Analysis of the influence of sample rates on the Allan variance

Abstract

The paper considers the problem of interpreting the Allan deviation plot for signals from sensors polled more frequently than data are refreshed. The Allan variance is a standard tool for analysis of noise terms inevitably present in signals of inertial sensors. There exists a well-defined algorithm for its calculation both for time domain and frequency domain. Having calculated the Allan variance as a function of time (or frequency) one fetches its square root, called Allan deviation, and builds its plot in a logarithmic format. Each region of the Allan deviation plot characterizes a specific noise kind (white noise, flicker noise, random walk, etc). The plot is expected to have a well recognizable, predefined shape. However, in practice it may be that a plot obtained for real time series does not follow its textbook pattern. In this case it is unobvious how to interpret the plot and whether it is applicable or not. We observed quite untypical Allan deviation plots for signals of a magnetometer sampled too frequently, which suggested that the sample rate can be responsible for the unusual shape of the plot. Our work is aimed at analyzing the influence of the sample rate on the Allan deviation plot and evaluating the applicability of such a plot obtained for signals sampled too frequently. We reproduced experimental results by simulation and detected that the sample rate for synthesized white noise signals impacts the shape of the Allan deviation plot. The same idea was corroborated by filtering out repeated measurement points from experimentally obtained magnetometer signals. The simulation results are backed up by analytical calculations. Therefore, all the applied approaches such as simulation, filtering reading of a real sensor and analytical considerations confirmed that the shape of the Allan deviation plot depends on the signal sample rate. Moreover, we have shown that the Allan deviation plot built under these conditions is completely inapplicable unless all repeated measurement points are filtered out. Our analytical explanation of this fact is confirmed by a set of experiments. We provide a detailed description of a procedure for evaluation of the applicability of the Allan deviation plot using a magnetometer.