A Distributed Algorithm That Finds Almost Best Possible Estimate Under Non-Vanishing and Time-Varying Measurement Noise

In this letter, we review an existing distributed least-squares solver and share some new insights on it. Then, by the observation that an estimation of a constant vector under output noise can be translated into finding the least-squares solution, we present an algorithm for distributed estimation of the state of linear time-invariant systems under measurement noise. The proposed algorithm consists of a network of local observers, where each of them utilizes local measurements and information transmitted from the neighbors. It is proven that even under non-vanishing and time-varying measurement noise, we could obtain an almost best possible estimate with arbitrary precision. Some discussions regarding the plug-and-play operation are also given.