Slot-Wise Maximum Likelihood Estimation of the Tag Population Size in FSA Protocols

Framed Slotted Aloha (FSA) is a popular anti-collision technique in state-of-the-art RF-ID systems, as in ISO/IEC CD 18000-6 for 900MHz or the EPCglobal HF Gen 2 draft for 13.56MHz. In many applications the number of tags entering and leaving the detection range of the reader is subject to a strong fluctuation and usually unknown. The current number of tags in the field is a crucial parameter to operate the FSA anti-collision 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. The contributions of this paper are: 1) 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 developed and empirically verified. 2) This formula is then modified to compute the probability for partly observed frames as well which is of great interest as the referred standards allow for the in-frame adjustment of the frame size without quitting the interrogation round. 3) Then, a maximum likelihood estimator is formulated to yield the estimated number of tags on a slot-wise basis. 4) Its superior estimation performance is compared to the known best estimators over the complete parameter set. While its performance is strongly superior compared to Schoute's estimate, compared to Vogt's MSE estimator only marginally improvement is obtained(1).