基于小波变换的无驱动结构微机械陀螺信号自旋频率的提取

Spin Frequency Extraction of Non-Driven Micro- Machined Gyroscope Signal via Wavelet Transform

针对一种新型陀螺,它能敏感旋转载体的俯仰、偏航和滚转角速度,敏感信号是一种调幅波信号,载波频率是自旋频率,包络是横向角速度。实际应用中,需要精确提取自旋频率。基于此,提出了一种提取载波频率的新的方法——小波变换构造解析函数法,对自旋频率解算算法进行了理论推导,并通过MATLAB软件对噪声比为30 dB的模拟陀螺调幅波信号进行了自旋频率的提取和误差分析,其中Hilbert变换相对误差为0.033 6,小波变换相对误差为0.017 8。对三轴精密转台实时测试的横向角速度为180°/s的陀螺信号进行了自旋频率的提取和误差分析,其中Hilbert变换相对误差为0.035 9,均方差MSE为7.915 9;小波变换相对误差为0.001 8,均方差MSE为0.293 7。小波变换较Hilbert变换求解自旋频率精度提高二十倍,降噪性能和频率稳定性更好。

As a new type of gyroscope,it can sense pitch,yaw and roll angular velocity of the rotating aircraft. The sensitive signal is an amplitude modulated wave signal,where the carrier frequency is the spin frequency and the envelope is the lateral angular velocity. Considering that the spin frequency is required to be precisely extracted in practical applications,a new method that using wavelet transform to construct analytic functions is proposed and the algorithm is theoretically derived. Besides, the spin frequency of analog gyroscope amplitude modulation wave signal,whose noise ratio is 30 dB,is extracted and the error is further analyzed through MATLAB,where the relative error is 0. 033 6 for Hilbert transform and 0. 017 8 for wavelet transform. Furthermore, the spin frequency of gyroscope signal tested in real-time by three-axis precision turntable is extracted and the error is further analyzed, where the lateral angular velocity is 180°/s. For Hilbert transform,the relative error is 0. 035 9 and the MSE is 7. 915 9,while for wavelet transform,the relative error is 0. 001 8 and the MSE is 0. 293 7. The accuracy of spin frequency calculated by Wavelet transform is twenty times higher than the Hilbert transform, and the anti-noise performance and frequency stability is better.