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Motivated by the need of observers that are both robust to disturbances andguarantee fast convergence to zero of the estimation error, we propose anobserver for linear time-invariant systems with noisy output that consists ofthe combination of N coupled observers over a connectivity graph. At each nodeof the graph, the output of these interconnected observers is defined as theaverage of the estimates obtained using local information. The convergence rateand the robustness to measurement noise of the proposed observer's output arecharacterized in terms of $\mathcal{KL}$ bounds. Several optimization problemsare formulated to design the proposed observer so as to satisfy a given rate ofconvergence specification while minimizing the $H_\infty$ gain from noise toestimates or the size of the connectivity graph. It is shown that that theinterconnected observers relax the well-known tradeoff between rate ofconvergence and noise amplification, which is a property attributed to theproposed innovation term that, over the graph, couples the estimates betweenthe individual observers. Sufficient conditions involving information of theplant only, assuring that the estimate obtained at each node of the graphoutperforms the one obtained with a single, standard Luenberger observer aregiven. The results are illustrated in several examples throughout the paper.

Interconnected Observers for Robust Decentralized Estimation with Performance Guarantees and Optimized Connectivity Graph