**6. Gyroscope denoising simulation and analysis**

In this section, several control experiments are taken on gyroscope signal denoising using wavelet methods. The experiment uses the real flight data recorded by the flight control system of ServoHeli-40. The flight data is recorded at the 100Hz rate, and each point represents 10ms. It is sufficient to describe the motion of ServoHeli-40 RUAV both in time domain and in frequency domain.

In this simulation experiment, the length of the data is 14,950 points. And it means the data continued about 2.5 minutes. During this period of time, the RUAV did the following actions: standing still, engine ignition, speed idle, hovering , and trajectory tracking. In these flying modes, the data of gyroscope have different amplitude characters. This reflects the vibration differences in different flying modes. The original signal of ServoHeli-40's Y axis gyroscope is shown in the figure 12.

Through the above analysis, the modulus maximum method and translation invariant method have large calculation amounts. And this will affect the real-time calculation of integrated navigation system. So considering the speed of calculation and the ease of

The step of thresholding denoising method is as follows (Song et al., 2009; Su & Zhou, 2009): 1. Selecting the Wavelet function. Then the signal with noise , 0,1,..., 1 *<sup>i</sup> yi N* is discrete using wavelet transformation. A group of wavelet transform coefficients *<sup>j</sup>*,*<sup>k</sup> d* is got. The

2. Thresholding the wavelet transforms coefficients *<sup>j</sup>*,*<sup>k</sup> d* . The hard threshold, soft threshold or other threshold method can be used to deal with the coefficients. After the

, ,

 

*d d*

*j k j k j*

, , ,

*dd d*

 

3. Wavelet reconstruction. Using the inverse of discrete wavelet transform formulas, we

In this section, several control experiments are taken on gyroscope signal denoising using wavelet methods. The experiment uses the real flight data recorded by the flight control system of ServoHeli-40. The flight data is recorded at the 100Hz rate, and each point represents 10ms. It is sufficient to describe the motion of ServoHeli-40 RUAV both in time

In this simulation experiment, the length of the data is 14,950 points. And it means the data continued about 2.5 minutes. During this period of time, the RUAV did the following actions: standing still, engine ignition, speed idle, hovering , and trajectory tracking. In these flying modes, the data of gyroscope have different amplitude characters. This reflects the vibration differences in different flying modes. The original signal of ServoHeli-40's Y axis

*j k j k j j k j*

,

*d*

*j k j*

,

*d*

*j k j*

*<sup>j</sup> <sup>k</sup> d* is got.

(11)

(12)

implementation, thresholding denoising method is used in our navigation system.

**5.3 Thresholding denoising method** 

subscript *j* is the wavelet scale.

computation, a new wavelet transforms coefficients , <sup>ˆ</sup>

,

*d*

0,

*j k*

, <sup>ˆ</sup> 0,

sgn( )( ), <sup>ˆ</sup>

The hard threshold estimation is defined as follows:

The soft threshold estimation is defined as follows:

,

*d*

*<sup>j</sup>* is the threshold constant.

can get the de-noised signal ˆ*<sup>i</sup> y* .

domain and in frequency domain.

gyroscope is shown in the figure 12.

Where

*j k*

**6. Gyroscope denoising simulation and analysis** 

Fig. 12. The original signal of ServoHeli-40's Y axis gyroscope

In order to find a appropriate wavelet functions and decomposition levels, the simulation compared the thresholding denoising method using harr, db2, db4, db6, sym2, sym4, coif2, bior1.5 and bior5.5 wavelet functions. The decomposition levels are respectively 2, 5 and 8. The standard deviation of de-noised signal's residuals is calculated to compare the wavelet denoising results. The results are shown in Table 3. And the standard deviation of the original data is 0.06606.


Table 3. Standard deviation of de-noised signal's residuals

In Table 3, when decomposition level increases to more than 5 layers, improvement in denoised signal's residuals is unobvious. When the de-noised signal's residuals approach to 0.06606, the de-noised signal is close to straight line. And the computation cost is increased as layers increasing. So decomposition level of 5 is a good choice.

Application of Wavelets Transform in Rotorcraft UAV's Integrated Navigation System 631

The periodogram power spectral density estimate of original gyroscope signal is shown in Figure 14. The normalized frequency is 50Hz in this diagram. At 0.87(about 37Hz), the signal has a gain of -10db. In ServoHeli-40 RUAV system, there is a 16.7-45Hz vibration band. This vibration is caused by the rotation of main rotor, engine and tail rotor. 37Hz

For the characters of the control system, actuator system, and airframe of helicopter, the motion response of ServoHeli-40 is no more than 3Hz. The vibration frequency larger than 3Hz is out of the control of flight control system. Using the denoising result of db6 wavelet function, the spectrum energy density is analyzed. The periodogram power spectral density estimate of de-noised signal is shown in Figure 15. In this diagram, the noise signal more than 2.5Hz are eliminated by the algorithm. The wavelet filter can just remove high frequency noise. The denoising results reflected the actual movement of the aircraft. This

Periodogram Power Spectral Density Estimate

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Normalized Frequency ( rad/sample)

In this chapter, wavelet-based algorithm is applied to fault diagnosis and gyroscope noise reduction. Its advantage is that it does not require a prior model of a sensor. The proposed wavelet-based algorithm for fault detection of the RUAV sensor system gives us a multiscale analysis approach to identify the feature of flight data failures, which are not readily identified by traditional approaches. The results presented in this chapter have shown that

Fig. 15. The periodogram power spectral density estimate of denoised signal using db6

signal is in this noise band, and it is need to be eliminated.

method is suitable for denoising the noise of gyroscope.


wavelet function

**7. Conclusion** 




Power/frequency (dB/rad/sample)



0

Fig. 13. Contrast of denoised signal and original signal

According to the simulation results, db4, db6 and bior5.5 may be good choice for wavelet functions, because the curve of these de-noised signal are smoother than the others. But bior5.5 have lager computation cost, it is not suitable for real time computation. In Figure 13, the de-noised signals of db4, db6 are compared with the original signal. The denoising result, got from db6 wavelet function, is smoother than the result of db4. And the de-noised signal of db6 is closer to the real angular moment of RUAV than the original signal.

Fig. 14. The periodogram power spectral density estimate of original signal

The periodogram power spectral density estimate of original gyroscope signal is shown in Figure 14. The normalized frequency is 50Hz in this diagram. At 0.87(about 37Hz), the signal has a gain of -10db. In ServoHeli-40 RUAV system, there is a 16.7-45Hz vibration band. This vibration is caused by the rotation of main rotor, engine and tail rotor. 37Hz signal is in this noise band, and it is need to be eliminated.

For the characters of the control system, actuator system, and airframe of helicopter, the motion response of ServoHeli-40 is no more than 3Hz. The vibration frequency larger than 3Hz is out of the control of flight control system. Using the denoising result of db6 wavelet function, the spectrum energy density is analyzed. The periodogram power spectral density estimate of de-noised signal is shown in Figure 15. In this diagram, the noise signal more than 2.5Hz are eliminated by the algorithm. The wavelet filter can just remove high frequency noise. The denoising results reflected the actual movement of the aircraft. This method is suitable for denoising the noise of gyroscope.

Fig. 15. The periodogram power spectral density estimate of denoised signal using db6 wavelet function
