Beyond Allan Variance - GMWM Framework For Sensor Calibration

Proposed 50 years ago for studying stability of oscillators, Allan Variance (AV) was accepted by IEEE as a standard for characterizing behavior of sensors. However, the inverse mapping, i.e. the estimation of noise-parameters from Allan Variance is less straightforward and considerably more difficult procedure. The parameters that can be reliably estimated via a linear regression on the AV log-log plots are limited to few possible models and this approach has recently been proven inconsistent. Alternative estimation with Maximum Likelihood Estimation (MLE) is computationally expensive while it was shown to diverge with increased model complexity. We describe a new framework that estimates efficiently time series models that are commonly used to describe many sensors. This method is called Generalized Method of Wavelet Moments (GMWM) as it exploits the relation between the model and its wavelet variance. The GMWM has been mathematically proven in our JASA 2013 publication as a general consistent estimator for composite stochastic processes. Here we explain its basic relation to Allan Variance, its principal functionality and demonstrate its benefits on simulated and practical examples in the field of integrated navigation. Finally, we introduce a newly developed library with GMWM functionality that is planned to be released as a package within the open statistical software R later this year from which the scientists and engineers can benefit.