Non-gaussian weather radar signal adaptive spectral moment estimation method based on clustering algorithm

Abstract

The application discloses a non-Gaussian weather radar signal adaptive spectral moment estimation method based on a clustering algorithm. Firstly, a Gaussian mixture model is used to model a non-Gaussian power spectrum, and an elbow rule is used to calculate the number K of Gaussian power spectrums contained in the non-Gaussian signal. Then, a K-means clustering algorithm is used to cluster sampling points of the power spectrum of the non-Gaussian signal, and the mean and variance of the clustering are used as initial values of spectral moments. Finally, an expectation maximization algorithm is used to further estimate the spectral moments. The application can effectively estimate the spectral moment parameters when the power spectrum of a weather signal is in a non-Gaussian distribution and traditional spectral moment estimation methods fail.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of weather radar, and particularly relates to a non-Gaussian weather radar signal adaptive spectral moment estimation method based on a clustering algorithm. BACKGROUND

[0002] For a weather radar, the detection target is mainly a spatially distributed target such as a cloud rain particle. These distributed targets are usually filled with the entire radar beam unit, so the signal received by the radar antenna is not the echo from a single target, but the sum of the backscattering echoes of many scatterers distributed in the radar irradiation direction. When the radar resolution volume (RVV) is uniformly filled by weather particles, the power spectrum of the weather signal is usually assumed to be Gaussian. After the echo is received and collected by the radar receiver, I and Q data are obtained, and the spectral moment is estimated by using the power spectral density (i.e. the FFT method) or the pulse pair processing (PPP) method, so that useful information such as target scattering intensity, average speed and speed spectrum width can be obtained, and the extraction of weather basic data is completed. However, for a fixed radar beam width, the size of the RVV increases with the increase of the detection distance, resulting in the possibility that the RVV is filled with various distributed weather particles, i.e. non-uniform filling. At this time, the power spectrum may deviate from the Gaussian type and present various forms such as double peaks, flat peaks, sharp peaks or skewed peaks. At this time, the basic data estimated by using the FFT method or the PPP method will have a large deviation, and therefore a new method is needed to estimate the basic data of the non-Gaussian signal.

[0003] The current spectral moment estimation method for non-Gaussian signals mainly uses the parameterization method. Dias et al. [5] proposed a band-limited estimator. Under the assumption that the signal power spectrum is band-limited, the maximum likelihood estimation of the spectral moment was derived and the spectral moment parameters were calculated. When the spectrum is asymmetric or the spectrum width is large, the performance of the band-limited estimator is better than that of the PPP method, but the calculation amount is large and real-time processing is not possible. Boyer et al. [6][7] proposed a method for estimating the spectral moment by using the random maximum likelihood estimation (SML) and the weighted pseudo subspace fitting (WPSF). Yu et al. [8] modeled the non-Gaussian signal power spectrum as a mixture of two Gaussian spectra, and used a nonlinear fitting algorithm to estimate six spectral moments. The Gauss-Newton iteration method was used to minimize the cost function. This method needs to select appropriate initial values, and the Gauss-Newton method increases the calculation complexity. Pinsky et al. [9] used adaptive filtering technology and a parameterized model to estimate the spectral moment parameters. This method has good performance in the case of low signal-to-noise ratio, but the performance decreases seriously when the number of sampling points is small. The above parameterization methods need to estimate the spectral moment by iteration, and are sensitive to the initial value. An inappropriate initial value will make the algorithm converge to the wrong estimate, and the algorithm has a large calculation amount and high complexity. SUMMARY

[0004] In view of this, the present invention provides an adaptive spectral moment estimation method for non-Gaussian weather radar signals based on clustering algorithms, which can effectively estimate spectral moment parameters when the power spectrum of the weather signal is non-Gaussian and traditional spectral moment estimation methods fail.

[0005] The technical solution for implementing the present invention is as follows:

[0006] An adaptive spectral moment estimation method for non-Gaussian weather radar signals based on clustering algorithms is proposed. First, a Gaussian mixture model (GMM) is used to model the non-Gaussian power spectrum, and the elbow rule is used to calculate the number K of Gaussian power spectra contained in the non-Gaussian signal. Then, the K-means clustering algorithm is used to cluster the sampling points of the power spectrum of the non-Gaussian signal, and the mean and variance of the clusters are used as the initial values ​​of the spectral moments. Finally, the expectation-maximization (EM) algorithm is used to further estimate the spectral moments.

[0007] Furthermore, the K-means clustering algorithm is used to cluster the sampling points of the power spectrum of the non-Gaussian signal, and the mean and variance of the clusters are used as the initial values ​​of the spectral moments. Specifically:

[0008] Step 21: Using the elbow rule, the K value represents that this dataset has K different categories. For each category, randomly select a value and guess its center point μ1, μ2, ..., μ. K ;

[0009] Step 22, calculate the values ​​of a sample up to μ1, μ2, ..., μ K The distance between the sample and μ k The distance is minimized, μ k ∈(μ1,μ2,…,μ K ), then r ik =1, that is:

[0010]

[0011] Step 23: Recalculate the cluster center for each category, letting the loss function J(K) be related to μ. k The derivative of is zero, which means that the initial mean, spectral width and weights in category k that minimize the loss function are obtained;

[0012] Step 24: Repeat steps 22 and 23, iterating until convergence. Where ε is the convergence threshold and P is the number of iterations, the optimal initial parameters are obtained when the convergence condition is met or the set number of iterations is reached. and

[0013] Furthermore,

[0014]

[0015]

[0016]

[0017] f i For the i-th sample in the data set, i = 1, …, M, M is the number of pulse accumulation, r ik Indicates the selection coefficient, S(f i ) is the signal power spectral density, μ k Indicates the mean of the k-th Gaussian spectrum component.

[0018] Further, the number of Gaussian power spectrum K is calculated for each distance gate signal, if the calculated K = 1, the traditional PPP method is used to estimate the spectrum moment; if K > 1, the remaining steps of the method are continued to be executed until the spectrum moment estimation of the entire area is completed.

[0019] Beneficial effects:

[0020] 1. The non-Gaussian weather radar signal adaptive spectrum moment estimation method based on the clustering algorithm can effectively estimate the spectrum moment parameters when the weather signal power spectrum is non-Gaussian distribution and the traditional spectrum moment estimation method fails.

[0021] 2. Compared with other parameterization methods for non-Gaussian power spectrum spectrum moment estimation, the power spectrum characteristics and power spectrum initial value do not need to be known in advance, and the calculation method based on the clustering algorithm is relatively simple, and the adaptive spectrum moment estimation can be realized. Therefore, the adaptive spectrum moment estimation of the non-Gaussian weather signal can be realized.

[0022] 3. In addition, the estimated each speed and spectrum width component can be used for modeling the particles with different drop spectrum distribution in the radar resolution unit, and the water content and other parameters are inverted; these results are also helpful for the suppression and separation research of ground clutter. Therefore, the present application has great research and application value. DETAILED DESCRIPTION

[0023] Figure 1 It is a flow chart of the non-Gaussian weather radar signal adaptive spectrum moment estimation method based on the clustering algorithm;

[0024] Figure 2 It is the reflectivity factor distribution of the observed supercell;

[0025] Figure 3 It is the distribution of the Gaussian spectrum number K of each resolution unit in the detection area;

[0026] Figure 4The cost function of three typical resolution units with the number of Gaussian spectrum and the corresponding K value, wherein the elbow rule can be used to obtain the K value corresponding to figures (a)-(c) K=1, K=2 and K=3 respectively;

[0027] Figure 5 The distribution of each velocity component estimated by the present application; wherein figure (a) is the velocity estimated by the traditional PPP method, and figures (c-d) are three velocity components estimated by the present application respectively;

[0028] Figure 6 The distribution of each spectrum width component estimated by the present application; wherein figure (a) is the spectrum width estimated by the traditional PPP method, and figures (c-d) are three spectrum width components estimated by the present application respectively. DETAILED DESCRIPTION

[0029] The present application will be described in detail below with reference to the accompanying drawings and examples.

[0030] The present application will be described in detail below with reference to the accompanying drawings and examples. Figures 1 to 6 The present application will be described in detail below with reference to the accompanying drawings and examples. Figure 2 The reflectivity factor distribution of the observation target.

[0031] Table 1 Radar parameters

[0032]

[0033] As shown in the figure, the steps of the non-Gaussian weather signal adaptive spectrum moment estimation algorithm based on the clustering algorithm of the present application include: Figure 1 Step 1, model the non-Gaussian power spectrum using the Gaussian mixture model, and calculate the number of Gaussian spectra contained in the non-Gaussian signal using the elbow rule. Specifically, it includes:

[0034] After obtaining the radar complex sequence Z(m) in a distance gate, Fourier transform Z(m) and take the square of the modulus to obtain the signal power spectrum density S(f i ) in the distance gate:

[0035]

[0036]

[0037] Wherein M is the number of pulse accumulation, m is the sampling sequence, T s is the pulse repetition time, f i ​is the i-th sample in the dataset.

[0038] Assume that the signal power spectral density within the distance gate is represented by a Gaussian Mixture Model (GMM), i.e. composed of K Gaussian power spectra, the normalized power spectrum (1) can be written as:

[0039]

[0040] where is the k-th Gaussian spectral component. w k , μ k is the weight, mean, and σ fk is the standard deviation of the k-th Gaussian spectral component.

[0041] Next, the elbow method is used to obtain the optimal number of Gaussian spectra K contained in the GMM. For the frequency sequence dataset {f1, f2, …, f i , …, f M} in the Doppler domain, define the cost function: the sum of the squared errors of all samples to the mean of the class to which they belong:

[0042]

[0043] where μ k is the mean of the k-th Gaussian spectrum, K is the number of Gaussian spectra, M is the number of samples in the dataset (i.e. the number of sampling points), r ik is the selection coefficient, and f i only belongs to one class, i.e.:

[0044]

[0045] Starting from the number of classes K = 1, when the number of classes K is less than the true number of classes, as the number of classes increases, J(K) will quickly decrease, and when the number of classes reaches the critical point of the true number of classes, J(K) starts to slowly decrease, that is, the relationship curve of J(K) and K is an elbow shape, and the K value corresponding to the elbow can be considered as the appropriate number of classes.

[0046] Draw the curve of the cost function J(K) with respect to the number of Gaussian spectra K, and according to the elbow method, the optimal K value can be found; in addition, if the overall curve does not change much, i.e. the maximum gradient of the curve is less than a certain threshold (such as 0.5), then the value of K is judged to be 1, i.e. only one Gaussian spectrum is contained.

[0047] Step 2, use the K-means clustering algorithm to obtain the initial value of the spectral moment. Specifically, it includes:

[0048] The K-means clustering algorithm is an iterative algorithm, and each iteration involves two consecutive steps, which correspond to {rik} and {μ k} are optimized.

[0049] Step 21, the K value obtained by elbow rule represents K different categories of the data set, and the center point μ1, μ2, …, μK of each category is randomly guessed. K ;

[0050] Step 22, the distance of a sample to μ1, μ2, …, μK is calculated, if the distance of the sample to μk is the smallest, μk is the center of the category, and μk ∈ (μ1, μ2, …, μK), k = 1, 2, …, K, then r = 1. K ; k k K ik ;

[0051] Step 23, the clustering center of each category is recalculated. Let the derivative of the loss function J(K) with respect to μk be zero, that is, the initial mean, spectral width and weight of the category k that minimizes the loss function are obtained. k ;

[0052] Step 24, steps 22 and 23 are repeated, and iteration is continuously performed until convergence, that is, where ε is the convergence threshold (such as 0.001), and P is the number of iterations. When the convergence condition is met or the set number of iterations (such as 1000) is reached, the optimal initial parameters μk and σk are obtained. ;

[0053]

[0054] Step 3, the spectral moment is further estimated by using the EM algorithm. Specifically, it includes:

[0055] The EM algorithm is used to find the maximum likelihood estimation of the parameters in the probability model that depends on the hidden variable (such as μk and σk). ; The main steps are as follows: E step: calculate the conditional expectation of the log-likelihood function with respect to the hidden variable; M step: maximize the expectation and update the parameter estimation value. This is repeated until the likelihood function converges to a local optimal solution, thereby obtaining the optimal spectral moment parameters.

[0056] Step 31, E step: using the initial parameters μk and σk obtained in step 2, the likelihood of each sample f i coming from model k is calculated. ;

[0057]

[0058] ​​​​Step 32, M step: calculate the log-likelihood function of formula (2):

[0059]

[0060] Maximize formula (7) and calculate the model parameters of a new round of iteration:

[0061]

[0062] Step 33, repeat step 31 and step 32, and iterate until convergence, that is And Where ε1 and ε2 are convergence thresholds (such as both taking 0.001), P is the number of iterations, when the convergence condition is met or the set number of iterations (such as 1000) is reached, the best model parameters And

[0063] Step 4, repeat step 1 for each distance gate signal, if K=1 calculated in step 1, then use the traditional PPP method to estimate the spectral moment; if K>1, then repeat steps 2 and 3 until the entire region is completed. Spectral moment estimation.

[0064] So far, all steps are completed.

[0065] Figure 3 To detect the distribution of the number of Gaussian spectra K of each resolution unit in the region; Figure 4 The change of the cost function with the number of Gaussian spectra in three typical resolution units and the corresponding K value, from the figure, it can be seen that the elbow rule can obtain the K values corresponding to figures (a)-(c) K=1, K=2 and K=3, respectively. The dotted circle represents the elbow position of the best K value, wherein, Figure 4 The maximum gradient of the curve of (a) is less than 0.5, so the value of K is judged to be 1, that is, only one Gaussian spectrum is contained.

[0066] Figure 5 (a-d) and Figure 6 (a-d) are the distributions of each velocity and spectral width component estimated by the present application, wherein figure (a) is the velocity and spectral width estimated by the traditional PPP method, and figures (c-d) are three velocity and spectral width components estimated by the present application. It can be seen from the figure that the power spectrum of most non-Gaussian regions (i.e. K>1) is mainly double Gaussian spectrum. In addition, from Figure 2 And Figure 3 It can be seen that position ① may be a non-uniform convective precipitation region, so the power spectrum presents a non-Gaussian distribution; position 2 is a uniform precipitation region, and the power spectrum presents a Gaussian distribution; and position three is because the target distance from the radar is too far, resulting in a large radar resolution unit, which is filled with non-uniform meteorological particles, resulting in a non-Gaussian power spectrum.

[0067] To sum up, the above is only the preferred embodiment of the present application, and is not used to limit the protection scope of the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. An adaptive spectral moment estimation method for non-Gaussian weather radar signals based on clustering algorithms, characterized in that, First, a Gaussian mixture model is used to model the non-Gaussian power spectrum, and the elbow rule is used to calculate the number K of Gaussian power spectra in the non-Gaussian signal. Then, the K-means clustering algorithm is used to cluster the sampling points of the power spectrum of the non-Gaussian signal, and the mean and variance of the clusters are used as the initial values ​​of the spectral moments. Finally, the expectation-maximization algorithm is used to further estimate the spectral moments. The K-means clustering algorithm is used to cluster the sampling points of the power spectrum of the non-Gaussian signal, and the mean and variance of the clusters are used as the initial values ​​of the spectral moments. Specifically: Step 21: Using the elbow rule, the K value represents that this dataset has K different categories. For each category, randomly select a value and guess its center point μ1, μ2, ..., μ. K ; Step 22, calculate the values ​​of a sample up to μ1, μ2, ..., μ K The distance between the sample and μ k The distance is minimized, μ k ∈(μ1,μ2,…,μ K ), then r ik =1, that is: Step 23: Recalculate the cluster center for each category, letting the loss function J(K) be related to μ. k The derivative of is zero, which means that the initial mean, spectral width and weights in category k that minimize the loss function are obtained; Step 24: Repeat steps 22 and 23, iterating until convergence. Where ε is the convergence threshold and P is the number of iterations, the optimal initial parameters are obtained when the convergence condition is met or the set number of iterations is reached. and f i Let r be the i-th sample in the dataset, i = 1, ..., M, where M is the number of accumulated impulses. ik S(f) represents the selection coefficient. i ) represents the signal power spectral density, μ k This represents the mean of the k-th Gaussian spectral component; Step 31, using the obtained initial parameters and Calculate f for each sample i Possibilities from model k in, For the k-th Gaussian spectral component, w k μ k σ represents the weight and mean of the k-th Gaussian spectral component. fk This represents the standard deviation of the k-th Gaussian spectral component; Step 32, calculate the log-likelihood function of the power spectrum: Maximize equation (7) and calculate the model parameters for the next iteration: Step 33: Repeat steps 31 and 32, iterating until convergence. and Where ε1 and ε2 are convergence thresholds, and P is the number of iterations. When the convergence condition is met or the set number of iterations is reached, the optimal model parameters can be estimated. and 2. The adaptive spectral moment estimation method for non-Gaussian weather radar signals based on clustering algorithm as described in claim 1, characterized in that, For each signal within a distance gate, calculate the number of Gaussian power spectra K. If the calculated K = 1, then use the traditional PPP method to estimate the spectral moments; if K > 1, then continue to perform the remaining operations of the method described in claim 1 until the spectral moment estimation of the entire region is completed.

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