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Distributed parameter estimation for large-scale systems is an activeresearch problem. The goal is to derive a distributed algorithm in which eachagent obtains a local estimate of its own subset of the global parametervector, based on local measurements as well as information received from itsneighbours. A recent algorithm has been proposed, which yields the optimalsolution (i.e., the one that would be obtained using a centralized method) infinite time, provided the communication network forms an acyclic graph. Ifinstead, the graph is cyclic, the only available alternative algorithm, whichis based on iterative matrix inversion, achieving the optimal solution, does soasymptotically. However, it is also known that, in the cyclic case, thealgorithm designed for acyclic graphs produces a solution which, although nonoptimal, is highly accurate. In this paper we do a theoretical study of theaccuracy of this algorithm, in communication networks forming cyclic graphs. Tothis end, we provide bounds for the sub-optimality of the estimation error andthe estimation error covariance, for a class of systems whose topologicalsparsity and signal-to-noise ratio satisfy certain condition. Our results showthat, at each node, the accuracy improves exponentially with the so-calledloop-free depth. Also, although the algorithm no longer converges in finitetime in the case of cyclic graphs, simulation results show that the convergenceis significantly faster than that of methods based on iterative matrixinversion. Our results suggest that, depending on the loop-free depth, thestudied algorithm may be the preferred option even in applications with cycliccommunication graphs.

Accuracy Analysis for Distributed Weighted Least-Squares Estimation in Finite Steps and Loopy Networks