Patent ID: 8299900

Claim:
A method for estimating the cardinality of a set of one or more tags in a system that comprises the set of one or more tags and one or more readers, wherein: the one or more readers are adapted to transmit a command requesting that each tag that receives the command determine whether to transmit a reply; each receiving tag is adapted to determine whether to transmit a reply based on a specified probability level; and each receiving tag that determines to transmit a reply (i) selects a timeslot of a frame in which to transmit the reply based on (1) a specified total number of timeslots in the frame and (2) a specified random-number seed and (ii) transmits the reply in the selected timeslot; the method comprising: (a) during each of a plurality of time intervals: (a1) transmitting a command requesting that each tag that receives the command determine whether to transmit a reply; and (a2) receiving, in one or more timeslots of a frame corresponding to the time interval, replies from one or more tags; and (b) providing an estimate of the cardinality of the set of one or more tags in the system based on (i) timeslots in each of the plurality of time intervals that are zero timeslots, wherein a zero timeslot is a timeslot having no received reply, and (ii) the total number of timeslots in each frame', wherein the estimate t 0 of the cardinality of the set of one or more tags in the system in step (b) is calculated using at least: (i) the total number f of timeslots in each frame, (ii) the probability p that a tag will reply in a timeslot, (iii) a load factor ρ 0 defined as a ratio of a number of tags to frame size, and (iv) the number z i of zero timeslots for time interval i, wherein the estimate t 0 of the cardinality of the set of one or more tags in the system in step (b) is derived using the equations ⅇ - p ⁢ ⁢ ρ 0 = ∑ i ⁢ z i f , ⁢ and ⁢ ⁢ t 0 = f ⁢ ⁢ ρ 0 .