Slot-by-slot maximum likelihood estimation of tag populations in framed slotted aloha protocols

Framed Slotted ALOHA (FSA) is an anti-collision technique in current and future standards of RF-ID systems, as in ISO/IEC CD 18000-6. The number of tags present in the field is a crucial parameter to apply FSA algorithms in an optimal manner. Therefore, a lot of effort is spent on the estimation of this parameter and a range of different estimation techniques exist. But until now, a maximum likelihood estimator has not been formulated. In this paper, a closed formula for the probability of any observed event defined by the number of empty, singleton, and collision slots in the observed frame is derived. Since the referred standard allows for the in-frame adjustment of the frame size (without quitting the interrogation round), this formula is then modified to compute the probability for partly observed frames. Finally, a maximum likelihood estimator is formulated to yield the estimated number of tags on a slot-by-slot basis.