Reduced-Drift Virtual Gyro from an Array of Low-Cost Gyros.

Richard Vaccaro,Ahmed Zaki

doi:10.3390/s17020352

Richard Vaccaro, Ahmed Zaki

Open Access

https://doi.org/10.3390/s17020352

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Abstract

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.

Highlights

The concept of combining the outputs of an array of high-drift sensors to produce a virtual low-drift sensor was introduced by Bayard and Ploen [1,2], who used a Kalman filter to produce the virtual sensor
Virtual gyro signals were created by taking linear combinations of the six gyro signals using the two coefficient vectors
We have presented an algorithm for estimating R and Q, the spectral density matrices for the ARW and RRW components, respectively, of an array of gyros

Summary

Introduction

The concept of combining the outputs of an array of high-drift sensors to produce a virtual low-drift sensor was introduced by Bayard and Ploen [1,2], who used a Kalman filter to produce the virtual sensor They showed, through analysis and simulation examples, that the reduced drift of the virtual sensor depends on the drift components of the individual sensors being “favorably correlated”. Several researchers have attempted to implement the Bayard approach (see [3,4,5,6]) None of these efforts were able to implement the full Bayard algorithm because they were not able to estimate the correlations between the drift components of the individual sensors. In this paper we present an algorithm for estimating these correlations

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