And are there any relatively cheap RFID solutions that can assess the real-time proximity of players on a sports field?
The answers to your question, respectively, are yes and no. Yes, RFID can measure distance. There is an English soccer club—I'm not permitted to say which one—that has deployed a solution for tracking players on the field. Its goal is to be better able to analyze plays after a game, and to devise better tactics.
That system is probably not what you would describe as "relatively cheap," though I suppose that depends on your perception of what qualifies as inexpensive. If you were to employ a similar solution, you would need to use ultra-wideband (UWB) RFID technology, which can measure a tagged object's location very precisely. Such tags typically cost around $50 apiece. You would also need to deploy RFID readers around a field in order to capture signals, as well as sophisticated software that can analyze streams of data in real time, and display players' locations on the field. My guess is that the price would be outside the reach of all but the most elite teams.
Researchers at Fudan University's Auto-ID Lab, in Shanghai, are developing less expensive distance-sensing reader technology, based on time of flight. The solution being developed measures the time it takes for a radio wave to travel from a reader antenna to a passive ultrahigh-frequency (UHF) tag antenna, and back to the interrogator. The distance from the reader to the tag is calculated based on the travel speed of a radio wave in the speed of light (approximately 300,000 kilometers per second—see Readers That Sense Distance). But these passive UHF tags have a maximum read range of 30 or 40 feet, so they would be unable to track players on a large field.
—Mark Roberti, Founder and Editor, RFID Journal
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