Removal of zero-point drift from AB data and the statistical cost

Often the result of a scientific experiment is given by the difference of measurements in two configurations, denoted by A and B. Since the measurements are not obtained simultaneously, the drift of the zero point can bias the result. In practice measurement patterns are used to minimize this bias. The time sequence AB followed by BA, for example, would cancel a linear drift in the average difference A - B. We propose taking data with an alternating series ABAB ... , and removing the drift with a post hoc analysis. We present an analysis method that removes the bias from the result for a drift up to polynomial order p. A statistical cost function c(N) is introduced to compare the uncertainty in the end result with that from using a raw data average. For a data set size N > 30 the statistical cost is negligible. For N < 30 the cost is plotted as a function of N and filter order p and the trade-off between the size of the data set and p is discussed.