesses a state-independent unobservable subspace. Consequently, its observability properties remain unaffected by the linearization points. We establish the relationship between the unobservable subspaces of the original and transformed systems, guiding the design of the time-varying transformation. We then present a novel estimator based on this method, referred to as the Transformed EKF (T-EKF), which utilizes the transformed system for state estimation, thereby ensuring correct observability and thus consistency. The proposed approach has been extensively validated through both Monte Carlo simulations and real-world experiments, demonstrating better performance in terms of both accuracy and consistency compared to state-of-the-art methods.