Single / dual-channel signal alternate adaptive processing method for pulse radar Doppler power spectrum
Patent Information
- Application Number
- CN202611142491.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2026-07-30
- Publication Date
- 2026-10-20
- Estimated Expiration
- 2046-07-30
AI Technical Summary
[0004]本发明的目的在于提供一种技术方案，以解决现有技术无法自动识别信号数量、初始参数估计不可靠、拟合结果易出现无物理意义负功率、谱矩估计精度不足的问题
1、本发明通过整合预处理、高斯混合模型与贝叶斯信息量准则自动定数、迭代拟合及谱矩计算，自适应确定脉冲雷达多普勒速度功率谱中的信号数量，显著提高了信号处理方法的通用性和自动化水平。
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Figure CN122654595B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of radar signal processing technology, specifically to an adaptive processing method for alternating single and dual-channel signals of pulse radar Doppler power spectrum. Background Technology
[0002] Atmospheric radar obtains clear-sky echoes through backscattering caused by fluctuations in atmospheric refractive index. Affected by precipitation signals, its Doppler power spectrum will show alternating single and dual signals. Therefore, accurately separating different signals and estimating their spectral moment parameters is a fundamental step in applying radar data to meteorological operations and scientific research.
[0003] Currently, in signal separation and spectral moment parameter estimation, although existing technologies can separate overlapping dual signals using probability distribution functions, there are still significant difficulties in automatically identifying the number of signals and reliably estimating initial parameters. When fitting superimposed signals with random or fixed initial values, although good fitting results can be achieved, the separated individual signals may exhibit negative power, causing the results to lose their physical meaning. At the same time, the spectral moment estimation of dual signals is prone to large deviations, making the estimation accuracy unstable and unable to meet the needs of batch processing of radar data. Summary of the Invention
[0004] The purpose of this invention is to provide a technical solution to solve the problems of existing technologies, such as the inability to automatically identify the number of signals, unreliable initial parameter estimation, the tendency for fitting results to contain meaningless negative power, and insufficient accuracy in spectral moment estimation.
[0005] To achieve the above objectives, the present invention provides the following technical solution: a method for alternating adaptive processing of single and dual-channel signals in the Doppler power spectrum of pulse radar, comprising:
[0006] S1. Read the power spectrum data of the radar, preprocess the power spectrum data, and obtain the stretched power spectral density. S2. Establish a velocity sequence based on the stretched power spectral density, automatically determine the optimal signal quantity based on the Gaussian mixture model and Bayesian information criterion, estimate the expectation, variance and mixing coefficient of each Gaussian component and use them as initial spectral moment parameters. S3. Using the optimal number of signals and the initial spectral moment parameters as initial values, iteratively fit the stretched power spectral density to obtain the amplitude, expectation, and variance of each Gaussian component. S4. Reconstruct the power spectral density for the non-negative Gaussian components and output the echo power, average Doppler velocity, and spectral width for each valid signal.
[0007] It should be noted that by integrating preprocessing, Gaussian mixture model and Bayesian information criterion for automatic number determination, iterative fitting and spectral moment calculation, the method can adapt to the complex situations of single or dual Doppler spectral signals under different weather conditions and different signal-to-noise ratios without manual intervention, which significantly improves the versatility and automation level of the processing method.
[0008] According to the above technical solution, the preprocessing in S1 includes: performing three-point smoothing filtering on the power spectrum data to suppress high-frequency noise and random interference; and performing linear stretching on the three-point smoothed power spectrum data to normalize the total power of the power spectrum to a preset range to obtain the stretched power spectrum density.
[0009] Based on the above technical solution, the steps for automatically determining the optimal signal quantity based on Gaussian mixture model and Bayesian information content criterion are as follows: S21. A preset variable k is used to determine the number of Gaussian components. The initial value of the variable k is 1, and the upper limit value is the preset maximum number of Gaussian components K. S22. Based on the current value k of the Gaussian component, initialize the expected value, variance and mixing coefficient of each Gaussian component, and use the expected value maximization algorithm to iteratively update the above parameters until the calculation result meets the preset convergence condition. S23. Based on the expected value, variance and mixing coefficient of each Gaussian component after iterative update, calculate the Bayesian information criterion value corresponding to the Gaussian component at the current value k. S24. Increment the value of variable k by 1, and repeat S21-S23 until the value of k is equal to the preset maximum number of Gaussian components K. S25. Based on the Bayesian information criterion values corresponding to each Gaussian component in S21-S24, select the k value corresponding to the minimum Bayesian information criterion value as the optimal signal quantity k. min It outputs the expected value, variance, and mixing coefficient of each Gaussian component after iterative updates as the initial spectral moment parameters.
[0010] According to the above technical solution, based on the power spectral density S after stretching N (v), establish a velocity sequence, obtain the probability distribution function p(v) of the velocity sequence, and divide the velocity sequence into K Gaussian components according to the preset maximum number of Gaussian components, and obtain the probability distribution of each Gaussian component: ; ; Where v represents the Doppler velocity; This represents the probability distribution of the velocity sequence in the k-th Gaussian component, specifically the power spectral density value of the k-th Gaussian component; This represents the expectation of the velocity sequence in the k-th Gaussian component, specifically the average velocity; This represents the variance of the velocity sequence in the k-th Gaussian component; This represents the mixing coefficient of the k-th Gaussian component.
[0011] It should be noted that by fitting a Gaussian mixture model, the expectation, variance, and mixing coefficient of each Gaussian component are obtained, thereby determining the probability distribution of each Gaussian component.
[0012] According to the above technical solution, the expectation-maximization algorithm includes: calculating the posterior probability of each velocity point in each Gaussian component based on the probability distribution of each Gaussian component, according to the calculation formula: ; in, This represents the velocity point v in the k-th Gaussian component before iteration. i The posterior probability; This represents the mixing coefficient of the k-th Gaussian component before iteration; Specifically, it is a one-dimensional Gaussian probability density function, representing the k-th Gaussian component at the velocity point v. i The probability density at that location; This indicates that all Gaussian components are at the velocity point v. i The sum of weighted densities at each point; K represents the maximum Gaussian component number; Based on the posterior probability, the expectation, variance, and mixing coefficient of each Gaussian component are iteratively updated using the following formula: ; ; ; in, N k N represents the number of valid samples for the k-th Gaussian component; N represents the total number of data samples. This represents the expectation of the velocity sequence in the k-th Gaussian component after iterative update; This represents the variance of the velocity sequence in the k-th Gaussian component after iterative update; This represents the mixing coefficient of the k-th Gaussian component after iterative update.
[0013] It should be noted that, assuming there are a total of K Gaussian components, and the preset maximum number of Gaussian components K=1, ...,6, then the above calculation must be performed for each Gaussian component. For example, when K=1, the initial value of variable k is 1, and the upper limit is 1; when K=2, the initial value of variable k is 1, and the upper limit is 2; and so on. When K=6, the initial value of variable k is 1, and the upper limit is 6.
[0014] It should be noted that by softly assigning the responsibility of each velocity point using the posterior probability formula and iteratively updating the parameters through explicit closed-form solutions, the efficiency and physical rationality of the expectation-maximization algorithm are guaranteed.
[0015] Based on the above technical solution, and using the expectation, variance, and mixing coefficients of the Gaussian components, the total log-likelihood value of this round is iterated to obtain the conditional value L: ; The preset convergence conditions include: a preset threshold value; if the condition value L is greater than the preset threshold value or the number of iterations has not reached the upper limit value, the expectation, variance and mixing coefficient of the Gaussian component are repeatedly updated iteratively.
[0016] It should be noted that after the iteration is complete, when there are a total of K Gaussian components, the output is the final expectation of each Gaussian component. and variance .
[0017] Based on the above technical solution, the formula for calculating the Bayesian Information Criterion (BIC) value with K Gaussian components is as follows: ;in, ; This represents the total number of independent free parameters.
[0018] Based on the above technical solution, the method steps for iteratively fitting the stretched power spectral density in S3 to re-obtain the amplitude, expectation, and variance of each Gaussian component are as follows: S31. Using the optimal signal quantity and initial spectral moment parameters as initial values, read the stretched power spectrum data S. N The initial expectation of each Gaussian component is obtained as follows: The corresponding power spectral density And determine the initial amplitude. and initial variance The overall power spectral density distribution function is obtained. According to the calculation formula: ;in, ; Let represent the power spectral density of the i-th Gaussian component; v represents the Doppler velocity. S32. Using a nonlinear least squares iterative fitting method, S N and The optimization objective is to minimize the sum of squared residuals; the mean, variance, amplitude, and baseline parameters of each Gaussian component are iteratively adjusted to continuously reduce the deviation between the calculated values of the Gaussian mixture model and the measured scatter points; after the iterative calculation converges, the optimal Gaussian mixture model parameters are determined, and the fitting is completed; the fitting results are then output. and the power spectral density of each Gaussian component .
[0019] It should be noted that the total power spectral density distribution function This is the stretched power spectral density; nonlinear least squares fitting is used with the goal of minimizing the sum of squared residuals to accurately correct the mean, variance, amplitude and baseline of each Gaussian component, significantly improving the estimation accuracy of spectral peak parameters.
[0020] Based on the above technical solution, the method for calculating the echo power, average Doppler velocity, and spectral width of each effective signal is as follows: S41. Based on the power spectral density of each Gaussian component output, determine the final parameters of each Gaussian component output, including: amplitude. ,expect and variance k=0,1,…,K; Reconstruct the power spectral density of each Gaussian component k: ; ; in, This represents the power spectral density of the reconstructed k-th Gaussian component; This represents the amplitude of the reconstructed k-th Gaussian component; This represents the peak value of the sum of all fitted signals; Represents the original power spectrum; Indicates the noise level; S42. Based on the reconstructed power spectral density of each Gaussian component, determine the amplitude of the power spectral density of each Gaussian component; if there is an amplitude less than 0, it indicates that the signal is missing; if the amplitude is greater than 0, the signal is a valid signal. Calculate the echo power, average Doppler velocity, and spectral width of the signal according to the calculation formula: ; ; ; ; in, This represents the echo power of signal k; This indicates the accumulation of the power spectral density of the Gaussian component in signal k; w represents the average Doppler velocity of signal k. k This represents the spectral width of signal k; This represents the standard deviation of the Doppler velocity in signal k; S43, outputs the echo power, average Doppler velocity, and spectral width of all valid signals.
[0021] It should be noted that invalid signals are automatically eliminated by judging the positive or negative amplitude, and the echo power, average velocity and spectral width of the valid signals are calculated by using the standard weighted moment method, which ensures the physical reliability of the output parameters.
[0022] Compared with the prior art, the beneficial effects of the present invention are: 1. This invention integrates preprocessing, Gaussian mixture model and Bayesian information criterion for automatic number determination, iterative fitting and spectral moment calculation to adaptively determine the number of signals in the Doppler velocity power spectrum of pulse radar, which significantly improves the versatility and automation level of the signal processing method.
[0023] 2. By fitting the Gaussian mixture model, the expectation, variance, and mixing coefficient of each Gaussian component are obtained, and the initial parameters of the probability distribution function are objectively determined, which greatly solves the problem of negative power of a single signal in traditional methods.
[0024] 3. By adaptively processing the power spectrum of pulse Doppler radar, no additional settings are required for either single-target or multi-target scenarios, greatly accelerating computational efficiency and improving the estimation accuracy of spectral moment parameters. Attached Figure Description
[0025] Figure 1 This is a schematic diagram of the process steps of the single-channel and dual-channel signal alternating adaptive processing method for the Doppler power spectrum of pulse radar according to the present invention. Figure 2 This is a diagram showing the preprocessing results of power spectrum data in an embodiment of the single / dual-channel signal alternating adaptive processing method for pulse radar Doppler power spectrum of the present invention; Figure 3 This refers to the optimal number of signals determined by the BIC value in the embodiment of the single / dual-channel signal alternating adaptive processing method for pulse radar Doppler power spectrum of the present invention. Figure 4 This is the initial parameter estimation of different Gaussian components in the embodiment of the single- and dual-channel signal alternating adaptive processing method for pulse radar Doppler power spectrum of the present invention. Figure 5 This is the classification result of the velocity sequence in an embodiment of the single- and dual-channel signal alternating adaptive processing method for pulse radar Doppler power spectrum of the present invention; Figure 6 This is the result of fitting the optimal Gaussian mixture model parameters in an embodiment of the single / dual-channel signal alternating adaptive processing method for pulse radar Doppler power spectrum of the present invention; Figure 7 This is the output result of the effective signal in the embodiment of the single- and dual-channel signal alternating adaptive processing method for pulse radar Doppler power spectrum of the present invention. Detailed Implementation
[0026] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0027] Example 1: As Figure 1 As shown, this invention provides an adaptive processing method for alternating single and dual-channel signals in the Doppler power spectrum of pulse radar, comprising: The power spectrum data of the radar is read, and a three-point smoothing filter is applied to suppress high-frequency noise and random interference. The smoothed power spectrum data is then linearly stretched to normalize the total power, yielding the stretched power spectral density S. N (v): ; M can be set by the user according to their needs; Represents the original power spectrum. The noise levels are all known values; for example... Figure 2 As shown, the original power spectrum is preprocessed, with the horizontal axis representing Doppler velocity and the vertical axis representing power spectral density. The curve represents the preprocessed result, and the shaded area represents the original power spectrum data. Based on the stretched power spectral density S... N (v) Establish the velocity sequence and obtain the probability distribution function p(v) of the velocity sequence.
[0028] Furthermore, a variable k is preset to represent the number of Gaussian components. The initial value of variable k is 1, and the upper limit is the preset maximum number of Gaussian components K. In this embodiment, K is 6. Based on the preset maximum number of Gaussian components, the velocity sequence is divided into 6 Gaussian components, and the probability distribution of each Gaussian component is obtained. ; ; Where v represents the Doppler velocity; This represents the probability distribution of the velocity sequence in the k-th Gaussian component, specifically the power spectral density value of the k-th Gaussian component; This represents the expectation of the velocity sequence in the k-th Gaussian component, specifically the average velocity; This represents the variance of the velocity sequence in the k-th Gaussian component; This represents the mixing coefficient of the k-th Gaussian component.
[0029] Furthermore, based on the current value k of the Gaussian component, the expectation, variance, and mixing coefficient of each Gaussian component are initialized as parameters, and the expectation-maximization algorithm is used to iteratively update these parameters. The update process includes: calculating the posterior probability of each velocity point in each Gaussian component according to the probability distribution of each Gaussian component, based on the calculation formula: ; in, This represents the velocity point v in the k-th Gaussian component before iteration. i The posterior probability; This represents the mixing coefficient of the k-th Gaussian component before iteration; Specifically, it is a one-dimensional Gaussian probability density function, representing the k-th Gaussian component at the velocity point v. i The probability density at that location; This indicates that the k-th Gaussian component is at the velocity point v. i Weighted density at; This indicates that all Gaussian components are at the velocity point v. i The sum of weighted densities at each point; K represents the maximum Gaussian component number; Based on the posterior probability, the expectation, variance, and mixing coefficient of each Gaussian component are iteratively updated using the following formula: ; ; ; in, N k N represents the number of valid samples for the k-th Gaussian component; N represents the total number of data samples. This represents the expectation of the velocity sequence in the k-th Gaussian component after iterative update; This represents the variance of the velocity sequence in the k-th Gaussian component after iterative update; This represents the mixing coefficient of the k-th Gaussian component after iterative update.
[0030] Furthermore, the expectation, variance, and mixing coefficients of each Gaussian component are iteratively updated until the calculation result meets a preset convergence condition. In this embodiment, the preset convergence condition includes: a preset threshold value for the condition value. If the condition value L is greater than the preset threshold value or the number of iterations has not reached the upper limit, the expectation, variance, and mixing coefficients of the Gaussian component are iteratively updated repeatedly. Specifically, based on the expectation, variance, and mixing coefficients of the Gaussian component, the total log-likelihood value of this round is iterated to obtain the condition value L. The formula for calculating the condition value L is: .
[0031] Furthermore, based on the expectation, variance, and mixing coefficient of each Gaussian component after iterative updates, the Bayesian Information Criterion (BIC) value for having K Gaussian components is calculated using the formula: ;in, ; This represents the total number of independent free parameters.
[0032] Furthermore, the value of variable k is incremented by 1, and the Bayesian information criterion value for each Gaussian component is repeatedly calculated until the value of k equals the preset maximum number of Gaussian components K. At this point, the k value corresponding to the minimum Bayesian information criterion value is selected as the optimal signal quantity k. min It outputs the expected value, variance, and mixing coefficient of each Gaussian component after iterative updates as the initial spectral moment parameters.
[0033] In this embodiment, as Figure 3 As shown, by calculating the BIC value of variable k under different values, the optimal number of signals is adaptively determined. At this point, it is found that the optimal number of signals k is k when the Bayesian information content criterion value is minimized. min The maximum number of Gaussian components K is set to 2; where the horizontal axis represents the number of Gaussian components and the vertical axis represents the calculated BIC value; when the minimum BIC value is 0, it indicates that there is no valid signal.
[0034] In this embodiment, since the preset maximum number of Gaussian components K is 2, such as Figure 4 As shown, the initial spectral moment parameters for Gaussian component 1 and Gaussian component 2 are estimated respectively, where the horizontal axis represents the Doppler velocity and the vertical axis represents the power spectral density; Figure 5 As shown, the velocity series is established based on the power spectral density after stretching, where the horizontal axis represents the sequence number of the data points and the vertical axis represents the magnitude of the Doppler velocity.
[0035] Furthermore, using the optimal signal quantity and initial spectral moment parameters as initial values, the stretched power spectrum data S is read. N The initial expectation of each Gaussian component is obtained as follows: The corresponding power spectral density And determine the initial amplitude. and initial variance The overall power spectral density distribution function is obtained. According to the calculation formula: ;in, ; represents the power spectral density of the i-th Gaussian component; v represents the Doppler velocity.
[0036] Furthermore, a nonlinear least squares iterative fitting method is employed to fit S... N and The optimization objective is to minimize the sum of squared residuals; the mean, variance, amplitude, and baseline parameters of each Gaussian component are iteratively adjusted to continuously reduce the deviation between the calculated values of the Gaussian mixture model and the measured scatter points; after the iterative calculation converges, the optimal Gaussian mixture model parameters are determined, and the fitting is completed; the fitting results are then output. and the power spectral density of each Gaussian component .
[0037] In this embodiment, as Figure 6 As shown, the horizontal axis represents Doppler velocity, and the vertical axis represents power spectral density. The blue and orange fill colors in the figure represent the Gaussian distributions of the two separated signals, respectively. The black scatter dots represent the original power spectrum, and the red dashed line represents the fitting result of the output. Based on the power spectral density of each Gaussian component and fitting results Calculate the echo power, average Doppler velocity, and spectral width of the signal, such as Figure 7 As shown, it includes: amplitude ,expect and variance k=0,1,…,K; Reconstruct the power spectral density of each Gaussian component k: ; ; in, This represents the power spectral density of the reconstructed k-th Gaussian component; This represents the amplitude of the reconstructed k-th Gaussian component; This represents the peak value of the sum of all fitted signals; Represents the original power spectrum; Indicates the noise level; Based on the reconstructed power spectral density of each Gaussian component, determine the amplitude of the power spectral density of each Gaussian component; if the amplitude is less than 0, the signal is missing; if the amplitude is greater than 0, the signal is valid. Calculate the echo power, average Doppler velocity, and spectral width of the signal according to the calculation formula: ; ; ; ; in, This represents the echo power of signal k; This indicates the accumulation of the power spectral density of the Gaussian component in signal k; w represents the average Doppler velocity of signal k. k This represents the spectral width of signal k; This represents the standard deviation of the Doppler velocity in signal k.
[0038] Furthermore, based on the above spectral moment estimation results, the stretched power spectral density S is obtained. N (v): ; M can be set by the user according to their needs; Represents the original power spectrum. The noise levels are all known values.
[0039] It should be noted that, Figure 7 The vertical red dashed lines represent the average Doppler velocities of the two signals; the blue and orange fill colors represent the spectral widths w of the two signals, respectively. k The black dots represent the original power spectrum; the horizontal axis represents the Doppler velocity, and the vertical axis represents the power spectral density.
[0040] Furthermore, the echo power, average Doppler velocity, and spectral width of all valid signals are output.
[0041] In this embodiment, compared with other mixed signal processing algorithms, this algorithm achieves automatic identification of single and dual signals, with a single signal identification accuracy of 96.29% and a dual signal identification accuracy of 92.37%, and requires no manual intervention, supporting batch processing of massive network data. By objectively estimating initial parameters through GMM, the non-physical results of negative power are effectively avoided, and the data validity is greatly improved. The weighted moment method is used to calculate spectral moment parameters. The average Doppler velocity RMSE for single signal is 0.84 m / s, and the spectral width RMSE is 0.18 m / s; the average Doppler velocity RMSE for dual signal is approximately 0.36 m / s, and the spectral width RMSE is approximately 0.46 m / s, which significantly improves the estimation accuracy.
[0042] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered in all respects as exemplary and non-limiting, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.
Claims
1. A method for alternating adaptive processing of single and dual-channel signals in the Doppler power spectrum of pulse radar, characterized in that: include: S1. Read the power spectrum data of the radar, preprocess the power spectrum data, and obtain the stretched power spectral density. S2. Establish a velocity sequence based on the stretched power spectral density, automatically determine the optimal signal quantity based on the Gaussian mixture model and Bayesian information criterion, estimate the expectation, variance and mixing coefficient of each Gaussian component and use them as initial spectral moment parameters. The steps of the method for automatically determining the optimal signal quantity based on Gaussian mixture model and Bayesian information content criterion are as follows: S21. A preset variable k is used to determine the number of Gaussian components. The initial value of the variable k is 1, and the upper limit value is the preset maximum number of Gaussian components K. S22. Based on the current value k of the Gaussian component, initialize the expected value, variance and mixing coefficient of each Gaussian component, and use the expected value maximization algorithm to iteratively update the above parameters until the calculation result meets the preset convergence condition. S23. Based on the expected value, variance and mixing coefficient of each Gaussian component after iterative update, calculate the Bayesian information criterion value corresponding to the Gaussian component at the current value k. S24. Increment the value of variable k by 1, and repeat S21-S23 until the value of k is equal to the preset maximum number of Gaussian components K. S25. Based on the Bayesian information criterion values corresponding to each Gaussian component in S21-S24, select the k value corresponding to the minimum Bayesian information criterion value as the optimal signal quantity k. min The output will include the expected value, variance, and mixing coefficient of each Gaussian component after iterative updates, which will be used as the initial spectral moment parameters. S3. Using the optimal signal quantity and initial spectral moment parameters as initial values, iteratively fit the stretched power spectral density to obtain the amplitude, expectation, and variance of each Gaussian component. The steps for iteratively fitting the stretched power spectral density to re-obtain the amplitude, expectation, and variance of each Gaussian component are as follows: S31. Using the optimal signal quantity and initial spectral moment parameters as initial values, read the stretched power spectrum data S. N The initial expectation of each Gaussian component is obtained as follows: The corresponding power spectral density and determine the initial amplitude. and initial variance The overall power spectral density distribution function is obtained. According to the calculation formula: ;in, ; Let v represent the power spectral density of the i-th Gaussian component; v represents the Doppler velocity. S32. Using a nonlinear least squares iterative fitting method, S N and The optimization objective is to minimize the sum of squared residuals; the mean, variance, amplitude, and baseline parameters of each Gaussian component are iteratively adjusted to continuously reduce the deviation between the calculated values of the Gaussian mixture model and the measured scatter points; after the iterative calculation converges, the optimal Gaussian mixture model parameters are determined, and the fitting is completed; the fitting results are then output. and the power spectral density of each Gaussian component ; S4. Reconstruct the power spectral density for the non-negative Gaussian components and output the echo power, average Doppler velocity, and spectral width for each valid signal.
2. The single / dual-channel signal alternating adaptive processing method for pulse radar Doppler power spectrum according to claim 1, characterized in that: Based on the power spectral density S after stretching N (v), establish a velocity sequence, obtain the probability distribution function p(v) of the velocity sequence, and divide the velocity sequence into K Gaussian components according to the preset maximum number of Gaussian components, and obtain the probability distribution of each Gaussian component: ； ； Where v represents the Doppler velocity; This represents the probability distribution of the velocity sequence in the k-th Gaussian component, specifically the power spectral density value of the k-th Gaussian component; This represents the expectation of the velocity sequence in the k-th Gaussian component, specifically the average velocity; This represents the variance of the velocity sequence in the k-th Gaussian component; This represents the mixing coefficient of the k-th Gaussian component.
3. The single / dual-channel signal alternating adaptive processing method for pulse radar Doppler power spectrum according to claim 2, characterized in that: The process of iteratively updating the parameters using the expectation-maximization algorithm includes: calculating the posterior probability of each velocity point in each Gaussian component based on the probability distribution of each Gaussian component, according to the calculation formula: ； in, This represents the velocity point v in the k-th Gaussian component before iteration. i The posterior probability; This represents the mixing coefficient of the k-th Gaussian component before iteration; Specifically, it is a one-dimensional Gaussian probability density function, representing the k-th Gaussian component at the velocity point v. i The probability density at that location; This indicates that all Gaussian components are at the velocity point v. i The sum of weighted densities at each point; K represents the maximum Gaussian component number; Based on the posterior probability, the expectation, variance, and mixing coefficient of each Gaussian component are iteratively updated using the following formula: ； ； ； in, N k N represents the number of valid samples for the k-th Gaussian component; N represents the total number of data samples. This represents the expectation of the velocity sequence in the k-th Gaussian component after iterative update; This represents the variance of the velocity sequence in the k-th Gaussian component after iterative update; This represents the mixing coefficient of the k-th Gaussian component after iterative update.
4. The single / dual-channel signal alternating adaptive processing method for pulse radar Doppler power spectrum according to claim 3, characterized in that: Based on the expectation, variance, and mixing coefficients of the Gaussian components, the total log-likelihood value for this round is iterated to obtain the conditional value L: ； The preset convergence conditions include: a preset threshold value; if the condition value L is greater than the preset threshold value or the number of iterations has not reached the upper limit value, the expectation, variance and mixing coefficient of the Gaussian component are repeatedly updated iteratively.
5. The single / dual-channel signal alternating adaptive processing method for pulse radar Doppler power spectrum according to claim 4, characterized in that: The formula for calculating the Bayesian Information Criterion (BIC) value with K Gaussian components is as follows: ;in, ; This represents the total number of independent free parameters.
6. The single / dual-channel signal alternating adaptive processing method for pulse radar Doppler power spectrum according to claim 1, characterized in that: The method for calculating the echo power, average Doppler velocity, and spectral width of each valid signal is as follows: S41. Based on the power spectral density of each Gaussian component output, determine the final parameters of each Gaussian component output, including: amplitude. ,expect and variance k=0,1,…,K; Reconstruct the power spectral density of each Gaussian component k: ； ； in, This represents the power spectral density of the reconstructed k-th Gaussian component; This represents the amplitude of the reconstructed k-th Gaussian component; This represents the peak value of the sum of all fitted signals; Represents the original power spectrum; Indicates the noise level; S42. Based on the reconstructed power spectral density of each Gaussian component, determine the amplitude of the power spectral density of each Gaussian component; if there is an amplitude less than 0, it indicates that the signal is missing; if the amplitude is greater than 0, the signal is a valid signal. Calculate the echo power, average Doppler velocity, and spectral width of the signal according to the calculation formula: ； ； ； ； in, This represents the echo power of signal k; This indicates the accumulation of the power spectral density of the Gaussian component in signal k; w represents the average Doppler velocity of signal k. k This represents the spectral width of signal k; This represents the standard deviation of the Doppler velocity in signal k; S43, outputs the echo power, average Doppler velocity, and spectral width of all valid signals.
7. The single / dual-channel signal alternating adaptive processing method for pulse radar Doppler power spectrum according to any one of claims 1-6, characterized in that: The preprocessing in S1 includes: performing three-point smoothing filtering on the power spectrum data to suppress high-frequency noise and random interference; and performing linear stretching on the three-point smoothed power spectrum data to normalize the total power of the power spectrum to a preset range to obtain the stretched power spectral density.