Radar pulse signal sorting method under time-frequency analysis based on Hough transform

Abstract

The invention discloses a radar pulse signal sorting method under time-frequency analysis based on Hough transform, and relates to the technical field of radar signal processing, and the method comprises the steps: carrying out the time-frequency analysis of a received radar pulse signal, and obtaining a two-dimensional time-frequency matrix; performing binarization processing on the two-dimensional time-frequency matrix to obtain a time-frequency graph, and performing edge extraction on the obtained time-frequency graph to obtain an edge time-frequency graph; for each edge point of the edge time-frequency graph, searching a peak value in the time-frequency graph through Hough transform calculation; converting the peak value from a polar coordinate to a linear equation in a Cartesian coordinate system to obtain a modulation slope of the current pulse signal; and repeating the steps to obtain the modulation slopes of all the pulse trains, carrying out sorting and differential calculation on the modulation slopes, marking the signal sources with the slope differences smaller than the error range as the same signal source, and completing radar pulse signal sorting. The method effectively improves the precision and robustness of signal sorting, and especially shows obvious advantages in a complex electromagnetic environment.

Description

Technical Field

[0001] The present invention relates to the technical field of radar signal processing, and particularly relates to a radar signal sorting algorithm, in particular to a method for sorting radar pulse signals based on time-frequency analysis of in-pulse characteristic parameters of the radar and the Hough transform. Background Art

[0002] Radar pulse signal sorting is one of the key technologies in electronic reconnaissance signal processing, and is of great significance for the accurate extraction and processing of target information. By effectively sorting radar signals, signals from the same target can be associated or fused, thereby providing users with a more comprehensive and accurate target description. In addition, radar signal sorting technology plays a crucial role in pulse matching, target positioning, and collaborative work in multi-satellite systems.

[0003] Radar pulse signal sorting is also known as radar emitter signal deinterleaving, and its core is to accurately separate the pulse sequences emitted by different radar emitters from a randomly interleaved pulse stream. This process mainly uses in-pulse or inter-pulse characteristic parameters, and classifies pulses from the same emitter into one category by comparing similarities, so as to distinguish pulses from different emitters and achieve effective signal sorting.

[0004] The histogram algorithm is one of the most classic algorithms. This method identifies the repeating pattern of signals by detecting the time intervals between adjacent pulses in the pulse sequence, and then realizes the grouping of signals emitted by different emitters. It is applicable to scenarios where pulse signals are sparse, the number of emitters is limited, and the PRI parameters are stable. Compared with the traditional histogram algorithm, the CDIF (Cumulative Difference Histogram) and SDIF (Sequential Difference Histogram) algorithms have significantly improved in terms of PRI estimation accuracy and sorting performance. However, when the PRI jitter amplitude is large or there are serious losses in pulse signals, harmonic interference is likely to occur in the histogram, leading to incorrect sorting results such as misclassification or missed classification. Existing research results show that when the pulse PRI jitter amount is higher than 3% or the pulse loss rate is higher than 6%, the above algorithms cannot obtain ideal sorting effects. The biggest feature of the PRI transform method lies in its almost complete ability to suppress harmonics. This method performs a PRI transform on the interleaved radar pulse sequence to generate a PRI spectrogram, sets a threshold on the spectrogram, and takes the value corresponding to the spectral peak exceeding the threshold as the possible PRI value, and further performs sequence retrieval to complete signal sorting. When there is a certain amount of PRI jitter, especially when the jitter amount exceeds 10%, the performance of the traditional PRI transform method drops significantly, and at this time the true PRI value is often submerged by noise.

[0005] To adapt to diverse radar signals and dynamic electromagnetic environments, sorting methods based on clustering have gradually evolved. The application of K-means clustering algorithm and density clustering (such as DBSCAN) in radar signal sorting has significantly improved the flexibility and adaptability of sorting. However, the clustering sorting method is usually an offline batch processing method with high algorithm complexity and large computational volume, making it difficult to meet the requirements of high-speed real-time processing. With the wide application of machine learning technology, support vector machines (SVMs) are used to identify and classify radar signals from different sources. Due to the high computational complexity of SVMs, their efficiency is low when dealing with large-scale data. Despite the continuous development and optimization of various sorting algorithms, radar signal sorting in complex electromagnetic environments still faces many challenges. Summary of the Invention

[0006] To overcome the above problems existing in the prior art, the present invention proposes a radar pulse signal sorting method based on time-frequency analysis under the Hough transform.

[0007] The technical solution adopted by the present invention to solve its technical problems is: a radar pulse signal sorting method based on time-frequency analysis under the Hough transform, including the following steps: Step 1: Perform time-frequency analysis on the received radar pulse signal to obtain a two-dimensional time-frequency matrix; Step 2: Binarize the two-dimensional time-frequency matrix obtained in Step 1 to obtain a time-frequency diagram, perform edge extraction on the obtained time-frequency diagram to obtain an edge time-frequency diagram; Step 3: For each edge point of the edge time-frequency diagram obtained in Step 2, calculate and find the peak value in the time-frequency diagram through the Hough transform; Step 4: Convert the peak value obtained in Step 3 from polar coordinates to a straight-line equation in the Cartesian coordinate system to obtain the modulation slope of the current pulse signal; Step 5: Repeat Steps 1-4 to obtain the modulation slopes of all pulse trains, sort the modulation slopes and perform differential calculation. Those with a slope difference less than the error range are marked as signals from the same source, and the sorting of radar pulse signals is completed.

[0008] In the above radar pulse signal sorting method based on time-frequency analysis under the Hough transform, the Wigner-Ville distribution algorithm is used for time-frequency analysis in Step 1, and the expression is: ; Among them, represents time, represents frequency, is the time-delay variable, is the signal 's complex conjugate, and j is the imaginary unit.

[0009] In the above radar pulse signal sorting method based on time-frequency analysis under the Hough transform, Step 2 specifically includes: Step 2.1, when binarizing the two-dimensional time-frequency matrix obtained in Step 1, the decision threshold is defined as th, and the specific calculation formula is: ; wherein, represents the maximum value in the two-dimensional time-frequency matrix , represents the dot product operation, is a threshold coefficient; Step 2.2, binarize the time-frequency matrix to obtain the time-frequency diagram The specific expression is: ; Step 2.3, perform noise exclusion processing on the small connected regions of the time-frequency diagram obtained in Step 2.2; Step 2.4, perform edge detection on the time-frequency diagram obtained in Step 2.3, and find the edge position by applying the derivative operation to the image.

[0010] For the above-mentioned radar pulse signal sorting method based on time-frequency analysis using the Hough transform, Step 2.4 is specifically: calculate the gradient values of the image in the horizontal and vertical directions through the following formula , : ; According to the gradients in the horizontal and vertical directions, calculate the gradient magnitude and the direction to identify the position of the edge: ; When the gradient magnitude exceeds the set threshold, this position is considered an edge point, and the expression is: ; wherein, is the threshold for edge detection.

[0011] For the above-mentioned radar pulse signal sorting method based on time-frequency analysis using the Hough transform, Step 3 is specifically: Step 3.1, for each edge point in the edge time-frequency diagram, calculate its corresponding polar coordinate parameters through the Hough transform: ; Step 3.2, the Hough transform calculates each edge point in the parameter space for all and Contribution; by accumulating these contributions, each straight line in the image forms a peak in the Hough space. The voting accumulation formula in the Hough space is: ; where is the voting accumulation function in the Hough space, representing and the voting result of the corresponding parameter space position; is the Dirac function, representing the contribution of each point in the image to the straight line; Step 3.3: By calculating the voting accumulation in the Hough space, find the most significant peaks. These peaks correspond to the straight lines in the edge time-frequency diagram. The peak detection formula in the Hough space is as follows: ; where represents the maximum value in the Hough space.

[0012] For the above-mentioned radar pulse signal sorting method based on Hough transform in time-frequency analysis, the expression of the peak converted from polar coordinates to the straight line equation in the Cartesian coordinate system in step 4 is: , the modulation slope of the current pulse signal.

[0013] For the above-mentioned radar pulse signal sorting method based on Hough transform in time-frequency analysis, step 5 is specifically as follows: Step 5.1: Estimate the modulation slopes of all pulse trains for the received data, and sort them in ascending order of slope to obtain a complete modulation slope array: ; where is the number of pulse trains; Step 5.2: Perform differential calculation on adjacent elements of the modulation slope array in step 5.1 to obtain the change trend of the modulation slope: ; where represents the difference between the and th modulation slopes; Step 5.3: Set an error range for each modulation slope . If the difference between two adjacent modulation slopes, it is marked as the same signal source. Otherwise, it indicates that the change in the modulation slope between them is significant and belongs to different radiation sources, and finally the sorting of radar pulse signals is completed.

[0014] The beneficial effects of the present invention are as follows: (1) Based on the intra-pulse characteristic parameters of the radar, the modulation slope of the pulse signal is extracted, and simulation scenarios are designed for various pulse signal modes such as fixed PRI, jittered PRI, and staggered PRI, verifying the applicability of the algorithm and improving the sorting accuracy in complex scenarios.

[0015] (2) The present invention introduces a process to remove noise clutter points in small connected regions, demonstrating excellent anti-noise performance under complex signal-to-noise ratio conditions. In the simulation experiment, when the signal-to-noise ratio is as low as -20 dB, the sorting performance of the traditional CDIF algorithm significantly deteriorates, while the algorithm of the present invention still maintains a high correct sorting probability of 87%, proving its robustness in a low signal-to-noise ratio environment.

[0016] (3) The present invention can effectively suppress noise interference under high false alarm conditions and significantly improve the sorting correct rate. In the simulation of the real working scenario, continuous noise interference is added. The correct rate of the traditional CDIF algorithm drops to 71.14% due to noise interference, and additional incorrect groupings occur. The algorithm proposed by the present invention can effectively suppress noise interference and improve the sorting correct rate to 99.35% under high false alarm conditions, significantly outperforming the traditional algorithm.

[0017] In summary, a method for sorting radar pulse signals based on time-frequency analysis using the Hough transform proposed by the present invention is significantly superior to traditional sorting methods in terms of adaptability and robustness in complex electromagnetic environments. Through the extraction of time-frequency features and the application of connected region decision, this algorithm can accurately identify multi-source pulse signals under complex conditions such as reduced signal-to-noise ratio, enhanced noise interference, PRI jitter, or staggering, providing strong technical support for radar signal sorting. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 is the algorithm flowchart of the present invention; Figure 2 is the time-frequency grayscale map corresponding to the two-dimensional time-frequency matrix in the algorithm of the present invention; Figure 3 is the time-frequency map after binary processing of the time-frequency matrix in the algorithm of the present invention; Figure 4 is the time-frequency map before and after processing to exclude small connected regions in the algorithm of the present invention, where (a) is the time-frequency map before processing to exclude small connected regions, and (b) is the time-frequency map after processing to exclude small connected regions; Figure 5 is the time-frequency map after edge detection processing in the algorithm of the present invention; Figure 6 is the mapping result map after Hough space transformation in the algorithm of the present invention; Figure 7 is the schematic diagram of straight line extraction by Hough transform in the algorithm of the present invention; Figure 8 It is the signal waveform diagram of the fixed PRI pulse generated by the embodiment of the present invention; Figure 9 It is the sorting result diagram of the fixed PRI pulse provided by the embodiment of the present invention. Specific embodiments

[0019] To enable those skilled in the art to better understand the technical solution of the present invention, the present invention will be described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0020] This embodiment discloses a method for sorting radar pulse signals based on time-frequency analysis using the Hough transform. The specific process is as Figure 1 shown and includes: Step 1: Perform time-frequency analysis on the received radar pulse signal using the Wigner-Ville Distribution (WVD) algorithm. The expression is: ; where, represents time, represents frequency, is the time-delay variable, is the complex conjugate of the signal .

[0021] Specifically, in this embodiment, the WVD calculates the distribution of the signal on the time-frequency plane by performing a Fourier transform on the autocorrelation function of the signal. Please refer to Figure 2 , Figure 2 which is the time-frequency grayscale diagram corresponding to the two-dimensional time-frequency matrix provided by the embodiment of the present invention. The horizontal axis is the time domain and the vertical axis is the frequency domain. It can be seen from the figure that the frequency of the signal changes linearly with time.

[0022] Step 2: Binarize the two-dimensional time-frequency matrix obtained in Step 1 to obtain a time-frequency diagram . To exclude the influence of noise false alarms on the subsequent signal sorting process, small connected regions need to be further excluded during binarization, and then edge extraction is performed on the time-frequency diagram to obtain an edge time-frequency diagram .

[0023] Specifically, Step 2 includes: Step 2.1: From the two-dimensional time-frequency matrix obtained in Step 1, when binarizing it, the decision threshold is defined as th, and its calculation expression is as follows: ; where, represents the two-dimensional time-frequency matrix The maximum value in represents the dot product operation, is a threshold coefficient, which is usually adjusted according to the experimental results in simulation and practical applications. According to the effect of the simulation statistical algorithm, is often taken. Specifically, this coefficient is used to adjust the sensitivity of the threshold value to ensure the effectiveness of the signal while suppressing possible noise interference. By setting an appropriate threshold value th, time-frequency points with low energy and possibly belonging to noise can be filtered out, and only significant signal features are retained.

[0024] Step 2.2: Perform binarization on the time-frequency matrix to obtain the time-frequency diagram The specific expression of is:

[0025] Specifically, in this embodiment, please refer to Figure 3 , Figure 3 is the time-frequency diagram after binarization processing of the time-frequency matrix provided by the embodiment of the present invention. The received radar pulse signal has a high signal-to-noise ratio, weak noise interference, and a reasonable decision threshold. It can be seen from Figure 3 that the binarized time-frequency diagram can effectively highlight the time-frequency characteristics of the signal. The purpose is to simplify the two-dimensional time-frequency matrix by setting most of the irrelevant time-frequency matrix values to 0, retaining the most important signal features, and reducing the influence of noise on subsequent processing.

[0026] Step 2.3: In a complex electromagnetic environment, to eliminate the influence of noise false alarms on the subsequent signal sorting process, small connected regions need to be further excluded during binarization. A connected region usually refers to a region composed of pixel points with the same pixel value and adjacent to each other in the time-frequency diagram. The calculation formula for the area of the connected region: ; where represents a certain connected region in the time-frequency diagram, is the area of this region, are all the time-frequency points in this region. If the area of a certain connected region is less than the set threshold ( can be selected according to the dimension of the binary time-frequency matrix, such as taking 30), then this region is considered noise and is excluded, that is, the time-frequency diagram is further optimized. The expression is: ; This step can effectively eliminate small-area signal components that may be caused by noise, and only retain regions that conform to the actual signal characteristics.

[0027] Specifically, in this embodiment, please refer to Figure 4 , Figure 4It is the time-frequency diagram before and after the processing of excluding small connected regions provided by the embodiments of the present invention. Among them, Figure 4 in (a) is the time-frequency diagram before the processing of excluding small connected regions, Figure 4 and in (b) is the time-frequency diagram after the processing of excluding small connected regions. As can be seen from Figure 4 the left side, it is the original time-frequency diagram without excluding small connected regions when the signal-to-noise ratio of the received signal is relatively poor. Among them, the signal and noise are intertwined, resulting in blurred signal features and making it difficult to clearly distinguish. In this diagram, the energy distributions of the noise and the signal overlap, making accurate signal recognition complex. However, the right side shows the time-frequency diagram after excluding small connected regions. Through morphological processing and connected region analysis, the noise region is effectively removed, the features of the signal region become more prominent, the noise is significantly suppressed, and the distinction between the signal and the interference becomes more obvious. This processing greatly improves the accuracy in the subsequent signal sorting and analysis processes, provides clearer and more reliable input data for the subsequent steps, and thus ensures the accuracy and robustness of the entire signal processing flow.

[0028] Step 2.4: After excluding noise through Step 2.3, the signal features in the time-frequency diagram become more prominent, and then the signal boundary is extracted, that is, edge detection. The edge position is found by applying derivative operations to the image. Specifically, the gradient values of the image in the horizontal and vertical directions can be calculated through the following mathematical formulas and : ; According to the gradients in these two directions, the magnitude and direction of the gradient can be calculated, which are used to identify the position of the edge: ; When the gradient magnitude exceeds the set threshold, this position is considered an edge point, and the expression is: ; Among them, is the threshold for edge detection, which is used to determine which regions have a large enough gradient change and should be regarded as edges.

[0029] Specifically, in this embodiment, please refer to Figure 5 and Figure 5 is the time-frequency diagram after edge detection processing provided by the embodiments of the present invention. The purpose of edge detection is to identify the significant boundaries of the signal in the image, clearly distinguish the signal region from the noise region, and provide key information for subsequent signal analysis. In radar signal processing, especially in time-frequency image analysis, edge detection can help extract the time-domain and frequency-domain features of the signal, so as to clarify the shape, directionality, and distribution of the signal.

[0030] Step 3. For each edge point in , calculate and find the peak in the time-frequency diagram through Hough transform .

[0031] Specifically, Step 3 includes: Step 3.1. For each edge point in , calculate its corresponding polar coordinate parameters through Hough transform: ; This process maps the coordinates of each point in the image space to the parameter space (Hough space), where and represent the polar coordinates of the line corresponding to that point.

[0032] Step 3.2. To identify the lines in the edge time-frequency diagram , Hough transform calculates the contribution of each edge point in the parameter space for all and . By accumulating these contributions, each line in the image will form a peak in the Hough space, and the presence of these peaks indicates the existence of line features in the image. The voting accumulation formula in the Hough space is: ; where is the voting accumulation function in the Hough space, indicating and the voting result at the corresponding parameter space position. is the Dirac function, indicating the contribution of each point in the image to the line.

[0033] Step 3.3. By calculating the voting accumulation in the Hough space, the most significant peaks can be found, and these peaks correspond to the lines in the edge time-frequency diagram . The peak detection formula in the Hough space is as follows: ; where represents the maximum value in the Hough space.

[0034] Specifically, in this embodiment, please refer to Figure 6 . Figure 6It is the mapping result diagram after the Hough space transformation provided by the embodiment of the present invention. In the Hough space, we can see the peak of the signal, and the peak indicates the corresponding straight-line feature in the image. The Hough transform successfully converts the signal structure feature in the time-frequency diagram into a local peak in the parameter space, and records the position of the point with the brightest color in the Hough space, which is the most consistent with the extracted straight line.

[0035] Step 4: Convert the found peak from polar coordinates to the straight-line equation in the Cartesian coordinate system, and the expression is: ; Estimate the modulation slope of the current pulse signal according to the straight line .

[0036] Specifically, in this embodiment, please refer to Figure 7 , Figure 7 which is the schematic diagram of straight-line extraction by the Hough transform provided by the embodiment of the present invention. The modulation slope represents the rate of change of frequency with time and reflects the frequency modulation characteristics of the signal.

[0037] Step 5: By performing time-frequency analysis on the received radar pulse signals one by one, the modulation slopes of all pulse trains can be estimated in sequence, obtaining a complete modulation slope array. Sort the modulation slopes and perform differential calculation. If the slope difference is less than the error range, it is marked as the same signal source, thereby realizing the classification of radiation source groups, that is, completing the sorting of radar pulse signals.

[0038] Specifically, Step 5 includes: Step 5.1: Estimate the modulation slopes of all pulse trains for the received data and sort them from small to large to obtain a complete modulation slope array: ; wherein, is the number of pulse trains.

[0039] Step 5.2: Perform differential calculation on adjacent elements of the modulation slope array in Step 5.1 to obtain the change trend of the modulation slope: ; wherein, represents the difference between the th and the th modulation slopes.

[0040] Step 5.3: Set an error range for each modulation slope , defined as 5% of the current slope value, and the expression is: ; If the difference between two adjacent modulation slopes , they are marked as from the same signal source; otherwise, it indicates that the modulation slope changes significantly between them, belonging to different radiation sources, and finally the sorting of radar pulse signals is completed.

[0041] The above method is based on the accurate calculation and differential analysis of the modulation slope, making full use of the frequency modulation characteristics of pulse signals. Compared with traditional simple classification methods based on time or frequency, this method shows higher sensitivity and adaptability in dealing with complex electromagnetic environments. Especially when facing pulse signals with jitter or stagger characteristics, the differential analysis of the modulation slope can accurately capture the subtle differences between signals, thus achieving efficient signal sorting.

[0042] In this embodiment, the performance of the above method is illustrated through simulation experiments. The traditional method and the algorithm proposed in the present invention respectively start from different perspectives of inter-pulse parameters and intra-pulse parameters to sort the radar pulse signal sequence. In order to comprehensively evaluate the performance advantages of the algorithm of the present invention, a comparison is made with the traditional CDIF algorithm, and the applicability under different environments and conditions is analyzed by simulation.

[0043] First, for several common pulse signal categories (fixed PRI, jitter PRI, stagger PRI), and based on these categories, multiple simulation scenarios are designed. PRI is one of the important characteristics of radar signals. In the fixed PRI mode, the pulse repetition interval always maintains a fixed value and does not change with time. When the PRI fluctuates around a central value and randomly changes within a certain range, such a pulse repetition pattern is called the PRI jitter mode. In addition, in some scenarios, the PRI is not fixed, nor does it randomly fluctuate around the central value, but consists of multiple different fixed PRI values alternating in a specific order. This pulse repetition pattern is called the stagger PRI mode. In the simulation experiment, pulse sequences of two radiation sources are generated, the observation time is set to 10 ms, the pulse bandwidth is 1 μs, the sampling rate is 160 MHz, and the signal-to-noise ratio is 0 dB. The signal waveform generated by the fixed PRI pulse can be seen in Figure 8 , which clearly reflects the overall timing distribution of the pulse signal.

[0044] The simulation results show that for fixed PRI signals, both algorithms can achieve accurate sorting. The sorting results can be seen in Figure 9 . It can be seen that the algorithm uses two needle diagrams with different amplitudes to distinguish the pulse sequences generated by the two radiation sources. However, in the jitter PRI and stagger PRI scenarios, the CDIF algorithm has incorrect sorting due to the interference of statistical characteristics, while the algorithm proposed in the present invention can overcome this problem by using the time-frequency characteristics of the signal, achieve high-precision sorting, and can effectively cope with diverse modulation signals in complex electromagnetic environments.

[0045] Secondly, under complex signal-to-noise ratio conditions, the algorithm proposed in this embodiment demonstrates stronger anti-noise ability and sorting accuracy. In the simulation experiment, the set observation time is 50 ms, the sampling rate is 160 MHz, including 3 groups of different radiation sources, with a total of 116 pulses. The simulation results of the two algorithms are shown in Table 1.

[0046] As can be seen from Table 1, by comparing the pulse radiation source sorting correct rates of the two algorithms, it is found that when the SNR is relatively low (such as -20 dB), the sorting performance of the CDIF algorithm significantly deteriorates, while the algorithm of the present invention still maintains a relatively high correct sorting probability of 87%.

[0047] Table 1 Comparison of recognition rates of two sorting algorithms under different SNRs

[0048] Finally, in order to further simulate the real working scenario of the receiver, continuous noise of 1.25 ms is added to the 1 s simulation data. The data contains the pulse sequences of 3 groups of different radiation sources, with a total of 2303 pulses. The sorting performances of the two algorithms under high false alarm conditions are evaluated. The results are shown in Table 2.

[0049] Table 2 Comparison of simulation algorithms for the real scenario of the receiver

[0050] As can be seen from Table 2, both algorithms sort the pulse sequences generated by the 3 groups of radiation sources into 4 groups. The CDIF algorithm adds a group caused by noise, and the correct rate drops to 71.14%. In contrast, the algorithm proposed in this embodiment effectively suppresses noise interference through the connected region decision method, and the sorting correct rate is as high as 99.35%.

[0051] The above embodiments are only exemplary embodiments of the present invention and are not used to limit the present invention. Those skilled in the art can make various modifications or equivalent replacements to the present invention within the essence and protection scope of the present invention, and such modifications or equivalent replacements should also be regarded as falling within the protection scope of the present invention.

Claims

1. A radar pulse signal sorting method based on time-frequency analysis of Hough transform, characterized in that: The steps include: Step 1, performing time-frequency analysis on the received radar pulse signal to obtain a two-dimensional time-frequency matrix; Step 2, binarizing the two-dimensional time-frequency matrix obtained in step 1 to obtain a time-frequency graph, and extracting edges from the obtained time-frequency graph to obtain an edge time-frequency graph; Step 3, for each edge point of the edge time-frequency graph obtained in step 2, find the peak value in the time-frequency graph by Hough transform calculation; Step 4, converting the peak value obtained in step 3 from polar coordinates to a straight line equation in a Cartesian coordinate system to obtain a modulation slope of the current pulse signal; Step 5, repeat steps 1-4 to obtain the modulation slopes of all pulse trains, sort the modulation slopes, and perform differential calculations. Those with slope differences less than the error range are marked as the same signal source, thus completing the radar pulse signal sorting.

2. The radar pulse signal sorting method based on time-frequency analysis of Hough transform according to claim 1 is characterized in that: In step 1, the Wigner-Wiley distribution algorithm is used to perform time-frequency analysis, and the expression is: ; in, Indicates time, Indicates frequency, is the time-lagged variable, It's a signal is the complex conjugate of , where j is the imaginary unit.

3. The radar pulse signal sorting method based on time-frequency analysis of Hough transform according to claim 1 is characterized in that: The step 2 specifically includes: Step 2.1, when the two-dimensional time-frequency matrix obtained in step 1 is binarized, the decision threshold is defined as th, and the specific calculation formula is: ; in, Represents a two-dimensional time-frequency matrix The maximum value in represents the dot product operation, is a threshold coefficient; Step 2.2, time-frequency matrix Perform binarization to obtain the time-frequency diagram The specific expression is: ； Step 2.3, performing noise elimination processing on the small connected area of ​​the time-frequency graph obtained in step 2.2; Step 2.4, edge detection is performed on the time-frequency image obtained in step 2.3, and the edge position is found by applying a derivative operation to the image.

4. The radar pulse signal sorting method based on time-frequency analysis of Hough transform according to claim 3 is characterized in that: The step 2.4 is specifically as follows: the gradient values ​​of the image in the horizontal and vertical directions are calculated by the following formula: , : ； According to the horizontal and vertical gradients, the gradient amplitude is calculated and direction , used to mark the edge position: ; When the gradient amplitude When the value exceeds the set threshold, the position is considered to be an edge point. The expression is: ; in, is the threshold for edge detection.

5. The radar pulse signal sorting method based on Hough transform time-frequency analysis according to claim 1 is characterized in that: The step 3 is specifically as follows: Step 3.1: for each edge point in the edge time-frequency graph , calculate its corresponding polar coordinate parameters through Hough transform: ； Step 3.2, Hough transform calculates each edge point In the parameter space, for all and By accumulating these contributions, each straight line in the image forms a peak in the Hough space. The voting accumulation formula of the Hough space is: ; in, is the voting accumulation function in Hough space, indicating and The voting results of the corresponding parameter space positions; is the Dirac function, which means that each point in the image Contribution to the line; Step 3.3, by calculating the vote accumulation in Hough space, find the most significant peaks, which correspond to the straight lines in the edge time-frequency diagram. The peak detection formula of Hough space is as follows: ; in, represents the maximum value in the Hough space.

6. The radar pulse signal sorting method based on Hough transform time-frequency analysis according to claim 1 is characterized in that: The linear equation expression of the peak value converted from polar coordinates to Cartesian coordinates in step 4 is: , the modulation slope of the current pulse signal .

7. The radar pulse signal sorting method based on Hough transform time-frequency analysis according to claim 1 is characterized in that: The step 5 is specifically as follows: Step 5.1, estimate the modulation slopes of all pulse trains for the received data, and sort them from small to large to obtain a complete modulation slope array: ; in, is the number of pulse trains; Step 5.2, for the modulation slope array of step 5.1 Perform differential calculation on adjacent elements to obtain the change trend of the modulation slope: ; in, Indicates and The difference between the modulation slopes; Step 5.3, for each modulation slope Set a margin of error , if the difference between two adjacent modulation slopes , they are marked as the same signal source, otherwise it means that the modulation slope between the two changes significantly and they belong to different radiation sources, and finally the radar pulse signal is sorted.

Images