We present an algorithm for the problem of linear distributed estimation of a parameter in a network where a set of agents are successively taking measurements. The approach considers a roaming token in a network that carries the estimate, and jumps from one agent to another in its vicinity according to the probabilities of a Markov chain. When the token is at an agent it records the agent's local information. We analyze the proposed algorithm and show that it is consistent and asymptotically optimal, in the sense that its mean-square-error (MSE) rate of decay approaches the centralized one as the number of iterations increases. We show these results for a scenario where the network changes over time, and we consider two different sets of assumptions on the network instantiations: (I) they are i.i.d. and connected on the average, or (II) that they are deterministic and strongly connected for every finite time window of a fixed size. Simulations show our algorithm is competitive with consensus+innovations and diffusion type of algorithms, achieving a smaller MSE at each iteration in all considered scenarios.

中文翻译：

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通过漫游令牌的分布式线性估计

我们提出了一种算法，用于解决网络中参数的线性分布估计问题，其中一组代理连续进行测量。该方法考虑网络中携带估计的漫游令牌，并根据马尔可夫链的概率从一个代理跳转到其附近的另一个代理。当令牌在代理处时，它记录代理的本地信息。我们分析了所提出的算法，并表明它是一致的和渐近最优的，因为随着迭代次数的增加，其均方误差 (MSE) 衰减率接近集中式。我们针对网络随时间变化的场景展示了这些结果，并且我们考虑了关于网络实例的两组不同假设：（I）它们是 iid 并且平均连接，或 (II) 对于每个固定大小的有限时间窗口，它们都是确定性的并且具有强连接性。模拟表明，我们的算法与共识+创新和扩散类型的算法相比具有竞争力，在所有考虑的场景中，每次迭代都实现了更小的 MSE。