Scale-Wise Variance Minimization for Optimal Virtual Signals: An Approach for Redundant Gyroscopes

The increased use of low-cost gyroscopes within inertial sensors for navigation purposes, among others, has brought to the development of a considerable amount of research in improving their measurement precision. An approach that has been put forward in recent years is to make use of arrays of such sensors to combine their measurements thereby reducing the impact of individual sensor noise. Nevertheless, combining these measurements is not straightforward given the complex stochastic nature of these errors and, although some solutions have been suggested, these are limited to certain specific settings which do not allow to achieve solutions in more general circumstances. Hence, in this work we put forward a non-parametric method that makes use of the wavelet cross-covariance at different scales to construct an optimal measurement signal with weak assumptions on the processes underlying the individual errors. We also study an appropriate non-parametric approach for the estimation of the asymptotic covariance matrix of the wavelet cross-covariance estimator which has important applications beyond the scope of this work. The theoretical properties of the proposed approach are studied and are supported by simulations and real applications, indicating that this method represents an appropriate and general tool for the construction of optimal virtual signals that are particularly relevant for arrays of gyroscopes. Moreover, the results of this work can support the creation of optimal signals for other types of inertial sensors other than gyroscopes as well as for redundant measurements in other domains beyond that of navigation.