An Enhanced Three-Dimensional Wind Retrieval Method Based on Genetic Algorithm-Particle Swarm Optimization for Coherent Doppler Wind Lidar

Abstract

In this paper, a wind retrieval method based on genetic algorithm-particle swarm optimization (GA-PSO) for the coherent Doppler wind lidar (CDWL) is proposed. The algorithm incorporates an advanced optimization framework that considers wind field spatial continuity, simultaneously enhancing retrieval accuracy and computational efficiency. Comprehensive validations of the GA-PSO algorithm are conducted using a 1.5 μm all-fiber CDWL through ground-based and airborne experiments. In ground-based experiments, the GA-PSO algorithm extends the detection range by 20%~30% compared with traditional methods. The validation against meteorological tower data demonstrates excellent agreement, with mean deviations better than 0.27 m/s for horizontal wind speed and 3.07° for horizontal wind direction and corresponding RMSE values better than 0.36 m/s and 6.04°, respectively. During high-altitude airborne experiments at 5.5 km, the GA-PSO algorithm recovers up to 31% more horizontal wind speed and direction information compared with traditional algorithms, demonstrating exceptional performance in low signal-to-noise ratio (SNR) conditions. Both simulation analysis and field experiments demonstrate that the GA-PSO algorithm achieves processing speeds comparable to traditional real-time methods, establishing its suitability for real-time, three-dimensional wind retrieval applications.

1. Introduction

Accurate three-dimensional (3D) wind retrieval plays a pivotal role in atmospheric science, supporting applications including numerical weather forecasting [1], gravity wave analysis [2], and boundary layer dynamics research [3]. The CDWL system, with its capabilities for remote sensing, high wind measurement accuracy, and high spatiotemporal resolution, has emerged as a research focus in wind detection research [4]. The CDWL utilizes the Doppler effect and coherent detection method to measure aerosol particle motion, enabling 3D wind retrieval [5]. In practical applications, CDWL directly measures the line-of-sight (LOS) wind information, representing the projection of the 3D wind vector along the laser path. To retrieve 3D wind information, the CDWL leverages the horizontal homogeneity assumption within the measurement volume [6]. By performing azimuthal scanning and combining multiple LOS measurements with corresponding azimuth angles, the 3D wind field can be reconstructed.

Wind retrieval algorithms can be classified into two primary categories. The first category utilizes sine wave fitting (SWF) methods, processing LOS wind speed data with corresponding azimuth angles through direct sine wave fitting (DSWF) and filtered sine wave fitting (FSWF). The second category directly retrieves 3D wind components from spectrum data across multiple azimuths, primarily utilizing maximum frequency accumulation spectrum (MFAS) and maximum velocity maximum likelihood (MVML) methods. SMALIKHO conducted a comparative study of these algorithms [7]. The study validated that DSWF offers computational efficiency but limited performance by poor adaptability to low-SNR conditions and dependence on the accuracy of LOS wind speed calculations. In contrast, MFAS algorithms achieve superior measurement accuracy and extended detection range, though at the expense of significantly increased computational complexity due to their lack of analytical solutions.

To address these limitations, researchers have pursued multiple studies. In SWF method development, Zhu et al. introduced a Levenberg–Marquardt (LM) based wind retrieval algorithm in 2016, experimentally validating its measurement accuracy [8]. In 2019, Rui et al. developed an adaptive iteratively reweighted SWF method, enhancing DSWF performance in low-SNR conditions through dynamic weighting of LOS wind speed contributions [9]. In 2022, Lin et al. further proposed the smoothed accumulated spectra-based wDSWF method, minimizing the effects of bad LOS wind estimates by considering both signal intensity and wind spatial continuity [10].

Despite these improvements, the performance of various new SWF-based algorithms still falls short of the MFAS algorithm, driving research focus toward developing real-time processing capabilities for MFAS-based algorithms. In 2018, Stephan et al. demonstrated the effectiveness of the MFAS algorithm for detecting 3D wind information using ground-based CDWL systems [11]. In 2019, the French Aerospace Lab (ONERA) confirmed the airborne applicability of the MFAS algorithm in low-SNR conditions [12]. From 2020 to 2023, researchers at the Shanghai Institute of Optics and Fine Mechanics integrated genetic algorithms with the MFAS algorithm, validating the hybrid approach through several field experiments [13,14,15]. However, the computational performance of the algorithms in these studies remains insufficient for real-time processing requirements, limiting their application to auxiliary methods for targeted wind retrieval in low-SNR regions.

In this paper, we propose a wind retrieval method based on genetic algorithm-particle swarm optimization (GA-PSO), combining the rapid convergence of the optimization framework with the excellent wind retrieval performance of the maximum function of the accumulated spectra method. This approach significantly enhances processing efficiency, enabling real-time 3D wind retrieval from multi-azimuth spectrum data with improved accuracy and extended detection range. The proposed method’s performance is validated through ground-based experiments, demonstrating superior capabilities compared with traditional approaches. Comparative analysis with meteorological tower reference data provided objective accuracy assessment. To further validate multi-scenario applicability, we conducted airborne experiments using an airborne CDWL system, confirming the algorithm’s effectiveness across different measurement platforms and atmospheric conditions.

2. Materials and Methods

2.1. Principle of Three-Dimensional Wind Retrieval

The velocity azimuth display (VAD) technique is a widely adopted method for 3D wind retrieval [16]. This technique requires maintaining a constant angle between the laser path and the vertical axis, specifically defined as the zenith angle in ground-based measurements and the nadir angle in airborne measurements. The CDWL system employs a servo-controlled scanning mechanism to perform wind measurements at predetermined angular intervals in the azimuthal plane. Considering the wind vector V = (v_x, v_y, v_z), where v_x, v_y, and v_z denote the orthogonal components of the 3D wind vector. The LOS wind speed can be expressed as:

V_LOS = v_xcosφsinθ + v_ysinφsinθ + v_zcosθ

(1)

where φ is the azimuth angle, and θ is the zenith angle. In order to achieve high precision in wind retrieval, multiple scanning azimuth angles are typically set in practical wind measurements. Figure 1 shows the scanning mode in ground-based and airborne wind measurement scenarios, respectively.

The relationship between the LOS wind speed and the 3D wind speed can be further expressed as:

$$\left\{\begin{array}{c}{V}_{\mathit{LOSi}}=\mathbf{V}·{\mathbf{S}}_i\\ \mathbf{V}=(v_x,v_y,v_z)\\ {\mathbf{S}}_i=(\cos {\phi }_i\sin \theta ,\sin {\phi }_i\sin \theta ,\cos \theta )\end{array}\right.$$

(2)

where φ_i is the i-th azimuth angle, and V_LOSi represents the LOS wind speed detected at the i-th azimuth angle. The 3D wind speed (v_x, v_y, v_z) obtained from Equation (2) provides the foundation for calculating two essential meteorological parameters: the horizontal wind speed (V_h) and wind direction (θ_h). These parameters are determined through the following relationships:

$$\left\{\begin{array}{c}{V}_h=\sqrt{v_x^2+v_y^2}\\ {\theta }_h=\arctan (v_y/v_x)\end{array}\right.$$

(3)

where θ_h is defined within the range of 0° to 360°. The error propagation principle indicates that inaccuracies in LOS wind speed calculations directly propagate into the 3D wind retrieval progress. This limitation poses substantial challenges for conventional SWF algorithms relying on LOS wind speed measurements. On order to mitigate retrieval errors, an alternative approach directly computes the 3D wind speed from spectrum data, which relies on the intrinsic relationship between wind speed and Doppler frequency shift. Based on the Doppler wind measurement principle, the spectrum frequency f_i in the i-th azimuth angle relates to 3D wind components (v_x, v_y, v_z) through the following expression:

f_i = 2/λ·(v_xcosφsinθ + v_ysinφsinθ + v_zcosθ) + f_AOM

(4)

where λ is the laser wavelength, and f_AOM is the frequency shift introduced by the acoustic-optic modulator (AOM) in the CDWL system. Based on Equation (4), the evaluation function E(V) is introduced to calculate the cumulative result of the spectrum amplitudes across multiple azimuth angles, which can be expressed as:

$$\mathrm{E}\left(\mathbf{V}\right)={\displaystyle \frac{1}{N}}\sum _{i=1}^{N}S\left(f_i\right)$$

(5)

where V is the estimated 3D wind vector, N is the number of azimuth angles, and S(f_i) is the spectrum amplitude corresponding to f_i. The estimated wind vector V is considered optimal when it maximizes the evaluation function E(V), thereby providing an accurate representation of the actual wind field.

This method directly processes spectrum information to retrieve 3D wind speeds, eliminating the influence of LOS wind speed errors. Additionally, the evaluation function’s computational process performs additional spectrum accumulation, further enhancing the SNR. These characteristics grant the method distinct advantages over SWF-based algorithms in both detection range and measurement accuracy. However, the wind speed estimation and the iterative calculations require a large amount of processing resources, making the MFAS-based algorithm unsuitable for applications requiring high real-time performance.

The method’s calculation process can be reformulated as a three-variable (v_x, v_y, v_z) optimization problem to enhance computational efficiency. This transformation enables the application of advanced optimization algorithms to accelerate processing. The optimization framework consists of three core elements: (i) the decision variables corresponding to 3D wind speed, (ii) constraints defining the feasible range of wind speeds, and (iii) an objective function as specified in Equation (4).

2.2. GA-PSO Algorithm

Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) are two classical optimization algorithms [17,18]. The optimization mechanism of GA is inspired by the concept of “survival of the fittest” in nature. Its basic optimization process involves generating a population, analyzing the fitness of individuals within the population, selecting high-fitness individuals for crossover and mutation, generating a new population, and analyzing fitness again. This process is iterated until the optimal solution is found. GA excels in global optimization but has limitations in local optimization due to its random search direction, which often results in longer computation times. Additionally, GA requires encoding and decoding of the parameters to be optimized when solving specific problems, which reduces its applicability.

Particle Swarm Optimization (PSO) represents another prominent optimization technique, drawing inspiration from the collective foraging behavior of bird flocks [19]. The algorithm initiates population initialization, where each particle explores the solution space independently. During iterative computations, PSO maintains the personal best (pbest), representing each particle’s optimal solution, and the global best (gbest), denoting the population’s overall optimal solution. Particles dynamically update their velocities and positions based on these parameters through the following equations:

v_d(i + 1) = w·v_d(i + 1) + c₁·rand₁·(p_d(i) − x_d(i)) + c₂·rand₂·(g_d(i) − x_d(i))

(6)

x_k,d(i + 1) = x_k,d(i) + v_k,d(i + 1)

(7)

where v_d represents the particle’s velocity in problem space dimension d, i denotes the iteration index, and k is the particle number. w is the inertia weight, c₁ is the cognitive learning factor (associated with the particle’s personal best position p_d), and c₂ is the social learning factor (related to the swarm’s global best position g_d). The w critically influences both computational efficiency and search behavior. The larger values promote global exploration, while smaller values enhance local refinement. We implement a dynamic adjustment strategy, initializing w at a relatively high value and gradually decreasing it during iterations to balance computational efficiency and optimization capability. The c₁ and c₂ require careful tuning. Insufficient c₁ may cause premature convergence to local optima, while inadequate c₂ will slow the convergence. As these parameters are problem-dependent, we recommend initializing the c₁ and c₂ with large values followed by performance-based adaptive tuning during optimization. The current position in the search space is denoted by x_d. The stochastic components rand₁ and rand₂ represent independent, uniformly distributed random numbers within the interval [0,1], introducing necessary randomness to the optimization process.

Compared with GA, PSO demonstrates superior computational efficiency through its information-sharing mechanism, which facilitates the population’s transition from disorder to order during optimization. This characteristic enables faster convergence while eliminating the need for encoding procedures and reducing the number of parameters [20,21]. However, PSO exhibits greater susceptibility to local optima, resulting in a narrower search range compared with GA and potentially compromising solution accuracy. To address this limitation, we develop a hybrid optimization method that integrates the PSO framework with GA operators. This method incorporates GA-inspired crossover and mutation operations after specified PSO iterations, effectively expanding the solution space exploration while maintaining computational efficiency. The GA-PSO optimization framework flow is as follows:

(1)

Experimental spectrum data often suffer from limited frequency resolution. In order to mitigate this limitation, Fourier interpolation is applied to the spectrum data, a method that has been proven effective in refining spectrum resolution [11]. After interpolation, the spectrum resolution is better than 0.05 MHz.

(2)

The particle swarm size is set to 50, and the maximum number of iterations is set to 200. The initial inertia weight w is set to 0.95 and decreases linearly with iterations. The cognitive learning factor c₁ is set to 0.85, and the social learning factor c₂ is set to 1.95. The crossover and mutation mechanisms of the genetic algorithm are introduced to enhance global search capabilities, with a crossover probability P_c of 0.2 and a mutation probability P_m of 0.35. The evaluation function is defined by Equation (5), and the total number of azimuths is set to 16. The length of the iterative evaluation register is set to 20.

(3)

The dimension of the problem space, d, is set to 3, corresponding to v_x, v_y, and v_z. For the first range gate, the DSWF method is employed to compute the 3D wind speeds v_x1, v_y1, and v_z1, which serve as the initial search center. The search range is defined as (v_x1 ± 7.5 m/s, v_y1 ± 7.5 m/s, v_z1 ± 1 m/s), with a search step size of 0.01 m/s. The initial positions of the particle swarm are randomly assigned within the search range, and their initial velocities are also randomized. Iterative optimization is then conducted for the first range gate. By leveraging the spatial continuity of the wind field, the optimization process propagates solutions sequentially through subsequent range gates. Upon convergence at the current range gate, the optimal solution is propagated forward as the search center for the next range gate while maintaining the same search range.

(4)

The fitness function is applied to quantitatively evaluate each particle’s performance, simultaneously identifying both pbest and gbest solutions for the current iteration. Subsequently, particle positions and velocities are systematically updated according to Equations (6) and (7).

(5)

GA operations are implemented every 5 iterations to prevent premature convergence. Following the crossover probability P_c, adjacent particle pairs undergo a simple crossover operation, generating two new particle positions. Subsequently, based on the mutation probability P_m, perturbations are introduced to individual positions, effectively preventing the algorithm from falling into local optima.

(6)

Following each iteration, the algorithm performs a left-shift operation on the iterative evaluation register and updates it with the current gbest. Convergence is determined through gradient analysis of this register array. When the gradient becomes zero (indicating no improvement in the gbest for 20 consecutive iterations), the optimization process terminates, outputting the optimal 3D wind speed results. If the number of iterations reaches the preset maximum, the iteration is also stopped.

The flow chart of the GA-PSO algorithm is shown in Figure 2.

The proposed algorithm achieves a balance between accuracy and computational efficiency through several design choices. The spectrum interpolation process employs moderate resolution enhancement, simultaneously optimizing spectrum processing and evaluation function computation. A fixed-length iteration escape mechanism ensures timely termination of the optimization process. These design features collectively enable high-precision 3D wind retrieval while maintaining real-time processing capabilities.

The aforementioned algorithm process is directly applicable to ground-based CDWL systems for wind measurement. In airborne applications, precise compensation for platform motion effects is essential to ensure accurate 3D wind retrieval. It is necessary to obtain the 3D motion velocities v_n, v_e, v_d of the flight platform, as well as motion angles such as the roll angle α, the pitch angle β, and the yaw angle γ. According to the platform motion compensation method proposed in [22], the azimuth angle φ_g and nadir angle θ_g in the geographic coordinate system can first be calculated. Define a vector, r_p, in the laser transmission path in the platform coordinate system. φ_p and θ_p represent the azimuth and nadir angles, respectively, in the platform coordinate system. After applying the coordinate transformation matrix, this vector can be expressed in the geographic coordinate system as:

$$r_g=\left[\begin{array}{c}{x}_g\\ y_g\\ z_g\end{array}\right]=\mathrm{H}·r_p={\mathrm{H}}_{\mathit{yaw}}·{\mathrm{H}}_{\mathit{pitch}}·{\mathrm{H}}_{\mathit{roll}}·\left[\begin{array}{c}m·\sin {\theta }_p\cos {\phi }_p\\ m·\sin {\theta }_p\sin {\phi }_p\\ m·\cos {\theta }_p\end{array}\right]$$

(8)

where m is the vector magnitude. The total rotation matrix H is composed of three elemental rotation matrices: H_roll, H_pitch, and H_yaw, which correspond to the aircraft’s roll, pitch, and yaw angular motions, respectively. These matrices can be expressed through the following equations:

$${\mathrm{H}}_{\mathit{roll}}=\left[\begin{array}{ccc}1& 0& 0\\ 0& \cos \mathsf{\alpha }& -\sin \mathsf{\alpha }\\ 0& \sin \mathsf{\alpha }& \cos \mathsf{\alpha }\end{array}\right]$$

(9)

$${\mathrm{H}}_{\mathit{pitch}}=\left[\begin{array}{ccc}\cos \beta & 0& \sin \beta \\ 0& 1& 0\\ -\sin \beta & 0& \cos \beta \end{array}\right]$$

(10)

$${\mathrm{H}}_{\mathit{yaw}}=\left[\begin{array}{ccc}\cos \gamma & -\sin \gamma & 0\\ \sin \gamma & \cos \gamma & 0\\ 0& 0& 1\end{array}\right]$$

(11)

Then, φ_g and θ_g can be calculated as:

φ_g = arctan(y_g/x_g)

(12)

θ_g = arccos(z_g/m)

(13)

The GA-PSO algorithm implements platform motion compensation through a streamlined approach that directly subtracts the platform’s 3D motion velocities during wind speed estimation. Following this subtraction, the algorithm applies coordinate transformation using φ_g and θ_g to calculate motion-compensated 3D wind speeds. This approach means modifying Equation (4) as follows:

f_i = 2/λ·[(v_x + v_n)cosφ_gisinθ_g + (v_y + v_e)sinφ_gisinθ_g + (v_z + v_d)cosθ_g] + f_AOM

(14)

where φ_gi represents i-th azimuth angle in the geographic coordinate system. The proposed GA-PSO algorithm demonstrates remarkable adaptability through its simple modification for airborne applications, as enabled by Equation (14). This flexibility facilitates deployment across multiple wind measurement scenarios while maintaining consistent retrieval performance.

3. Results

3.1. Experiments Based on Simulated Signal

3.1.1. CDWL Signal Simulation

A thorough evaluation of the GA-PSO algorithm’s performance necessitates simulated spectrum data spanning multiple azimuths and range gates. Although atmospheric layered models can generate time-domain signals of the CDWL [23], followed by range gate segmentation and fast Fourier transform (FFT) processing, this approach proves computationally intensive for large-scale simulations. Alternatively, we adopt an efficient spectrum simulation method proposed by Yoshiki et al. [24], which provides comparable simulation accuracy with significantly reduced computational overhead. The method is mathematically expressed as:

S(f) = C_s·(B_w/B)SNR_w·exp[(f − f_i²)/2σ²] + C_n

(15)

where f is the frequency, σ is the spectrum width, B_w is the wideband receiving bandwidth, and f_i represents the spectrum peak frequency determined through Equation (4) using the predefined 3D wind speed (v_x, v_y, v_z). C_s, representing the speckle effect of the atmosphere [25], follows an exponential distribution with unit mean. C_n, modeling system noise, is characterized by a normal distribution with a mean of zero and a standard deviation of one. SNR_w is the wideband signal-to-noise ratio (SNR) calculated according to Kameyama et al. [23,26].

The simulation initializes 3D wind speeds across all range gates with v_x = 12 m/s, v_y = 12 m/s, and v_z = 1.5 m/s, establishing a constant 45° horizontal wind direction throughout the simulation range. The scanning mode encompasses a full 360° azimuth range with 45° angular resolution, executed over two complete cycles. Through Equation (4), we determine the spectrum peak frequency for each azimuth position. Utilizing the system parameters detailed in

Table 1. System parameters in signal simulation.

Parameters	Value
Laser wavelength	1550 nm
Pulse energy	300 μJ
Sampling rate	400 MHz
Intermediate frequency	80 MHz
Bandwidth	200 MHz
Telescope diameter	100 mm
Accumulated number	5000
Zenith angle	20°
System efficiency	0.193
Pulse width	600 ns

, we generate spectrum data across 16 azimuth angles and 100 range gates.

Figure 3 presents the simulated spectrum characteristics for the 10th, 30th, 50th, and 70th range gates, generated using the parameters specified in Table 1.

The 10th range gate exhibits distinct spectrum peaks with a pronounced sinusoidal distribution across azimuth angles, clearly demonstrating the expected wind field signature. However, signal degradation becomes evident at the 50th range gate, where spectrum peaks begin to merge with noise, accompanied by an obvious reduction in SNR. This degradation progresses to the 70th range gate, where spectrum peaks become virtually indistinguishable from background noise.

3.1.2. Performance Analysis

Following spectrum data simulation, we conduct the performance evaluation of three wind retrieval algorithms: (1) the LM-based DSWF algorithm (LM-DSWF) [27], (2) the FSWF algorithm [7], and (3) the proposed GA-PSO algorithm. The LM-DSWF algorithm processes spectrum data in 8-azimuth segments, with subsequent averaging of retrieval results. In comparison, both the FSWF and GA-PSO algorithms employ the full 16-azimuth dataset for 3D wind retrieval. In order to align with practical applications, this study calculates and analyzes horizontal wind speed and direction from the retrieved 3D wind speeds in both simulations and field experiments.

To quantitatively assess algorithm performance, we conduct 500 independent spectrum simulations followed by wind retrievals. All computational analyses, including spectrum simulations and the algorithm implementations, are conducted on an industrial-grade computer featuring an Intel Core i7-1255U processor and 16 GB RAM. The horizontal wind speed and direction results are systematically compared with preset values, enabling statistical analysis of retrieval accuracy through root mean square error (RMSE) calculations for both parameters. Figure 4 presents the comprehensive statistical results from the evaluation.

Within the near-range region (1st~40th range gates), all algorithms achieve exceptional precision, maintaining horizontal wind speed RMSE better than 1 m/s. However, as the range gate increases, the SNR progressively decreases, leading to significant performance divergence among different algorithms. The LM-DSWF algorithm shows rapid accuracy degradation, while both FSWF and GA-PSO maintain RMSE within 5 m/s up to the 60th range gate. Beyond this, the FSWF algorithm’s performance deteriorates, whereas the GA-PSO algorithm demonstrates consistent accuracy, sustaining sub-5 m/s precision throughout all 100 range gates. Similar trends are observed in horizontal wind direction results, with the GA-PSO algorithm achieving sustained horizontal wind direction RMSE better than 10° across all 100 range gates. Based on 500 simulations, these results demonstrate the GA-PSO algorithm’s superior accuracy and remarkable robustness in low-SNR conditions, making it particularly suitable for extended-range wind measurements.

We further evaluate the computational efficiency of each algorithm through 500 times wind retrievals, processing spectrum data across 100 range gates per retrieval. In the simulation, the LM-DSWF algorithm completes all calculations in approximately 175 s (including average calculation), equivalent to 1.7 ms per range gate. The proposed GA-PSO algorithm requires 180 s total, averaging 3.6 ms per range gate, which is approximately twice the LM-DSWF’s processing time. In contrast, the FSWF algorithm exhibits significantly higher computational demands, consuming more than 1500 s for complete processing. These results highlight the GA-PSO algorithm’s balanced performance, offering substantial accuracy improvements with moderate increases in computational time.

3.2. Field Experiments

3.2.1. CDWL System

In field experiments, we utilized the airborne CDWL developed by our research group to conduct ground-based and airborne experiments [27], validating the performance of the proposed GA-PSO algorithm. The system structure of the airborne CDWL is shown in Figure 5. The system parameters of the airborne CDWL are listed in

Table 2. System parameters of the airborne CDWL in field experiments.

Parameters	Value
Laser wavelength	1550 nm
Maximum pulse energy	300 μJ
Pulse width	100 ns~600 ns selectable
Pulse repetition frequency	10 kHz
Telescope aperture	100 mm
Vertical range resolution	20 m~100 m
Typical accumulated number	5000
Nadir angle	20°
Sampling frequency	400 MHz
Data rate	~2 Hz
Weight	~20 kg
Size	250 mm × 250 mm × 400 mm
Consumption	≤200 W

.

The airborne CDWL utilizes an all-fiber single-frequency laser source, delivering a maximum pulse energy of 300μJ at a 10 kHz pulse repetition frequency (PRF), with corresponding pulse durations of 600 ns. The telescope aperture is 100 mm. When combined with a wedge prism and a rotor, the system can achieve full 360° conical scanning capability with a fixed 20° nadir angle. The core board integrates real-time spectrum processing, wind retrieval algorithms, and comprehensive system control functionalities. In previous work [27], we designed an LM-based DSWF algorithm and implemented it in the core board, achieving airborne real-time 3D wind retrieval with a data rate of approximately 2 Hz. In this paper, we utilize the core board to record spectrum data and process it using both the LM-DSWF algorithm and the GA-PSO algorithm in the aforementioned industrial-grade computer, enabling direct comparison of their retrieval accuracy and computational efficiency. The combined navigation system (CNS, KY-INS300) delivers high-precision platform motion data with a velocity accuracy of 0.05 m/s and an angle accuracy of 0.02°. Previous research has demonstrated the airborne CDWL capability for accurate 3D wind retrieval at an altitude exceeding 6 km. This paper primarily utilizes the airborne CDWL to collect spectrum data and compare the performance of different wind retrieval algorithms.

3.2.2. Ground-Based Experiments

From 9 to 21 March 2023, we conducted ground-based wind measurement experiments using the airborne CDWL in Taiyuan, Shanxi Province, China. The airborne CDWL, configured in an upward-looking orientation for vertical wind profiling, continuously acquired and archived real-time spectrum data. The airborne CDWL acquired real-time spectrum data with a pulse accumulation of 5000, corresponding to a 0.5 s temporal resolution. The spatial configuration consisted of 150 range gates with a vertical range gate length of 30 m. We process the collected data using both the LM-DSWF and GA-PSO algorithms, analyzing real-time results and time-averaged results to evaluate algorithm performance. Figure 6 presents a comparative analysis of three real-time datasets.

As shown in Figure 6, the comparative analysis reveals obvious performance characteristics between the two algorithms. The effective detection range is determined by examining the maximum distance where continuous, stable wind speed and direction distributions are maintained with sufficient SNR levels. Given the proposed algorithm’s enhanced capability in low-SNR conditions, the evaluation of effective range focuses on the distance over which stable wind speed and direction distributions are maintained with reliable data continuity. For the three datasets presented in Figure 6, the effective detection ranges achieved through the LM-DSWF algorithm are 2.82 km, 2.46 km, and 2.16 km, respectively. In comparison, the GA-PSO algorithm demonstrates superior performance with effective detection ranges of 3.78 km, 3.15 km, and 2.76 km, respectively. Within the lower detection height (<2 km), both LM-DSWF and GA-PSO algorithms demonstrate comparable horizontal wind speed and direction retrievals, showing consistent trends and similar values. However, in the 2 km~3 km detection height, the GA-PSO algorithm exhibits significantly improved performance, maintaining reliable retrievals where the LM-DSWF results become increasingly scattered.

To assess the algorithm’s long-term operational stability, we perform an extended analysis using time-averaged data from the aforementioned three separate 5 min intervals. The evaluation process involved two steps. First, we process real-time spectrum data using both LM-DSWF and GA-PSO algorithms, followed by cumulative averaging over 5 min periods to determine mean horizontal wind speed and direction. Second, we apply the accumulation to the 5 min spectrum data before processing with the LM-DSWF algorithm to generate reference results. Figure 7 illustrates the comparative results from these three processing approaches.

The averaging of wind speed and direction results primarily serves to evaluate algorithm stability over the 5 min processing period, with minimal impact on detection range. In contrast, spectrum averaging enhances the SNR substantially, resulting in detection range improvements. For the three datasets presented in Figure 7, the effective detection ranges from the LM-DSWF algorithm are 2.75 km, 2.28 km, and 2.16 km, respectively. The effective detection ranges from GA-PSO are 3.60 km, 3.12 km, and 2.73 km, respectively. As shown in the comparative analysis, the LM-DSWF algorithm demonstrates an effective detection range typically limited to 2.5 km for averaged wind profile calculations. In contrast, the GA-PSO algorithm achieves detection ranges approaching 3 km. The effective detection ranges of the reference results are 3.54 km, 2.79 km, and 2.70 km, respectively. While the reference results incorporating additional spectrum accumulation show an improved range compared with standard LM-DSWF processing, they still fall short of the GA-PSO algorithm’s capabilities. This comparison demonstrates that the GA-PSO algorithm’s real-time processing (0.5 s accumulation) achieves detection range performance comparable to traditional methods using 300 s accumulation. The analysis of the three datasets in Figure 7 shows the GA-PSO algorithm increasing the effective detection range by 31%, 37%, and 26%, respectively, compared with the LM-DSWF algorithm. Figure 8 compares the continuous wind retrieval results obtained from the GA-PSO and LM algorithms, demonstrating the superior performance of the GA-PSO algorithm. The results show that while the LM algorithm is typically confined to detection ranges of about 2 km, the GA-PSO algorithm consistently maintains effective wind measurements beyond 2.5 km. This performance comparison establishes the GA-PSO algorithm’s enhanced capability for reliable long-range wind measurement.

To further evaluate the wind measurement accuracy of the GA-PSO algorithm, the ground-based comparison experiment between the airborne CDWL and a 255-m meteorological tower were conducted from 20 January to 5 February 2025 in Tianjin, China. The meteorological tower, located in southern urban Tianjin, features 15 measurement platforms equipped with EL15 series anemometers (manufactured by ZhongHuan TIG Co., Ltd., Tianjin, China) at different altitudes, providing wind measurements with a wind speed accuracy of 0.5 m/s and a wind direction accuracy of 3°. During the experiment, the airborne CDWL was placed adjacent to the meteorological tower, with the laser pulse width modified to 100 ns and the vertical range resolution adjusted to 20 m by changing the range gate length. On this basis, the measurement positions of the airborne CDWL were spatially matched with the measurement platforms of the meteorological tower at altitudes of 80 m, 120 m, and 220 m. The airborne CDWL measurement data are processed using the GA-PSO algorithm. Figure 9 presents a detailed comparison of horizontal wind speed and direction measurements at these three altitudes.

In order to ensure temporal alignment, both CDWL and tower measurements are averaged over 10 min intervals, which is commonly used in the CDWL validation [28,29,30]. The comparative analysis shows excellent agreement between the airborne CDWL measurements and meteorological tower reference data. Compared with the reference data from different altitude levels, the CDWL demonstrates mean wind speed and direction deviations better than 0.27 m/s and 3.07°, respectively, with corresponding RMSE better than 0.36 m/s and 6.04°. The linear analysis yields correlation coefficients R² exceeding 0.9803 for wind speed and 0.9971 for wind direction between the airborne CDWL measurements and the reference data from the meteorological tower. The urban location of the meteorological tower introduces significant turbulence effects that influence CDWL measurement accuracy by inducing instantaneous flow disturbances and reducing heterodyne efficiency. These turbulent conditions increase wind retrieval error in the comparison experiments. Additionally, the GA-PSO algorithm’s computational efficiency prioritization involves trade-offs in wind speed estimation resolution, optimization cycles, and iteration requirements. While enabling real-time processing, this design approach may result in suboptimal solutions in some cases, representing another potential source of errors in wind retrieval.

In similar studies, MFAS-based algorithms are typically employed as auxiliary methods for processing wind retrievals in low-SNR regions, primarily due to their longer processing times [11,12,13,14]. The proposed algorithm in this paper fundamentally addresses this limitation, enabling the direct replacement of traditional methods while fully leveraging its performance advantages throughout the entire wind measurement range.

3.2.3. Airborne Experiments

The GA-PSO algorithm’s enhanced performance significantly extends the detection range in ground-based measurements. For airborne applications, atmospheric conditions at higher altitudes often create irregular SNR distributions along the measurement path, potentially compromising full-path wind profile retrieval. To validate the algorithm’s advantages in airborne scenarios, we conducted airborne experiments using the Y-12E aircraft equipped with the CDWL. With the CNS providing precise flight altitude data, we present subsequent experiment results with altitude as the vertical axis parameter. An airborne wind measurement experiment was conducted on 22 July 2024, in Shanxi Province, China. Figure 10a illustrates the SNR distribution observed during the airborne experiment. The aircraft executed an altitude transition from 5.5 km to 5 km before maintaining horizontal flight. The SNR distribution exhibited distinct characteristics. Above 4.5 km, sparse aerosol concentrations maintain consistently low SNR values, while the 4 km~4.5 km range showed significant SNR enhancement from aerosol accumulation and cloud effects. Below 4 km, despite increased aerosol backscatter, progressive atmospheric attenuation leads to gradually declining SNR with decreasing altitude. High SNR values observed at 2 km altitude likely result from strong backscattering by mountainous terrain. The presence of dense clouds in the 4 km~4.5 km altitude range (dash line 1) creates strong backscatter signals while inducing complete laser attenuation, preventing valid wind retrieval using conventional algorithms. Similarly, the LM-DSWF algorithm and the GA-PSO algorithm are used to process the measured spectrum data, and the comparative results are shown in Figure 10.

The LM-DSWF algorithm produces significant anomalies in retrieving horizontal wind speed and direction between 3.3 km~3.9 km and 4.2 km~5.3 km altitudes, as shown in Figure 10b,c. In contrast, the GA-PSO algorithm successfully obtains valid horizontal wind speed and direction measurements within the aforementioned 1.7 km range at the aircraft’s 5.5 km flight altitude. This represents a 31% improvement in recoverable wind information compared with the LM-DSWF method. To validate its accuracy, we analyze data at the dashed line 2, which exhibits temporal proximity to dashed line 1 with minimal wind variation and improved SNR conditions. Figure 10d,e demonstrates that the LM-DSWF algorithm achieves consistent wind retrievals in this scenario, showing good agreement with results from the GA-PSO algorithm. The wind field structure from dashed line 2 maintains temporal continuity with GA-PSO results from dashed line 1, confirming the proposed algorithm’s reliability in low-SNR conditions.

As shown in Figure 10f,g, dashed line 3 presents a more uniform SNR distribution along the measurement path, with both algorithms producing effective horizontal wind speed and direction profiles. The GA-PSO algorithm demonstrates consistent spatial continuity in horizontal wind speed and direction results between consecutive measurement periods. This additional dataset further demonstrates the effectiveness of the proposed GA-PSO algorithm, proving its superior performance in airborne wind detection applications.

The airborne experiment conducted on 20 September 2024 exhibits similar findings. Figure 11 displays the SNR distribution obtained during the flight campaign, along with comparative results from both LM-DSWF and GA-PSO processing. During this experiment, the aircraft executed a descent from 3.2 km to 2.5 km before maintaining horizontal flight.

The analysis of Figure 11d,f demonstrates that the LM-DSWF algorithm produces erroneous wind retrievals during periods of low-SNR conditions, corresponding to Figure 11a. The GA-PSO algorithm maintains robust performance throughout. A representative case occurred at 11:20:04 when the LM-DSWF algorithm generated invalid wind profiles from 2.5 km to ground level. In contrast, the GA-PSO algorithm successfully reconstructs complete and physical wind profiles while maintaining temporal consistency and spatial continuity with adjacent measurements.

We further evaluate the computational performance of the GA-PSO algorithm using the airborne dataset presented in Figure 11. Given the flight altitude, each spectrum dataset requires processing across 70 range gates. Figure 11b presents the computational performance analysis, showing that wind retrieval across 70 range gates requires an average processing time of 0.40 s with a standard deviation of 0.056 s. Although slightly slower than DSWF methods, this processing speed satisfies real-time processing requirements for airborne wind retrieval applications.

4. Discussion

In this study, the proposed GA-PSO algorithm realizes real-time, long-range, and high-precision 3D wind retrieval through optimization of the algorithm architecture and integration of MFAS principles, effectively balancing retrieval accuracy and computational efficiency. Experimental results demonstrate the algorithm’s capability to extend the effective detection range, though this enhancement varies depending on specific spectrum characteristics. As illustrated in Figure 7, when wind speeds at higher altitudes obviously change, the algorithm’s detection range enhancement gradually decreases. This phenomenon likely results from decreased SNR due to aerosol dilution under high wind speed conditions. This observation is consistent with the principle of spectrum accumulation, demonstrating that the algorithm’s range-enhancing capability is inherently constrained by spectrum limitations.

The GA-PSO algorithm proposed in this study has been implemented across diverse wind measurement scenarios, including both ground-based and airborne applications. Through extended ground-based experiments at multiple geographical locations, the GA-PSO algorithm has consistently outperformed conventional wind retrieval methods in long-term operation. For the airborne experiments, the results confirm that the GA-PSO algorithm maintains consistent effectiveness under different flight altitudes and aerosol distribution characteristics. Validation experiments confirm the algorithm’s robust generalization across diverse conditions, with field verification remaining ongoing. The robust performance of the GA-PSO algorithm benefits from optimized wind speed estimation and spectrum accumulation processes. Computational efficiency represents a critical performance criterion that demands careful assessment. Initial validation employs simplified spectrum simulations assuming homogeneous wind fields, where the algorithm demonstrates accelerated processing speeds of 3.6ms per range gate, facilitated by idealized spectrum characteristics, including stable peak locations and uniform SNR distributions. In operational airborne experiments, the processing speed of the GA-PSO algorithm decreases to about 5.7ms per range gate. This reduction primarily stems from the more complex SNR distributions and the increased noise levels in actual airborne spectrum data, which extend optimization iterations. Nevertheless, these processing speeds remain well within real-time processing constraints for airborne wind retrieval applications.

In computational resource-abundant scenarios, the GA-PSO algorithm’s performance can be further enhanced by implementing higher-resolution spectrum interpolation, increasing iteration counts for improved convergence, employing finer search step sizes, and incorporating additional azimuth angles in the retrieval process. These enhancements collectively extend the effective detection range while significantly improving wind retrieval accuracy.

5. Conclusions

In summary, we present a novel wind retrieval algorithm based on a GA-PSO optimization framework, demonstrating superior performance in low-SNR conditions through ground-based and airborne experiments. The ground-based validation shows the GA-PSO algorithm’s advantages over the LM-DSWF method, extending the detection range by 20%~30%. Comparative analysis with meteorological tower data reveals excellent agreement, with horizontal wind speed and direction R² better than 0.9803 and 0.9971, respectively. The mean deviations between the GA-PSO results and meteorological tower data are better than 0.27m/s for horizontal wind speed and 3.07° for horizontal wind direction, respectively. The corresponding RMSE values are better than 0.36m/s and 6.04°, confirming the algorithm’s accuracy. In airborne experiments, the GA-PSO algorithm effectively mitigates measurement challenges caused by complex atmospheric conditions. During a 5.5km altitude airborne experiment, the GA-PSO algorithm recovered 31% of the effective measurement range and achieved complete path coverage for 3D wind retrieval. The airborne experiment results demonstrate that the GA-PSO algorithm achieves a mean processing time of 0.40s for 70 range gates. Although the computational speed exhibits fluctuations caused by spectrum variability, the proposed algorithm maintains computational efficiency comparable to the LM-DSWF algorithm. This enables the replacement of traditional algorithms for real-time wind retrieval.

Overall, field experiment results conclusively demonstrate the GA-PSO algorithm’s advantages in measurement accuracy, detection range, and real-time processing capability. Future research will focus on enhancing computational efficiency and exploring broader application scenarios. We will expand the geographical coverage of testing sites and include more atmospheric conditions, further enhancing the algorithm’s utility for diverse wind measurement requirements.