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In this paper, we revisit the inconsistency problem of EKF-based cooperativelocalization (CL) from the perspective of system decomposition. By transformingthe linearized system used by the standard EKF into its Kalman observablecanonical form, the observable and unobservable components of the system areseparated. Consequently, the factors causing the dimension reduction of theunobservable subspace are explicitly isolated in the state propagation andmeasurement Jacobians of the Kalman observable canonical form. Motivated bythese insights, we propose a new CL algorithm called KD-EKF which aims toenhance consistency. The key idea behind the KD-EKF algorithm involves performstate estimation in the transformed coordinates so as to eliminate theinfluencing factors of observability in the Kalman observable canonical form.As a result, the KD-EKF algorithm ensures correct observability properties andconsistency. We extensively verify the effectiveness of the KD-EKF algorithmthrough both Monte Carlo simulations and real-world experiments. The resultsdemonstrate that the KD-EKF outperforms state-of-the-art algorithms in terms ofaccuracy and consistency.

KD-EKF: A Consistent Cooperative Localization Estimator Based on Kalman Decomposition