So I'm having the same issue. R1 is connected to my iOS device. I open Collector and by natural common sense told it under the Location Provider to use the Trimble R1. When doing that I get no GPS location when opening any web map (do not see dot on map or cannot collect a feature). If I am reading comments above right, you are actually suppose to choose Integrated Receiver and I'll still get the accuracy of the R1? I have an ESRI person working a ticket for me right now and claims they have no issue when setting up an R1 and Collector.
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