  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. Aside
from developing methods that allow to model and account for the deterministic
and stochastic components that contribute to the measurement errors of these
devices, an approach that has been put forward in recent years is to make use
of arrays of such sensors in order 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 and common circumstances. Hence, in this work we put forward a
non-parametric method that makes use of the wavelet cross-covariance at
different scales to combine the measurements coming from an array of gyroscopes
in order to deliver an optimal measurement signal without needing any
assumption on the processes underlying the individual error signals. 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, our results
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
other than navigation.
