Federated Smoothing ADMM for Localization

This paper addresses the challenge of localization in federated settings, which are characterized by distributed data, non-convexity, and non-smoothness. To tackle the scalability and outlier issues inherent in such environments, we propose a robust algorithm that employs an $\ell_1$-norm formulation within a novel federated ADMM framework. This approach addresses the problem by integrating an iterative smooth approximation for the total variation consensus term and employing a Moreau envelope approximation for the convex function that appears in a subtracted form. This transformation ensures that the problem is smooth and weakly convex in each iteration, which results in enhanced computational efficiency and improved estimation accuracy. The proposed algorithm supports asynchronous updates and multiple client updates per iteration, which ensures its adaptability to real-world federated systems. To validate the reliability of the proposed algorithm, we show that the method converges to a stationary point, and numerical simulations highlight its superior performance in convergence speed and outlier resilience compared to existing state-of-the-art localization methods.

Distributed Filtering Design with Enhanced Resilience to Coordinated Byzantine Attacks

This paper proposes a Byzantine-resilient consensus-based distributed filter (BR-CDF) wherein network agents employ partial sharing of state parameters. We characterize the performance and convergence of the BR-CDF and study the impact of a coordinated data falsification attack. Our analysis shows that sharing merely a fraction of the states improves robustness against coordinated Byzantine attacks. In addition, we model the optimal attack strategy as an optimization problem where Byzantine agents design their attack covariance or the sequence of shared fractions to maximize the network-wide mean squared error (MSE). Numerical results demonstrate the accuracy of the proposed BR-CDF and its robustness against Byzantine attacks. Furthermore, the simulation results show that the influence of the covariance design is more pronounced when agents exchange larger portions of their states with neighbors. In contrast, the performance is more sensitive to the sequence of shared fractions when smaller portions are exchanged.