Scalable Distributed Least-Squares Algorithm for Time-Varying Observation Vectors via Scheduling

In this work, we propose a novel discrete-time distributed algorithm for finding least-squares solutions of linear algebraic equations, utilizing a scheduling protocol to further enhance its scalability. Unlike typical distributed algorithms, our approach accounts for communication bandwidth limits by allowing agents to transmit only a portion of their guessed solution, regardless of its dimension. A cyclic scheduling protocol determines which portion is transmitted at each iteration. Assuming a small fixed step size and a diagonalizable algorithm matrix, we prove via a matrix-theoretic approach that the agents' guessed solutions converge to a least-squares solution, even if the problem admits non-unique least-squares solutions. Furthermore, when observation vectors are time-varying, we show that the tracking error is bounded by the single-step variation in the observation vector. Simulations and comparisons with state-of the-art algorithms validate the feasibility and scalability of our proposed method.