Low-altitude slow small target threat evaluation method and system based on LSTM model combined with KAN network

Abstract

The application discloses a low-altitude slow target threat evaluation method and system based on an LSTM model combined with a KAN network, and the method steps are as follows: S1, obtaining low-altitude slow target pulse data in a set time period, and taking pulse data with a length of N as a sample for preprocessing; S2, preprocessing the pulse data in a fuzzy data mode; S3, constructing a model based on the LSTM model combined with the KAN network, and initializing parameters; S4, processing according to the credibility of data, inputting the processed data into the model constructed in step S3 for network training, and saving the feature extractor and the classifier weight obtained through the training; and S5, inputting the preprocessed low-altitude slow target pulse data to be tested into the model trained in step S4 for evaluation, and obtaining a low-altitude slow target threat evaluation result. The application can improve the threat evaluation accuracy of low-altitude slow small targets in a dynamic environment.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of radar reconnaissance, and particularly relates to a low-altitude slow small target threat assessment method and system based on an LSTM (Long Short-Term Memory) model combined with a KAN network (KAN, Kolmogorov-Arnold Networks), and the application can be used for low-altitude slow small target threat assessment. BACKGROUND

[0002] In the low-altitude area of cities and battlefields, identifying and responding to low-altitude slow small (LSS) flying targets is one of the major challenges faced by defense monitoring and early warning systems. For incoming LSS targets, accurate threat assessment is crucial for the efficiency of firepower deployment and command decision-making, which has become an increasingly growing demand. At the present stage, threat assessment mainly relies on analyzing trajectory data obtained through detection and tracking. Since the trajectory reflects the observable motion characteristics of the target, specific trajectory features can be used to infer the true intention of the target. In threat assessment, target type and motion characteristics are one of the most intuitive, most effective and most commonly used indicators, because these attributes directly affect the response capability of weapon systems and the efficiency of reconnaissance and attack. By integrating various features extracted from the trajectory, threat assessment can more accurately determine the potential threat level of the target. Therefore, in-depth research on target classification and threat assessment based on trajectories is the key to improving defense capabilities.

[0003] The core of threat level assessment lies in the quantitative analysis and description of the threat intention of the target. Although existing multiple attribute decision-making algorithms (MADM) and Bayesian networks have achieved certain results in threat recognition, there are obvious limitations in these existing methods. They usually assess the threat at each moment independently, ignoring the temporal relationship between different time points, and cannot effectively capture the continuously changing threat patterns or comprehensively analyze the overall threat intention of the target. This makes it difficult for them to exhibit sufficient accuracy and coherence when dealing with dynamic threats.

[0004] There are two main challenges in threat assessment. First, the threat level has inertia over time, so the assessment process needs to consider the correlation between different time points to capture the continuous threat intention of the target. Second, the accuracy of assessment depends on the quality of trajectory data, and random noise and trajectory fluctuations can make it difficult to accurately extract the true intention and threat level of the target. SUMMARY

[0005] Aiming at the phenomenon that the existing network structure has uncertainty to data parameter change and data credibility in dynamic environment under complex electromagnetic environment, in order to improve the threat level evaluation performance of LSS target, the application provides a LSS target threat evaluation method and system based on LSTM model combined with KAN network.

[0006] In order to achieve the above object, the application adopts the following technical scheme:

[0007] The low-altitude slow small target threat evaluation method based on LSTM model combined with KAN network comprises the following steps:

[0008] S1, obtaining low-altitude slow small target pulse data for a period of time, taking pulse data with a length of N as a sample for preprocessing;

[0009] S2, for uncertain information of reconnaissance data, preprocessing the pulse data by using fuzzy data;

[0010] S3, constructing a model based on LSTM model combined with KAN network, and initializing and setting parameters;

[0011] S4, according to different data credibility, different processing is carried out, the processed data is input into the model constructed in S3 for network training, and the feature extractor and classifier weight obtained by training are saved;

[0012] S5, inputting the preprocessed low-altitude slow small target pulse data to be tested into the model trained in step S4 for evaluation, and obtaining the threat evaluation result of the low-altitude slow small target.

[0013] Further, in step S1, the preprocessing process comprises introducing a membership function, and normalizing the attribute value to f(x) [0, 1]. Wherein, x is a specific threat attribute value, and f is a function in the membership space F. In the application, the rising exponential function and the descending half normal distribution function are used to normalize the quantitative attribute, so as to ensure the comparability between different attributes and provide a basis for subsequent dynamic threat evaluation. The specific steps are as follows:

[0014] If the threat attribute is positively correlated with the threat degree, the rising exponential function is adopted, such as:

[0015]

[0016] Wherein, x0 is a constant, representing the threshold value of the attribute; x is the input value, i.e. the true value of the attribute of the reconnaissance data; δ L is a constant, representing a coefficient, and when the true value is less than the threshold value, the function is a constant; k is a constant, representing the growth rate and attenuation rate of the function, which determines the change speed of the function;

[0017] When the attribute value x is less than x0, the quantization f(x) equals δ L When x is greater than x0, f(x) is positively correlated with x, and is expressed as an ascending exponential function. f(x) = 0.5 if and only if x = x1. k is used to fit the above conditions:

[0018] k = -(ln(f(x1) / (1-δ L )) / (x1-x0)

[0019] If the threat attribute is negatively correlated with the threat degree, a descending half-normal distribution function is used. For example:

[0020]

[0021] There are three parameters: δ H , x0, x1 (x0 < x1), when the attribute value x is less than x0, the quantization f(x) equals δ H When x is greater than x0, f(x) is negatively correlated with x, and is expressed as a descending half-normal distribution function. f(x) = 0.5 if and only if x = x1. k is used to fit the above conditions:

[0022] k = -(ln(f(x1) / (1-δ H )) / (x1-x0)

[0023] Different types of parameters have different criteria when normalizing the membership of data:

[0024] Distance: Distance is one of the important factors that determine the difficulty of target reconnaissance and attack. As the target gradually approaches, the reaction time of the defense system shortens, the defense difficulty increases significantly, and the possibility of the target successfully breaking through the defense also rises accordingly. Therefore, the closer the distance, the greater the threat posed by the target to the defense, and the threat level also rises accordingly. In order to accurately quantify the relationship between this threat and distance, a descending half-normal distribution function is used to model the distance attribute. This function can well reflect the non-linear characteristics of the threat decreasing with distance, ensure that close-range targets are given higher weights in threat assessment, and the threat of long-range targets gradually weakens, thus providing a more reasonable basis for threat assessment.

[0025] Speed: Speed is one of the important indicators to measure the maneuverability of the target. In some cases, the faster the target speed, the stronger its maneuverability and flexibility, which increases the difficulty of the target to evade reconnaissance or defense systems, and thus increases its danger. Therefore, the increase in speed usually means greater threat. In order to accurately reflect this feature, the rising exponential function is used to model the speed attribute. This function can effectively capture the non-linear relationship between the increase in speed and the increase in threat level, ensuring that high-speed targets receive higher threat ratings during threat assessment, thus providing more accurate basis for defense decision-making.

[0026] Altitude: Altitude is one of the important parameters reflecting the operational purpose of the flying target. Generally, targets performing high-risk attack or reconnaissance tasks tend to fly at low altitudes to evade radar detection. Such low-altitude flight increases the possibility of successful penetration of defense systems, thus posing a greater threat to the defender. In this case, low-altitude flying targets must be given priority due to their higher threat. To quantify the impact of altitude on threat assessment, a decreasing semi-normal distribution function is used to model the altitude attribute. This function can effectively reflect the non-linear relationship between target altitude and threat, ensuring that low-altitude flying targets are given higher threat weights in threat assessment, while high-altitude flying targets are correspondingly reduced in threat level.

[0027] Shortcut: Shortcut represents the horizontal distance from the current flight direction of the target to the defense area. Generally, a longer shortcut may imply that the target's attack intention is weak, and the direct threat of the target is relatively small. As the shortcut shortens, the target is more likely to enter the key defense area, and the threat level also increases. Therefore, the change of shortcut is inversely related to the threat level. In order to accurately quantify the impact of shortcut on threat assessment, a decreasing semi-normal distribution function is used to model this attribute. This function can effectively reflect the non-linear impact of shortcut length on threat level, ensuring that targets with shorter shortcuts are given higher threat weights, while long-shortcut targets are considered to be less threatening.

[0028] Further, in step S2, in a dynamically changing environment, especially when encountering extreme conditions such as bad weather, the collected pulse data is often disturbed, thereby affecting the accuracy and effectiveness of the data. Such unreliable data, if directly used for decision-making or analysis, may have serious consequences. Therefore, by introducing the relative MAE (Mean Absolute Error) as a reliability parameter, the reliability of the data can be quantified, and the data with high reliability and data with low reliability are processed in two ways. Specifically:

[0029] S21, introduce relative mean absolute error to judge data accuracy, the mean absolute error expression is:

[0030]

[0031] where n represents the number of samples; X i represents the ith prediction value; X 真实值 represents the corresponding true value.

[0032] In order to determine whether the MAE is too large, the relative MAE can be considered, that is, the percentage of the data MAE to the average value or true value of the data is calculated, and the expression is:

[0033]

[0034] S22, accuracy judgment of data: when the relative MAE is too large (usually more than 20%) or exceeds the error standard of a specific field, the credibility of the data is considered to be insufficient.

[0035] S23, in the reconnaissance data processing, although the credibility of part of the data is low, the error is usually maintained within a certain range. Based on this feature, the data can be divided into five levels according to the numerical interval, so as to more flexibly manage and apply the data. Even if the data is judged to be low in credibility because of large error, as long as its value meets the corresponding level interval, it can still be classified into the corresponding level. This hierarchical mode can improve the overall utilization rate under the premise of ensuring the effectiveness of the data, and provide orderly support for subsequent analysis.

[0036] Further, in step S3, in order to extract the correlation of the LSS target time sequence pulse signal in time, the LSTM network model is used to extract the correlation in time sequence.

[0037] Further, in step S3, the model design is as follows:

[0038] In step S31, four LSTM layers are used to extract features of the time sequence signal, and a convolution block is used to extract hidden information of the time sequence signal; a gating mechanism, a cell state and a hidden state are used to fuse the hidden information of the time sequence signal feature extraction; specifically:

[0039] In order to extract the correlation of the LSS target time sequence pulse signal in time, the LSTM network model is used to extract the correlation in time sequence:

[0040] The LSTM network is a recurrent neural network widely used in time series data processing, and its main advantage is to effectively capture the long and short term dependence relationship in time series through the internal "memory" unit. LSTM controls the flow process of information by setting the forget gate, input gate and output gate. Specifically:

[0041] Forget gate: responsible for selecting the historical information to be discarded, avoiding the interference of useless data to the model.

[0042] Input Gate: decides which new information should be added to the current memory cell.

[0043] Output Gate: controls what the model outputs at the current time step, ensuring that critical temporal information is passed to the next time step.

[0044] LSTM network structure: Cell state represents the cell state (memory state) and has C t , the current cell state C t is determined by the cell state C t-1 of the previous time step and the newly generated Forget Gate: represents the forget gate and has f t = σ(W f · [h t-1 , x t ] + b f ), which operates on the cell state C t-1 of the previous time step and the current input x t , the previous hidden state h t-1 , and outputs a value f t , indicating the part of the cell state that needs to be "forgotten". Input Gate represents the input gate and has i t = (W i · [h t-1 , x t ] + b i ), The input gate consists of two parts: i t controls which values need to be updated, generated from the current input and the previous hidden state; generate candidate cell state, decide the new content. Output Gate represents the output gate and has o t = σ(W o · [h t-1 , x t ] + b o ), h t = o t *tanh(C t ), the role of o t is to control how much information in the current cell state C t can be output as the hidden state h t of the current time step, playing a "screening" role, when approaching 0, indicating that little information is output, the hidden state h t will be greatly inhibited, when approaching 1, indicating that more information is output, the hidden state h t accepts more from the cell state C tinformation. The output gate value o t After that, it will be combined with the current cell state C t The values processed by the tanh function are multiplied element by element to generate the hidden state of the current time step.

[0045] This design allows LSTM to maintain the memory of long-span information while filtering out short-term noise. Therefore, when dealing with complex data containing trajectory jitter or measurement noise, LSTM performs particularly well. It can dynamically track and capture the threat intent of the target, greatly improving the accuracy and stability of threat assessment.

[0046] Step S32, using KAN model instead of traditional multilayer perceptron (MLP, Multilayer Perceptron), to get the output, so as to realize the representation of multi-dimensional features of signal.

[0047] Although LSTM performs well in capturing time series information, it still has limitations in dealing with complex multivariate data. To improve the accuracy and noise suppression ability of threat assessment, KAN network is innovatively combined to effectively decompose complex trajectory features into single variable function processing through multivariate function approximation. KAN network complements the shortcomings of LSTM in high-dimensional data processing, enhances the model's ability to identify target movement intent, and significantly improves the accuracy and stability of threat assessment. After the combination of the two, the model has stronger dynamic response ability and robustness in complex environments with noise interference.

[0048] KAN network is a network architecture based on Kolmogorov-Arnold representation theorem, which is used to approximate complex multivariate functions. According to the theorem, any continuous multivariate function f(x1, x2, …, xn) can be represented as the superposition of multiple single variable functions, that is:

[0049]

[0050] where ψ i and φ ij are continuous single variable functions. KAN network uses this representation theorem to decompose complex multi-dimensional input data into a series of simple single variable functions, and completes accurate modeling of multi-dimensional data through the combination of these functions. This decomposition method allows KAN network to extract deep motion features when dealing with complex trajectory data, making it particularly suitable for threat assessment of LSS targets.

[0051] The advantages of KAN network mainly lie in its strong multivariate function approximation ability and excellent noise reduction effect. Through function decomposition, KAN network can convert high-dimensional trajectory data into a simpler form for processing, significantly reducing the influence of noise and measurement error. For example, when facing a trajectory with serious noise interference, KAN can separate noise from the main features through function decomposition, thereby improving the stability and accuracy of threat assessment. In addition, KAN network can efficiently extract the key motion features of the target, especially in complex environments, it can capture subtle changes of the target, enhancing the robustness of the model.

[0052] By combining KAN network with LSTM, the advantages of both are complementary. LSTM network is good at processing time series data and can capture the dynamic changes of target threats, while KAN network complements its shortcomings in processing multi-dimensional data. After combination, the model can not only accurately analyze the time series features of the target, but also approximate complex multi-dimensional trajectories through KAN network, greatly improving the recognition accuracy of the target's motion intention. Finally, the combination of KAN and LSTM provides a more robust and efficient threat assessment scheme for dealing with complex environments with serious noise.

[0053] Further, in step S4, different data is processed differently. Specifically: first, according to the relative MAE, the error between the true data and the reconnaissance data is judged, if the error range is within the threshold, the membership function is directly used for normalization; if the parameter range exceeds the threshold, the data is first fuzzified, and then the membership function is used for normalization.

[0054] Further, in step S4, the specific steps of model training are as follows:

[0055] Step S41, the obtained time series pulse information is analyzed for credibility, and in the case of high credibility, the data is directly input into the network; when the data credibility is not strong, the data needs to be fuzzified through fuzzy logic first, and then input into the network;

[0056] Step S42, set the training optimizer to Adam optimizer, the sample Batch Size to 32, the hidden layer feature dimension to 32, and the initial learning rate l r 0.01;

[0057] Step S43, after the data is initialized, the data is input into the network, the output result is obtained, and the root mean square error and R2 determination coefficient are calculated;

[0058] Step S44, using the gating mechanism, cell state, hidden state in the LSTM model, and KAN network using a learnable activation function on the edges (i.e. weights) of the network, the parameters of the model are optimized to obtain the optimal parameters, and the trained feature extractor and classifier model are saved.

[0059] Further, in step S4, the network is trained based on the LSTM combined with KAN model, and the root mean square error (RMSE) and R2 coefficient of determination are used to judge the performance of the network model.

[0060] The calculation formula of RMSE is:

[0061]

[0062] Where N represents the number of samples, Y i represents the predicted value of the i-th sample, f(x i ) represents the actual value of the i-th sample, Y i -f(x i ) is the prediction error, which represents the difference between the predicted value and the actual value.

[0063] Compared with MSE, RMSE has more advantages in interpretation and intuition. RMSE reflects the deviation between the predicted value and the true value, and the smaller the value, the closer the predicted result is to the actual value, and the higher the accuracy of the model. Therefore, RMSE can more clearly measure the prediction effect of the model.

[0064] R2 coefficient of determination:

[0065] It is an index to measure the fitting degree of the regression model to the data, which is used to represent the proportion of the model to explain the variation of the dependent variable. R 2 The value of R

[0066] The regression sum of squares (SSR) is represented as:

[0067]

[0068] That is, the error of the estimated value and the average value, which reflects the deviation sum of squares of the correlation between the independent variable and the dependent variable;

[0069] Where, represents the predicted value of the i-th observation, represents the mean of all observations, represents the square of the difference between the predicted value of the i-th observation and the mean of all observations;

[0070] The residual sum of squares (SSE) is represented as:

[0071]

[0072] i.e. the error of the estimated value from the true value, reflecting the fitting degree of the model;

[0073] where y i represents the i-th observation, represents the i-th predicted value, represents the square of the difference between the i-th observation and the corresponding predicted value;

[0074] The total sum of squared deviations (SST) is expressed as:

[0075]

[0076] i.e. the error between the mean value and the true value, reflecting the deviation from the mathematical expectation;

[0077] The R2 coefficient of determination is expressed as:

[0078]

[0079] Further simplified as:

[0080]

[0081] In the above formula, MSE represents the mean square error, and Var represents the variance. R 2 has the meaning that: when 0≤R 2 ≤1, the closer R 2 is to 1, the better the fitting effect of the model, indicating that the independent variable can explain a larger proportion of the variation of the dependent variable. R 2 equal to 1 indicates that the model can perfectly explain all the variation of the dependent variable, i.e. the predicted value completely matches the actual value. R 2 equal to 0 means that the model cannot explain the variation of the dependent variable, and the effect of the model is the same as that of a simple average value prediction. R 2 is negative, which indicates that the model fitting is very poor, even worse than directly using the mean value for prediction.

[0082] S42, for parameter training based on LSTM combined with KAN network, includes the following parts:

[0083] The LSTM network parameters include:

[0084] Input gate (Input Gate) parameters: the input gate weight is used to control the influence of the current input on the state of the LSTM unit. W ix represents the weight matrix between the input and the input gate, W ix represents the weight matrix between the hidden state and the input gate, b i represents the offset for adjusting the input gate.

[0085] Forget Gate parameters: Forget gate weights are used to control the influence of the previous cell state on the current state. W fx denotes the weight matrix between the input and the forget gate, W fh denotes the weight matrix between the hidden state and the forget gate. b f denotes the bias used to adjust the forget gate.

[0086] Cell State parameters: Cell state weights are used to control the influence of the current cell state on the final output. W cx denotes the weight matrix between the input and the cell state, W ch denotes the weight matrix between the hidden state and the output gate, b c denotes the bias used to adjust the output gate.

[0087] Output Gate parameters: Output gate weights are used to control the influence of the current cell state on the final output. W ox denotes the weight matrix between the input and the output gate, W oh denotes the weight matrix between the hidden state and the output gate, b o denotes the bias used to adjust the output gate.

[0088] KAN network parameters include:

[0089] φ ij (x j ) denotes a continuous one-dimensional function that acts on the input variable x j . The purpose is to perform a nonlinear transformation on each input variable x j , converting each dimension of high-dimensional input data into a new set of feature representations. In this network, each input x j is processed through multiple φ ij functions, which can help the model capture different input feature patterns and subtle changes.

[0090] ψ i denotes a one-dimensional combination function that acts on . The purpose is to further nonlinearly combine the results of φ ij transformation of all input dimensions to form the output of the model. These combination functions can be seen as a summary or weighting of the dimensions of the features. ψ i function can integrate the outputs of multiple one-dimensional transformations to represent more complex high-dimensional relationships. By summing multiple ψ i functions, the model can approximate more complex multi-dimensional functions.

[0091] The model is back-propagated by using the minimum cross-entropy loss, and the parameters of the model are optimized to obtain optimal parameters:

[0092] W m ←Adam(▽w m ,L,lr,W m )

[0093] Wherein, L represents a loss function, lr is a hyperparameter representing a network learning rate, W m represents the parameters of the current network, and▽w m represents the gradient of the network parameters, then the weights of the feature extractor and the prediction layer of the trained LSTM and KAN network are saved for subsequent prediction tasks.

[0094] Further, in step S5, the time sequence pulse data of the LSS target received in the complex electromagnetic environment is preprocessed and input into the trained LSTM model combined with the KAN network model to obtain the threat assessment result.

[0095] The application also discloses a low-altitude slow small target threat assessment system based on an LSTM model combined with a KAN network.

[0096] The time sequence pulse data acquisition and preprocessing module acquires the time sequence pulse data of the low-altitude slow small target in a set time period, takes pulse data with a length of N as a sample and pre-processes the sample.

[0097] The abnormal data processing module mainly processes data with low credibility, and pre-processes the acquired time sequence pulse data by using fuzzy data.

[0098] The model construction module constructs a model based on the LSTM combined with the KAN, and initializes and sets parameters.

[0099] The sample training module processes data according to the credibility of different data, inputs the processed data into the model based on the LSTM combined with the KAN for network training, and saves the feature extractor and the classifier weight obtained by training.

[0100] The threat assessment module inputs the pulse data of the to-be-tested low-altitude slow small target after preprocessing into the model based on the LSTM combined with the KAN for threat assessment, and obtains the low-altitude slow small target threat assessment result.

[0101] Compared with the prior art, the application has the following beneficial effects:

[0102] 1. The application introduces the concept of dynamic environment, considers influencing factors such as target distance, speed change and external environmental noise, and dynamically adjusts the threat assessment under different conditions. At the same time, in order to deal with the uncertainty and measurement error in the actual data, an uncertain value processing method is proposed to enhance the robustness of the model under abnormal data conditions. Through reasonable processing of uncertain values, the model can still maintain high-precision threat assessment in the case of large data noise or measurement error.

[0103] 2. The application proposes a dynamic threat assessment model combining Kolmogorov-Arnold network (KAN) and long short-term memory network (LSTM). Through the multivariate function approximation ability of KAN network, the complex trajectory data is effectively decomposed and modeled, the potential motion pattern of the target is accurately captured, and more detailed feature extraction is provided. At the same time, the LSTM network uses its powerful time sequence processing and memory unit function to capture the time correlation in the trajectory data, filter out the influence of short-time noise and trajectory fluctuations on the evaluation results. This combined model not only significantly improves the accurate identification of target threat intentions, but also continuously tracks the changes in target threats through dynamic assessment, enhances the algorithm's ability to suppress measurement noise, and ultimately improves the overall robustness and precision of threat assessment.

[0104] 3. The application uses experimental simulation data as experimental simulation. The technical solution proposed in the application is more significant than traditional methods and single LSTM network in harsh environments and distance influence. As the distance and environmental noise continue to increase, the accuracy of the technical solution proposed in the application is continuously improved compared with the LSTM model without KAN and the traditional MADM algorithm.

[0105] In summary, the application proposes a low-altitude slow small target threat assessment method and system based on LSTM model combined with KAN. In view of the harsh weather processing and distance influence faced by radar reconnaissance in actual combat scenarios, the LSTM method is introduced into the LSS threat assessment problem, the LSTM network can learn long-term dependencies, and the KAN network module core feature is to use a learnable activation function on the edge of the network (i.e. weight), which can better train the network model and get higher recognition accuracy with fewer labeled samples. BRIEF DESCRIPTION OF DRAWINGS

[0106] Figure 1 The flowchart of the preferred embodiment of the application, a low-altitude slow small target threat assessment method based on LSTM model combined with KAN network, is shown in the figure.

[0107] Figure 2 The preferred embodiment of the application, an LSTM structure diagram, is shown in the figure.

[0108] Figure 3 Figure 1 is a network structure diagram of a preferred embodiment of the present application;

[0109] Figure 4 Figure 4 is a comparison chart of accuracy rate with distance change of the present application and a single LSTM network when the data has credibility;

[0110] Figure 5 Figure 5 is a comparison chart of accuracy rate with distance change of the present application and a traditional method when the data does not have credibility;

[0111] Figure 6 Figure 6 is a system block diagram of a low-altitude slow small target threat assessment system based on an LSTM model combined with a KAN network according to a preferred embodiment of the present application. DETAILED DESCRIPTION

[0112] The implementation process of the present application is described below through a preferred embodiment, and other advantages and effects of the present application can be easily understood by those skilled in the art from the disclosure of the present specification. The present application can also be implemented or applied through other different specific embodiments, and various modifications or changes can be made to the details in the present specification based on different views and applications without departing from the spirit of the present application.

[0113] Reference Figure 1 The embodiment provides a low-altitude slow small target threat assessment method based on an LSTM model combined with a KAN network, and specifically comprises the following steps:

[0114] S1, for a period of low-altitude slow small target pulse data, taking pulse data with a length of N as a sample for preprocessing, specifically as follows:

[0115] A membership function is introduced, and the attribute value is normalized to f(x) [0, 1], wherein x is a specific threat attribute value, and f is a function in the membership space F. In the present application, an ascending exponential function and a descending half-normal distribution function are used to normalize the quantitative attribute, so as to ensure the comparability between different attributes and provide a basis for subsequent dynamic threat assessment. Specifically as follows:

[0116] If the threat attribute is positively correlated with the threat degree, an ascending exponential function is used as follows:

[0117]

[0118] When the attribute value x is less than x0, the quantization f(x) is equal to δ L When x is greater than x0, f(x) is positively correlated with x, and is expressed as an ascending exponential function, f(x) = 0.5 if and only if x = x1. k is used to fit the above conditions:

[0119] k = -(ln(f(x1) / (1-δL ))) / (x1-x0)

[0120] If the threat attribute is negatively correlated with the threat degree, a decreasing semi-normal distribution function is adopted. For example:

[0121]

[0122] There are three parameters: δ H , x0, x1 (x0 < x1) (where x0 is a constant representing the attribute threshold value; x is the input value, i.e. the true value of the reconnaissance data for this attribute; δ H is a constant representing a coefficient, and the function is a constant when the true value is less than the threshold value; k is a constant representing the growth rate and decay rate of the function, which determines the speed of change of the function), when the attribute value x is less than x0, the quantification f(x) is equal to δ H . When x is greater than x0, f(x) is negatively correlated with x, and is represented as a decreasing semi-normal distribution function. f(x) = 0.5 if and only if x = x1. Use k to satisfy the above conditions:

[0123] k = -(ln(f(x1) / (1-δ H ))) / (x1-x0)

[0124] Specifically, the quantification method of the threat attribute is as follows:

[0125] Distance: Distance is one of the important factors that determine the difficulty of target reconnaissance and attack. As the target gradually approaches, the reaction time of the defense system shortens, the defense difficulty increases significantly, and the possibility of the target successfully breaking through the defense also rises accordingly. Therefore, the closer the distance, the greater the threat posed by the target to the defense party, and the threat level also rises accordingly. In order to accurately quantify the relationship between this threat and distance, the present invention adopts a decreasing semi-normal distribution function to model the distance attribute. This function can well reflect the non-linear characteristics of the threat decreasing with distance, ensure that the near-distance target gets a higher weight in threat assessment, and the threat of the far-distance target gradually weakens, thereby providing a more reasonable basis for threat assessment.

[0126] Speed: Speed is one of the important indicators to measure the maneuverability of the target. In some cases, the faster the target speed, the stronger its maneuverability and flexibility, which increases the difficulty of the target evading reconnaissance or defense systems, and thus its danger also rises. Therefore, the increase in speed usually means greater threat. In order to accurately reflect this characteristic, the present invention adopts an increasing exponential function to model the speed attribute. This function can effectively capture the non-linear relationship between the increase in speed and the rise in threat degree, ensuring that high-speed targets get a higher threat rating in the threat assessment process, thereby providing a more accurate basis for defense decision-making.

[0127] Height: Height is one of the important parameters reflecting the operational purpose of the flying target. Generally, targets performing high-risk attack or reconnaissance tasks tend to fly at low altitudes to evade radar detection. Such low-altitude flight increases the likelihood of their successful penetration of defense systems, thus posing a greater threat to the defenders. In this case, low-flying targets must be given priority attention due to their higher threat. To quantify the impact of height on threat assessment, the present invention uses a reduced semi-normal distribution function to model the height attribute. This function effectively reflects the non-linear relationship between target height and threat, ensuring that low-flying targets are given a higher threat weight in threat assessment, while high-flying targets correspondingly reduce their threat level.

[0128] Shortcut: Shortcut represents the horizontal distance from the current flight direction of the target to the defense area. Generally, a longer shortcut may imply a weaker attack intention of the target, and the direct threat of the target is relatively small. As the shortcut shortens, the target is more likely to enter the key defense area, and the threat level also increases. Therefore, the change of shortcut is inversely related to the threat level. To accurately quantify the impact of shortcut on threat assessment, the present invention uses a reduced semi-normal distribution function to model this attribute. This function effectively reflects the non-linear impact of shortcut length on threat level, ensuring that targets with shorter shortcuts are given a higher threat weight, while long-shortcut targets are considered to be less threatening.

[0129] S2, for uncertain information of reconnaissance data (the uncertain information here is a definition of the data obtained by reconnaissance, when receiving the reconnaissance data, the information credibility is judged by calculating the relative MAE, if it exceeds the threshold, it belongs to uncertain information), the data is preprocessed in a fuzzy data manner. The specific steps are as follows:

[0130] S21, the relative average absolute error is introduced to judge the accuracy of the data, and the average absolute error expression is:

[0131]

[0132] In order to judge whether MAE is too large, the relative MAE can be considered, that is, the percentage of data MAE to the average value or true value of the data is calculated, and the expression is:

[0133]

[0134] S22, accuracy judgment of data: when the relative MAE is too large (usually more than 20%) or exceeds the error standard of a specific field, the credibility of the data will be considered insufficient.

[0135] S23、In the reconnaissance data processing, although the reliability of part of the data is low, the error is usually maintained within a certain range. Based on this feature, the data can be divided into five levels according to the numerical interval, so as to more flexibly manage and apply the data. Even if the data is judged to be low in reliability due to large error, as long as its value meets the corresponding level interval, it can still be classified into the corresponding level. This hierarchical mode can improve the overall utilization rate under the premise of ensuring the effectiveness of the data, and provide orderly support for subsequent analysis.

[0136] Step S3, a model based on LSTM combined with KAN network is constructed, and the parameters are initialized and set; the specific steps are as follows:

[0137] Step S31, in order to extract the correlation of LSS target time sequence pulse signal in time, the network model of LSTM is used to extract the correlation in time sequence.

[0138] LSTM network is a recurrent neural network widely used in time series data processing, and its main advantage is to effectively capture the long and short term dependence relationship in time series through internal "memory" unit. LSTM controls the flow process of information by setting forget gate, input gate and output gate. Specifically:

[0139] Forget gate: responsible for selecting the historical information that needs to be discarded, avoiding the interference of useless data to the model.

[0140] Input gate: decides which new information should be added to the current memory unit.

[0141] Output gate: controls the content output by the model at the current time, ensuring that the key time information can be passed to the next time.

[0142] The structure of LSTM network is as shown in Figure 2 : 1 represents Cell state and has C t , which represents the cell state (memory state), the current cell state C t is determined by the cell state C t-1 of the previous time step and the newly generated . 2 represents Forget Gate and has f t =σ(W f ·[h t-1 ,x t ]+b f ), the operation process is to act on the cell state C t-1 of the last time, the current input x t and the last hidden state h t-1 , and output a value f t, which represents the part of the cell state that needs to be "forgotten". 3 represents the Input Gate and has i t = (W i ·[h t-1 ,x t ]+b i ), The input gate consists of two parts: i t controls which values need to be updated, generated from the current input and the previous hidden state; generates a candidate cell state, deciding the new content. 4 represents the Output Gate and has o t = σ(W o ·[h t-1 ,x t ]+b o ), t = o t *tanh(C t ), o t 's role is to control how much information in the current cell state C t can be output as the hidden state h t at the current time step, playing the role of "filtering". When approaching 0, it means that little information is output, and the hidden state h t will be greatly inhibited. When approaching 1, it means that more information is output, and the hidden state h t accepts more information from the cell state C t . After obtaining the output gate value o t , it will be multiplied element by element with the value of the current cell state C t processed by the tanh function, thus generating the hidden state at the current time step.

[0143] This design enables LSTM to maintain the memory of long-time span information while filtering out short-time noise. Therefore, when dealing with complex data containing trajectory jitter or measurement noise, LSTM performs particularly well. It can dynamically track and capture the threat intent of the target, greatly improving the accuracy and stability of threat assessment.

[0144] Step S32, replace the traditional MLP with the KAN model to obtain the output. The specific network structure is shown in Figure 3 , so as to realize the representation of the multi-dimensional features of the signal.

[0145] Although LSTM performs well in capturing time series information, it still has limitations in handling complex multivariate data. To improve the accuracy and noise suppression ability of threat assessment, the invention innovatively combines KAN network, effectively decomposes complex trajectory features into single variable functions through multivariate function approximation. KAN network complements the shortcomings of LSTM in high-dimensional data processing, enhances the model's ability to identify target motion intent, and significantly improves the accuracy and stability of threat assessment. After combining the two, the model has stronger dynamic response ability and robustness in complex environments with severe noise interference.

[0146] KAN network is a network architecture based on Kolmogorov-Arnold representation theorem, which is used to approximate complex multivariate functions. According to the theorem, any continuous multivariate function f(x1, x2, …, xn) can be represented as the superposition of multiple single variable functions, that is:

[0147]

[0148] where ψ i and φ ij are continuous single variable functions. KAN network uses this representation theorem to decompose complex multi-dimensional input data into a series of simple single variable functions, and completes accurate modeling of multi-dimensional data through these function combinations. This decomposition method enables KAN network to extract deep motion features when processing complex trajectory data, especially suitable for threat assessment of LSS targets.

[0149] The advantages of KAN network mainly lie in its powerful multivariate function approximation ability and excellent noise reduction effect. Through function decomposition, KAN network can convert high-dimensional trajectory data into a simpler form for processing, significantly reducing the influence of noise and measurement error. For example, when facing trajectories with severe noise interference, KAN can separate noise from the main features through function decomposition, thereby improving the stability and accuracy of threat assessment. In addition, KAN network can efficiently extract key motion features of the target, especially in complex environments, it can capture subtle changes of the target, enhancing the robustness of the model.

[0150] By combining KAN network with LSTM, the advantages of the two complement each other. LSTM network is good at processing time series data and can capture the dynamic changes of target threat, while KAN network complements its shortcomings in processing multi-dimensional data. After combining, the model not only can accurately analyze the time series characteristics of the target, but also can approximate complex multi-dimensional trajectories through KAN network, greatly improving the recognition accuracy of target motion intent. Finally, the combination of KAN and LSTM provides a more robust and efficient threat assessment scheme for complex environments with severe noise.

[0151] Step S4, different data are processed differently (since the scout data has a bias in reliability, the data sources are divided into two types, one is that the input network can be directly initialized, and the other is that the fuzzy data operation needs to be performed before the data is normalized by the membership function (see Figure 1 )), the processed data are input into the model based on LSTM combined with KAN for network training, and the feature extractor and classifier weights obtained by training are saved; the specific steps are as follows:

[0152] Step S41, the network training based on the model of LSTM combined with KAN is performed, and the root mean square error (RMSE) and R2 determination coefficient are used to determine the performance of the network model;

[0153] The calculation formula of RMSE is:

[0154]

[0155] Where N represents the number of samples, Y i represents the predicted value of the i-th sample, f(x i ) represents the actual value of the i-th sample, Y i -f(x i ) is the prediction error, which represents the difference between the predicted value and the actual value.

[0156] Compared with MSE, RMSE has more advantages in interpretation and intuition. RMSE reflects the deviation between the predicted value and the true value, and the smaller the value, the closer the predicted result is to the actual value, and the higher the accuracy of the model. Therefore, RMSE can more clearly measure the prediction effect of the model.

[0157] R2 determination coefficient:

[0158] It is an index for measuring the fitting degree of the regression model to the data, which is used to represent the proportion of the model to explain the variation of the dependent variable. R 2 The value is usually between 0 and 1, and the closer the value is to 1, the better the fitting degree of the model to the data.

[0159] Regression sum of squares (SSR) is represented as:

[0160]

[0161] That is, the error of the estimated value and the average value, which reflects the deviation sum of squares of the correlation degree between the independent variable and the dependent variable;

[0162] Residual sum of squares (SSE) is represented as:

[0163]

[0164] i.e. the error of the estimated value and the true value, reflecting the fitting degree of the model;

[0165] The total sum of squares (SST) is expressed as:

[0166]

[0167] i.e. the error between the mean value and the true value, reflecting the deviation from the mathematical expectation;

[0168] The R2 coefficient of determination is expressed as:

[0169]

[0170] Further simplified as:

[0171]

[0172] R 2 means: when 0≤R 2 ≤1, R 2 is closer to 1, the fitting effect of the model is better, indicating that the independent variable can explain a larger proportion of the dependent variable variation. R2 equal to 1 means that the model can perfectly explain all the variation of the dependent variable, i.e. the predicted value completely matches the actual value. R 2 equal to 0 means that the model cannot explain the variation of the dependent variable, and the effect of the model is the same as the simple average prediction. R 2 is negative, which means that the model fitting is very poor, even worse than directly using the mean value prediction.

[0173] Step S42, for the LSTM combined with KAN network parameter training contains the following parts:

[0174] LSTM network parameters include:

[0175] Input gate (Input Gate) parameters: Input gate weight is used to control the influence of current input on the state of LSTM unit. W ix represents the weight matrix between input and input gate, W ix represents the weight matrix between hidden state and input gate, b i represents the offset used to adjust the input gate.

[0176] Forget gate (Forget Gate) parameters: Forget gate weight is used to control the influence of the unit state at the last moment on the current state. W fx represents the weight matrix between input and forget gate, W fh represents the weight matrix between hidden state and forget gate. b f represents the offset used to adjust the forget gate.

[0177] Cell State parameters: Cell state weights are used to control the influence of the current cell state on the final output. W cx denotes the weight matrix between inputs and cell state, W ch denotes the weight matrix between hidden state and output gate, b c denotes the bias used to adjust the output gate.

[0178] Output Gate parameters: Output gate weights are used to control the influence of the current cell state on the final output. W ox denotes the weight matrix between inputs and output gate, W oh denotes the weight matrix between hidden state and output gate, b o denotes the bias used to adjust the output gate.

[0179] KAN network parameters include:

[0180] φ ij (x j ) denotes a continuous one-dimensional function acting on input variable x j , which is used to perform nonlinear transformation on each input variable x j , converting each dimension of high-dimensional input data into a new set of feature representations. In this network, each input x j is processed through multiple φ ij functions, which can help the model capture different input feature patterns and subtle changes.

[0181] ψ i denotes a one-dimensional combination function acting on . The function is used to further nonlinearly combine the results of φ ij transformation of all input dimensions to form the output of the model. These combination functions can be seen as a summary or weighting of the dimensions of the features. ψ i function can integrate the outputs of multiple one-dimensional transformations to represent more complex high-dimensional relationships. By summing multiple ψ i functions, the model can approximate more complex multi-dimensional functions.

[0182] Step S43, use the minimum cross-entropy loss to back-propagate the model, and optimize the parameters of the model to obtain the optimal parameters:

[0183] W m ← Adam(▽w m ,L,lr,W m )

[0184] W m denotes the current network parameters, and ▽wm The gradient of the network parameters is represented, and then the trained feature extractor and classifier weights of the LSTM and KAN networks are saved for direct loading and use in subsequent prediction tasks, achieving efficient prediction of complex time series.

[0185] Step S5, the pre-processed low-altitude slow small target pulse data to be tested (the pre-processing method of this pulse data is the same as that of S1 or S2, and the data with high reliability can be directly input into the network after normalization by the membership function; the data with low reliability needs to go through a data fuzzification step before pre-processing, and the pre-processing method is the same as that of S1 or S2 (judged by relative MAE, if the result is lower than the threshold, the pre-processing method of S1 is adopted; if the result exceeds the threshold, the pre-processing method of S2 is adopted)) is input into the model trained in step S4 for evaluation, and the threat evaluation result of the low-altitude slow small target is obtained.

[0186] The time series pulse data received in the complex electromagnetic environment is classified, and the classification basis is whether the data needs to be fuzzified. After pre-processing the data, the time series pulse data received in the complex electromagnetic environment is input into the trained LSTM combined with KAN model for threat evaluation of LSS targets after normalization by the membership function.

[0187] According to the above embodiment, experiments are carried out, and training and testing are carried out by taking the experimental simulation data set as an example. The total training sample amount is 500, and the training set and test set are divided by 8:2. Different intensity of interference noise is added in different environments, and data preprocessing and initialization operation is carried out in the case of low data reliability. In the simulation experiment, two groups of different parameters are used to train the LSTM combined with KAN model, and the results are compared with the LSTM model without KAN and the traditional MADM algorithm. Reference Figure 4 、 5 , Figure 4 、 5 It is shown that under different environments and low data reliability, the threat assessment prediction accuracy of the LSTM combined with KAN model in this embodiment is significantly higher than that of the other two methods. Therefore, the LSTM combined with KAN module model in this embodiment has superior prediction accuracy in low-altitude slow small target threat assessment.

[0188] As Figure 6 shown, the embodiment discloses a low-altitude slow small target threat assessment system based on an LSTM model combined with a KAN network, which is used to execute the above method, and specifically includes the following modules:

[0189] Timing pulse data acquisition and preprocessing module: the timing pulse data of the LSS target is taken as a sample with a fixed length of N and preprocessed;

[0190] Abnormal data processing module: abnormal data processing mainly includes processing of low credibility data, credibility analysis and preprocessing of the acquired timing pulse data;

[0191] Model construction module: a model based on LSTM combined with KAN is constructed, and the parameters are initialized and set;

[0192] Sample training module: according to the credibility of different data, the timing pulse data is input into the model based on LSTM combined with KAN for network training, and the feature extractor and classifier weight obtained by training are saved;

[0193] Threat assessment module: after the timing pulse data of the LSS target to be tested is normalized by the membership function and analyzed for timing pulse data credibility, it is input into the model based on LSTM combined with KAN obtained by training for threat assessment, and the LSS target threat assessment result is obtained.

[0194] Other contents of the embodiment can refer to the above method embodiments.

[0195] The above is only the preferred embodiment of the present application and the technical principle applied. Those skilled in the art will understand that the present application is not limited to the specific embodiments described herein, and those skilled in the art can make various obvious changes, readjustments and substitutions without departing from the scope of the present application. Therefore, although the present application has been described in more detail through the above embodiments, the present application is not limited to the above embodiments, and can include more other equivalent embodiments without departing from the concept of the present application, and the scope of the present application is determined by the scope of the appended claims.

Claims

1. A low-altitude slow-speed small target threat assessment method based on an LSTM model combined with a KAN network, characterized by The specific steps include: S1. Obtain pulse data of a low-altitude, slow-moving, small target within a set time period, and take pulse data of length N as a sample for preprocessing; S2. To address the uncertain information in the reconnaissance data, the pulse data is preprocessed using fuzzy data. S3. Build a model based on the LSTM model combined with the KAN network and initialize the parameters. The details of this step are as follows: S31, using LSTM model to extract the correlation in time series; S32, using the KAN model to characterize the multi-dimensional features of the signal; S4. Perform different processing according to the credibility of different data, input the processed data into the model constructed in step S3 for network training, and save the feature extractor and classifier weights obtained from the training; S5. Pre-process the pulse data of the low-altitude, slow-moving small target to be measured and input it into the model trained in step S4 for evaluation to obtain a threat assessment result of the low-altitude, slow-moving small target.

2. The method according to claim 1, wherein, In step S1, the membership function is introduced and the attribute value is normalized to f(x) ∈ [0, 1], where x is the specific threat attribute value and f is the function in the membership space F. The ascending exponential function and descending half-normal distribution function are used to normalize the quantitative attributes. The specific steps are as follows: If the threat attribute is positively correlated with the threat level, an ascending exponential function is used as follows: f(x) = x where x0is the threshold of the attribute; x is the input value; δ L is a constant, and the function is a constant when the real value is less than the threshold; k is the growth rate and decay rate of the function; When the attribute value x is less than x0, the quantification f(x) is equal to δ L ; when x is greater than or equal to x0, f(x) is positively related to x and is expressed as an ascending exponential function, f(x) = 0.5 if and only if x = x1; k is used to fit: k = -(ln(f(x1) / (1-δ L )) / (x1-x0) If the threat attribute is negatively correlated with the threat level, the descending half-normal distribution function is used as follows: f(x) = x There are three parameters: δ H , x0, x1, x0 < x1, when the attribute value x is less than x0, the quantization f(x) is equal to δ H ; when x is greater than or equal to x0, f(x) is negatively correlated with x, and is expressed as a decreasing semi-normal distribution function; f(x) = 0.5 if and only if x = x1; k is used for fitting: k = -(ln(f(x1) / (1-δ H )) / (x1-x0).

3. The method according to claim 2, wherein, When normalizing the membership of attribute values, different types of parameters have different criteria: Distance: The descending half normal distribution function is used to model the distance attribute; Speed: The speed attribute is modeled using a rising exponential function; Height: The height attribute is modeled using the descending half normal distribution function; Shortcut: Use the descending half normal distribution function to model this attribute.

4. The method according to claim 1, wherein the method is characterized in that, Step S2 is specifically as follows: S21. Introduce the relative mean absolute error to judge the accuracy of the data, where the mean absolute error expression is: where n represents the number of samples; X i represents the ith prediction value; X 真实值 represents the corresponding true value; Relative MAE is introduced to determine whether MAE is greater than the threshold, that is, the percentage of MAE of the calculated data to the average value or true value of the data. The relative MAE expression is: Among them, relative means relative; S22. Judgment of data accuracy: If the relative MAE exceeds the set standard, the credibility of the data is considered insufficient; S23. Divide the data into five levels according to the numerical range.

5. The method according to claim 1, wherein, In step S4, different data are processed differently. Specifically, the error between the real data and the reconnaissance data is judged according to the relative MAE. If the error range is within the threshold, the membership function is directly used for normalization. If the parameter range exceeds the threshold, the data is first fuzzified and then normalized using the membership function.

6. The method according to claim 5, wherein, In step S4, the root mean square error (RMSE) and the R2 coefficient of determination are used to judge the performance of the model based on the LSTM model combined with the KAN network; The calculation formula of RMSE is: wherein n, N represent the number of samples, Y i represents the predicted value of the i-th sample, f(x i ) represents the actual value of the i-th sample, Y i -f(x i ) is the prediction error, representing the difference between the predicted value and the actual value; The R2 coefficient of determination is as follows: The regression sum of squares SSR is expressed as: It represents the error between the estimated value and the mean value; wherein, represents the predicted value of the i-th observation, represents the mean of all observations, represents the square of the difference between the predicted value of the i-th observation and the mean of all observations; The residual sum of squares SSE is expressed as: Indicates the error between the estimated value and the true value; where y i represents the ith observation, represents the ith prediction, represents the square of the difference between the ith observation and the corresponding prediction. The total sum of squared deviations SST is expressed as: Indicates the error between the mean and the true value; The R2 coefficient of determination is expressed as: Further expressed as: Where MSE represents mean square error and Var represents variance.

7. The method according to claim 6, wherein, In step S4, network training for the model based on the LSTM model combined with the KAN network includes the following: LSTM model parameters include: Input gate parameters: input gate weights control the influence of the current input on the LSTM cell state; W ix denotes the weight matrix between the input and the input gates, W ix denotes the weight matrix between the hidden state and the input gates, b i denotes the bias for adjusting the input gate; forget gate parameter: a forget gate weight is used to control the influence of the cell state at the previous time on the current state; W fx denotes a weight matrix between the input and the forget gate, W fh denotes a weight matrix between the hidden state and the forget gate; b f denotes an offset used to adjust the forget gate; Cell state parameters: Cell state weights are used to control the influence of the current cell state on the final output; W cx denotes the weight matrix between the input and the cell state, W ch denotes the weight matrix between the hidden state and the output gate, b c denotes the bias used to adjust the output gate; Output gate parameters: output gate weights to control the influence of the current cell state on the final output; W ox denotes the weight matrix between the input and the output gate, W oh denotes the weight matrix between the hidden state and the output gate, b o denotes the bias for adjusting the output gate; KAN network parameters include: φ ij (x j ) denotes a continuous one-dimensional function acting on input variable x j , each input x j is processed through multiple φ ij functions; Ψ i represents a one-dimensional combination function acting on Ψ The model is back-propagated by minimizing the cross entropy loss, and the parameters of the model are tuned to obtain the optimal parameters: W m ← Adam(▽w m , L, lr, W m ) wherein L represents a loss function, lr is a hyper-parameter representing a network learning rate, W m represents a parameter of a current network, and m represents a gradient of the network parameter.

8. A low-altitude slow-moving small target threat assessment system based on an LSTM model combined with a KAN network, configured to perform the method of any one of claims 1-7, characterized in that Specifically, it includes the following modules: Time series pulse data acquisition and preprocessing module: obtains pulse data of low-altitude, slow-moving small targets in a set time period, takes pulse data of length N as a sample and performs preprocessing; Abnormal data processing module: pre-process the pulse data using fuzzy data; Model construction module: Build a model based on the LSTM model combined with the KAN network and initialize the parameters; Sample training module: Processes data based on their credibility, inputs the processed data into a model based on the LSTM model combined with the KAN network for network training, and saves the trained feature extractor and classifier weights; Threat assessment module: The pulse data of the low-altitude, slow-moving small target to be tested is preprocessed and input into the trained LSTM model combined with the KAN network model for evaluation to obtain the threat assessment results of the low-altitude, slow-moving small target.

Images