LFM signal parameter estimation method based on ranksvm-frft

Abstract

The RankSVM-FRFT-based LFM signal parameter estimation method relates to a signal parameter estimation method, solves the problems that the existing maximum, negative Shannon entropy and other traditional single evaluation functions are easily affected by noise, the optimal order of FRFT is deviated, false extreme values are formed, and the estimation of the frequency modulation rate and the center frequency of the LFM signal is affected, and the like. The present application constructs a noisy LFM signal training sample, extracts the fractional domain energy aggregation features under different FRFT orders, and then learns the good and bad order ranking relationship of the FRFT through RankSVM; the optimal FRFT order of the signal to be estimated is determined by using the evaluation function, and finally the frequency modulation rate and the center frequency of the LFM signal are estimated. The present application can significantly improve the estimation accuracy of the center frequency and the frequency modulation rate of the LFM signal under the condition of low signal-to-noise ratio [‑13,‑9] dB, and has better noise resistance and robustness.

Description

Technical Field

[0001] This invention relates to signal parameter estimation methods, specifically to a linear frequency modulation (LFM) signal parameter estimation method based on ranked support vector machine-fractional Fourier transform (RankSVM-FRFT). Background Technology

[0002] The frequency of an LFM signal changes linearly with time. It is a typical non-stationary signal with good time-domain and frequency-domain compression characteristics as well as Doppler frequency shift characteristics. It has wide applications in communication, sonar, seismic exploration and biomedicine.

[0003] Traditional spectral analysis methods, based on the Fast Fourier Transform (FFT), cannot reflect the frequency-time variation characteristics of non-stationary signals. Time-frequency analysis methods, however, can characterize the evolution of a signal's time and frequency domain characteristics over time, accurately capturing the distribution and changes in signal frequency at different moments. Therefore, they are often used to process such non-stationary signals. Commonly used time-frequency analysis methods include the Short-Time Fourier Transform (STFT), Continuous Wavelet Transform (CWT), S-Transform, and Wegener-Weil Distribution (WVD), among others.

[0004] Among these methods, STFT uses a fixed window function for analysis, which is computationally simple, but the choice of window length determines the trade-off between time-domain and frequency-domain clustering, making it difficult to achieve a fine characterization of both time and frequency. CWT adjusts the analysis resolution through variable scaling, enabling multi-resolution capabilities, but the choice of basis functions significantly affects the results, and there is currently no unified theory or criterion to guide the optimal selection of basis functions. S-transform combines the characteristics of STFT and wavelets, improving time-frequency clustering to some extent through frequency-adaptive windows, but its computational cost is high. WVD does not rely on window function limitations and has high time-frequency clustering, but its bilinear characteristics lead to cross-term interference when processing multi-component signals, easily masking the true signal characteristics. In contrast, the fractional Fourier transform (FRFT) exhibits unique advantages in LFM signal processing. FRFT can highly concentrate the energy of linear frequency modulated signals in a specific fractional domain, facilitating parameter detection and extraction. Especially when processing multi-component LFM signals, FRFT does not have the cross-term interference problem common in WVD-like methods, making FRFT-based LFM signal parameter estimation stand out among many methods.

[0005] However, the accuracy of the FRFT method largely depends on the evaluation function's determination of the optimal transform order. The evaluation function quantifies and assesses the FRFT result of the LFM signal, determining the optimal order by optimizing within the search space constructed by this function, thus transforming the problem of determining the optimal order into a numerical optimization problem. Traditional FRFT typically uses maximum values, negative Shannon entropy, etc., as evaluation functions. Under low signal-to-noise ratio (SNR) conditions, these evaluation functions can deviate in their representation of the optimal order, creating spurious extrema and misleading the search to local optima or even incorrect solutions.

[0006] To address this problem, this invention proposes a RankSVM-FRFT-based method for estimating LFM signal parameters. This method constructs a training dataset covering multiple modulation frequencies, multiple center frequencies, and multiple signal-to-noise ratios, extracts fractional-domain energy aggregation features, and trains a RankSVM ranking model. This model is then used to evaluate the FRFT search order of the signal to be estimated to determine the optimal value, thereby completing the estimation of the modulation frequency and center frequency of the LFM signal. Summary of the Invention

[0007] This invention addresses the problems in existing technologies, such as the susceptibility of traditional single evaluation functions like maximum value and negative Shannon entropy to noise, which can shift the optimal order representation of FRFT, leading to false extrema and affecting the estimation of LFM signal modulation frequency and center frequency. It provides a RankSVM-FRFT-based method for estimating LFM signal parameters.

[0008] The LFM signal parameter estimation method based on RankSVM-FRFT is implemented by the following steps:

[0009] Step 1: Construct training samples of noisy LFM signals with multiple tuning frequencies, multiple center frequencies, and multiple signal-to-noise ratios, and construct a set of effective candidate orders for each noisy LFM signal training sample.

[0010] Step 2: Extract the fractional domain amplitude spectrum features of each noisy LFM signal training sample at different FRFT orders to obtain the standardized feature matrix;

[0011] Step 3: Learn the ranking relationship of FRFT orders through the RankSVM ranking model to obtain the RankSVM evaluation function for candidate orders;

[0012] Step 4: Input the noisy LFM signal to be estimated, use the RankSVM evaluation function to determine the optimal FRFT order estimate, and calculate the estimated frequency modulation frequency and center frequency of the noisy LFM signal to be estimated.

[0013] The beneficial effects of the present invention are as follows: The estimation method described in the present invention transforms the FRFT optimal order optimization into a candidate order ranking learning task. By extracting the eight-dimensional energy aggregation features in the fractional domain to train the RankSVM ranking model, the merits of each order are comprehensively evaluated. This overcomes the shortcomings of single evaluation functions such as maximum value and negative Shannon entropy, which are easily affected by noise interference and have the disadvantage of bias in optimal order determination.

[0014] Simulation results show that, under strong noise conditions of [-13, -9] dB, the root mean square error of LFM signal modulation frequency and center frequency estimation can be significantly reduced, the parameter estimation accuracy can be greatly improved, and it has stable adaptability to LFM signals with different modulation frequencies. The overall noise resistance and algorithm robustness are better than the traditional FRFT parameter estimation scheme, which can provide a more reliable technical means for LFM signal detection and parameter extraction in strong noise scenarios such as communication and sonar. Attached Figure Description

[0015] Figure 1 This is a flowchart of the LFM signal parameter estimation method based on RankSVM-FRFT described in this invention;

[0016] Figure 2 This is a schematic diagram of the LFM signal in this invention; wherein, (a) is an ideal time-domain waveform diagram, (b) is an ideal time-frequency relationship diagram, (c) is a time-domain waveform diagram with SNR=0dB, (d) is a time-frequency relationship diagram with SNR=0dB, (e) is a time-domain waveform diagram with SNR=-20dB, and (f) is a time-frequency relationship diagram with SNR=-20dB.

[0017] Figure 3 This is a schematic diagram of coordinate axis rotation in FRFT transformation;

[0018] Figure 4 The energy concentration of FRFT; where (a) is a schematic diagram of the fractional domain transform of the LFM signal; (b) is a schematic diagram of the fractional domain signal when the transform order p=0.7; (c) is a schematic diagram of the fractional domain signal when the transform order p=1.14656; (d) is a schematic diagram of the fractional domain signal when the transform order p=1.3.

[0019] Figure 5 Flowchart for training the RankSVM model;

[0020] Figure 6 A flowchart for LFM parameter estimation using FRFT;

[0021] Figure 7 This is a schematic diagram illustrating the performance of the RankSVM model in evaluating the FRFT order.

[0022] Figure 8A comparison of the accuracy of various evaluation functions FRFT (Maximum-FRFT, Peak Energy Ratio-FRFT, Negentropy-FRFT, and RankSVM-FRFT) under different SNRs. =0, =30) Renderings; where (a) is a schematic diagram of the frequency modulation estimation RMSE; (b) is a schematic diagram of the starting frequency estimation RMSE;

[0023] Figure 9 A comparison of the accuracy of various evaluation functions FRFT (Maximum-FRFT, Peak Energy Ratio-FRFT, Negentropy-FRFT, and RankSVM-FRFT) under different SNRs. =0, =50) Renderings; where (a) is a schematic diagram of the frequency modulation estimation RMSE; (b) is a schematic diagram of the starting frequency estimation RMSE;

[0024] Figure 10 A comparison of the accuracy of various evaluation functions FRFT (Maximum-FRFT, Peak Energy Ratio-FRFT, Negentropy-FRFT, and RankSVM-FRFT) under different SNRs. =0, =70) Renderings; where (a) is a schematic diagram of the frequency modulation estimation RMSE; (b) is a schematic diagram of the starting frequency estimation RMSE. Detailed Implementation

[0025] Specific Implementation Method 1: Combination Figures 1 to 6 This embodiment describes an LFM signal parameter estimation method based on RankSVM-FRFT, which is implemented through the following steps:

[0026] Step S1. Construct training samples of noisy LFM signals with multiple tuning frequencies, multiple center frequencies, and multiple signal-to-noise ratios, and obtain the effective candidate order set for each training sample; the specific implementation process is as follows:

[0027] Step S11: Generate ideal LFM signal samples;

[0028] Set amplitude Modulation period Number of sampling points In frequency tuning and center frequency Parameters are randomly selected uniformly within the range of values, and ideal LFM signal samples are generated based on the selected parameters. ;

[0029] The ideal LFM signal formula is defined as follows:

[0030] (1)

[0031] In the formula, , , , These represent the amplitude, center frequency, frequency modulation (FM), and frequency modulation period of the LFM signal, respectively.

[0032] In this embodiment, the LFM signal parameters are set as follows: , , , =0, then the time-domain waveform and time-frequency relationship of the signal are as follows: Figure 2 As shown.

[0033] As can be seen from the time-domain waveform (a), the density of the signal waveform changes regularly over time: since k>0 in this example, the waveform gradually becomes denser from left to right, corresponding to a linear increase in instantaneous frequency, while the negative half-axis shows the opposite. The time-frequency relationship (b) more directly demonstrates the time-frequency coupling characteristics of the LFM signal: the straight line with a slope of k=30 clearly shows the linear change of instantaneous frequency over time, which is fundamentally different from the characteristic of a horizontal straight line in the time-frequency diagram of a single-frequency signal. In (c) and (d), noise makes the time-domain waveforms blurry and difficult to identify, but time-frequency analysis can still extract the frequency evolution trajectory; however, due to noise interference, the energy distribution in (d) shows obvious dispersion, and the clarity of the time-frequency ridge and the energy concentration are lower than in (b), reflecting the weakening of energy concentration by noise. In (e) and (f), as the signal-to-noise ratio further decreases to -20dB, strong noise overwhelms the regular changes of the LFM signal, and the time-domain waveform becomes unrecognizable. In the corresponding time-frequency relationship diagram, the dispersion of energy distribution intensifies, the time-frequency ridge is completely obscured, and the energy concentration is completely lost, which intuitively demonstrates the serious interference of noise on time-frequency analysis under low signal-to-noise ratio.

[0034] Step S12: Add noise to construct noisy LFM signal training samples;

[0035] For each generated ideal LFM signal sample Add Gaussian white noise The SNR is randomly sampled within a set range of [-15, 5] dB (90% probability of noise, 10% probability of no noise) to obtain a noisy LFM signal. As shown in Equation 2:

[0036] (2)

[0037] In the formula, This is Gaussian white noise, representing environmental interference with the signal.

[0038] Step S13: Calculate the theoretical optimal FRFT order for each noisy LFM signal training sample;

[0039] For each noisy LFM signal training sample, the signal parameters (frequency modulation) are calculated according to formula (3). Modulation period Sampling frequency Calculate the theoretically optimal FRFT order for this signal. ,according to Figure 3 , Figure 4 As can be seen, FRFT is essentially a fractional coordinate rotation transformation. Figure 3 , Figure 4 In this context, t represents the time axis in the time domain, and f... sig denoted as the frequency axis in the frequency domain, u is the fractional-domain coordinate axis obtained by the FRFT transform, and |FRFT| is the fractional-domain amplitude. denoted as the time-frequency plane rotation angle; p represents the FRFT transform order, and the rotation angle and transform order satisfy the following relationship: The degree of energy concentration of the LFM signal in the fractional domain is directly determined by the transform order. The optimal transform order can make the LFM signal achieve the strongest energy concentration effect in the fractional domain. This order is set as the optimal order of the signal benchmark, providing a benchmark label for subsequent RankSVM ranking learning.

[0040] (3)

[0041] Step S14: Construct a set of valid candidate orders;

[0042] For each noisy LFM signal training sample, the theoretically optimal FRFT order obtained in step S13 is used. Centered on this, and combining a preset fixed offset set Δ∈{±0.12, ±0.09, ±0.06, ±0.04, ±0.025, ±0.015, ±0.008, 0} with several transformation orders randomly generated within [0.7, 1.3], such as... Figure 4 As shown. After combining and deduplication, the effective candidate order set of all noisy LFM signal training samples is obtained.

[0043] Step S2. For each set of valid candidate orders of the noisy LFM signal training samples, calculate the fractional-domain amplitude spectrum under different FRFT orders one by one, and extract 8-dimensional fractional-domain amplitude spectrum features. All the obtained 8-dimensional fractional-domain amplitude spectrum features form a feature matrix. Standardize the features by calculating the mean and standard deviation of each dimension, obtaining a standardized feature matrix. Store the mean and standard deviation standardization parameters for each dimension for use in subsequent steps. The specific implementation process is as follows:

[0044] Step S21: For each noisy LFM signal training sample and all candidate orders in its corresponding effective candidate order set, calculate FRFT and take the modulus to obtain the fractional domain amplitude spectrum;

[0045] For the Noisy LFM signal training samples and its i-th candidate order Calculate its fractional-domain amplitude spectrum:

[0046] (4)

[0047] In the formula, Indicates doing something to the signal FRFT.

[0048] Step S22: For each fractional-domain amplitude spectrum of the noisy LFM signal training sample, extract its 8-dimensional fractional-domain amplitude spectrum features: Based on each fractional-domain amplitude spectrum, extract 8-dimensional fractional-domain amplitude spectrum features; specifically as follows:

[0049] For the Noisy LFM signal training samples and its i-th candidate order The calculated fractional-domain amplitude spectrum B, let the total spectral energy be:

[0050] (5)

[0051] in, It is a very small positive number to prevent the denominator from being 0 in subsequent calculations.

[0052] The normalized spectral energy distribution is as follows:

[0053] (6)

[0054] The location of the main peak is:

[0055] (7)

[0056] The 8-dimensional fractional-domain amplitude spectrum features extracted based on this fractional-domain amplitude spectrum are as follows.

[0057] (8)

[0058] The specific calculation is as follows: the first dimension fractional domain amplitude spectrum feature is the peak energy ratio, that is, the proportion of the energy of the peak point to the total energy of the entire spectrum. This value is the largest under the optimal order, as shown in formula (9);

[0059] (9)

[0060] The second-dimensional fractional domain amplitude spectrum feature is the energy percentage of the top 1%. The top 1% of points with the largest amplitude squares are selected, and their energy and proportion of the total energy are calculated to measure the overall energy concentration.

[0061] (10)

[0062] Where L is the set of u-axis points representing the top one percent of the total spectral energy; This is the index of discrete sampling points in the fractional domain, belonging to L.

[0063] The third-dimensional fractional domain amplitude spectrum feature is the proportion of energy in the peak neighborhood. It takes the energy of 3 points to the left and right of the peak point (7 points in total) and the proportion of the total energy, focusing on the local clustering of the peak.

[0064] (11)

[0065] In the formula, The neighborhood half-width is [value], and the total neighborhood length is [value]. In this embodiment, the following is adopted: ; This is an index for discrete sampling points in the fractional domain, belonging to... .

[0066] The fourth-dimensional fractional-domain amplitude spectrum feature is the Shannon entropy; the smaller the entropy, the more concentrated the energy distribution.

[0067] (12)

[0068] The fifth-dimensional fractional-domain amplitude spectrum feature is the second-order Renyi entropy;

[0069] (13)

[0070] The sixth-dimensional fractional-domain amplitude spectrum feature measures the contrast between the peak region and the background noise;

[0071] (14)

[0072] In the formula, and To remove the mean and standard deviation of the background amplitude from the five points to the left and right of the peak;

[0073] The seventh-dimensional fractional domain amplitude spectrum feature compares the global peak value with the peak value of the background region excluding the peak's neighborhood.

[0074] (15)

[0075] In the formula, The fractional-domain amplitude spectrum at the main peak position. The fractional-domain amplitude spectrum of the background region after removing the neighborhood of the main peak; For discrete sampling point indices in the fractional domain, corresponding to Figure 3 Fractional domain shown Axis coordinates;

[0076] The eighth-dimensional fractional-domain amplitude spectrum is characterized by the maximum peak amplitude.

[0077] (16)

[0078] Step S23: Feature Standardization: Construct a feature matrix from the 8-dimensional fractional-domain amplitude spectrum features obtained from all fractional-domain amplitude spectra of all noisy LFM signal training samples. Calculate the mean and standard deviation of each dimension's features, and standardize the features according to the following formula to obtain the standardized feature matrix; simultaneously store the mean and standard deviation parameters of each dimension for use in subsequent step S4.

[0079] (17)

[0080] In the formula, The h-th dimension feature vector is extracted from all fractional domain amplitude spectra obtained from all noisy LFM signal training samples. The total number of training samples for the noisy LFM signal; for Standardized results; and These are the mean and standard deviation parameters of the h-th dimension fractional domain amplitude spectrum feature in the training set, respectively.

[0081] Step S3. Learn the ranking relationship of FRFT order using the RankSVM ranking model; such as Figure 5 As shown, the specific implementation process is as follows:

[0082] Step S31: For each noisy LFM signal training sample, iterate through any two orders within its candidate order set. and Calculate the order of each and the theoretical optimal order respectively. distance and .like Then determine The corresponding fractional domain features are better than For the corresponding fractional domain features, extract the standardized feature vectors corresponding to these two orders. and Construct a pair of difference samples: Assign sorting labels Simultaneously, by utilizing the antisymmetry of the ordering relation, generate And assign sorting labels .like If the two are not significantly superior, the sample pair should be discarded to avoid the influence of ambiguous labels on model training.

[0083] Step S32: Train the RankSVM ranking model;

[0084] Using all paired difference samples as input, a linear kernel SVM is trained according to the objective function and constraints in formulas (18) and (19) to obtain the ranking weight vector. and bias The details are as follows:

[0085] The RankSVM ranking model is trained using a sample set consisting of all paired difference samples, and its objective function is:

[0086] (18)

[0087] In the formula, j is the index of the paired difference sample. The total number of paired difference samples constructed; This is the sorting weight vector. For bias terms, The penalty coefficient is... Let be the slack variable for the j-th paired difference sample. The constraints are:

[0088] (19)

[0089] In the formula, Let be the feature vector of the j-th paired difference sample; for The corresponding sorting label.

[0090] Step S33: After training, obtain the RankSVM evaluation function (including weight vector) for candidate orders. Bias The function (including the standardized parameters stored in step 2) is as follows:

[0091] (20)

[0092] in, The fractional-domain amplitude spectrum characteristics of f after standardization; The function value is the evaluation function value for that order; the higher the value, the better the order.

[0093] Save the RandSVM evaluation function of the candidate order for subsequent step S4.

[0094] Step S4. Figure 6As shown, after inputting the signal to be estimated, the optimal FRFT order is determined using the RankSVM evaluation function trained in step S33, ultimately achieving the estimation of the LFM signal's modulation frequency and center frequency. The specific implementation process is as follows:

[0095] Step S41: Input the noisy LFM signal x_test(t) with unknown parameters to be estimated, and determine the FRFT order search interval. And within this interval, a candidate order sequence is generated according to a preset step size for subsequent scoring and optimal order search;

[0096] Step S42: For each candidate order, calculate the FRFT amplitude spectrum sequentially, extract the 8-dimensional amplitude spectrum features as in step S2, and then call the data stored in step S23. Standardize the data and then substitute it into the RankSVM evaluation function obtained in step S33 to calculate the scores for each order.

[0097] Step S43: Compare the scores of all candidate orders, and take the order corresponding to the maximum score as the optimal FRFT transform order estimate of the signal to be estimated. ;

[0098] Step S44: Solve for LFM signal parameters: In The fractional domain coordinates corresponding to the peak amplitude in the FRFT results of order X The frequency modulation can be calculated by simultaneously solving formulas (21), (22), and (23). and center frequency .

[0099] By searching for the optimal order The optimal FRFT transformation angle can be determined. As shown in the following formula:

[0100] (twenty one)

[0101] Under this optimal transform domain, the LFM signal will exhibit energy concentration characteristics, forming a significant pulse peak. The coordinate position corresponding to this peak is denoted as... According to the time-frequency rotation geometric interpretation of FRFT, there is a definite mapping relationship between this peak point and the time-frequency parameters of the original signal. Therefore, it can be derived from... and Jointly estimate the modulation frequency of the LFM signal and center frequency As shown in the following formula:

[0102] (twenty two)

[0103] (twenty three)

[0104] Specific Implementation Method Two: Combination Figures 7 to 10 This embodiment describes a verification example of the LFM signal parameter estimation method based on RankSVM-FRFT described in Specific Embodiment 1:

[0105] To comprehensively evaluate the performance of the RankSVM-FRFT method proposed in this invention for LFM signal parameter estimation, two sets of simulation experiments were designed in this embodiment. Experiment 1 is an effectiveness experiment, which visually verifies the correctness of the proposed method in identifying the optimal FRFT order under different signal-to-noise ratio conditions; Experiment 2 is a performance comparison experiment, which compares the parameter estimation accuracy of the proposed method and the maximum value criterion FRFT method in the low signal-to-noise ratio range through Monte Carlo simulation.

[0106] In this implementation, the training settings for the RankSVM model are as follows:

[0107] LFM signal model: Amplitude Modulation period Number of sampling points Frequency modulation The value range is [10, 90] Hz / s, and the center frequency is... The value range is [0, 30] Hz.

[0108] FRFT order search range: The search range for order p is [0.7, 1.3].

[0109] Training dataset construction: Number of training samples numTrain=2000. Frequency of each sample. and center frequency Uniformly and randomly sampled within their respective ranges. The signal-to-noise ratio (SNR) has a 90% probability of being within [a certain range]. Randomly and uniformly sampled within a dB range, with a 10% probability of being noise-free. For each training sample, its theoretically optimal order is used. Construct a candidate order set centered at:

[0110]

[0111] in, This is the set of valid candidate orders for the training samples; For relative to A fixed offset, belonging to a set , The set consists of 5 orders randomly generated within the FRFT search range [0.7, 1.3]. After merging and removing duplicate elements from the set, the set of valid candidate orders is obtained.

[0112] Feature extraction and standardization: Eight-dimensional fractional-domain amplitude spectrum features are extracted from the FRFT amplitude spectrum of each candidate order for each noisy LFM signal training sample. The eight-dimensional feature vectors of all noisy LFM signal training samples form a feature matrix, and the mean is calculated dimension by dimension. and standard deviation After standardization, the standardized feature matrix is ​​obtained. .

[0113] Sorting sample construction: For any two candidate orders within the same training signal Let their absolute distances from the theoretically optimal order be respectively .like If the superiority / inferiority relationship is unclear, the sample pair is discarded; otherwise... At that time, pairwise difference samples are generated: Assign sorting labels Simultaneously, by utilizing the antisymmetry of the ordering relation, generate And assign labels .

[0114] The RankSVM model is trained using a linear kernel support vector machine with a penalty coefficient. The RankSVM evaluation function is obtained through training. .

[0115] To verify the effectiveness of the trained RankSVM model in evaluating order ranking, a parameter of... , , , Number of sampling points Verification experiments were conducted using LFM signals. The experimental results are as follows: Figure 7 As shown:

[0116] In the figure, the FRFT evaluation results of each order output by RankSVM achieve a global peak at the theoretical optimal order, and the score decreases as the order deviates from the optimal value. Although the evaluation results of orders far from the optimal order rise when SNR=−10dB, the peak at the optimal order is obviously prominent and there are no false extreme points. This indicates that the trained model can accurately represent the relative merits of the FRFT order and can effectively locate the optimal FRFT order.

[0117] This embodiment also includes a comparison experiment of the accuracy of different evaluation functions under different SNRs;

[0118] To verify the performance advantage of the proposed RankSVM evaluation function over the traditional maximum value criterion at low signal-to-noise ratios, a Monte Carlo simulation experiment was designed. The signal-to-noise ratio interval was set to... Step length There are 16 SNR nodes in total. Each node undergoes 1000 independent and repeated experiments, with Gaussian white noise randomly generated for each experiment. Parameter estimation is performed using the maximum value criterion, peak energy ratio, negative Shannon entropy, and RankSVM scoring function, and the frequency modulation frequency is calculated. and center frequency The root mean square error (RMSE) was calculated. To verify the consistency of the results, three independent control experiments were conducted.

[0119] Let the parameters of the LFM signal be... , =0, , Number of sampling points The experimental results are as follows: Figure 8 As shown.

[0120] Let the parameters of the LFM signal be... , =0, , Number of sampling points The experimental results are as follows: Figure 9 As shown.

[0121] Let the parameters of the LFM signal be... , =0, , Number of sampling points The experimental results are as follows: Figure 10 As shown.

[0122] In this embodiment, Figures 8-10 The parameter estimation results for modulation frequencies k=30, 50, and 70Hz / s show a consistent overall trend:

[0123] In the figure, Maximum-FRFT, PER-FRFT, Negentropy-FRFT, and RankSVM-FRFT are FRFT algorithms using maximum value, peak energy ratio, negative Shannon entropy, and the method of this invention as evaluation functions, respectively. When the signal-to-noise ratio is higher than -5dB, the performance of each method tends to be similar. In the low signal-to-noise ratio range of [-13dB, -9dB], the errors of the three traditional single criteria—maximum value, peak energy ratio, and negative Shannon entropy—all increase rapidly, with the negative Shannon entropy criterion showing the most significant performance degradation. The RMSE of the RankSVM-FRFT method of this invention is consistently lower than that of the comparative methods, effectively suppressing the optimal order shift caused by noise. As the modulation frequency k increases, the overall estimation error of each method increases slightly, but the accuracy advantage of RankSVM-FRFT remains stable, demonstrating good adaptability to LFM signals with different modulation frequencies.

[0124] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0125] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of this invention patent should be determined by the appended claims.

Claims

1. A parameter estimation method for LFM signals based on RankSVM-FRFT, characterized by: This method is implemented by the following steps: Step 1: Construct training samples of noisy LFM signals with multiple tuning frequencies, multiple center frequencies, and multiple signal-to-noise ratios, and construct a set of effective candidate orders for each noisy LFM signal training sample. Step 2: Extract the fractional domain amplitude spectrum features of each noisy LFM signal training sample at different FRFT orders to obtain the standardized feature matrix; Step 3: Learn the ranking relationship of FRFT orders through the RankSVM ranking model to obtain the RankSVM evaluation function for candidate orders; Step 4: Input the noisy LFM signal to be estimated, use the RankSVM evaluation function to determine the optimal FRFT order estimate, and calculate the estimated frequency modulation frequency and center frequency of the noisy LFM signal to be estimated.

2. The LFM signal parameter estimation method based on RankSVM-FRFT according to claim 1, characterized in that: The specific process of step one is as follows: Step 1: Generate ideal LFM signal samples; Step 1 and Step 2: Add noise to the ideal LFM signal samples to construct noisy LFM signal training samples; Step 13: Calculate the theoretically optimal FRFT order of the noisy LFM signal training samples; Step 14: Using the theoretically optimal FRFT order as the center, obtain the effective candidate order set of noisy LFM signal training samples according to the pre-set fixed offset set and the randomly generated transformation order.

3. The LFM signal parameter estimation method based on RankSVM-FRFT according to claim 1, characterized in that: In step two, the fractional domain amplitude spectrum of each noisy LFM signal training sample is calculated, and the eight-dimensional fractional domain amplitude spectrum features are extracted based on each fractional domain amplitude spectrum. An eight-dimensional fractional-domain amplitude spectrum feature matrix is ​​constructed for all fractional-domain amplitude spectrum features of all noisy LFM signal training samples. The mean and standard deviation of the fractional-domain amplitude spectrum features in each dimension are statistically analyzed, and the features are standardized to obtain a standardized feature matrix.

4. The LFM signal parameter estimation method based on RankSVM-FRFT according to claim 3, characterized in that: The specific implementation process of step two is as follows: Step Two One, for the first Noisy LFM signal training samples and its i-th candidate order Calculate its fractional-domain amplitude spectrum: ； In the formula, For training samples of noisy LFM signals Candidate order FRFT; Step 22: Set the energy spectrum corresponding to the fractional-domain amplitude spectrum as follows: ； In the formula, It is a very small positive number; the total energy of the fractional domain amplitude spectrum is normalized to obtain the normalized total energy: ； Steps two and three: The eight-dimensional fractional-domain amplitude spectrum features are represented as follows: ； In the formula, These are the first-dimensional fractional-domain amplitude spectrum features, the second-dimensional fractional-domain amplitude spectrum features, and the eighth-dimensional amplitude spectrum features, respectively. Step 24: Calculate the mean and standard deviation of the amplitude spectrum features in each dimension of the fractional domain and standardize them to obtain the standardized feature matrix. ; ； In the formula, This is the h-th eigenvector extracted from all fractional-domain amplitude spectra obtained from all noisy LFM signal training samples. The total number of training samples for the noisy LFM signal; for Standardized results; and denoted as the mean and standard deviation parameters of the h-th dimension fractional domain amplitude spectrum feature, respectively.

5. The LFM signal parameter estimation method based on RankSVM-FRFT according to claim 4, characterized in that: The first-dimensional fractional-domain amplitude spectrum feature, the second-dimensional fractional-domain amplitude spectrum feature, and the third-dimensional fractional-domain amplitude spectrum feature are respectively expressed by the following formulas: ； ； ； In the formula, The location of the main peak. Let L be the neighborhood half-width, and L be the set of u-axis points representing the top 1% of the total spectral energy. , All are discrete sampling point indices in the fractional domain.

6. The LFM signal parameter estimation method based on RankSVM-FRFT according to claim 5, characterized in that: ； In the formula, To remove the neighborhood of the main peak, the fractional-domain amplitude spectrum of the background region, For discrete sampling point indexes in the fractional domain, The fractional-domain amplitude spectrum of the main peak position.

7. The LFM signal parameter estimation method based on RankSVM-FRFT according to claim 5, characterized in that: The specific process of step three is as follows: Construct pairs of difference samples; For each noisy LFM signal training sample, iterate through any two orders within its candidate order set. and Calculate the distances between the two orders and the theoretically optimal order, respectively; if Then determine The corresponding fractional-domain amplitude spectrum characteristics are better than For the corresponding fractional-domain amplitude spectrum features, extract the standardized feature vectors corresponding to the two orders. and Constructing a pair of differential samples ; A sample set is formed by combining all paired difference samples, and a RankSVM ranking model is trained. An objective function and constraints are set to obtain the RankSVM evaluation function for candidate orders. ; ； In the formula, This is the sorting weight vector. For bias terms, This represents the fractional-domain amplitude spectrum characteristics of f after standardization.

8. The LFM signal parameter estimation method based on RankSVM-FRFT according to claim 7, characterized in that: The objective function and constraints are expressed as follows: ； ； In the formula, j is the index of the paired difference sample. The total number of paired difference samples constructed; The penalty coefficient is... Let be the slack variable for the j-th pairwise difference sample; Let be the feature vector of the j-th paired difference sample; To and The corresponding sorting label.

9. The LFM signal parameter estimation method based on RankSVM-FRFT according to claim 8, characterized in that: The specific implementation process of step four is as follows: To determine the FRFT order search interval for the noisy LFM signal to be estimated, a candidate order sequence is generated within the search interval at a set step size. For each candidate order noisy LFM signal, calculate the FRFT amplitude spectrum, extract the eight-dimensional fractional domain amplitude spectrum features, and perform feature standardization; The RankSVM evaluation function is used to calculate the score of each order. The scores of all candidate orders are compared, and the order corresponding to the maximum score is taken as the optimal FRFT transform order estimate of the noisy LFM signal to be estimated. The estimated values ​​of the frequency modulation frequency and the center frequency are calculated based on the optimal FRFT transform order estimate.

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