邱林茂 , 高文冀 , 李磊 , 等 . 导引头中MEMS陀螺漂移补偿算法研究 [J ] . 火控雷达技术 , 2013 , 42 ( 2 ): 10 - 14 .

QIU L M , GAO W J , LI L , et al. Study on algorithm for MEMS gyro drift compensation in seeker [J ] . Fire Control Radar Technology , 2013 , 42 ( 2 ): 10 - 14 . (in Chinese)

熊必凤 . 低成本MEMS陀螺仪随机漂移误差的建模及修正 [D ] . 重庆 : 西南大学 , 2017 .

XIONG B F . Research on the modeling and correction technology of random drift error of low cost MEMS gyroscope [D ] . Chongqing : Southwest University , 2017 . (in Chinese)

刘孝博 , 陈光武 , 王迪 , 等 . MEMS陀螺仪漂移和噪声的分析和补偿 [J ] . 传感技术学报 , 2018 , 31 ( 3 ): 368 - 373 .

LIU X B , CHEN G W , WANG D , et al. Analysis and compensation of drift and noise in MEMS gyroscope [J ] . Chinese Journal of Sensors and Actuators , 2018 , 31 ( 3 ): 368 - 373 . (in Chinese)

刘文超 , 郑小兵 , 王荣颖 , 等 . 基于角速度估计的MEMS陀螺随机误差动态滤波方法 [J ] . 电光与控制 , 2021 , 28 ( 5 ): 79 - 84 .

LIU W C , DENG X B , WANG R Y , et al. MEMS gyroscope random error dynamic filtering method based on angular velocity estimation [J ] . Electronics Optics & Control , 2021 , 28 ( 5 ): 79 - 84 . (in Chinese)

段志强 , 刘洁瑜 , 汪立新 , 等 . BPNN辅助KF的MEMS陀螺仪数据处理方法 [J ] . 压电与声光 , 2020 , 42 ( 2 ): 284 - 288 .

DUAN Z Q , LIU J Y , WANG L X , et al. Research on data processing method of MEMS gyroscope based on BPNN assisted Kalman filter [J ] . Piezoelectric & Acoustooptics , 2020 , 42 ( 2 ): 284 - 288 . (in Chinese)

程章 , 许江宁 , 许微 , 等 . 基于神经网络的MEMS陀螺标定与补偿 [J ] . 压电与声光 , 2018 , 40 ( 1 ): 111 - 114 .

CHENG Z , XU J N , XU W , et al. Calibration and compensation of MEMS gyroscope based on neural network [J ] . Piezoelectric & Acoustooptics , 2018 , 40 ( 1 ): 111 - 114 . (in Chinese)

BHATT D , AGGARWAL P , BHATTACHARYA P , et al. An enhanced MEMS error modeling approach based on nu-support vector regression [J ] . Sensors , 2012 , 12 ( 7 ): 9448 - 9466 . DOI: 10.3390/s120709448 http://doi.org/10.3390/s120709448 Micro Electro Mechanical System (MEMS)-based inertial sensors have made possible the development of a civilian land vehicle navigation system by offering a low-cost solution. However, the accurate modeling of the MEMS sensor errors is one of the most challenging tasks in the design of low-cost navigation systems. These sensors exhibit significant errors like biases, drift, noises; which are negligible for higher grade units. Different conventional techniques utilizing the Gauss Markov model and neural network method have been previously utilized to model the errors. However, Gauss Markov model works unsatisfactorily in the case of MEMS units due to the presence of high inherent sensor errors. On the other hand, modeling the random drift utilizing Neural Network (NN) is time consuming, thereby affecting its real-time implementation. We overcome these existing drawbacks by developing an enhanced Support Vector Machine (SVM) based error model. Unlike NN, SVMs do not suffer from local minimisation or over-fitting problems and delivers a reliable global solution. Experimental results proved that the proposed SVM approach reduced the noise standard deviation by 10-35% for gyroscopes and 61-76% for accelerometers. Further, positional error drifts under static conditions improved by 41% and 80% in comparison to NN and GM approaches.

DRAGOMIRETSKIY K , ZOSSO D . Variational mode decomposition [J ] . IEEE Transactions on Signal Processing , 2014 , 62 ( 3 ): 531 - 544 .

DING M K , SHI Z Y , DU B H , et al. A signal de-noising method for a MEMS gyroscope based on improved VMD-WTD [J ] . Measurement Science and Technology , 2021 , 32 : 095112 . DOI: 10.1088/1361-6501/abfe33 http://doi.org/10.1088/1361-6501/abfe33

刘宇 , 付乐乐 , 邹新海 , 等 . 基于RBF神经网络的MEMS惯性传感器误差补偿方法 [J ] . 重庆理工大学学报(自然科学) , 2021 , 35 ( 1 ): 197 - 202 .

LIU Y , FU L L , ZOU X H , et al. Error compensation method for MEMS inertial sensor based on RBF neural networks [J ] . Journal of Chongqing University of Technology(Natural Science) , 2021 , 35 ( 1 ): 197 - 202 . (in Chinese)

孙伟 , 段顺利 , 文剑 , 等 . 阈值去噪与RBF神经网络在MEMS陀螺仪误差补偿中的应用 [J ] . 传感技术学报 , 2017 , 30 ( 1 ): 115 - 119 .

SUN W , DUAN S L , WEN J , et al. Application of threshold denoising and RBF neural network in the error compensating of MEMS gyro [J ] . Chinese Journal of Sensors and Actuators , 2017 , 30 ( 1 ): 115 - 119 . (in Chinese)

郭宏伟 , 侯宏录 , 李光耀 . 基于Kalman滤波和神经网络的MEMS陀螺温度漂移补偿 [J ] . 自动化与仪表 , 2020 , 35 ( 1 ): 1 - 4 ,9.

GUO H W , HOU H L , LI G Y . Temperature drift compensation of MEMS gyroscope based on Kalman filter and neural network [J ] . Process Automation Instrumentation , 2020 , 35 ( 1 ): 1 - 4 ,9. (in Chinese)

禹忠 , 黄一超 , 郭畅 . 卡尔曼滤波结合神经网络在MEMS传感器上的应用 [J ] . 传感器与微系统 , 2021 , 40 ( 11 ): 154 - 156 ,160.

YU Z , HUANG Y C , GUO C . Application of Kalman filtering combines with neural network in Mems sensors [J ] . Transducer and Microsystem Technologies , 2021 , 40 ( 11 ): 154 - 156 ,160. (in Chinese)

ZHU C H , CAI S , YANG Y F , et al. A combined method for MEMS gyroscope error compensation using a long short-term memory network and Kalman filter in random vibration environments [J ] . Sensors , 2021 , 21 ( 4 ): 1181 . DOI: 10.3390/s21041181 http://doi.org/10.3390/s21041181 https://www.mdpi.com/1424-8220/21/4/1181 https://www.mdpi.com/1424-8220/21/4/1181 In applications such as carrier attitude control and mobile device navigation, a micro-electro-mechanical-system (MEMS) gyroscope will inevitably be affected by random vibration, which significantly affects the performance of the MEMS gyroscope. In order to solve the degradation of MEMS gyroscope performance in random vibration environments, in this paper, a combined method of a long short-term memory (LSTM) network and Kalman filter (KF) is proposed for error compensation, where Kalman filter parameters are iteratively optimized using the Kalman smoother and expectation-maximization (EM) algorithm. In order to verify the effectiveness of the proposed method, we performed a linear random vibration test to acquire MEMS gyroscope data. Subsequently, an analysis of the effects of input data step size and network topology on gyroscope error compensation performance is presented. Furthermore, the autoregressive moving average-Kalman filter (ARMA-KF) model, which is commonly used in gyroscope error compensation, was also combined with the LSTM network as a comparison method. The results show that, for the x-axis data, the proposed combined method reduces the standard deviation (STD) by 51.58% and 31.92% compared to the bidirectional LSTM (BiLSTM) network, and EM-KF method, respectively. For the z-axis data, the proposed combined method reduces the standard deviation by 29.19% and 12.75% compared to the BiLSTM network and EM-KF method, respectively. Furthermore, for x-axis data and z-axis data, the proposed combined method reduces the standard deviation by 46.54% and 22.30% compared to the BiLSTM-ARMA-KF method, respectively, and the output is smoother, proving the effectiveness of the proposed method.

孙俊 . 量子行为粒子群优化算法研究 [D ] . 无锡 : 江南大学 , 2009 .

SUN J . Particle swarm optimization with particles having quantum behavior [D ] . Wuxi : Jiangnan University , 2009 . (in Chinese)

陈一鸣 . 基于卡尔曼滤波的陀螺仪随机误差分析 [J ] . 电子测量技术 , 2020 , 43 ( 17 ): 97 - 100 .

CHEN Y M . Analysis of gyro random error based on Kalman filter [J ] . Electronic Measurement Technology , 2020 , 43 ( 17 ): 97 - 100 . (in Chinese)

周克良 , 王威 , 郭春燕 . 基于NAR-KF的心音信号仿真研究 [J ] . 现代电子技术 , 2021 , 44 ( 21 ): 35 - 38 .

ZHOU K L , WANG W , GUO C Y . Research on heart sound signal denoising based on NAR and Kalman filtering [J ] . Modern Electronic Technology , 2021 , 44 ( 21 ): 35 - 38 . (in Chinese)

张敏 , 李凯 , 韩焱 , 等 . 基于卡尔曼滤波的陀螺仪降噪处理 [J ] . 传感技术学报 , 2018 , 31 ( 2 ): 223 - 227 .

ZHANG M , LI K , HAN Y , et al. The noise reduction of gyroscope based on Kalman filter [J ] . Chinese Journal of Sensors and Actuators , 2018 , 31 ( 2 ): 223 - 227 . (in Chinese)

谷鹏 , 王大龙 , 张世仓 . 基于粒子群优化的扩展卡尔曼滤波方法研究 [J ] . 工业控制计算机 , 2019 , 32 ( 11 ): 80 - 82 .

GU P , WANG D L , ZHANG S C . Extended Kalman filter method based on particle swarm optimization [J ] . Industrial Control Computer , 2019 , 32 ( 11 ): 80 - 82 . (in Chinese)

杨辉 , 杨川 , 姜湖海 , 等 . 基于改进极限学习机的MEMS陀螺随机误差补偿方法研究 [J ] . 传感技术学报 , 2021 , 34 ( 2 ): 244 - 248 .

YANG H , YANG C , JIANG H H , et al. Research on compensation method of MEMS gyroscope random error based on improved extreme learning machine [J ] . Chinese Journal of Sensors and Actuators , 2021 , 34 ( 2 ): 244 - 248 . (in Chinese)

WANG X L , CAO H L , JIAO Y Z , et al. Research on novel denoising method of variational mode decomposition in MEMS gyroscope [J ] . Measurement Science Review , 2021 , 21 ( 1 ): 19 - 24 . (in Chinese) DOI: 10.2478/msr-2021-0003 http://doi.org/10.2478/msr-2021-0003 https://www.sciendo.com/article/10.2478/msr-2021-0003 https://www.sciendo.com/article/10.2478/msr-2021-0003 The noise signal in the gyroscope is divided into four levels: sampling frequency level, device bandwidth frequency level, resonant frequency level, and carrier frequency level. In this paper, the signal in the dual-mass MEMS gyroscope is analyzed. Based on the variational mode decomposition (VMD) algorithm, a novel dual-mass MEMS gyroscope noise reduction method is proposed. The VMD method with different four-level center frequencies is used to process the original output signal of the MEMS gyroscope, and the results are analyzed by the Allan analysis of variance, which shows that the ARW of the gyroscope is increased from 1.998*10−1°/√h to 1.552*10−4°/√h, BS increased from 2.5261°/h to 0.0093°/h.

吴保锋 , 夏林元 , 吴东金 , 等 . MEMS陀螺仪随机误差分析与小波阈值去噪研究 [J ] . 电子设计工程 , 2020 , 28 ( 15 ): 1 - 5 .

WU B F , XIA L Y , ZHU H Y , et al. Random error analysis and wavelet threshold denoising of MEMS gyroscope [J ] . Electronic Design Engineering , 2020 , 28 ( 15 ): 1 - 5 . (in Chinese)

李世银 , 张楠 , 武中文 , 等 . 基于小波分析的MEMS加速度计去噪优化算法 [J ] . 传感技术学报 , 2018 , 31 ( 5 ): 705 - 709 .

LI S Y , ZHANG N , WU Z W , et al. An optimized MEMS accelerometer de-noising algorithm based on wavelet analysis [J ] . Chinese Journal of Sensors and Actuators , 2018 , 31 ( 5 ): 705 - 709 . (in Chinese)