In this paper, we revisit the inconsistency problem of EKF-based cooperative localization (CL) from the perspective of system decomposition. By transforming the linearized system used by the standard EKF into its Kalman observable canonical form, the observable and unobservable components of the system are separated. Consequently, the factors causing the dimension reduction of the unobservable subspace are explicitly isolated in the state propagation and measurement Jacobians of the Kalman observable canonical form. Motivated by these insights, we propose a new CL algorithm called KD-EKF which aims to enhance consistency. The key idea behind the KD-EKF algorithm involves perform state estimation in the transformed coordinates so as to eliminate the influencing factors of observability in the Kalman observable canonical form. As a result, the KD-EKF algorithm ensures correct observability properties and consistency. We extensively verify the effectiveness of the KD-EKF algorithm through both Monte Carlo simulations and real-world experiments. The results demonstrate that the KD-EKF outperforms state-of-the-art algorithms in terms of accuracy and consistency.

翻译：摘要：本文从系统分解的角度重新审视了基于扩展卡尔曼滤波（EKF）的协同定位（CL）的不一致性问题。通过将标准EKF所使用的线性化系统转换为其卡尔曼可观测规范形式，系统的可观测分量与不可观测分量得以分离。因此，在卡尔曼可观测规范形式的状态传播和测量雅可比矩阵中，导致不可观测子空间维度缩减的因素被明确隔离。基于这些发现，我们提出了一种名为KD-EKF的新型CL算法，旨在增强一致性。KD-EKF算法的核心思想是在变换后的坐标中进行状态估计，以消除卡尔曼可观测规范形式中影响可观测性的因素。从而，KD-EKF算法确保了正确的可观测性属性与一致性。我们通过蒙特卡洛仿真和实际实验广泛验证了KD-EKF算法的有效性。结果表明，KD-EKF在精度和一致性方面均优于现有最先进算法。