Obtaining a correlation factor is a prerequisite for fusing multiple outputs of a mircoelectromechanical system (MEMS) gyroscope array and evaluating accuracy improvement. In this paper, a mathematical statistics method is established to analyze and obtain the practical correlation factor of a MEMS gyroscope array, which solves the problem of determining the Kalman filter (KF) covariance matrix Q and fusing the multiple gyroscope signals. The working principle and mathematical model of the sensor array fusion is briefly described, and then an optimal estimate of input rate signal is achieved by using of a steady-state KF gain in an off-line estimation approach. Both theoretical analysis and simulation show that the negative correlation factor has a favorable influence on accuracy improvement. Additionally, a four-gyro array system composed of four discrete individual gyroscopes was developed to test the correlation factor and its influence on KF accuracy improvement. The result showed that correlation factors have both positive and negative values; in particular, there exist differences for correlation factor between the different units in the array. The test results also indicated that the Angular Random Walk (ARW) of 1.57°/h^0.5 and bias drift of 224.2°/h for a single gyroscope were reduced to 0.33°/h^0.5 and 47.8°/h with some negative correlation factors existing in the gyroscope array, making a noise reduction factor of about 4.7, which is higher than that of a uncorrelated four-gyro array. The overall accuracy of the combined angular rate signal can be further improved if the negative correlation factors in the gyroscope array become larger.

A micro-inertial measurement unit (MIMU) is usually used to sense the angular rate and acceleration of the flight carrier. In this study, multiple MEMS gyroscopes were used to form a spatial non-orthogonal array to construct a redundant MIMU system, and an optimal Kalman filter (KF) algorithm was established by a steady-state KF gain to combine array signals to improve the MIMU’s accuracy. The noise correlation was used to optimize the geometric layout of the non-orthogonal array and reveal the mechanisms of influence of correlation and geometric layout on MIMU’s performance improvement. Additionally, two different conical configuration structures of a non-orthogonal array for 4,5,6,8-gyro were designed and analyzed. Finally, a redundant 4-MIMU system was designed to verify the proposed structure and KF algorithm. The results demonstrate that the input signal rate can be accurately estimated and that the gyro’s error can also be effectively reduced through fusion of non-orthogonal array. The results for the 4-MIMU system illustrate that the gyro’s ARW and RRW noise can be decreased by factors of about 3.5 and 2.5, respectively. In particular, the estimated errors (1σ) on the axes of X_b, Y_b and Z_b were 4.9, 4.6 and 2.9 times lower than that of the single gyroscope.

Attitude estimation has increasingly relied on MEMS inertial measurement units (IMUs) owing to the low cost and miniature size, but the inherent high random noise and error accumulation limit long-term measurement accuracy. This article proposes an integrated attitude estimation algorithm based on data fusion from a MIMU inertial array and magnetometer to address this challenge. First, a redundant inertial array is constructed using homogeneous gyroscopes, and a Kalman filter (KF) is designed to fuse output signals from multiple gyroscopes to estimate true angular rate. Second, an integrated error state Kalman filter (ESKF) for the MIMU/magnetometer system is developed. Using the attitude quaternion calculated by the strapdown inertial solution as the nominal state and combining it with measurements from the accelerometer and magnetometer as observations, the attitude error is estimated and corrected. Both simulations and field experiments were conducted to validate the effectiveness of the proposed algorithm. The experimental results show that the ESKF algorithm performs best in estimation accuracy and addresses the issue of error accumulation and fluctuation. In particular, the Root Mean Square Error (RMSE) of the ESKF algorithm was significantly reduced, with the roll angle reduced by 55.34%, the pitch angle by 30.25%, and the yaw angle by 55.71%.