A Study of the Allan Variance for Constant-Mean Nonstationary Processes

Haotian Xu, Stephane Guerrier, Roberto Molinari, Yuming Zhang

Research output: Contribution to journalArticlepeer-review


The Allan variance (AV) is a widely used quantity in areas focusing on error measurement as well as in the general analysis of variance for autocorrelated processes in domains such as engineering and, more specifically, metrology. The form of this quantity is widely used to detect noise patterns and indications of stability within signals. However, the properties of this quantity are not known for commonly occurring processes whose covariance structure is nonstationary and, in these cases, an erroneous interpretation of the AV could lead to misleading conclusions. This letter generalizes the theoretical form of the AV to some nonstationary processes while at the same time being valid also for weakly stationary processes. Some simulation examples show how this new form can help to understand the processes for which the AV is able to distinguish these from the stationary cases and hence allow for a better interpretation of this quantity in applied cases.

Original languageEnglish (US)
Article number7964734
Pages (from-to)1257-1260
Number of pages4
JournalIEEE Signal Processing Letters
Issue number8
StatePublished - Aug 2017


  • Bias-instability
  • Haar wavelet variance
  • heteroscedasticity
  • longitudinal studies
  • metrology
  • sensor calibration

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering
  • Applied Mathematics


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