Appendix A Rolling Average Algorithm

Transcription

1 Appendix A Roing Average Agorith 98

2 ROLLING AVERAGE ALGORITHM Let be a ink between two reader fied sites with aributes th, the ink threshod for ink,, the current roing average trave tie for ink, and s, the current roing average speed for ink. Let t c be the current tie and t w be the duration of the roing average window in seconds. Let be the set of a tag atches,, received for ink. Let each atch have the foowing aributes: t, the tie that atch was received,, the trave tie easured by atch, and s, the speed easured by atch. Let the current set of vaid tag atches,, be defined by the foowing: { tc tw t tc and ( th) ( th)} The roing average trave tie for ink,, and the roing average speed, s, can be cacuated by the foowing equations: s Roing Average Exapes A tag atch is produced whenever a tag is received by an adjacent pair of reader sites that are defined as a source-destination pair in the configuration fie. Tag atches are stored in a tabe aong with the tie that they were received and the trave tie and speed easured for the tag as it passed between the two readers. Tabe A.1 shows an exape of a tabe for ink identifier IN003I-RANDO-WALZE, which is one (1) ie in ength. s 99

3 MATCH NUMBER Tabe A.1 - Tag Match Tabe for ink IN003I-RANDO-WALZE TAG IDENTIFIER TIME TRAVEL TIME (SEC) :0: :0: :0: :0: :0: :0: :0: :0: :0: :0: :0: :0: :06: :06: :06: Periodicay, the average trave tie and speed for each ink are cacuated using a roing-average agorith. Two paraeters are used to contro the function of this agorith: the roing-average window and the ink threshod. SPEED (MPH) The roing-average window is used to deterine the period of tie that shoud be considered when cacuating the roing-average. For exape, if the roing-average window is 60 seconds, ony the tag atches received in the past 60 seconds wi be used to cacuate the roing average. The average that is produced fro this cacuation woud be referred to as a 60-second roing-average. The second paraeter, the ink threshod, is used to fiter tag atches. For exape, if the ink threshod is 20%, any atch which is 20% greater or ess than the previous roingaverage trave tie wi not be incuded in the cacuation. The roing-average is cacuated by taking the su of a tag atches which were recorded within the past roing-average window and which have trave tie vaues that 100

4 fa within the ink threshod. This su is then divided by the nuber of atches that were incuded in the su. Exape A.1 Assue that the current tie is 10:0:20, the tag atch tabe for ink IN003I-RANDO- WALZE is as presented in Tabe A.1, and the previous cacuation for the roing-average trave tie was 9 seconds. Using a roing-average window of 20 seconds and a threshod of 20%, a atches received since 10:0:00 with a trave tie between 7.2 seconds and 70.8 seconds wi be considered. This produces the foowing equation: 1, {1, 2, 3,,, 6, 7, 8, 2, 3,, } ,10,11,12,13,1,1 Equation A.1 - Cacuation of Roing-Average Trave Tie for Exape A.1 The ink roing-average speed, s, can be cacuated in a siiar fashion by repacing the atch trave tie,, with the atch speed, s. This woud produce a roing-average speed of 8.2 ph. Exape A.2 Assue that the current tie is 10:06:10, the tag atch tabe for ink IN003I-RANDO- WALZE is as presented in Tabe A.1, and the previous cacuation for the roing-average trave tie was 62 seconds. Using a roing-average window of 30 seconds and a threshod of 20%, a atches received since 10:0:0 with a trave tie between 9.6 seconds and 7. seconds wi be considered. This produces the foowing cacuation: 101

5 1, 2, 3,,, 6, 7, 8, 9,10,11,12,13,1,1 {10,12,13,1} 9.0 Equation A.2 - Cacuation of Roing-Average Trave Tie for Exape A.2 Note that in Equation A.2, tag atch nuber 11 is not incuded in the current atch set,, because its trave tie vaue, 90, fas outside the vaid range of trave ties. The ink roing-average speed, s, can be cacuated in a siiar fashion by repacing the atch trave tie,, with the atch speed, s. This woud produce a roing-average speed of 61.7 ph. 102