Analytical Solution for BPM Reading the Multi-bunch Average in Booster
  The BPM system in Booster only can provide the beam position from the average of about 15 bunches due to the electronic limitation. Numerically calculating the difference made by this average can nearly give all the information, which is needed for extrapolating the BPM data. It is still useful to derive the analytical expression for the BPM reading, which can be helpful in getting the insight for the BPM system optimization. 
Xi Yang