Vaccaro Richard J, Zaki Ahmed S
Department of Electrical, Computer, and Biomedical Engineering, University of Rhode Island, Kingston, RI 02881, USA.
Naval Undersea Warfare Center, Division Newport, Newport, RI 02840, USA.
Sensors (Basel). 2017 Feb 11;17(2):352. doi: 10.3390/s17020352.
A Kalman filter approach for combining the outputs of an array of high-drift gyros to obtain a virtual lower-drift gyro has been known in the literature for more than a decade. The success of this approach depends on the correlations of the random drift components of the individual gyros. However, no method of estimating these correlations has appeared in the literature. This paper presents an algorithm for obtaining the statistical model for an array of gyros, including the cross-correlations of the individual random drift components. In order to obtain this model, a new statistic, called the "Allan covariance" between two gyros, is introduced. The gyro array model can be used to obtain the Kalman filter-based (KFB) virtual gyro. Instead, we consider a virtual gyro obtained by taking a linear combination of individual gyro outputs. The gyro array model is used to calculate the optimal coefficients, as well as to derive a formula for the drift of the resulting virtual gyro. The drift formula for the optimal linear combination (OLC) virtual gyro is identical to that previously derived for the KFB virtual gyro. Thus, a Kalman filter is not necessary to obtain a minimum drift virtual gyro. The theoretical results of this paper are demonstrated using simulated as well as experimental data. In experimental results with a 28-gyro array, the OLC virtual gyro has a drift spectral density 40 times smaller than that obtained by taking the average of the gyro signals.
一种用于组合高漂移率陀螺仪阵列输出以获得虚拟低漂移率陀螺仪的卡尔曼滤波器方法在文献中已出现十多年。该方法的成功取决于各个陀螺仪随机漂移分量的相关性。然而，文献中尚未出现估计这些相关性的方法。本文提出了一种用于获取陀螺仪阵列统计模型的算法，包括各个随机漂移分量的互相关性。为了获得该模型，引入了一种新的统计量，称为两个陀螺仪之间的“艾伦协方差”。陀螺仪阵列模型可用于获得基于卡尔曼滤波器（KFB）的虚拟陀螺仪。相反，我们考虑通过对各个陀螺仪输出进行线性组合得到的虚拟陀螺仪。陀螺仪阵列模型用于计算最优系数，并推导所得虚拟陀螺仪漂移的公式。最优线性组合（OLC）虚拟陀螺仪的漂移公式与先前为KFB虚拟陀螺仪推导的公式相同。因此，无需卡尔曼滤波器即可获得最小漂移虚拟陀螺仪。本文的理论结果通过模拟数据和实验数据进行了验证。在使用28个陀螺仪阵列的实验结果中，OLC虚拟陀螺仪的漂移谱密度比通过取陀螺仪信号平均值得到的结果小40倍。
