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.
翻译:在惯性传感器中为导航目的更多地使用低成本陀螺仪,除其他外,这已导致在改进测量精确度方面进行大量研究,除了开发能够建模和核算有助于测量这些装置误差的确定性和随机性组件的方法外,近年来提出的一种方法是使用这些传感器的阵列,以便结合测量结果,从而减少单个传感器噪音的影响;然而,鉴于这些误差的虚拟分析性质复杂,综合这些测量结果并非直截了当,尽管提出了一些解决办法,但仅限于某些特定环境,无法在更一般和共同的情况下找到解决办法。因此,在这项工作中,我们提出了一种非参数方法,利用不同尺度的波板交叉变异性,将来自这些传感器阵列的测量结果结合起来,以便提供最佳测量信号,而无需对单个误差信号所依据的过程作任何假设。 我们还研究了一种适当的非对数值方法,用以估计在一般情况下无法在一般情况下找到解决办法。