Estimating the extrema of large-scale RFID systems

In some large-scale RFID systems where tags carry values, the extrema are critical statistics. We consider estimating the extrema, i.e., estimating the maximum and minimum values simultaneously. A straightforward approach is to perform binary search on the possible values, each time requesting tags with values in a certain range to respond. We show that this approach is suboptimal due to the inter frame overhead between two frames in practical RFID systems. We propose a class of protocols to find the minimum value or maximum value separately, and show how to select the best protocol according to the hardware parameters of RFID systems. We then revise the protocol to estimate the minimum and maximum values simultaneously, and give the optimal parameters. Extensive simulations show that our protocol gives the smallest estimation error within any allocated time.