An optimal virtual inertial sensor framework using wavelet cross covariance

The practice of inertial sensor calibration has commonly been carried out by taking into account the deterministic and stochastic components of the error measurements issued from a calibration session. Once the deterministic components have been taken into account through physical models, the remaining stochastic component has always been dealt with for each sensor separately. The latter process involves estimating complex probabilistic models for each sensor which has been proven to be extremely complicated over the past years, although recent proposals have allowed to overcome most of the limitations that have characterized this task. However, the separate stochastic calibration of the individual sensors composing an inertial measurement unit may not be wise in many cases since there can be considerable degrees of dependence between the sensors, especially between the gyroscopes. For this reason, there has been growing attention towards this issue in order to consider the influence of the stochastic behaviour of the sensors on each other, with few proposals that address this problem. Among these proposals there has been the idea of integrating the information coming from the different gyroscopes so as to build a virtual gyroscope. In this paper we build on this idea and, using a recently proposed method for multivariate signal modelling, we deliver a general and flexible framework that allows to consider many different modelling options which provide the basis to construct a virtual sensor that optimally combines the information from the individual sensors and considerably improves navigation accuracy.