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.

💡 Research Summary

The paper addresses a common problem in precision experiments where the quantity of interest is obtained as the difference between two measurement configurations, A and B. Because the two measurements are not taken simultaneously, slow variations of the instrument’s zero‑point (offset) can introduce a systematic bias. Traditional approaches mitigate this by pre‑defining measurement sequences such as AB BA or ABA that cancel linear (or higher‑order) drifts. However, these sequences have practical drawbacks: they are asymmetric, they require a priori knowledge of the drift order, and any missing data point forces the discard of the whole block.

The authors propose a radically simpler data‑acquisition scheme: record an alternating series ABAB… without any special timing or pattern, then remove drift in post‑processing. They model each raw datum as

 u_i = z₀(i) + (−1)^i η + ε_i,

where z₀(i) is the slowly varying zero‑point, η is the true signal that flips sign with each measurement, and ε_i is zero‑mean white noise with variance σ². A naïve estimator that simply multiplies by (−1)^i and averages yields E