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Abstract
Wind vector estimation method that provides more available data in low signal-to-noise ratio (SNR) regime improves the performance of pulsed coherent Doppler lidar. The adaptive iteratively reweighted sine wave fitting (airSWF) method proposed here reweights the contribution of each radial wind velocity adaptively and iteratively when estimating the wind vector. Based on the processing results of both the simulated and real-captured signal, the airSWF method provides more available wind vector estimates with little computational time increment, compared with the direct sine wave fitting (DSWF) and weighted DSWF methods. Specifically, the proportion of available wind vector estimates determined using the airSWF method increases by >20% when the detection height exceeds 1 km. Another significant advantage of the airSWF method over the filtered sine wave fitting (FSWF) method is that no prior knowledge is required. Moreover, the computational complexity of the airSWF method is lower than that of the FSWF and maximum of the function of accumulated spectra methods.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Pulsed coherent Doppler lidar (PCDL) systems have been widely used for rapid detection of atmospheric wind field, including for wind energy assessment [1–3], wake vortex visualization of wind turbines and aircrafts [4–10], atmospheric turbulence investigation [10–14], and other research on atmospheric dynamics [15–17]. A PCDL system can only detect radial wind velocities in different range bins along the probing laser beam, thus requiring at least three radial wind velocities detected from different directions to retrieve a wind vector.
Various estimators, including periodogram (PM) maximum estimator, maximum likelihood (ML) estimator, signal match (SM) estimator, autoregressive (AR) estimator, minimum variance (MV) estimator, and weighted subspace fitting (WSF), have been studied to increase the proportion of reliable radial wind velocity estimates [18–21]. For a PCDL system featuring real-time signal processing, the PM maximum estimator is preferred [9,22,23]. Regardless of which frequency estimator is used, some of the radial wind velocity estimates are unreliable. Therefore, it is essential to decide which ones should be included and how much they “contribute” toward estimating the wind vector.
A novel nonlinear adaptive Doppler frequency shift estimation technique (NADSET) has been proposed to replace unreliable radial wind velocity estimates by interpolating the nearby reliable ones before estimating the wind vector. As proven by the validation lidar (VALIDAR) system, this method can significantly improve the quality of radial wind velocity estimates in the regime of low signal-to-noise ratio (SNR) [24].
Another widely used technique involves screening the radial wind velocity estimates with a user-defined SNR threshold, as the probability of a reliable estimate depends on the SNR of the corresponding power spectral density (PSD) [25]. The radial wind velocities estimated from the PSD whose SNR is below the threshold can be discarded [9,16,26] or replaced by the median value of the 20 closest ones that have an SNR value greater than the threshold [27]. However, because the SNR not only depends on the configuration of the PCDL system, but also on the atmospheric condition (atmospheric backscatter coefficient, extinction ratio, and refractive turbulence), the SNR threshold can only be derived under a relatively stable wind condition (a vertical wind velocity close to zero) for a specified system [26,28].
After filtering the radial wind velocity estimates, sine wave fitting (SWF) methods, including direct sine wave fitting (DSWF) and filtered sine wave fitting (FSWF), can be used to estimate the wind vectors, as proposed by Smalikho [29]. The FSWF method can also be used without having to filter the radial wind velocity estimates. Besides the SWF methods, the maximum of the function of accumulated spectra (MFAS) and maximum likelihood for wind vector (WV ML) methods can be used to estimate the wind vector directly from the PSD data. As compared with the DSWF method, FSWF, MFAS and WV ML methods are more computationally intensive. Moreover, a prior knowledge of the relationship between the SNR and the standard deviation (SD) of the reliable radial wind velocity estimates is required by the FSWF method. For PCDL systems with different configurations, the relationships vary from each other. This is a significant limitation of the FSWF method.
In this paper, we propose an adaptive iteratively reweighted sine wave fitting (airSWF) method to estimate wind vector for the PCDL system that uses velocity-azimuth display (VAD) scanning technique. The contributions of each radial wind velocity estimates toward estimating the wind vector are weighted adaptively and iteratively. Based on the simulated signals, the performance of the airSWF method is compared with those of four other methods: DSWF, weighted DSWF (wDSWF), FSWF, and MFAS methods. The airSWF method shows three significant advantages. The calculation speed of the airSWF method is significantly higher than those of the FSWF and the MFAS methods; moreover, the proposed method can be deployed in a VAD scanning PCDL system in a real-time manner. The second advantage is that proportion of available wind vector determined using the airSWF method is higher than those of the DSWF and wDSWF methods when the SNR is low. Besides, prior knowledge of the relationship between the SNR and the SD of the reliable radial wind velocity estimates is not required by the airSWF method, which makes it easy to deploy the airSWF method in a VAD scanning PCDL system. We also perform a comparison using a real signal captured with a custom-made portable PCDL system. The airSWF method once again exhibits the same performance improvement.
2. airSWF wind vector estimation technique
2.1 Velocity-azimuth display scanning technique
To estimate the wind vector, the radial wind velocities from different directions are first determined using the well-known VAD scanning technique, whereby the elevation angles of the probe beams are fixed (e.g., φ = 70°) and the azimuth angles (θi) are evenly distributed from 0 to 360° [29]. Under the assumption of a homogeneous wind vector in the scanning area, the radial wind velocities detected in the range bins at same height will show a sine wave dependence on the azimuth angles.
Figure 1 shows a scheme of the VAD scanning technique for a ground-based PCDL system. We assume that V = [Vz, Vn, Ve]T is the true wind vector, where Vz is the vertical component, and Vn and Ve are the north and east components, respectively. Si = [sinφ, cosφcosθi, cosφsinθi]T is the unit column vector along the ith probing beam with an azimuth angle of θi and an elevation angle of φ. The radial wind velocity along the probing beam can be represented in the following form
2.2 Review of sine wave fitting methods
The probability density function (PDF) of the radial wind velocity estimate ${\hat{V}_{ri}}$ is defined in [25] and expressed in a biased Gaussian model as follows
2.3 Adaptive iteratively reweighted sine wave fitting
Inspired by the weighting process in the FSWF method, the least-squares function for the DSWF method can be weighted in the following form:
The adaptive iteratively reweighted procedure is similar to the weighted least-squares except for iteratively reweighting the least squares with different weighting coefficients, which can be obtained during the iterative procedure. This procedure is generally used to find the baseline of the Raman spectrum [31,32]. To estimate the wind vector, the procedure can be modified as follows:
- A. The initial weighting coefficients $w_i^{({t = 0} )} = 1({i = 1, \ldots ,n} )$ should be given, and the initial estimated wind vector ${\hat{\textbf{V}}^{({t = 0} )}}$ is calculated with the input radial wind velocity estimates ${\hat{V}_{ri}}$ using Eq. (8).
- B. The initial projected radial wind velocities $V_{ri}^{({t = 0} )}$ corresponding to ${\hat{\textbf{V}}^{({t = 0} )}}$ are calculated using Eq. (1). The absolute errors $d_i^{({t = 0} )}$ between input radial wind velocity estimates ${\hat{V}_{ri}}$ and initial projected radial wind velocities $V_{ri}^{({t = 0} )}$ can be calculated using
- C. The new weighting coefficients for the next step are calculated using$$w_i^{({t + 1} )} = \frac{2}{{1 + \exp \left\{ {2\left[ {\frac{{d_i^{(t )} - ({2s_d^{(t )} - m_d^{(t )}} )}}{{s_d^{(t )}}}} \right]} \right\}}},$$where $s_d^{(t )}$ and $m_d^{(t )}$ are the standard deviation and mean of $d_i^{(t )}$, respectively.
In summary, the procedure of the airSWF method involves finding the sine wave baseline step by step among the “outliers” (unreliable radial wind velocity estimates) polluted radial wind velocity estimates. During each step, the “contributions” (weighting coefficients) from all the radial wind velocity estimates toward determining wind vector are reweighted according to how much they deviate from the sine wave baseline derived in the previous step, rather than derived from the relationship between the SNR and the standard deviation (SD) of the reliable radial wind velocity estimates. Therefore, as compared with the wDSWF and FSWF methods, the proposed airSWF method needs no prior information. Usually, after several iterations, the “contributions” from all the radial wind velocity estimates vary little and so does the sine wave baseline. Then the wind vector can be determined from the sine wave baseline derived in last step. However, under extreme wind condition such as severe turbulence, the radial wind velocity estimates show no sine wave dependence on the azimuth angles, the airSWF method cannot work anymore.
Figure 2 shows a flowchart describing the proposed procedure. This method along with the other four methods have been implemented using MATLAB R2018b on an Intel i5-8400 CPU computer, with 8G RAM and 64-bit Windows 10 operation system. The performance of these methods is analyzed in the following two sections based on the simulated signal and the real-captured lidar data.
3. Experiments on simulated signal
3.1 Time-domain simulated signal
The output signal in the time domain of a pulsed coherent lidar system can be expressed as the summation of the heterodyne signal and noise. The heterodyne signal is the voltage converted from the mixed power of the incoherent backscattered light within a small atmospheric range and the local oscillator (LO) light. If the power of the total noise is normalized to one, the output complex signal of single range gate from a single detection in the digital domain can be expressed as [33,34]
Figure 3(a) shows the real part of the complex simulated signal of a single pulse in the time domain. The radial wind velocities in the small atmospheric range and the td-SNR are set to 0 m/s and −15 dB, respectively. The remaining parameters of the simulated signal are set according to Table 1.
Fig. 3. Simulated signal: (a) real part of the amplitude of a single pulse; (b) averaged noise and signal PSD of the real part.
Table 1. Parameters of the Simulated Signal
3.2 Frequency-domain SNR and radial wind velocity estimation method
Although the wind band SNR is predefined in the time domain for the simulated signal, it is impossible to estimate the SNR without processing the time domain signal captured from the real PCDL system. For a PCDL system featuring a real-time signal processing function, the SNR is usually estimated from the average PSD data in the frequency domain.
Figure 3(b) shows the averaged PSD of the real part of the simulated signal of 100 pulses. The PSD of the signal of a single pulse is calculated with 1024 points discrete Fourier transformation (DFT)-based PM method. The frequency-domain wideband SNR (fd-SNR) of the signal is defined as the ratio of the integration of the signal PSD to the integration of the noise PSD, as shown in Fig. 3(b). Although the td-SNR is set to −15 dB, the estimated fd-SNR is −16.21 dB. This difference is mainly because a part of the signal PSD is buried in the fluctuation of the noise PSD.
The radial wind velocity is estimated in the search band ranging from 70 to 170 MHz (centered at an AOM frequency shift of 120 MHz) as shown in Fig. 3(b). Thus, the frequency domain search band SNR (fds-SNR) is defined as the ratio of the integration of the signal PSD to the integration of the noise PSD in the search band. As the search bandwidth (100 MHz) is limited to half the total bandwidth (200 MHz), the fds-SNR is approximately 3 dB greater than the fd-SNR and is estimated to be −13.10 dB.
The radial wind velocity is estimated using the following equation:
where the frequency shift fshift is the frequency of the centroid of the signal PSD. The radial wind velocity is estimated to be 0.052 m/s.3.3 Statistical analysis of estimated radial wind velocities
Statistical studies are carried out to demonstrate the reliability of the estimated radial wind velocities. The relationship between the fds-SNR and the SD of the reliable radial wind velocity estimates is studied using the Monto Carlo simulation method. This relationship is the prior knowledge required by the wDSWF and FSWF methods, which are to be compared with the airSWF method in terms of the performance in estimating the wind vector. To retrieve the relationship, a series of signals with different td-SNRs and the same radial wind velocity of 0 m/s are simulated. The td-SNRs are set from −30 to −10 dB with an interval of 0.5 dB. Other parameters are set according to Table 1. For each td-SNR, the Monto Carlo iteration number is 10k. Thus, a total of 410k signals are simulated.
Figure 4 shows the histogram distribution of the fds-SNRs of these signals. The bin width of the histogram is set to 0.25 dB. Hence, the signal numbers counted in most of the fds-SNR bins (from −18 to −7 dB) are approximately 5k. As the td-SNR decreases, the signal PSD is buried in the fluctuations of the noise PSD, and the estimated fds-SNR fluctuates more. Most of the estimated fds-SNRs at a low level are distributed in the range of −23–−18 dB. Therefore, the counts in these bins exceed 5k, and there are largely no counts when the search band SNR is lower than −25 dB.
In each fds-SNR bin, the PDF of the radial wind velocity estimates are modeled according to Eq. (2). The parameters b and σi are determined by fitting the histogram count distribution into Eq. (2) using the least-squares method. Figures 5(a) and 5(b) show the histogram and the PDF of the radial wind velocity estimates, when the fds-SNRs are −16 and −22 dB, respectively. When the fds-SNR is −16 dB, most of the radial wind velocity estimates are distributed within ± 2 m/s in a Gaussian form. The detection probability of the radial wind velocity is close to 100%, and the SD of the reliable radial wind velocity estimates is 0.5408 m/s. When the fds-SNR drops to −22 dB, 76.21% of the radial wind velocity estimates are unreliable, and they are uniformly distributed in the search band of the radial wind velocity. The reliable radial wind velocity estimates are still distributed in a Gaussian form; however, the SD of the reliable radial wind velocity estimates increases to 2.038 m/s. Figure 5(c) shows the relationship between the fds-SNR and the detection probability and the SD of the reliable radial wind velocity estimates. As the fds-SNR decreases, the SD of the reliable radial wind velocity estimates increases.
Fig. 5. Histogram and PDF of the estimated radial wind velocities with fds-SNRs of (a) −16 dB and (b) −22 dB; (c) Relationship between the fds-SNR and the SD of reliable radial wind velocity estimates and the detection probability.
3.4 Performance analysis
To demonstrate the performance and advantages of the proposed airSWF methods, we run the airSWF method as well as the DSWF, wDSWF, FSWF, and MFAS methods on the simulated signals. The signals are the numerical simulation of a scanning PCDL working in the VAD pattern. The total number of detection directions is assumed to be 24 for a full VAD scan, the elevation angles of the detection directions are fixed at 70°, and the azimuth angles of the detection directions are evenly distributed from 0° to 360° with an interval of 15°.
To simulate the signals of a VAD scanning PCDL system according to Eq. (12), two assumptions are required. For a real PCDL system, the SNRs of the signals drop with the increasement of the detection range. However, during a single full scan, the SNRs of the signals detected in the range gates at same height can be assumed to vary little from each other. Therefore, the first assumption we make is that the td-SNRs of the signals detected at different azimuth angles of a single full scan at same height are constant. As explained in section 3.2, although the td-SNRs of these signals are assumed to be constant, the fds-SNRs of these signals detected in the range gates at same height are slightly different from each other. Another assumption to be required is that the wind field at same height is homogeneous during a single full scan.
Simulated signals with different td-SNRs can represent the signals detected in the range gates at different heights. The td-SNRs are set from −25 to −14 dB with an increasing step of 0.5 dB. For each td-SNR, signals of 1k full scans are generated. Meanwhile, for different scans, the north and east components of the wind field are randomly generated except the vertical components are fixed at 0 m/s. The true radial wind velocities Vri at different azimuth angles are the projections of the true wind vector V onto each detection direction. The other parameters are set according to Table 1.
Figure 6 shows the true radial wind velocities Vri, the radial wind velocities ${\hat{V}_{ri}}$ estimated from the simulated signals of a single scan with td-SNRs of −19 dB and −22 dB, and the fitting radial wind velocities estimated using the DSWF, wDSWF, FSWF, MFAS, and airSWF methods. Although the td-SNRs of the signals simulated at different azimuth angles of a full scan are the same, the fds-SNRs estimated at different azimuth angles are slightly different. Therefore, the mean fds-SNR is estimated, and the values are (a) −16.01 dB and (b) −19.30 dB.
Fig. 6. Radial wind velocities vs. azimuth angles; the mean fds-SNRs are: (a) −16.01 dB and (b) −19.3 dB.
As shown in Fig. 6(a), when the mean fds-SNR is −16.01 dB, the radial wind velocity estimates are quite consistent with the true radial wind velocities. The same is true for the radial wind velocities fitted from the wind vectors estimated using all the methods. When the fds-SNR decreases to −19.30 dB, a quarter of the radial wind velocity estimates are unreliable, as shown in Fig. 6(b). The radial wind velocities fitted from the wind vectors estimated using the DSWF and wDSWF methods significantly deviate from the true radial wind velocities. However, the radial wind velocities fitted from the wind vectors estimated using the airSWF, FSWF, and MFAS methods are quite consistent with the true radial wind velocities.
The residual and correlation between the fitting radial velocities and the true radial velocities Vri are analyzed using the simulated signals with various td-SNRs. For each scan, the residual and correlation between the fitting radial velocities and the true radial velocities are determined. Figures 7(a) and 7(b) respectively show the mean of the residuals and the correlations between the fitting radial velocities and the true radial velocities of the 1k scans with respect to the different fds-SNRs. The estimated wind vector estimate $\hat{\textbf{V}} = {[{{{\hat{V}}_z},{{\hat{V}}_n},{{\hat{V}}_e}} ]^T}$ is assumed to be acceptable if the relative error, which is defined as ${{|{\hat{\textbf{V}} - {\textbf V}} |} \mathord{\left/ {\vphantom {{|{\hat{\textbf{V}} - {\textbf V}} |} {|{\textbf V} |}}} \right.} {|{\textbf V} |}}$, does not exceed 10%. Figure 7(c) shows the proportion of available wind vectors with respect to different fds-SNRs when using the different wind vector estimation methods.
Fig. 7. (a) Residual and (b) correlation between the fitting radial wind velocities and the true radial wind velocities vs. different mean frequency search band SNRs; (c) Proportion of available wind vectors estimated using the different methods vs. different mean frequency search band SNRs; (d) Time required (in seconds) for the different wind vector estimation methods.
As shown in Figs. 7(a)–7(c), the performances of all the methods decrease with the decreasing fds-SNR, but the fds-SNR thresholds from where the performances of these methods begin to decrease rapidly are different. For DSWF, wDSWF, airSWF, MFAS and FSWF methods, the fds-SNR thresholds where the proportion of available estimated wind vectors below 90% are −16.5 dB, −17 dB, −19 dB, −20 dB and −20.5 dB. Specifically, when the fds-SNR drops to −18 dB, the proportion of available wind vectors estimated using the DSWF method is less than 50%; however, when using the airSWF method, this proportion is still near 100%.
Since the DSWF method cannot weight the contributions from the radial wind velocity estimates used to determine the wind vector, its performance begins to decrease rapidly as the fds-SNR decreases below the level (−16.5 dB) where unreliable estimates emerge. However, for the other four methods, the “contributions” from the unreliable radial wind velocity estimates can be weighted to a low level, thus, as the fds-SNR drops, the performance of the DSWF method begins to decrease first. When the fds-SNR drops to the levels below −19 dB, the proportion of unreliable radial wind velocity estimates becomes larger as the fds-SNR keeps dropping. For the airSWF method, the more the unreliable radial wind velocity estimates exist, the lower the probability of deriving the correct sine wave baseline becomes. The performance of the airSWF method begins to decrease as the fds-SNR drops below −19 dB. Nevertheless, thanks to the global searching procedure in the MFAS and FSWF methods, these two methods can still derive the available wind vector from the “outliers” heavily polluted radial wind velocity estimates.
In summary, in the regime of low fds-SNR, the FSWF and MFAS methods significantly outperform the DSWF and wDSWF methods in estimating the wind vector. However, as shown in Fig. 7(d), the computational time of processing the simulated signals of 1k scans required by the FSWF and MFAS methods are over a thousand times that of the DSWF and the wDSWF methods. The airSWF method outperforms the DSWF and the wDSWF methods, with acceptable increment in the computational time required. In the next section, the performances of these wind vector estimation methods are validated using the real wind lidar signals captured with a custom-made portable PCDL system.
4. Experiments on real wind lidar signals
4.1 System description
The custom-made portable PCDL system can be divided into three main units, namely a laser transmitter, an optical antenna, and a receiver unit, as shown in Fig. 8(a). Figure 8(b) shows a photo of the custom-made portable PCDL system. The output signal from the balanced detector is digitized, and the PSD is estimated in the digital data acquisition and processing system. The accumulated PSD data are transferred to an industrial tablet through a USB 2.0 port. The wind vector is estimated from these data in real-time and is displayed on the tablet. Table 2 lists the specifications of this system.
Table 2. Specifications of the Portable PCDL System
4.2 Wind vector estimation
From March 20 to 23, 2018, we carried out a series of experiments in the urban Najiao Meteorological Center of China Meteorological Administration to calibrate the detection accuracy of the portable PCDL system. The wind vectors estimated from the system are compared with those measured from the radiosonde. The results have already been published in [35].
During the night, when the wind was very weak, the system began to stare in the vertical direction and collected the accumulated PSD data. A statistical analysis of the radial wind velocities estimated from the real captured data was performed on these data under the assumption that the vertical wind velocity is 0 m/s. Figure 9 shows the relationship between the fds-SNR and the SD of the reliable radial wind velocity estimates and the relationship between the fds-SNR and the detection probability for the real captured signal. As the accumulation pulse number and the search band range of the real captured signal are different from those of the simulated signal, the fds-SNR threshold where the detection probability begins to drop for the real captured signal is different from that for the simulated signal and is approximately 6.5 dB less, compared with the result shown in Fig. 5(c). The relationship between the fds-SNR and the SD of the reliable radial wind velocity estimates for the real captured signal is the prior knowledge when estimating the wind vector from the real captured lidar signal using the wDSWF and the FSWF methods.
Fig. 9. Relationship between the frequency-domain search band SNR and the SD of reliable radial wind velocity estimates and the detection probability for the real captured signal.
Figure 10 shows the spatial-temporal pseudo-color map of the horizontal wind velocities estimated from the continuous signal acquired in over 20 min. The points where the horizontal wind velocity exceeds 10 m/s are considered as the error estimates and are indicated in white. As shown in Fig. 10, when the height is below 800 m, the horizontal wind velocities estimated using the airSWF method are similar to those estimated using the DSWF, wDSWF, and FSWF methods. When the height exceeds 1 km, the horizontal wind velocities estimated using the DSWF and wDSWF methods exhibit significant data loss; however, the horizontal wind velocities estimated using the airSWF method are more continuous.
Fig. 10. Spatial-temporal pseudo-color map of horizontal wind velocities estimated using (a) DSWF; (b) wDSWF; (c) airSWF; and (d) FSWF methods.
When the height exceeds 1 km, the proportion of reliable wind vector estimates determined using the DSWF and wDSWF methods is 75%. The proportion increases to 95% when the airSWF method is used. Figure 11(a) shows the spatial-temporal pseudo-color map of the fds-SNR in approximately 2 min. Between 19:51:54 and 19:52:36, there exists a signal whose SNR is very low for all the height bins. This is because someone got too close to the system and blocked the transmitted laser pulse accidentally. Figure 11(b) shows the horizontal wind velocities estimated using the DSWF method. As the error radial velocity estimates are not weighted when using the DSWF method, the horizontal wind velocities estimated from these error radial velocity estimates exceed 10 m/s. Clearly, the horizontal wind velocity estimates are unreliable. When using the airSWF and FSWF methods, the contribution of the unreliable radial wind velocity estimates to the wind vector can be weighted to a very low level, and the horizontal wind velocities are reliable, as shown in Figs. 11(c) and (d).
Fig. 11. Spatial-temporal pseudo-color map of (a) fds-SNR and horizontal wind velocities estimated using (b) DSWF; (c) airSWF; and (d) FSWF methods.
5. Conclusions
The airSWF method is proposed in this paper to estimate the wind vector in a real-time PCDL system. This method adaptively and iteratively reweights the contribution of the different radial wind velocity estimates, which are used to estimate the wind vector. To demonstrate its advantages, its performance in estimating the wind vector was compared with those of previously proposed DSWF, wDSWF, FSWF, and MFAS methods. Both the simulated signal and real captured lidar signal are used to perform the comparison.
When the SNR of the simulated signal was low, the DSWF and wDSWF methods were prone to unreliable radial wind velocity estimates and could not provide reliable wind vector estimates. The FSWF and MFAS methods could provide much more reliable wind vector estimates; however, the computational time required for the two methods were over a thousand times those of the DSWF and wDSWF methods. When the airSWF method was used, a better trade-off might be obtained between wind vector estimation performance and the calculation speed. The computation time required by the airSWF method was only approximately two times those required by the DSWF and wDSWF methods. The proportion of available wind vector estimates when using the airSWF method increased over 25 and 40% compared with that using the wDSWF and DSWF methods, when the mean fds-SNR dropped to −18 dB. The same performance improvement could be seen when processing on the real-captured lidar signal. When the height exceeded 1 km, the proportion of available wind vector estimates determined using the airSWF methods increased by over 20% compared with that using the DSWF methods. Moreover, as compared with the wDSWF and FSWF methods, the airSWF method does not require the prior knowledge of the relationship between the SNR and the SD of the reliable radial wind velocity estimates, thus, the deployment of the airSWF method in a real PCDL system is easier than those of the wDSWF and FSWF methods.
In conclusion, the airSWF method has three advantages: 1) It is much faster in terms of the calculation speed than the FSWF and MFAS methods and can be easily deployed in PCDL system; 2) In the low SNR regime, the proportion of available wind vector estimates determined using the airSWF method is higher than those of the DSWF and wDSWF methods; 3) No prior knowledge is required for deploying the airSWF method in a real PCDL system. Although we studied the performance of the proposed method based on the calculation speed and proportion of available wind vector it can provide in the low SNR regime, there still exists some more studies should be carried on. In the future, we will focus on optimizing the terminative criterion threshold of the proposed method to improve the wind vector estimation accuracy.
Funding
national advanced science research of China (30502040203).
Acknowledgment
The authors thank the editor and the anonymous reviewers for their insightful comments on the manuscript.
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