Dynamic Performance Comparison of Two Kalman Filters for Rate Signal Direct Modeling and Differencing Modeling for Combining a MEMS Gyroscope Array to Improve Accuracy.

In this paper, the performance of two Kalman filter (KF) schemes based on the direct estimated model and differencing estimated model for input rate signal was thoroughly analyzed and compared for combining measurements of a sensor array to improve the accuracy of microelectromechanical system (MEMS) gyroscopes. The principles for noise reduction were presented and KF algorithms were designed to obtain the optimal rate signal estimates. The input rate signal in the direct estimated KF model was modeled with a random walk process and treated as the estimated system state. In the differencing estimated KF model, a differencing operation was established between outputs of the gyroscope array, and then the optimal estimation of input rate signal was achieved by compensating for the estimations of bias drifts for the component gyroscopes. Finally, dynamic simulations and experiments with a six-gyroscope array were implemented to compare the dynamic performance of the two KF models. The 1σ error of the gyroscopes was reduced from 1.4558°/s to 0.1203°/s by the direct estimated KF model in a constant rate test and to 0.5974°/s by the differencing estimated KF model. The estimated rate signal filtered by both models could reflect the amplitude variation of the input signal in the swing rate test and displayed a reduction factor of about three for the 1σ noise. Results illustrate that the performance of the direct estimated KF model is much higher than that of the differencing estimated KF model, with a constant input signal or lower dynamic variation. A similarity in the two KFs' performance is observed if the input signal has a high dynamic variation.

A Microgripper with a Post-Assembly Self-Locking Mechanism.

In this work, we report a new design for an electrostatically actuated microgripper with a post-assembly self-locking mechanism. The microgripper arms are driven by rotary comb actuators, enabling the microgripper to grip objects of any size from 0 to 100 µm. The post-assembly mechanism is driven by elastic deformation energy and static electricity to produce self-locking and releasing actions. The mechanism enables the microgripper arms to grip for long periods without continuously applying the external driving signal, which significantly reduces the effects and damage to the gripped objects caused by these external driving signals. The microgripper was fabricated using a Silicon-On-Insulator (SOI) wafer with a 30 µm structural layer. Test results show that this gripper achieves a displacement of 100 µm with a driving voltage of 33 V, and a metal wire with a diameter of about 1.6 mil is successfully gripped to demonstrate the feasibility of this post-assembly self-locking mechanism.

Signal processing of MEMS gyroscope arrays to improve accuracy using a 1st order Markov for rate signal modeling.

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.

An Integrated MEMS Gyroscope Array with Higher Accuracy Output.

In this paper, an integrated MEMS gyroscope array method composed of two levels of optimal filtering was designed to improve the accuracy of gyroscopes. In the firstlevel filtering, several identical gyroscopes were combined through Kalman filtering into a single effective device, whose performance could surpass that of any individual sensor. The key of the performance improving lies in the optimal estimation of the random noise sources such as rate random walk and angular random walk for compensating the measurement values. Especially, the cross correlation between the noises from different gyroscopes of the same type was used to establish the system noise covariance matrix and the measurement noise covariance matrix for Kalman filtering to improve the performance further. Secondly, an integrated Kalman filter with six states was designed to further improve the accuracy with the aid of external sensors such as magnetometers and accelerometers in attitude determination. Experiments showed that three gyroscopes with a bias drift of 35 degree per hour could be combined into a virtual gyroscope with a drift of 1.07 degree per hour through the first-level filter, and the bias drift was reduced to 0.53 degree per hour after the second-level filtering. It proved that the proposed integrated MEMS gyroscope array is capable of improving the accuracy of the MEMS gyroscopes, which provides the possibility of using these low cost MEMS sensors in high-accuracy application areas.

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

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°/h0.5 and bias drift of 224.2°/h for a single gyroscope were reduced to 0.33°/h0.5 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.