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, 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 drift with a post-hoc analysis. We present an analysis method that removes bias from the result for 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.