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Cooperative positioning is an emerging topic in wireless sensor networks and navigation. It can improve the positioning accuracy and coverage in GPS-challenged conditions such as inside tunnels, in urban canyons, and indoors. Different algorithms have been proposed relying on iteratively exchanging and updating positional information. For the purpose of computational complexity, network traffic, and latency, it is desirable to minimize the amount of information shared between devices, while still maintaining acceptable performance. We show that information that is not reliable should not be shared, and information that is not informative should not be used. This naturally leads to censoring schemes. We consider different censoring schemes based on the Cramér Rao bound (CRB). We find that by blocking the broadcasts of the nodes that do not have reliable estimates (transmit censoring) and selecting the most usable links after receiving signals from neighbors (receive censoring), complexity and traffic can be reduced significantly without degrading positioning performance.