Rayleigh Lidar Signal Denoising Method Combined with WT, EEMD and LOWESS to Improve Retrieval Accuracy
<p>Schematic diagram of the Rayleigh lidar system.</p> "> Figure 2
<p>The ideal echo signals and the noisy signals in the case of integration time of 1200 s.</p> "> Figure 3
<p>Flowchart of the proposed WT-EEMD-LOWESS algorithm.</p> "> Figure 4
<p>The absolute error of (<b>a</b>) density and (<b>b</b>) temperature retrieval with the WT method.</p> "> Figure 5
<p>The <math display="inline"><semantics> <mrow> <mi>S</mi> <mi>N</mi> <msub> <mi>R</mi> <mi>m</mi> </msub> </mrow> </semantics></math> changes with height.</p> "> Figure 6
<p>Denoising performance of WT-EEMD-LOWESS algorithm.</p> "> Figure 7
<p>The variation of (<b>a</b>) density and (<b>b</b>) temperature retrievals with WT-EEMD-LOWESS algorithm.</p> "> Figure 8
<p>The absolute error of (<b>a</b>) density and (<b>b</b>) temperature retrievals with the WT-EEMD-LOWESS method.</p> "> Figure 9
<p>The variation of the maximum detection range with the integration time under the condition that (<b>a</b>) the error of density retrieval was less than 5% and (<b>b</b>) the error of temperature retrieval was less than 10 K.</p> "> Figure 10
<p>The noisy echo signal and the signal after denoising of ground-based lidar.</p> "> Figure 11
<p>The variation of (<b>a</b>) density and (<b>b</b>) temperature retrievals with WT-EEMD-LOWESS algorithm of ground-based lidar.</p> ">
Abstract
:1. Introduction
2. Rayleigh Lidar Simulation System
3. Methodology Descriptions
3.1. Brief Description of the WT Algorithm
3.2. Basic Theory of EEMD
- 1.
- Identifying the local extrema of .
- 2.
- Using the cubic spline interpolation function to form the upper envelope and the lower envelope .
- 3.
- Calculating the mean value of the upper and lower envelopes.
- 4.
- Denoting the difference in value between and as . If satisfies conditions for IMFs, then is defined as the first IMF. If not, is represented as . Repeating the steps 1 to 3 K times until meets IMF conditions and will be the first IMF of the signal.
- 5.
- Separating the first IMF from . The residue item can be computed with the following equation:
- 1.
- Adding white noise, which follows a normal distribution with mean 0 and standard deviation , N times to the original signal .Then, the new data series can be computed as follows:
- 2.
- Decomposing the signal added with Gaussian white noise by EMD to obtain the ith set of decomposition results, which includes IMF components (j = 1, 2, …, m) and a residual .
- 3.
- Repeating the above steps n times, the overall average values and are used as the results of the jth IMF component and the residual decomposed by EEMD, respectively.
3.3. Principle of DFA
- 1.
- Integrating the time series of the mean detached signal and the cumulative series can be computed as follows:
- 2.
- The integrated series was then divided into equal and non-overlapping windows of length n. For each window, the local linear trend is calculated by a polynomial fitting of order l. The root mean square fluctuation is given by the equation
- 3.
- The scaling exponent is calculated as a slope of the curve as follows:
3.4. Brief Description of the LOWESS Method
- 1.
- Estimating the span width, which usually contains more than 13 data points and the initial weight of points within the span width is defined as a cubic weighting function as follows:
- 2.
- The first-order polynomial fit with the formula is used to estimate the value of at x. The slope a and constant b are defined as:
- 3.
- The robust weight function is defined to calculate the new weight using the residual of the estimated formula. The robust weighting is:
- 4.
- Repeating steps 2–3 with the new weighting so that the smoothed value of any point could be obtained after several cycles. The theoretical cycles were repeated less than four times.
3.5. Proposed WT-EEMD-LOWESS Algorithm
- 1.
- The echo signal is divided into two segments according to Equation (20), and the high SNR signals are imported into the WT method for denoising.
- 2.
- The low SNR signals are decomposed by EEMD and the scaling exponent is calculated through the DFA algorithm to select IMFs for the signal reconstruction. Then a LOWESS algorithm is performed on the reconstructed signal for further denoising.
- 3.
- The two denoised signals are spliced to obtain the final signals.
4. Results and Discussion
4.1. Experiments with Simulated Signals
4.2. Real Experiment on a Lidar Echo Signal
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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System Parameter | Value |
---|---|
Laser pulse energy/mJ | 40 |
Telescope diameter/mm | 350 |
Field of view/rad | 165 |
Detection quantum efficiency | 0.5 |
Total optical transmittance | 0.4 |
Dark counts/counts per second | 50 |
Range resolution/m | 100 |
Filter bandwidth/nm | 0.25 |
Pulse repetition frequency/Hz | 50 |
Platform height/km | 20 |
Height Range/km | RAW | MA | WTH | WTS | EEMD | VMD-WOA |
---|---|---|---|---|---|---|
30–40 | 59.7109/1233.5 | 38.9091/1352.8 | 58.1694/1473.0 | 60.7532/1094.0 | 57.1453/1657.4 | 23.8776/7634.9 |
30–50 | 60.1029/837.7 | 34.2279/1647.4 | 60.9346/761.2 | 62.7611/616.8 | 56.6552/837.7 | 22.4360/6403.4 |
30–60 | 58.9623/780.6 | 32.1997/1700.4 | 59.1537/763.6 | 60.3729/663.6 | 55.7952/1124.0 | 22.4334/5234.4 |
30–70 | 59.2095/657.3 | 31.2823/1637.3 | 59.6589/624.2 | 61.2158/521.7 | 55.5927/996.8 | 22.4416/4530.8 |
40–70 | 42.6718/349.4 | 34.0989/937.5 | 44.6919/276.9 | 47.8397/192.7 | 47.2425/206.4 | 24.6075/2795.9 |
50–70 | 28.4629/297.1 | 35.5781/130.9 | 32.1896/193.4 | 35.8858/132.5 | 35.0250/139.6 | 26.3373/379.4 |
60–70 | 16.3705/282.9 | 26.1785/91.4 | 18.1742/229.8 | 20.8954/167.9 | 23.7415/121.1 | 26.1806/91.4 |
0.19 | 0.12 | 0.42 | 1.00 | 1.48 | 1.99 |
1–6 IMFs | 2–6 IMFs | 3–6 IMFs | 4–6 IMFs | 5–6 IMFs | 6th IMF | |
---|---|---|---|---|---|---|
SNR/dB | 18.22 | 21.43 | 25.11 | 28.88 | 25.00 | 24.73 |
RMSE | 286.97 | 198.32 | 129.87 | 84.11 | 131.53 | 135.67 |
RAW | EMD | EEMD | CEEMDAN | VMD-WOA | |
---|---|---|---|---|---|
/dB | 18.56 | 27.34 | 28.56 | 27.71 | 26.47 |
Best times | 12 | 55 | 18 | 15 |
RAW | EEMD | EEMD-NLM | EEMD-WTS | EEMD-SVD | EEMD-LOWESS | |
---|---|---|---|---|---|---|
SNR/dB | 18.56 | 28.56 | 20.92 | 28.97 | 26.46 | 30.54 |
System Parameter | Value |
---|---|
Laser pulse energy/mJ | 500 |
Telescope diameter/m | 1 |
Average power/W | >10 |
Wavelength/nm | 532 |
Pulse width/ns | 8 |
Quantum efficiency | 0.4 |
Filter transmittance | 0.8 |
System optical efficiency | 0.02 |
Pulse repetition frequency/Hz | 30 |
Degree from zenith/° | 0 |
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Zhang, Y.; Wu, T.; Zhang, X.; Sun, Y.; Wang, Y.; Li, S.; Li, X.; Zhong, K.; Yan, Z.; Xu, D.; et al. Rayleigh Lidar Signal Denoising Method Combined with WT, EEMD and LOWESS to Improve Retrieval Accuracy. Remote Sens. 2022, 14, 3270. https://doi.org/10.3390/rs14143270
Zhang Y, Wu T, Zhang X, Sun Y, Wang Y, Li S, Li X, Zhong K, Yan Z, Xu D, et al. Rayleigh Lidar Signal Denoising Method Combined with WT, EEMD and LOWESS to Improve Retrieval Accuracy. Remote Sensing. 2022; 14(14):3270. https://doi.org/10.3390/rs14143270
Chicago/Turabian StyleZhang, Yijian, Tong Wu, Xianzhong Zhang, Yue Sun, Yu Wang, Shijie Li, Xinqi Li, Kai Zhong, Zhaoai Yan, Degang Xu, and et al. 2022. "Rayleigh Lidar Signal Denoising Method Combined with WT, EEMD and LOWESS to Improve Retrieval Accuracy" Remote Sensing 14, no. 14: 3270. https://doi.org/10.3390/rs14143270