-
摘要:
为提高微机电系统(MEMS)陀螺的精度,提出一种基于松弛Chebyshev中心(RCC)的最优定界椭球(OBE)算法,并用于陀螺阵列信号的融合。以单个陀螺误差输出模型为基础,建立了阵列系统的机动融合模型;由于噪声统计特性的不确定会导致传统融合方法精度下降,引入仅要求噪声未知但有界的集员估计理论,运用OBE算法实现角速率信号的稳健估计;在OBE算法中,往往采用椭球几何中心作为真实值的点估计,但该中心并没有理论上的最优特性,而可行集的Chebyshev中心具有很多优良特性,同时,考虑到准确的Chebyshev中心求解十分困难,转而求解可行集的RCC,作为速率信号的点估计,设计了以RCC作为输出的OBE更新过程和新的参数优化准则。采用6个陀螺构成的阵列进行了验证试验,结果表明基于该算法的阵列估计融合方法在获得角速率保证边界的基础上,可以进一步提高MEMS陀螺精度。
-
关键词:
- 微机电系统(MEMS)陀螺 /
- 陀螺阵列 /
- 最优定界椭球(OBE)算法 /
- 数据融合 /
- Chebyshev中心
Abstract:In order to improve the accuracy of micro-electro-mechanical system (MEMS) gyro, an optimal bounding ellipsoid (OBE) algorithm based on relaxed Chebyshev center (RCC) is proposed and used to fuse gyro array signals. On the basis of the error model of single gyro, the maneuvering fusion model of the array system is established. Because of the uncertainty of the noise statistics, the accuracy of the traditional fusion method is reduced. The set-membership estimation theory with unknown but bounded disturbances is introduced and the OBE algorithm is used to achieve the robust estimation of the angular rate. In the OBE algorithm, the ellipsoid geometry center is often used as the point estimate of the true value, but it is not optimal theoretically. The Chebyshev center of the feasible set has many excellent features. Meanwhile, considering that it is very difficult to solve the exact Chebyshev center, the relaxed Chebyshev center is used as a substitute for the point estimate of the true angular rate. Then an OBE update process with RCC as output is designed and a novel parameter optimization criterion is proposed. The verification experiment is performed by using a gyro array composed by six gyroscopes. The experimental results show that the estimation fusion method based on the proposed algorithm can obtain the angle rate guaranteed boundary and further improve the MEMS gyroscope accuracy.
-
表 1 A=10°,T=2 s条件下处理结果
Table 1. Results of signal processed with A=10° and T=2 s
指标 单个陀螺 Kalman滤波 OBE RCC-OBE SNR/dB 31.903 4 42.008 7 40.953 4 43.690 4 RMSE/((°)·s-1) 0.564 2 0.176 3 0.199 1 0.145 3 表 2 A=10°,T=4 s条件下处理结果
Table 2. Results of signal processed with A=10° and T=4 s
指标 单个陀螺 Kalman滤波 OBE RCC-OBE SNR/dB 33.246 1 43.224 3 42.655 7 45.274 6 RMSE/((°)·s-1) 0.532 8 0.135 4 0.150 1 0.113 2 表 3 A=20°,T=2 s条件下处理结果
Table 3. Results of signal processed with A=20° and T=2 s
指标 单个陀螺 Kalman滤波 OBE RCC-OBE SNR/dB 27.215 2 39.854 2 39.002 5 43.011 2 RMSE/((°)·s-1) 0.602 5 0.195 2 0.213 4 0.151 6 -
[1] KIM D, M'CLOSKEY R T.Spectral analysis of vibratory gyro noise[J].IEEE Sensors Journal, 2013, 13(11):4361-4374. doi: 10.1109/JSEN.2013.2269797 [2] 王鼎杰, 王广才, 吴杰.微惯性/卫星组合导航高精度事后基准确定方法[J].中国惯性技术学报, 2017, 25(1):97-102. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=zggxjsxb201701020WANG D J, WANG G C, WU J.Fixed-interval smoothing post-processing algorithm for low-cost MEMS-based integrated navigation system[J].Journal of Chinese Intertial Technology, 2017, 25(1):97-102(in Chinese). http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=zggxjsxb201701020 [3] 郝燕玲, 刘博, 史宏洋.新型反相位驱动双解耦微机械陀螺设计[J].哈尔滨工业大学学报, 2014, 46(9):105-110. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=hebgydxxb201409019HAO Y L, LIU B, SHI H Y.The novel design of anti-phase double-decoupled micromachined gyroscope[J].Journal of Harbin Institute of Technology, 2014, 46(9):105-110(in Chinese). http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=hebgydxxb201409019 [4] BAYARD D S, PLOEN S R.High accuracy inertial sensors from inexpensive components: US patent, 6882964[P].2005-04-19. [5] CHANG H L, XUE L, QIN W, et al.An integrated MEMS gyroscope array with higher accuracy output[J].Sensors, 2008, 8(4):2886-2899. doi: 10.3390/s8042886 [6] 吉训生, 王寿荣.硅微陀螺阵列信号处理技术研究[J].宇航学报, 2009, 30(1):235-239. doi: 10.3873/j.issn.1000-1328.2009.00.041JI X S, WANG S R.Research on signal procession of silicon micro-gyroscope array[J].Journal of Astronautics, 2009, 30(1):235-239(in Chinese). doi: 10.3873/j.issn.1000-1328.2009.00.041 [7] XUE L, JIANG C Y, CHANG H L, et al.A novel Kalman filter for combining outputs of MEMS gyroscope array[J].Measurement, 2012, 12(1):745-754. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=fb35252378dc9299af167bc33781ada1 [8] XUE L, JIANG C Y, WANG L X, et al.Noise reduction of MEMS gyroscope based on direct modeling for an angular rate signal[J].Micromachines, 2015, 6(2):266-280. doi: 10.3390/mi6020266 [9] LIU J Y, SHEN Q, QIN W W.Signal processing technique for combining numerous MEMS gyroscopes based on dynamic conditional correlation[J].Micromachines, 2015, 6(6):684-698. doi: 10.3390/mi6060684 [10] VACCARO R J, ZAKI A S.Reduced-drift virtual gyro from an array of low-cost gyros[J].Sensors, 2017, 17(2):352. doi: 10.3390/s17020352 [11] LE B F, SLIWKA J, JAULIN L, et al.Set-membership state estimation with fleeting data[J].Automatica, 2012, 48(2):381-387. doi: 10.1016/j.automatica.2011.11.004 [12] 周波, 樊帅权, 戴先中.基于集员滤波的移动机器人动态环境建模[J].东南大学学报(自然科学版), 2011, 41(1):107-112. doi: 10.3969/j.issn.1001-0505.2011.01.021ZHOU B, FAN S Q, DAI X Z.Dynamic environment modeling of mobile robots based on set membership filter[J].Journal of Southeast University(Natural Science Edition), 2011, 41(1):107-112(in Chinese). doi: 10.3969/j.issn.1001-0505.2011.01.021 [13] LIU Y, ZHAO Y, WU F.Ellipsoidal state-bounding-based set-membership estimation for linear system with unknown-but-bounded disturbances[J].IET Control Theory and Applications, 2016, 10(4):431-442. doi: 10.1049/iet-cta.2015.0654 [14] 周波, 钱堃, 马旭东, 等.一种新的基于保证定界椭球算法的非线性集员滤波器[J].自动化学报, 2013, 39(2):150-158. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=QK201300112539ZHOU B, QIAN K, MA X D, et al.A new nonlinear set membership filter based on guaranteed bounding ellipsoid algorithm[J].Acta Automatica Sinica, 2013, 39(2):150-158(in Chinese). http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=QK201300112539 [15] 刘玉双, 赵剡, 吴发林.基于外定界椭球集员估计的纯方位目标跟踪[J].北京航空航天大学学报, 2017, 43(3):497-505. http://bhxb.buaa.edu.cn/CN/abstract/abstract14117.shtmlLIU Y S, ZHAO Y, WU F L.Bearing-only target tracking based on ellipsoidal outer-bounding set-membership estimation[J].Journal of Beijing University of Aeronautics and Astronautics, 2017, 43(3):497-505(in Chinese). http://bhxb.buaa.edu.cn/CN/abstract/abstract14117.shtml [16] ELDAR C Y, BECK A, TEBOULLE M.A minimax Chebyshev estimator for bounded error estimation[J].IEEE Transactions on Signal Processing, 2008, 56(4):1388-1397. doi: 10.1109/TSP.2007.908945