Combining Numerous Uncorrelated MEMS Gyroscopes for Accuracy Improvement Based on an Optimal Kalman Filter

Abstract

In this paper, an approach to improve the accuracy of microelectromechanical systems (MEMS) gyroscopes by combining numerous uncorrelated gyroscopes is presented. A Kalman filter (KF) is used to fuse the output signals of several uncorrelated sensors. The relationship between the KF bandwidth and the angular rate input is quantitatively analyzed. A linear model is developed to choose suitable system parameters for a dynamic application of the concept. Simulation and experimental tests of a six-gyroscope array proved that the presented approach was effective to improve the MEMS gyroscope accuracy. The experimental results indicate that six identical gyroscopes with a noise density of 0.11 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$^{\circ}/\hbox{s}/\surd\hbox{Hz}$</tex></formula> and a bias instability of 62 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$^{\circ}/\hbox{h}$</tex></formula> can be combined to form a virtual gyroscope with a noise density of 0.03 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$^{\circ}/\hbox{s}/\surd\hbox{Hz}$ </tex></formula> and a bias instability of 16.8 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$^{\circ}/\hbox{h}$</tex></formula> . The accuracy improvement is better than that of a simple averaging process of the individual sensors.