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The increased use of low-cost gyroscopes within inertial sensors fornavigation purposes, among others, has brought to the development of aconsiderable amount of research in improving their measurement precision. Asidefrom developing methods that allow to model and account for the deterministicand stochastic components that contribute to the measurement errors of thesedevices, an approach that has been put forward in recent years is to make useof arrays of such sensors in order to combine their measurements therebyreducing the impact of individual sensor noise. Nevertheless combining thesemeasurements is not straightforward given the complex stochastic nature ofthese errors and, although some solutions have been suggested, these arelimited to certain specific settings which do not allow to achieve solutions inmore general and common circumstances. Hence, in this work we put forward anon-parametric method that makes use of the wavelet cross-covariance atdifferent scales to combine the measurements coming from an array of gyroscopesin order to deliver an optimal measurement signal without needing anyassumption on the processes underlying the individual error signals. We alsostudy an appropriate non-parametric approach for the estimation of theasymptotic covariance matrix of the wavelet cross-covariance estimator whichhas important applications beyond the scope of this work. The theoreticalproperties of the proposed approach are studied and are supported bysimulations and real applications, indicating that this method represents anappropriate and general tool for the construction of optimal virtual signalsthat are particularly relevant for arrays of gyroscopes. Moreover, our resultscan support the creation of optimal signals for other types of inertial sensorsother than gyroscopes as well as for redundant measurements in other domainsother than navigation.

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