A radar active jamming weighted joint optimization threshold positioning method

Abstract

This invention discloses a radar active interference weighted joint optimization threshold localization method, comprising: obtaining a discrete domain received signal sequence based on the radar received baseband echo signal; obtaining a final time-frequency map sequentially based on a first time-frequency map; obtaining a probability distribution result based on the final time-frequency map; obtaining the inter-class variance based on the foreground probability and background probability; obtaining the optimal Otsu segmentation threshold based on the inter-class variance; obtaining the optimal Tsallis segmentation threshold based on the non-additive combined entropy; determining adaptive joint weights based on normalized inter-class variance index and normalized Tsallis gain index; fusing the optimal Otsu segmentation threshold and the optimal Tsallis segmentation threshold through a weighted method to obtain a joint segmentation threshold; and segmenting a standard grayscale image based on the joint segmentation threshold to obtain the interference localization result. This invention improves the accuracy of radar active interference localization under low interference-to-signal ratio conditions and enhances the robustness of interference localization in complex electromagnetic environments.

Description

Technical Field

[0001] This invention belongs to the field of radar signal processing and electronic countermeasures technology, specifically relating to a radar active interference weighted joint optimization threshold localization method. Background Technology

[0002] Modern radar systems play a crucial role in both military and civilian fields, but their performance consistently faces the severe challenge of active jamming. Active radar jamming, through the proactive transmission of jamming signals, aims to overwhelm, obscure, or confuse the echoes of genuine radar targets, thereby drastically reducing the radar's detection, tracking, and identification capabilities. Therefore, rapid and accurate detection and localization of jamming signals are prerequisites for effective electronic countermeasures. The core of jamming localization is to separate the time-frequency energy distribution of the jamming signal from the target echo, environmental clutter, and internal system noise in the time-frequency domain. In real-world complex electromagnetic environments, when the jamming source is far away or its power is limited, the jamming signal may be very weak when it reaches the radar receiver, with energy comparable to or even weaker than the target echo, strong sea clutter, or system noise. This makes the jamming characteristics extremely inconspicuous and difficult to extract from the background. Against this backdrop, designing a jamming localization method that maintains high detection probability and high localization accuracy even at low signal-to-interference ratios has become a critical technical challenge urgently needing to be solved in the field of radar signal processing.

[0003] Currently, existing radar active jamming localization technologies generally rely on a single threshold segmentation criterion. However, a single, universal segmentation criterion is difficult to maintain optimal performance in low interference-to-signal ratio scenarios, resulting in the robustness, adaptability, and overall positioning accuracy of existing methods failing to meet the needs of modern radar electronic countermeasures. Summary of the Invention

[0004] To address the aforementioned problems in the existing technology, this invention provides a radar active interference weighted joint optimization threshold localization method.

[0005] The technical problem to be solved by this invention is achieved through the following technical solution: This invention provides a radar active interference weighted joint optimization threshold localization method, comprising: Based on the radar received baseband echo signal containing interference, which is obtained from radar active interference echo signal, linear frequency modulated signal and additive white Gaussian noise, a discrete domain received signal sequence is obtained. The first time-frequency graph obtained from the discrete domain received signal sequence is sequentially denoised and enhanced to obtain the final time-frequency graph. The final time-frequency graph is preprocessed to obtain the probability distribution result; The foreground probability and background probability are obtained based on the probability distribution results, and the inter-class variance is obtained based on the foreground probability and the background probability. Based on the Otsu maximum inter-class variance criterion, the optimal Otsu segmentation threshold is obtained according to the inter-class variance. Based on the Tsallis entropy criterion, a non-additive combined entropy is obtained according to the foreground probability, the background probability, and the probability distribution results, and the optimal Tsallis segmentation threshold is obtained according to the non-additive combined entropy. The adaptive joint weights are determined based on the normalized inter-class variance index obtained from the inter-class variance and the normalized Tsallis gain index obtained from the non-additive combination entropy. Based on the adaptive joint weight, the optimal Otsu segmentation threshold and the optimal Tsallis segmentation threshold are fused by a weighted method to obtain the joint segmentation threshold; The standard grayscale image is segmented according to the joint segmentation threshold to locate the active interference region, thereby obtaining the interference localization result.

[0006] In one embodiment of the present invention, a discrete-domain received signal sequence is obtained based on the radar received baseband echo signal containing interference, obtained from radar active interference echo signal, linear frequency modulated signal, and additive white Gaussian noise. The sequence includes: Obtain the linear frequency modulated signal, the time-domain expression of which is:

[0007] in, It is a linear frequency modulated signal. For time, For signal amplitude, For rectangular window functions, The modulation frequency of a linear frequency modulation signal. , The time-domain pulse width of the linear frequency modulated signal. This represents the frequency domain bandwidth of the linear frequency modulated signal. The center frequency point of the linear frequency modulated signal; Acquire radar active interference echo signals; The linear frequency modulated signal, the radar active interference echo signal, and the additive white Gaussian noise are combined to form the radar received baseband echo signal, which is represented as follows:

[0008] in, To receive baseband echo signals for radar, This is an active interference signal for radar echo. It is additive white Gaussian noise; Based on the radar received baseband echo signal obtained by equal-interval sampling according to the Nyquist sampling theorem, the discrete-domain received signal sequence is obtained, which is expressed as:

[0009] in, For discrete domain received signal sequences, The sampling period is n For discrete sampling point numbers, N This represents the total number of sampling points. In one embodiment of the present invention, the radar active jamming echo signal includes one of the following: multi-false target jamming signal, comb spectrum jamming, and linear frequency sweep jamming signal; The multi-false-target interference signal is represented as follows:

[0010] in, This is a signal interference from multiple false targets. K The number of false target interferences, For time delay, For Doppler frequency shift; The comb-like interference is represented as:

[0011]

[0012] in, This is due to comb-like interference. It is a comb-like spectrum signal. The number of comb teeth. For the first m The modulation amplitude corresponding to each comb tooth For the first m The frequency position corresponding to each comb tooth; The linear sweep frequency interference signal is represented as follows:

[0013] in, It is a linear frequency sweep interference signal. For interference power, This is the highest frequency of the sweep. This is the lowest frequency for frequency sweep. For the frequency sweep period, 0≤ ≤ T . In one embodiment of the present invention, the first time-frequency graph obtained from the discrete-domain received signal sequence is subjected to denoising and enhancement processing sequentially to obtain the final time-frequency graph, including: A first time-frequency diagram is obtained by performing a short-time Fourier transform on the radar received baseband echo signal. The first time-frequency diagram is represented as follows:

[0014] in, In the first time-frequency diagram The amplitude value at that point, For time frame indexing, For frequency index, For discrete domain received signal sequences, n For discrete sampling point numbers, N This represents the total number of sampling points. For window functions Shift to the right along the time axis x After sampling points, at discrete time n The value at; The background noise in the first time-frequency image is removed using the mean denoising method to obtain the second time-frequency image, which is represented as follows:

[0015] in, For the second time-frequency diagram The amplitude value at that point, To obtain the modulo value, To take the average value; The second time-frequency graph is subjected to amplitude enhancement processing using the amplitude squaring method to obtain the final time-frequency graph, which is represented as follows:

[0016] in, For the final time-frequency plot The amplitude value at that point. In one embodiment of the present invention, the final time-frequency graph is preprocessed to obtain a probability distribution result, including: The final time-frequency graph is normalized and mapped to a preset grayscale range of 0~255 to generate an 8-bit standard grayscale image, which is represented as follows:

[0017] in, For standard grayscale images grayscale at that location For the final time-frequency plot The amplitude value at that point, This represents the minimum amplitude value in the final time-frequency plot. This represents the maximum amplitude value in the final time-frequency plot. Rounding to the nearest integer; Histogram analysis was performed on the standard grayscale image to obtain statistical results, which are expressed as follows:

[0018] in, The grayscale value is The frequency of the pixels appearing in the standard grayscale image, and ; The grayscale probability distribution is calculated based on the statistical results, and the probability distribution result is expressed as follows:

[0019] in, The grayscale value is The probability of a pixel appearing in a standard grayscale image. This represents the total number of pixels in a standard grayscale image. .

[0020] In one embodiment of the present invention, foreground probability and background probability are obtained based on the probability distribution result, and inter-class variance is obtained based on the foreground probability and the background probability, including: Based on the probability distribution results, the foreground probability and the background probability are obtained, and the foreground probability and the background probability are respectively expressed as:

[0021]

[0022] in, Foreground probability, For background probability, The segmentation threshold is... The grayscale value is The probability of a pixel appearing in a standard grayscale image; The foreground mean is obtained based on the foreground probability and the probability distribution result, and the background mean is obtained based on the background probability and the probability distribution result. The foreground mean and the background mean are respectively expressed as follows:

[0023]

[0024] in, Foreground mean The mean value is the background value. The inter-class variance is obtained based on the foreground probability, the background probability, the foreground mean, and the background mean, and is expressed as follows:

[0025] in, The variance is between classes.

[0026] In one embodiment of the present invention, the optimal Otsu segmentation threshold is expressed as:

[0027] in, The optimal Otsu segmentation threshold is... The independent variable is the one that takes the maximum value. For inter-class variance, This is the segmentation threshold. In one embodiment of the present invention, based on the Tsallis entropy criterion, a non-additive combined entropy is obtained according to the foreground probability, the background probability, and the probability distribution result, and an optimal Tsallis segmentation threshold is obtained according to the non-additive combined entropy, including: Based on the foreground probability and the probability distribution result, the normalized probability within the foreground class and the normalized probability within the background class are obtained, and the normalized probability within the foreground class and the normalized probability within the background class are respectively expressed as:

[0028]

[0029] in, The normalized probability within the foreground class. The normalized probability within the background class. Foreground probability, For background probability, The segmentation threshold is... The grayscale value is The probability of a pixel appearing in a standard grayscale image; The Tsallis entropy of the foreground class is obtained based on the normalized probability within the foreground class, and the Tsallis entropy of the background class is obtained based on the normalized probability within the background class. The Tsallis entropy of the foreground class and the Tsallis entropy of the background class are respectively expressed as follows:

[0030]

[0031] in, For the foreground class, Tsallis entropy The Tsallis entropy for the background class. It is a non-extensive entropy exponent; The non-additive combined entropy is obtained based on the Tsallis entropy of the foreground class and the Tsallis entropy of the background class, and the non-additive combined entropy is expressed as:

[0032] in, It is the non-additive combinatorial entropy; The optimal Tsallis segmentation threshold is obtained based on the non-additive combined entropy, and the optimal Tsallis segmentation threshold is expressed as follows:

[0033] in, The optimal Tsallis segmentation threshold is... The independent variable is the value when the maximum value is obtained. In one embodiment of the present invention, determining adaptive joint weights based on a normalized inter-class variance index obtained from the inter-class variance and a normalized Tsallis gain index obtained from the non-additive combination entropy includes: Based on the inter-class variance, a normalized inter-class variance index is obtained, which is expressed as follows:

[0034] in, The normalized inter-class variance index , , 10 -6 , For inter-class variance, The segmentation threshold is... The grayscale value is The probability of a pixel appearing in a standard grayscale image; The normalized Tsallis gain index is obtained based on the non-additive combination entropy, and the normalized Tsallis gain index is expressed as follows:

[0035] in, The normalized Tsallis gain metric. , for The mean, It is the non-additive combinatorial entropy; The adaptive joint weights are obtained based on the normalized inter-class variance index and the normalized Tsallis gain index, and the adaptive joint weights are expressed as follows:

[0036] in, For adaptive joint weights. In one embodiment of the present invention, the joint segmentation threshold is expressed as:

[0037] in, For joint segmentation threshold, For adaptive joint weights, The optimal Otsu segmentation threshold is... The optimal Tsallis segmentation threshold is used. Compared with the prior art, the beneficial effects of the present invention are as follows: The localization method provided by this invention constructs a joint optimization objective based on the Otsu criterion and Tsallis entropy, and introduces adaptively adjustable joint weights. Through multi-criteria fusion, entropy statistical enhancement, and joint threshold optimization, it effectively overcomes the technical bottlenecks of insufficient adaptability and low localization accuracy of single segmentation criteria under complex conditions such as low interference-to-signal ratio and non-uniform backgrounds. Through the joint entropy-threshold optimization mechanism, this invention can improve interference localization accuracy under low interference-to-signal ratio conditions while maintaining low computational complexity. This invention improves the accuracy of radar active interference localization under low interference-to-signal ratio conditions, solves the problem of single threshold segmentation criteria easily misdetecting target signals as interference and missing interference detection under low interference-to-signal ratio conditions, and enhances the robustness of interference localization in complex electromagnetic environments.

[0038] The tracking method provided by this invention can be directly applied to the engineering implementation of motion platforms.

[0039] The present invention will now be described in further detail with reference to the accompanying drawings. Attached Figure Description

[0040] Figure 1 This is a flowchart illustrating a radar active interference weighted joint optimization threshold localization method provided in an embodiment of the present invention; Figure 2 This is a simulated interference time-frequency diagram provided in an embodiment of the present invention; Figure 3 This is a comparison chart of the interference positioning effect provided in the embodiments of the present invention. Detailed Implementation

[0041] The present invention will be further described in detail below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.

[0042] Example 1 Zhao et al. in *Remote Sensing* used the Otsu algorithm to perform threshold segmentation on radar echo intensity maps for pedestrian detection. This method performs well when the interference-to-signal ratio is high, but when the time-frequency energy distribution has multiple peaks or a non-uniform background, Otsu may produce false positives or under-detections. Marcelo Portes de Albuquerque et al. in *Pattern Recognition Letters* proposed an image threshold segmentation method based on Tsallis entropy. This method is more robust in image segmentation with complex textures or non-uniform backgrounds, but it usually requires parameter tuning and may miss detections in low-energy segments.

[0043] However, the aforementioned methods suffer from insufficient robustness and adaptability in complex scenarios. Both the Otsu method and the Tsallis entropy method rely on a single criterion for decision-making. The Otsu method suffers from inaccurate threshold selection when interference and background contrast are low (low interference-to-signal ratio), due to the decrease in inter-class variance. The performance of the Tsallis entropy method is highly dependent on the preset value of the non-extensive parameter q, making it difficult to select a universally optimal q value for radar time-frequency maps with highly variable statistical characteristics. Therefore, existing methods cannot maintain stable and reliable segmentation performance in various complex scenarios ranging from high to low interference-to-signal ratios and from uniform to non-uniform backgrounds.

[0044] Furthermore, the Tsallis entropy calculation is extremely sensitive to the setting of the non-extensive parameter q, and the optimal q usually depends on the true energy distribution of the image. In actual radar jamming scenarios, the structure of the time-frequency image is complex and variable, making it impossible to pre-select a fixed q that is applicable to all jamming types and signal-to-noise ratio conditions. If q is set improperly, the threshold calculation will deviate from the optimal solution, leading to unstable segmentation or even failure.

[0045] To overcome the shortcomings of existing technologies, this invention proposes a radar active interference weighted joint optimization threshold localization method. Please refer to [link to relevant documentation]. Figure 1 , Figure 1 This is a flowchart illustrating a radar active interference weighted joint optimization threshold localization method provided by an embodiment of the present invention. The radar active interference weighted joint optimization threshold localization method provided by the present invention includes: Step 1: Obtain the discrete domain received signal sequence based on the radar received baseband echo signal containing interference, obtained from the radar active interference echo signal, linear frequency modulated signal and additive white Gaussian noise.

[0046] Specifically, this embodiment establishes a mathematical model of radar active interference based on the different radar active interference echo generation principles, and simulates and generates radar interference echo signals as a dataset for interference localization methods.

[0047] In one specific embodiment, step 1 may include: Step 1.1: Obtain the linear frequency modulated (LFM) signal.

[0048] Specifically, a linear frequency modulated (LFM) signal is used as a typical radar transmitted waveform to construct the corresponding radar active interference model, providing a dataset for subsequent analysis and verification. The time-domain expression of the LFM signal is:

[0049] in, It is a linear frequency modulated signal. For time, For signal amplitude, The signal pulse width, The frequency modulation frequency of a linear frequency modulation signal. , The time-domain pulse width of the linear frequency modulated signal. This represents the frequency domain bandwidth of the linear frequency modulated signal. The center frequency point of the linear frequency modulated signal. The mathematical expression is:

[0050] in, This is a rectangular window function.

[0051] Step 1.2: Acquire radar active interference echo signal.

[0052] In this embodiment, the radar active jamming echo signal includes one of the following: multi-false target jamming signal, comb spectrum jamming, and linear frequency sweep jamming signal.

[0053] (1.2a) Multiple false target interference signals.

[0054] Specifically, Multiple False Target Jamming (MFTJ) signals are generated by a jammer capturing radar-transmitted signals, storing them in a digital radio frequency memory (DRFM), and then transmitting them with a designed delay and amplitude. Assuming the generation... K If there are one false target interference, then the multi-false target interference signal is represented as:

[0055] in, This is a signal interference from multiple false targets. K The number of false target interferences, For time delay, This is the Doppler frequency shift.

[0056] (1.2b) Comb spectrum interference.

[0057] Specifically, Comb Spectrum Jamming (CSJ) is obtained by modulating a cosine signal at multiple frequency points. During modulation, the frequency difference between each frequency point generally remains constant. Assume the comb spectrum signal is represented as:

[0058] in, It is a comb-like spectrum signal. The number of comb teeth. For the first m The modulation amplitude corresponding to each comb tooth For the first m The frequency position corresponding to each comb tooth.

[0059] Therefore, comb-like interference is represented as:

[0060] in, This is due to comb-like interference.

[0061] (1.2c) Linear sweep frequency interference signal.

[0062] Specifically, Linear Sweeping Frequency Jamming (LSFJ) signals are a type of suppressive interference signal characterized by linearly varying instantaneous frequencies. A linear sweeping frequency jamming signal is represented as:

[0063] in, It is a linear frequency sweep interference signal. For interference power, This is the highest frequency of the sweep. This is the lowest frequency for frequency sweep. For the frequency sweep period, 0≤ ≤ T .

[0064] Step 1.3: Combine the linear frequency modulated signal, the radar active interference echo signal, and the additive white Gaussian noise to form the radar receiving baseband echo signal.

[0065] Specifically, to construct a simulation dataset for subsequent processing, the linear frequency modulated signal emitted by the radar is mixed with specific types of interference signals. ( for , or One of the following is synthesized with additive white Gaussian noise to form a radar baseband echo signal containing interference. The radar baseband echo signal is represented as:

[0066] in, To receive baseband echo signals for radar, It is additive white Gaussian noise.

[0067] Step 1.4: Obtain the discrete domain received signal sequence by sampling the radar baseband echo signal at equal intervals according to the Nyquist sampling theorem.

[0068] Here, the discrete-domain received signal sequence is represented as:

[0069] in, For discrete domain received signal sequences, The sampling period is n For discrete sampling point numbers, N This represents the total number of sampling points.

[0070] Step 2: Perform denoising and enhancement processing on the first time-frequency diagram obtained from the discrete domain received signal sequence to obtain the final time-frequency diagram.

[0071] Specifically, the interference echo is processed by short-time Fourier transform to obtain a time-frequency diagram, and then image enhancement is performed to amplify the difference between the interference and the signal.

[0072] In one specific embodiment, step 2 may include: Step 2.1: Perform a short-time Fourier transform on the radar received baseband echo signal to obtain the first time-frequency diagram.

[0073] Here, the first time-frequency diagram is represented as:

[0074] in, In the first time-frequency diagram The amplitude value at that point, For time frame indexing, For frequency index, The window function is a Hamming window, and its discrete expression is:

[0075] Then after time shift The expression is:

[0076] in, For window functions The value at discrete time n is obtained after shifting x sampling points to the right along the time axis.

[0077] Step 2.2: Use the mean denoising method to remove background noise from the first time-frequency image to obtain the second time-frequency image.

[0078] Here, the second time-frequency diagram is represented as:

[0079] in, For the second time-frequency diagram The amplitude value at that point, To obtain the modulo value, To take the average value.

[0080] Step 2.3: Use the amplitude squaring method to perform amplitude enhancement processing on the second time-frequency graph to obtain the final time-frequency graph.

[0081] Here, the final time-frequency diagram is represented as follows:

[0082] in, For the final time-frequency plot The amplitude value at that point.

[0083] This embodiment amplifies the difference between the signal and the interference by denoising and squaring the time-frequency graph, thus providing a basis for subsequent interference localization.

[0084] Step 3: Preprocess the final time-frequency graph to obtain the probability distribution results.

[0085] Specifically, the probability distribution results are obtained by performing preprocessing operations such as normalization, quantization, and histogram statistics on the final time-frequency graph.

[0086] In one specific embodiment, step 3 may include: Step 3.1: Normalize the final time-frequency image and map it to a preset grayscale range of 0 to 255 to generate an 8-bit standard grayscale image, which will provide a probability distribution basis for the subsequent calculation of the Otsu threshold and Tsallis threshold. The preset grayscale range is 0 to 255.

[0087] Here, the standard grayscale image is represented as:

[0088] in, For standard grayscale images grayscale at that location This represents the minimum amplitude value in the final time-frequency plot. This represents the maximum amplitude value in the final time-frequency plot. Rounding to the nearest integer.

[0089] Step 3.2: Perform histogram statistics on the standard grayscale image to obtain the statistical results.

[0090] Here, the statistical results are expressed as follows:

[0091] in, The grayscale value is The frequency of the pixels appearing in the standard grayscale image, and .

[0092] Step 3.3: Calculate the gray-scale probability distribution based on the statistical results to obtain the probability distribution results.

[0093] Here, the probability distribution results are expressed as:

[0094] in, The grayscale value is The probability of a pixel appearing in a standard grayscale image. This represents the total number of pixels in a standard grayscale image. .

[0095] Step 4: Obtain the foreground probability and background probability based on the probability distribution results, and obtain the inter-class variance based on the foreground probability and background probability.

[0096] In one specific embodiment, step 4 may include: Step 4.1: Obtain the foreground probability and background probability based on the probability distribution results.

[0097] Here, the foreground probability and background probability are expressed as follows:

[0098]

[0099] in, Foreground probability, For background probability, This is the segmentation threshold.

[0100] Step 4.2: Obtain the foreground mean based on the foreground probability and probability distribution results, and obtain the background mean based on the background probability and probability distribution results.

[0101] Here, the foreground mean and background mean are expressed as follows:

[0102]

[0103] in, Foreground mean This represents the background mean.

[0104] Step 4.3: Calculate the inter-class variance based on the foreground probability, background probability, foreground mean, and background mean.

[0105] Here, the inter-class variance is expressed as:

[0106] in, The variance is between classes.

[0107] Step 5: Based on the Otsu maximum inter-class variance criterion, obtain the optimal Otsu segmentation threshold according to the inter-class variance.

[0108] Specifically, the Otsu method determines the optimal threshold by maximizing the inter-class variance between the foreground and background classes. The idea is that an optimal threshold should maximize the mean difference and separability between the two classes. Otsu finds the optimal threshold by maximizing the inter-class variance, essentially seeking the dividing point that makes the two classes statistically the "farthest" apart. The larger the inter-class variance, the more pronounced the difference between the foreground and background, and the more stable and reliable the threshold segmentation. However, in radar active jamming localization, especially under low signal-to-interference ratio or non-uniform background conditions, the signal and jamming energy distributions overlap significantly, resulting in a significant decrease in inter-class variance, making it difficult for the classic Otsu method to find an effective threshold. Therefore, while the Otsu criterion has the advantages of strong statistical stability and low computational cost, its performance depends on "separability," and its performance is limited in areas with weak jamming or complex backgrounds.

[0109] Therefore, the optimal Otsu segmentation threshold, as defined by the optimal Otsu threshold definition, is expressed as:

[0110] in, The optimal Otsu segmentation threshold is... The independent variable is the value when the maximum value is obtained.

[0111] Otsu utilizes the principle of maximizing inter-class variance to achieve the maximum grayscale difference between the foreground and background, thus obtaining the optimal Otsu segmentation threshold. The larger the inter-class variance, the stronger the separation effect; therefore, the grayscale value corresponding to the maximum inter-class variance is selected as the optimal Otsu segmentation threshold. .

[0112] Step 6: Based on the Tsallis entropy criterion, obtain the non-additive combined entropy according to the foreground probability, background probability and probability distribution results, and obtain the optimal Tsallis segmentation threshold according to the non-additive combined entropy.

[0113] Specifically, Tsallis entropy is a non-additive entropy measure widely used in complex systems. It is naturally sensitive to the skewness, clustering structure, and multi-scale statistical properties of distributions, and is defined as follows:

[0114] in, For Tsallis entropy, It is a non-extensive entropy index (non-extensive factor). q >0 and q Not equal to 1 q When the value is greater than 1, Tsallis entropy can emphasize the dominant component in the probability distribution; it highlights clustered or textured structures; and it adapts to complex statistical environments that are non-uniform and non-stationary. In radar time-frequency maps, interference typically presents as clustered structures or energy anomaly regions; background noise exhibits a relatively flat random distribution. Therefore, Tsallis entropy can more effectively reveal intra-class consistency and structural differences, especially under complex conditions such as low interference-to-signal ratio, multi-scale interference, and non-uniform backgrounds, demonstrating stronger discriminative power than Otsu.

[0115] In one specific embodiment, step 6 may include: Step 6.1: Obtain the normalized probability within the foreground class and the normalized probability within the background class based on the foreground probability and probability distribution results.

[0116] Here, the normalized probabilities within the foreground class and the normalized probabilities within the background class are expressed as follows:

[0117]

[0118] in, The normalized probability within the foreground class. The normalized probability within the background class.

[0119] Step 6.2: Obtain the Tsallis entropy of the foreground class based on the normalized probability within the foreground class, and obtain the Tsallis entropy of the background class based on the normalized probability within the background class.

[0120] Here, the Tsallis entropy of the foreground class and the Tsallis entropy of the background class are expressed as:

[0121]

[0122] in, For the foreground class, Tsallis entropy The Tsallis entropy for the background class.

[0123] Step 6.3: Obtain the non-additive combined entropy based on the Tsallis entropy of the foreground class and the Tsallis entropy of the background class to enhance the detectability of weak interference.

[0124] Here, the non-additive combinatorial entropy is expressed as:

[0125] in, It is the non-additive combinatorial entropy.

[0126] Step 6.4: Obtain the optimal Tsallis segmentation threshold based on the non-additive combination entropy.

[0127] Specifically, to reduce computational load and facilitate engineering implementation, this embodiment adopts the additive approximation model of Tsallis entropy. Therefore, the optimal Tsallis segmentation threshold is expressed as:

[0128] in, The optimal Tsallis segmentation threshold is used.

[0129] Step 7: Determine the adaptive joint weights based on the normalized inter-class variance index obtained from the inter-class variance and the normalized Tsallis gain index obtained from the non-additive combination entropy.

[0130] In one specific embodiment, step 7 may include: Step 7.1: Obtain the normalized inter-class variance index based on the inter-class variance.

[0131] Here, the normalized inter-class variance index is expressed as:

[0132] in, The normalized inter-class variance index , , For small quantities, 10 -6 To prevent division by zero.

[0133] The maximum inter-class variance varies under different TFRs and different interference-to-information ratios, and the original variance values ​​cannot be directly compared. Therefore, a normalized inter-class variance index is used. .

[0134] It can reflect whether the histogram shows bimodality or significant differences between classes. The larger the value, the more obvious the bimodality of the histogram, the more significant the differences between classes, and the more reliable the Otsu's algorithm. The smaller the value, the more severe the overlap between signal and interference, and the smaller the difference between classes. It is difficult to distinguish them using Otsu alone, and Tsallis entropy enhancement is required.

[0135] Step 7.2: Obtain the normalized Tsallis gain index based on the non-additive combinatorial entropy.

[0136] Here, the normalized Tsallis gain metric is expressed as:

[0137] in, The normalized Tsallis gain metric. , for The mean.

[0138] It can reflect the degree of improvement of the Tsallis target relative to the overall level at the optimal threshold. The larger the threshold, the better it can capture weak interference or complex structures, making Tsallis more reliable; The smaller the value, the more Tsallis entropy considers the threshold division meaningless, requiring Otsu enhancement.

[0139] Step 7.3: Obtain the adaptive joint weights based on the normalized inter-class variance index and the normalized Tsallis gain index.

[0140] Specifically, the normalized inter-class variance index and the normalized Tsallis gain index are used as the confidence scores of Otsu and Tsallis, respectively, and mapped to the adaptive joint weights. Therefore, the adaptive joint weights are expressed as:

[0141] in, For adaptive joint weights.

[0142] Step 8: Based on the adaptive joint weight, the optimal Otsu segmentation threshold and the optimal Tsallis segmentation threshold are fused by weighting to obtain the joint segmentation threshold.

[0143] Here, the joint segmentation threshold is expressed as:

[0144] in, This is the joint segmentation threshold.

[0145] By fusing the optimal Otsu segmentation threshold and the optimal Tsallis segmentation threshold in a weighted manner, the resulting joint segmentation threshold comprehensively considers inter-class variance and non-additive entropy information, which can improve robustness in the case of low JSR.

[0146] Step 9: Segment the standard grayscale image according to the joint segmentation threshold to locate the active interference region and obtain the interference localization result.

[0147] Specifically, the final joint segmentation threshold The interference mask is applied to a standard grayscale image to obtain a binarized interference mask, which is then used to determine the interference localization result. The binarized interference mask is represented as follows:

[0148] in, For binary interference masking, Interference area This refers to the background / target signal region.

[0149] like Figure 2 As shown, the simulation dataset sets the radar transmission parameters as follows: bandwidth of 80MHz, pulse width of 12μs, sampling frequency of 160MHz, and pulse repetition frequency of 5000Hz; the number of false targets in multi-false target jamming is 3; the number of false targets in frequency sweep jamming is 4; and the number of comb teeth in comb spectrum jamming is 4. Figure 2 Simulated time-frequency diagrams of interference for multiple false targets, comb-spectrum interference, and linear sweep frequency interference. For example... Figure 3 As shown, the interference localization effects of three methods—Otsu interference localization, Tsallis interference localization, and Otsu and Tsallis weighted joint threshold interference localization—are compared. At this point, JSR = 6 dB. Figure 3 It can be seen that the Otsu and Tsallis weighted joint threshold interference localization method has a lower probability of false detection and a better interference localization effect.

[0150] This invention constructs a joint optimization objective function that integrates the Otsu's inter-class variance criterion and the Tsallis entropy criterion, fully leveraging the statistical stability of the Otsu's method in terms of inter-class separation and the ability of the Tsallis entropy to describe complex systems, thus achieving a complementary advantage of both. Furthermore, it proposes a method for calculating adaptive joint weights. The adaptive adjustment mechanism dynamically determines the relative weights of Otsu and Tsallis in joint optimization by introducing a normalized inter-class variance index (measuring separation) and a normalized Tsallis gain index (measuring intra-class consistency). This adaptive joint weight can automatically compensate for inappropriate weights. q The value of the parameter affects the Tsallis result, thus weakening the effect of the Tsallis entropy on the parameter. qThe sensitivity to interference allows the method of this invention to select a reasonable optimization threshold under different interference structures and interference-to-signal ratio (ISR) conditions. Ultimately, this invention guides the search for a balanced threshold that simultaneously satisfies "high inter-class separation" (dominated by the Otsu component) and "high intra-class consistency" (dominated by the Tsallis entropy component) through a joint optimization criterion and an adaptive weighting mechanism. Addressing the problem of low positioning accuracy in existing methods under low ISR conditions, this invention improves interference positioning accuracy.

[0151] It should be noted that the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Therefore, features defined as "first" or "second" may explicitly or implicitly include one or more features. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0152] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features or characteristics described may be combined in any suitable manner in one or more embodiments or examples. In addition, those skilled in the art can combine and integrate the different embodiments or examples described in this specification.

[0153] Although the invention has been described herein in conjunction with various embodiments, those skilled in the art will understand and implement other variations of the disclosed embodiments by reviewing the accompanying drawings and the disclosure in carrying out the claimed invention. In this specification, the word "comprising" does not exclude other components or steps, and "a" or "an" does not exclude a plurality. While certain measures are described in different embodiments, this does not mean that these measures cannot be combined to produce good results.

[0154] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A radar active interference weighted joint optimization threshold localization method, characterized in that, include: Based on the radar received baseband echo signal containing interference, which is obtained from radar active interference echo signal, linear frequency modulated signal and additive white Gaussian noise, a discrete domain received signal sequence is obtained. The first time-frequency graph obtained from the discrete domain received signal sequence is sequentially denoised and enhanced to obtain the final time-frequency graph. The final time-frequency graph is preprocessed to obtain the probability distribution result; The foreground probability and background probability are obtained based on the probability distribution results, and the inter-class variance is obtained based on the foreground probability and the background probability. Based on the Otsu maximum inter-class variance criterion, the optimal Otsu segmentation threshold is obtained according to the inter-class variance. Based on the Tsallis entropy criterion, a non-additive combined entropy is obtained according to the foreground probability, the background probability, and the probability distribution results, and the optimal Tsallis segmentation threshold is obtained according to the non-additive combined entropy. The adaptive joint weights are determined based on the normalized inter-class variance index obtained from the inter-class variance and the normalized Tsallis gain index obtained from the non-additive combination entropy. Based on the adaptive joint weight, the optimal Otsu segmentation threshold and the optimal Tsallis segmentation threshold are fused by a weighted method to obtain the joint segmentation threshold; The standard grayscale image is segmented according to the joint segmentation threshold to locate the active interference region, thereby obtaining the interference localization result.

2. The radar active interference weighted joint optimization threshold localization method according to claim 1, characterized in that, Based on the radar received baseband echo signal containing interference, obtained from the radar active interference echo signal, linear frequency modulated signal, and additive white Gaussian noise, a discrete domain received signal sequence is obtained, including: Obtain the linear frequency modulated signal, the time-domain expression of which is: in, It is a linear frequency modulated signal. For time, For signal amplitude, For rectangular window functions, The frequency modulation frequency of a linear frequency modulation signal. , The time-domain pulse width of the linear frequency modulated signal. This represents the frequency domain bandwidth of the linear frequency modulated signal. The center frequency point of the linear frequency modulated signal; Acquire radar active interference echo signals; The linear frequency modulated signal, the radar active interference echo signal, and the additive white Gaussian noise are combined to form the radar received baseband echo signal, which is represented as follows: in, To receive baseband echo signals for radar, This is an active jamming echo signal for radar. It is additive white Gaussian noise; Based on the radar received baseband echo signal obtained by equal-interval sampling according to the Nyquist sampling theorem, the discrete-domain received signal sequence is obtained, which is expressed as: in, For discrete domain received signal sequences, The sampling period is n For discrete sampling point numbers, N This represents the total number of sampling points.

3. The radar active interference weighted joint optimization threshold localization method according to claim 2, characterized in that, The radar active jamming echo signal includes one of the following: multi-false target jamming signal, comb spectrum jamming, and linear sweep frequency jamming signal; The multi-false-target interference signal is represented as follows: in, This is a signal interference from multiple false targets. K The number of false target interferences, For time delay, For Doppler frequency shift; The comb-like interference is represented as: in, This is due to comb-like interference. It is a comb-like spectrum signal. The number of comb teeth. For the first m The modulation amplitude corresponding to each comb tooth For the first m The frequency position corresponding to each comb tooth; The linear sweep frequency interference signal is represented as follows: in, It is a linear frequency sweep interference signal. For interference power, This is the highest frequency of the sweep. This is the lowest frequency for frequency sweep. For the frequency sweep period, 0≤ ≤ T .

4. The radar active interference weighted joint optimization threshold localization method according to claim 1, characterized in that, The first time-frequency graph obtained from the discrete-domain received signal sequence is sequentially subjected to denoising and enhancement processing to obtain the final time-frequency graph, including: A first time-frequency diagram is obtained by performing a short-time Fourier transform on the radar received baseband echo signal. The first time-frequency diagram is represented as follows: in, In the first time-frequency diagram The amplitude value at that point, For time frame indexing, For frequency index, For discrete domain received signal sequences, n For discrete sampling point numbers, N This represents the total number of sampling points. For window functions Shift to the right along the time axis x After sampling points, at discrete time n The value at; The background noise in the first time-frequency image is removed using the mean denoising method to obtain the second time-frequency image, which is represented as follows: in, For the second time-frequency diagram The amplitude value at that point, To obtain the modulo value, To take the average value; The second time-frequency graph is subjected to amplitude enhancement processing using the amplitude squaring method to obtain the final time-frequency graph, which is represented as follows: in, For the final time-frequency plot The amplitude value at that point.

5. The radar active interference weighted joint optimization threshold localization method according to claim 1, characterized in that, The final time-frequency graph is preprocessed to obtain the probability distribution result, including: The final time-frequency graph is normalized and mapped to a preset grayscale range of 0~255 to generate an 8-bit standard grayscale image, which is represented as follows: in, For standard grayscale images grayscale at that location For the final time-frequency plot The amplitude value at that point, This represents the minimum amplitude value in the final time-frequency plot. This represents the maximum amplitude value in the final time-frequency plot. Rounding to the nearest integer; Histogram analysis was performed on the standard grayscale image to obtain statistical results, which are expressed as follows: in, The grayscale value is The frequency of the pixels appearing in the standard grayscale image, and ; The grayscale probability distribution is calculated based on the statistical results, and the probability distribution result is expressed as follows: in, The grayscale value is The probability of a pixel appearing in a standard grayscale image. This represents the total number of pixels in a standard grayscale image. .

6. The radar active interference weighted joint optimization threshold localization method according to claim 1, characterized in that, Based on the probability distribution results, foreground probabilities and background probabilities are obtained, and based on the foreground probabilities and background probabilities, inter-class variance is obtained, including: Based on the probability distribution results, the foreground probability and the background probability are obtained, and the foreground probability and the background probability are respectively expressed as: in, Foreground probability, For background probability, The segmentation threshold is... The grayscale value is The probability of a pixel appearing in a standard grayscale image; The foreground mean is obtained based on the foreground probability and the probability distribution result, and the background mean is obtained based on the background probability and the probability distribution result. The foreground mean and the background mean are respectively expressed as follows: in, Foreground mean The mean value is the background value. The inter-class variance is obtained based on the foreground probability, the background probability, the foreground mean, and the background mean, and is expressed as follows: in, The variance is between classes.

7. The radar active interference weighted joint optimization threshold localization method according to claim 1, characterized in that, The optimal Otsu segmentation threshold is expressed as: in, The optimal Otsu segmentation threshold is... The independent variable is the one that takes the maximum value. For inter-class variance, This is the segmentation threshold.

8. The radar active interference weighted joint optimization threshold localization method according to claim 1, characterized in that, Based on the Tsallis entropy criterion, a non-additive combined entropy is obtained according to the foreground probability, the background probability, and the probability distribution results. The optimal Tsallis segmentation threshold is then obtained based on the non-additive combined entropy, including: Based on the foreground probability and the probability distribution result, the normalized probability within the foreground class and the normalized probability within the background class are obtained, and the normalized probability within the foreground class and the normalized probability within the background class are respectively expressed as: in, The normalized probability within the foreground class. The normalized probability within the background class. Foreground probability, For background probability, The segmentation threshold is... The grayscale value is The probability of a pixel appearing in a standard grayscale image; The Tsallis entropy of the foreground class is obtained based on the normalized probability within the foreground class, and the Tsallis entropy of the background class is obtained based on the normalized probability within the background class. The Tsallis entropy of the foreground class and the Tsallis entropy of the background class are respectively expressed as follows: in, For the foreground class, Tsallis entropy The Tsallis entropy for the background class. It is a non-extensive entropy exponent; The non-additive combined entropy is obtained based on the Tsallis entropy of the foreground class and the Tsallis entropy of the background class, and the non-additive combined entropy is expressed as: in, It is the non-additive combinatorial entropy; The optimal Tsallis segmentation threshold is obtained based on the non-additive combined entropy, and the optimal Tsallis segmentation threshold is expressed as follows: in, The optimal Tsallis segmentation threshold is... The independent variable is the value when the maximum value is obtained.

9. The radar active interference weighted joint optimization threshold localization method according to claim 1, characterized in that, Based on the normalized inter-class variance index obtained from the inter-class variance and the normalized Tsallis gain index obtained from the non-additive combination entropy, the adaptive joint weights are determined, including: Based on the inter-class variance, a normalized inter-class variance index is obtained, which is expressed as follows: in, The normalized inter-class variance index , , 10 -6 , For inter-class variance, The segmentation threshold is... The grayscale value is The probability of a pixel appearing in a standard grayscale image; The normalized Tsallis gain index is obtained based on the non-additive combination entropy, and the normalized Tsallis gain index is expressed as follows: in, The normalized Tsallis gain metric. , for The mean, It is the non-additive combinatorial entropy; The adaptive joint weights are obtained based on the normalized inter-class variance index and the normalized Tsallis gain index, and the adaptive joint weights are expressed as follows: in, For adaptive joint weights.

10. The radar active interference weighted joint optimization threshold localization method according to claim 1, characterized in that, The joint segmentation threshold is expressed as: in, For joint segmentation threshold, For adaptive joint weights, The optimal Otsu segmentation threshold is... The optimal Tsallis segmentation threshold is used.

Images