Abstract
This paper presents a signal processing technique to improve angular rate accuracy of the gyroscope by combining the outputs of an array of MEMS gyroscope. A mathematical model for the accuracy improvement was described and a Kalman filter (KF) was designed to obtain optimal rate estimates. Especially, the rate signal was modeled by a first-order Markov process instead of a random walk to improve overall performance. The accuracy of the combined rate signal and affecting factors were analyzed using a steady-state covariance. A system comprising a six-gyroscope array was developed to test the presented KF. Experimental tests proved that the presented model was effective at improving the gyroscope accuracy. The experimental results indicated that six identical gyroscopes with an ARW noise of 6.2 °/√h and a bias drift of 54.14 °/h could be combined into a rate signal with an ARW noise of 1.8 °/√h and a bias drift of 16.3 °/h, while the estimated rate signal by the random walk model has an ARW noise of 2.4 °/√h and a bias drift of 20.6 °/h. It revealed that both models could improve the angular rate accuracy and have a similar performance in static condition. In dynamic condition, the test results showed that the first-order Markov process model could reduce the dynamic errors 20% more than the random walk model.
Highlights
Micro Electromechanical System (MEMS) gyroscopes have been used for measuring rate or angle of rotation in various inertial measurement fields thanks to their attractive advantages such as small size, low cost, possible batch fabrication and low power consumption [1,2]
Due to the actual statistical model of the rate signal is difficult to accurately obtain, and even qω varies with changes of the environment, if the choice of qω could accurately or closely reflect the dynamic characteristics of the input rate signal, the Kalman filter (KF) will reach the best performance and the virtual gyroscope signal with the best accuracy can be obtained; while qω is smaller than such ‘value’, the performance of the KF will be degraded, it would result in a signal attenuation; while qω is higher than such ‘value’, the performance of the KF will be degraded and eventually reach the level of a simple averaging process with increasing of qω
Reduction is greater than that of the rate random walk (RRW) and bias drift, the main reason being that the angular random walk (ARW) is the dominant noise in the single gyroscope and the virtual gyroscope adopts a simple error model to describe the relationship of the input angular rates and gyroscope outputs
Summary
Micro Electromechanical System (MEMS) gyroscopes have been used for measuring rate or angle of rotation in various inertial measurement fields thanks to their attractive advantages such as small size, low cost, possible batch fabrication and low power consumption [1,2]. An optimal rate estimate can be obtained by the optimal filter to fuse these multiple measurements This approach can further reduce the noise, the bias instability and improve the overall accuracy beyond the performance limitations of individual gyroscopes. It can be seen that the technology of the virtual gyroscope is essentially identical with the VIMU, since both of them fuse multiple measurements to create a combined signal from a sensor array for improving the overall performance. The key of combining multiple gyroscopes for accuracy improvement lies in rate signal modeling and the optimal filter design. The angular rate signal ωk+1 for the subsequent time point tk+1 usually can be thought as related to ωk for the former time point tk Such dynamic characteristics and property can be suitably represented by a Markov process model. The hardware of the virtual gyroscope system is implemented and the performance of the virtual gyroscope with two different rate signal models are tested and compared
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