小波分析在MEMS陀螺信号降噪中的应用研究
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摘要
陀螺漂移是惯性导航系统误差的主要误差源,因此有效地补偿陀螺漂移误差是保证惯性导航系统精度的关键。MEMS陀螺的随机漂移误差往往表现为非平稳性、弱线性、慢时变的特性,同时受外部环境等不确定性因素影响,在惯性导航系统中不能用简单方法加以补偿。小波分析以其优良的多分辨率特性特别适合非平稳信号的处理,本文从MEMS陀螺信号的特性出发,研究基于小波分析的去噪方法应用于MEMS陀螺信号降噪。主要对小波变换模极大值降噪方法、基于小波变换尺度间相关性的去噪方法以及小波阈值去噪方法进行了研究,对实际应用过程中的效果进行了对比分析。论文的主要内容包括:
1.分析和总结了小波变换方法产生的脉络、背景知识及其在MEMS陀螺信号降噪的应用情况;阐述了连续小波变换、离散小波变换、二进小波变换的基础理论以及小波多分辨率分析的相关理论;并着重介绍了常用的基于小波变换的模极大值降噪方法、尺度间相关性的去噪方法以及小波阈值去噪方法的原理、算法的实现以及各方法的特点。
2.以MATLAB生成的MEMS陀螺仿真信号为对象,分别运用基于小波分析的模极大值降噪方法、尺度间相关性降噪法和小波阈值去噪法对其进行降噪处理,并得出以上三种方法的最优小波基和最优降噪尺度。其中,采用Birge-Massart阈值对陀螺仿真信号进行12尺度降噪取得的效果最佳,几乎完全抑制了噪声信号,保留了94.91%的信号能量,使信号的标准差由1.3270(°/s)降低到0.0477(°/s),改善了信号的稳定性。
3.基于MEMS陀螺的测试系统,进行了硅微陀螺标定实验,获取了硅微陀螺静态、匀速转动和变速转动的角速度数据。依据MALAB仿真信号降噪的参数选取结论,分别对实测数据进行基于小波分析的降噪处理。通过对三种方法降噪结果的分析,发现采用Birge-Massart阈值去噪法进行降噪效果最好,能够几乎完全抑制噪声并保留较高的能量比例。同时,Birge-Massart阈值去噪法对陀螺静态信号的标准差由0.1987(°/s)降低到0.0069(°/s),对匀速转动信号的标准差由0.2169(°/s)降低到0.0138(°/s),对变速转动信号的降噪信号幅值没有造成较大的衰减,能够几乎完全抑制噪声。
本文通过对MEMS陀螺仿真信号以及实测数据的降噪处理,表明运用基于小波分析的降噪方法,在提高MEMS陀螺性能方面,有较好的应用价值。
The drift error is the main error source in Gyro inertial navigation system, and compensating gyro drift error effectively is the key point to ensure the accuracy of inertial navigation system. MEMS gyroscope drift error is random non-stationary, weak linear and slow time-varying, which is difficult to be compensated in the inertial navigation system with simple methods for the influence of uncertain external environment factors. Wavelet analysis is particularly suitable for non-stationary signal processing for its multi resolution attribute. In this paper, wavelet based analysis is applied to eliminate the MEMS gyro signal noise base on attributes of MEMS gyro signal. The wavelet transform modulus maxima denoising method, inter scale correlations of wavelet transform denoising method and wavelet threshold method are analyzed, and compared the effects of the three methods in practical applications. The main contents include:
Firstly, background theories and application of wavelet thansform methods for MEMS gyro signal denoising are analyzed. The basic theories of continuous wavelet transform, discrete wavelet thansform, dyadic wavelet transform and wavelet multiresolution analyses are expounded. Especially, the principles, algorithms and characteristics of wavelet transform modulus maxima denoising method, inter scale correlations of wavelet transform denoising method and wavelet threshold method are emphatically introduced.
Secondly, based on the MEMS gyro simulation signals which are generated by MATLAB, wavelet transform modulus maxima denoising method, inter scale correlations of wavelet transform denoising method and wavelet threshold method are applied to eliminate signal noises. Optimal wavelet basis and scale are concluded by the three methods, and Birge-Massart threshold method with scale 12 is proved the best for denoising, which eliminats most of the signal noise, keeps 94.91% signal energy, reduces standard deviation from 1.3270(°/s) to 0.0477(°/s) and promotes the signal stability.
Thirdly, MEMS gyro experiments are carried based on test system, and angular velocity data of statistic, uniform rotation, and variable rotation are sampled. With the parameters that concluded in MATLAB simulations above, the sampled data is denoised with wavelet analysis methods. The results indicate that Birge-Massart threshold method shows the best denoising effect, which almost eliminats all the noise and keeps the highest energy ratio. At the same time, Birge-Massart threshold method reduces standard deviation from 1.3270(°/s) to 0.0477(°/s) for the gyro static signal; reduces standard deviation from 0.2169(°/s) to 0.0138(°/s) for the gyro uniform rotation signal; and almost eliminats all the noise for the ununiform rotation signal.
In this paper, simulation signals generated by MATLAB and experimental signals sampled by MEMS gyro test system are denoised with different wavelet analysis methods, and it is proved that wavelet analysis based denoising methods have meaningful application value for promoting the performance of MEMS gyro.
1.分析和总结了小波变换方法产生的脉络、背景知识及其在MEMS陀螺信号降噪的应用情况;阐述了连续小波变换、离散小波变换、二进小波变换的基础理论以及小波多分辨率分析的相关理论;并着重介绍了常用的基于小波变换的模极大值降噪方法、尺度间相关性的去噪方法以及小波阈值去噪方法的原理、算法的实现以及各方法的特点。
2.以MATLAB生成的MEMS陀螺仿真信号为对象,分别运用基于小波分析的模极大值降噪方法、尺度间相关性降噪法和小波阈值去噪法对其进行降噪处理,并得出以上三种方法的最优小波基和最优降噪尺度。其中,采用Birge-Massart阈值对陀螺仿真信号进行12尺度降噪取得的效果最佳,几乎完全抑制了噪声信号,保留了94.91%的信号能量,使信号的标准差由1.3270(°/s)降低到0.0477(°/s),改善了信号的稳定性。
3.基于MEMS陀螺的测试系统,进行了硅微陀螺标定实验,获取了硅微陀螺静态、匀速转动和变速转动的角速度数据。依据MALAB仿真信号降噪的参数选取结论,分别对实测数据进行基于小波分析的降噪处理。通过对三种方法降噪结果的分析,发现采用Birge-Massart阈值去噪法进行降噪效果最好,能够几乎完全抑制噪声并保留较高的能量比例。同时,Birge-Massart阈值去噪法对陀螺静态信号的标准差由0.1987(°/s)降低到0.0069(°/s),对匀速转动信号的标准差由0.2169(°/s)降低到0.0138(°/s),对变速转动信号的降噪信号幅值没有造成较大的衰减,能够几乎完全抑制噪声。
本文通过对MEMS陀螺仿真信号以及实测数据的降噪处理,表明运用基于小波分析的降噪方法,在提高MEMS陀螺性能方面,有较好的应用价值。
The drift error is the main error source in Gyro inertial navigation system, and compensating gyro drift error effectively is the key point to ensure the accuracy of inertial navigation system. MEMS gyroscope drift error is random non-stationary, weak linear and slow time-varying, which is difficult to be compensated in the inertial navigation system with simple methods for the influence of uncertain external environment factors. Wavelet analysis is particularly suitable for non-stationary signal processing for its multi resolution attribute. In this paper, wavelet based analysis is applied to eliminate the MEMS gyro signal noise base on attributes of MEMS gyro signal. The wavelet transform modulus maxima denoising method, inter scale correlations of wavelet transform denoising method and wavelet threshold method are analyzed, and compared the effects of the three methods in practical applications. The main contents include:
Firstly, background theories and application of wavelet thansform methods for MEMS gyro signal denoising are analyzed. The basic theories of continuous wavelet transform, discrete wavelet thansform, dyadic wavelet transform and wavelet multiresolution analyses are expounded. Especially, the principles, algorithms and characteristics of wavelet transform modulus maxima denoising method, inter scale correlations of wavelet transform denoising method and wavelet threshold method are emphatically introduced.
Secondly, based on the MEMS gyro simulation signals which are generated by MATLAB, wavelet transform modulus maxima denoising method, inter scale correlations of wavelet transform denoising method and wavelet threshold method are applied to eliminate signal noises. Optimal wavelet basis and scale are concluded by the three methods, and Birge-Massart threshold method with scale 12 is proved the best for denoising, which eliminats most of the signal noise, keeps 94.91% signal energy, reduces standard deviation from 1.3270(°/s) to 0.0477(°/s) and promotes the signal stability.
Thirdly, MEMS gyro experiments are carried based on test system, and angular velocity data of statistic, uniform rotation, and variable rotation are sampled. With the parameters that concluded in MATLAB simulations above, the sampled data is denoised with wavelet analysis methods. The results indicate that Birge-Massart threshold method shows the best denoising effect, which almost eliminats all the noise and keeps the highest energy ratio. At the same time, Birge-Massart threshold method reduces standard deviation from 1.3270(°/s) to 0.0477(°/s) for the gyro static signal; reduces standard deviation from 0.2169(°/s) to 0.0138(°/s) for the gyro uniform rotation signal; and almost eliminats all the noise for the ununiform rotation signal.
In this paper, simulation signals generated by MATLAB and experimental signals sampled by MEMS gyro test system are denoised with different wavelet analysis methods, and it is proved that wavelet analysis based denoising methods have meaningful application value for promoting the performance of MEMS gyro.
引文
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[3] A.Abbaspour-Tamijani,L.Dussopt,and G.M.Rebeiz.Miniature and tunable filters using MEMS capacitors[J] . IEEE Transactions Microwave Theory and Techniques,2003,51(7):1878~1885.
[4] K.Van Caekenberghe.RF MEMS on the radar[J].IEEE Microwave Magazine,2009,10(6):99~116.
[5] A.Q.Liu.Photonic MEMS tunable laser sources[J].Journal of China Universities of Posts and Telecommunications,2009,16(3):1~3.
[6] C.G.Hindrichsen,R.Lou-Mller,K.Hansen,E.V.Thomsen.Advantages of PZT thick film for MEMS sensors[J].Sensors and Actuators A:Physical,2010,163(1):9~14.
[7] C.L.Cobb,A.M.Agogino.Case-based reasoning for evolutionary MEMS design[J].Journal of Computing and Information Science in Engineering,2010,10(3):31005.
[8]李荣冰,刘建业,曾庆化,华冰.基于MEMS技术的微型惯性导航系统的发展现状[J].中国惯性技术学报,2004,12(6):88~94.
[9]程建华,赵琳,黄卫权,周建明,郝燕玲.基于惯导系统模型的自对准陀螺测漂方法研究[J].哈尔滨工程大学学报,2006,27(1):66~74.
[10]张海鹏,房建成.石英MEMS陀螺漂移周期性误差补偿研究[J].仪器仪表学报,2008,29(6):1225~1230.
[11]汤巍,李士心.关于陀螺信号处理中小波基选取的研究[J].中国惯性技术学报,2002,10(5):27~29.
[12]刘鲁源,李士心.双正交小波在陀螺信号去噪中的应用[J].信号处理,2002,18(5):386~389.
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