Wavelet-Based Moment-Matching Techniques for Inertial Sensor Calibration

The task of inertial sensor calibration has required the development of various techniques to take into account the sources of measurement error coming from such devices. The calibration of the stochastic errors of these sensors has been the focus of increasing amount of research in which the method of reference has been the so-called “Allan variance (AV) slope method” which, in addition to not having appropriate statistical properties, requires a subjective input which makes it prone to mistakes. To overcome this, recent research has started proposing “automatic” approaches where the parameters of the probabilistic models underlying the error signals are estimated by matching functions of the AV or wavelet variance with their model-implied counterparts. However, given the increased use of such techniques, there has been no study or clear direction for practitioners on which approach is optimal for the purpose of sensor calibration. This article, for the first time, formally defines the class of estimators based on this technique and puts forward theoretical and applied results that, comparing with estimators in this class, suggest the use of the Generalized method of Wavelet moments (GMWM) as an optimal choice. In addition to analytical proofs, experiment-driven Monte Carlo simulations demonstrated the superior performance of this estimator. Further analysis of the error signal from a gyroscope was also provided to further motivate performing such analyses, as real-world observed error signals may show significant deviation from manufacturer-provided error models.