Statistical Interpretation of the Allan Variance as a Characteristic of Measuring and Navigation Devices

Abstract— The Allan variance was originally meant to be a characteristic of time and frequency standards, but now it is widely used in many fields, including the development of navigation devices. The paper considers different applications of the Allan variance to various tasks, among which is estimation of characteristics of navigation devices. However, sometimes the Allan variance does not seem to be very effective; besides, its physical interpretation may be vague. This is due to its empirical definition as an alternative estimate of variance. The paper considers the definition of the Allan variance based on a model of random processes with stationary increments that include both stationary and Wiener processes. In this model, the main characteristic is the structure function, whereas the Allan variance turns out to be its empirical estimate. This representation makes the statistical meaning of the Allan variance clear and explains its high effectiveness in the analysis of nonstationary signals and noise. It also allows the Allan variance to be used as a general characteristic describing stability of measuring and navigation devices, the one that is different from variance.