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 • /s/ √ Hz and a bias instability of 62 • /h can be combined to form a virtual gyroscope with a noise density of 0.03 • /s/ √ Hz and a bias instability of 16.8 • /h. The accuracy improvement is better than that of a simple averaging process of the individual sensors.

Analysis of Correlation in MEMS Gyroscope Array and its Influence on Accuracy Improvement for the Combined Angular Rate Signal

“…In previous research [15,17,20], a typical stochastic error model is used to describe the MEMS gyroscope as follows:$yfalse(tfalse)=\omega false(tfalse)+bfalse(tfalse)+nfalse(tfalse),\dot{b}false(tfalse)=w_{b}false(tfalse)$ where y ( t ) is the output rate signal of gyroscope, ω ( t ) is the input true rate signal, b ( t ) is the bias drift, driven by a white noise w b denoted as Rate Random Walk (RRW), and n ( t ) is a white noise denoted as Angular Random Walk (ARW).…”

“…The KF coefficient matrices F and H can be referred to in [17]. If we suppose that correlation exists in the sensor array between the RRW noises of the component gyroscopes, the correlated covariance matrix Q b in Equation (5) can be determined by the correlation factor and RRW noise variance in an off-diagonal form as:${\mathbf{Q}}_b={\left[\begin{array}{cccc}{\sigma }_{b1}^2& {\rho }_{12}\cdot \sqrt{{\sigma }_{b1}^2{\sigma }_{b2}^2}& \cdots & {\rho }_{1N}\cdot \sqrt{{\sigma }_{b1}^2{\sigma }_{bN}^2}\\ {\rho }_{21}\cdot \sqrt{{\sigma }_{b2}^2{\sigma }_{b1}^2}& {\sigma }_{b2}^2& \cdots & {\rho }_{2N}\cdot \sqrt{{\sigma }_{b2}^2{\sigma }_{bN}^2}\\ ⋮& ⋮& \ddots & ⋮\\ {\rho }_{N1}\cdot \sqrt{{\sigma }_{bN}^2{\sigma }_{b1}^2}& {\rho }_{N2}\cdot \sqrt{{\sigma }_{bN}^2{\sigma }_{b2}^2}& \cdots & {\sigma }_{bN}^2\end{array}\right]}_{N\times N}$ where ${\sigma }_{b,i}^2$ is the variance for RRW of the i th gyroscope, and ρ ij is the correlation factor between the i th and j th gyroscopes of the array corresponding to the RRW noise ( i = 1,2,…, N , j = 1,2,…, N ).…”

“…With regard to the KF system, it determines the KF bandwidth. When setting the parameter q ω as a larger value, the KF bandwidth will become much larger than that of the component gyroscopes [17], and then the system bandwidth is only determined by the component gyroscopes, which will be close to the bandwidth of the component gyroscopes. In this case, the drift of combined angular rate signal is mainly influenced by the correlation factor and number of array N , making it easy to analyze the effect of correlation on noise reduction.…”

“…In addition, a MEMS gyroscope array composed of three individual gyroscopes was presented by Chang et al [16], in which a two-level Kalman filter (KF) scheme was designed to reduce the gyroscope’s drift and improve the accuracy. In particular, the performance of a KF approach for fusing six fully uncorrelated MEMS gyroscopes was further analyzed and evaluated in [17], and it demonstrated that performance can be better than that of an averaging process. Additionally, Tanenhaus et al reported a method for constructing a MIMU [9,11] in which multiple gyroscopes are placed on each sensitive axis of the MIMU, and a wavelet de-noising method was used to combine outputs of the gyroscope array.…”

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

“…In order to implement the Bayard approach it is necessary to estimate these correlations from sensor data, but no such estimation algorithm has appeared in the literature. Several researchers have attempted to implement the Bayard approach (see [3,4,5,6]). However, 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.…”