A guidance law identification method based on signal decomposition and support vector machine

Abstract

This invention discloses a guidance law identification method based on signal decomposition and support vector machine. Based on the relative motion information of different guidance laws within a short time, it eliminates the need for step-by-step iteration and state fusion. Employing signal decomposition and support vector machine classification, it achieves rapid and high-precision identification of guidance laws, representing a novel guidance law identification method. No similar technologies have been observed to date.

Description

Technical Field

[0001] This invention belongs to the field of aircraft system identification technology, specifically relating to a guidance law identification method based on signal decomposition and support vector machine. Background Technology

[0002] In modern warfare, air strikes have become a primary method in localized conflicts. When our aircraft attack key enemy targets, such as early warning aircraft, their escort aircraft often launch defensive missiles to intercept them. If our aircraft can identify the guidance law of these defensive missiles based on the information obtained, it will be of great significance for our aircraft to penetrate enemy defenses or launch missiles to counter-intercept them.

[0003] Currently, there is relatively little literature on guidance law identification. Hu Zhiheng and Zhou Di studied the guidance law identification problem in three-dimensional space. Based on the observability conditions of the system, they designed an extended Kalman filter to output guidance law parameter information. Yun et al. used an improved interactive multi-model filtering algorithm to identify the guidance law of anti-ship missiles, thereby improving the survivability of naval vessels. Cai Yuanli et al. addressed the typical TDM problem of active defense, using a nonlinear multi-model adaptive filtering method and multiple Kalman filters running in parallel to identify the guidance law of incoming interceptor missiles. Furthermore, guidance law identification based on Kalman filters is combined with other methods to enhance the adaptability and accuracy of the method. For example, the Kalman filter algorithm is combined with a low-pass filter to construct a frequency-domain separation adaptive Kalman filter method, enabling real-time processing of observation data to identify the guidance law. The above guidance law identification methods are mainly based on Kalman filtering and its improved algorithms.

[0004] In existing schemes, a relative motion model of the aircraft and the enemy's defensive missile is first established. Then, assuming the missile employs several typical guidance laws, an unscented Kalman filter algorithm is combined with a nonlinear missile kinematics model to construct a parallel Kalman filter. By iteratively updating the estimated covariance and prediction error at each step, the corresponding Gaussian likelihood function value is calculated, achieving probability updates at each step. The overall state of the system model is corrected by fusing radar measurements with state predictions from different guidance law models. When the probability of one guidance law is higher than the probabilities of others, the incoming missile is considered to be using the more probable guidance law, thus identifying the guidance law and guidance coefficients used by the incoming missile.

[0005] The mainstream method for guidance law identification mainly employs Kalman filtering and its improved algorithms. Kalman filtering requires a large number of kinematic parameters during the identification process, necessitating continuous parameter iteration and information fusion before obtaining the identification result. Furthermore, Kalman filtering takes a considerable amount of time to identify the guidance law, which negatively impacts online applications. Summary of the Invention

[0006] In view of this, the purpose of this invention is to provide a novel guidance law identification method that differs from the Kalman filter algorithm, eliminating the need for iterative updates and state fusion estimation based on continuous motion information. Instead, it can quickly identify the guidance law used by the defensive missile based solely on short-term relative motion information measured by radar, which is beneficial for online applications.

[0007] A guidance law identification method based on signal decomposition and support vector machine includes:

[0008] Step 1: Simulate the line-of-sight angular velocity of defensive missiles intercepting maneuvering combat aircraft using different guidance laws. and distance change rate Signal;

[0009] Step 2: Based on the Empirical Mode Decomposition (EMD) method, analyze the line-of-sight angular velocity under different guidance laws. and distance change rate signal The two signals are decomposed and extracted to obtain all IMF components and a residual res;

[0010] Step 3: Calculate the line-of-sight angular velocity The energy of each IMF component and residual res, and the distance change rate signal The energy of each IMF component and the residual res is arranged into a vector to form the characteristic vector energy band T corresponding to each guidance law. The guidance law category label is labeled for each characteristic vector energy band T.

[0011] Step 4: Traverse the pairwise combinations of guidance law categories, construct a binary support vector machine (SVM) for each combination, and train the SVM using the feature vector energy band T corresponding to the two guidance laws.

[0012] Step 5: Line-of-sight angular velocity of the defensive missile to be identified. and distance change rate The signal is first decomposed using the Empirical Mode Decomposition (EMD) method to obtain the corresponding feature vector energy band T, which is then input into each trained SVM. The recognition result of each binary SVM is counted as 1 vote, and the guidance law category with the most votes is the category of the signal to be identified.

[0013] Preferably, the specific method of step 2 is as follows:

[0014] Step 1: Find the signal or signal For all extreme points, the upper and lower envelopes e are fitted using cubic spline interpolation. max and e min ;

[0015] Step 2: Calculate the mean value of the upper and lower envelopes as m(t);

[0016] Step 3: Send the signal or signal Subtracting m(t) yields the sequence c(t);

[0017] Step 4: Check whether the sequence c(t) meets the set conditions:

[0018] If the condition is met, c(t) is separated as an IMF component, yielding the remaining sequence r(t), i.e. or

[0019] If the conditions are not met, the sequence c(t) is used as a new signal and Step 1 to Step 3 are repeated until the sequence c(t) meets the set conditions. Then, all IMF components and a residual of the signal are extracted.

[0020] The set conditions are as follows: on the entire time axis, the number of extreme points and zero crossings of the signal sequence are the same or differ by at most one, and at any time point, the average value of the upper envelope and lower envelope formed by the local maxima and local minima of the signal sequence must be 0, that is, the waveform of the signal sequence must be locally symmetrical.

[0021] Preferably, in step 2, for the signal or signal The data is mirrored at both ends of the signal to symmetrically extend the original signal into a closed loop signal, and then the decomposition is performed.

[0022] Preferably, in step 3, when the number of T elements in the energy band of the feature vector corresponding to different guidance laws is different, zero features are added after the lowest frequency IMF, so that the length of the sample data in the subsequent guidance law identification step based on machine learning is consistent.

[0023] Preferably, in step 3, the energy band T elements of the feature vector are normalized.

[0024] Ideally, SVM uses a Gaussian kernel function.

[0025] Preferably, in step 3, the energy calculation formula is:

[0026]

[0027]

[0028] In the formula, c i r represents the value of each IMF component at time i; i This represents the value of the residual at time i.

[0029] The present invention has the following beneficial effects:

[0030] This invention, based on the relative motion information of different guidance laws within a short period of time, eliminates the need for step-by-step iteration and state fusion. It employs signal decomposition and support vector machine classification to achieve rapid and high-precision identification of guidance laws, representing a novel guidance law identification method. No similar technologies have been observed to date. Attached Figure Description

[0031] Figure 1 This is a schematic diagram illustrating the relative motion of the defensive missile aircraft.

[0032] Figure 2 The results are the line-of-sight angular velocity signal decomposition results based on EMD;

[0033] Figure 3 Comparison of the mirror-extended and unextended envelopes;

[0034] Figure 4 For comparison between mirror-extended and unextended sequences;

[0035] Figure 5 This is a "one-to-one" multi-class SVM model;

[0036] Figure 6 The flowchart of the guidance law identification method based on empirical mode decomposition of the present invention is as follows;

[0037] Figure 7 The trajectories of both sides under four guidance laws;

[0038] Figure 8 The line-of-sight angular velocity under four guidance laws;

[0039] Figure 9 The rate of change of distance under four guidance laws;

[0040] Figure 10 The line-of-sight angular velocity (EMD) results for PPN.

[0041] Figure 11 EMD results for PPN distance change rate;

[0042] Figure 12 EMD results for TPN line-of-sight angular velocity;

[0043] Figure 13 EMD results for the TPN distance change rate;

[0044] Figure 14 EMD results for IPN line-of-sight angular velocity;

[0045] Figure 15 EMD results for the rate of change of IPN distance;

[0046] Figure 16 The results are the APN line-of-sight angular velocity EMD values.

[0047] Figure 17 This is the EMD result of the APN distance change rate. Detailed Implementation

[0048] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0049] I. Modeling and Scenario Design of Defensive Missiles and Combat Aircraft

[0050] If an aircraft encounters enemy defensive missiles during combat, and assuming both move within a vertical plane, their relative motion is shown in the diagram below. Figure 1 As shown.

[0051] Figure 1 In the middle, M and A represent defensive missiles and aircraft, respectively; V M and V A The speeds of the defensive missile and the aircraft are respectively; θ M θ A For the ballistic inclination angle of the defensive missile and the heading angle of the aircraft; R is the relative distance between the defensive missile and the aircraft; q is the line-of-sight angle; η M η A The leading angle for defense against missiles and aircraft; Let V' be the angle between the line of sight and the relative velocity V′, where V′ = V A -V M All angles shown in the diagram are positive.

[0052] As shown in the diagram, the equations of relative motion between the defensive missile and the aircraft are:

[0053]

[0054] The kinematic models of the defensive missile and the aircraft are as follows:

[0055]

[0056]

[0057] In the formula, (x M ,y M ), (x A ,y A ) represent the coordinates of the defensive missile and the aircraft, respectively; a M a A These are the normal accelerations of the defensive missile and the aircraft, respectively.

[0058] Proportional guidance laws are simple in form and easy to implement, making them a commonly used guidance law when intercepting aircraft with defensive missiles. They may take one of the following forms: Pure Proportional Navigation (PPN), True Proportional Navigation (TPN), Ideal Proportional Navigation (IPN), or Augmented Proportional Navigation (APN). The guidance commands for these four guidance laws are as follows:

[0059]

[0060]

[0061]

[0062]

[0063] In equation (4), a PPN The PPN command acceleration is perpendicular to the velocity direction of the defensive missile; K is the proportional guidance coefficient; in equation (5), a TPN For TPN command acceleration, perpendicular to the line of sight; V r For approximate velocity; in equation (6), a IPN The acceleration is the IPN command acceleration, perpendicular to the direction of the relative velocity between the projectile and the aircraft; V k For the velocity of the defensive missile and the aircraft along the perpendicular line of sight; in equation (7), a APN For APN command acceleration, perpendicular to the line of sight; a Ak For a A The component of acceleration along the direction perpendicular to the line of sight.

[0064] When a defensive missile intercepts a combat aircraft using one of the four guidance laws mentioned above, the combat aircraft first performs empirical mode decomposition on the measured line-of-sight angular velocity and range change rate signals to construct the guidance law characteristic energy band. This energy band is then used as input for machine learning to train an optimal model for classifying samples. Through accurate classification of the guidance law characteristic energy band, the identification of unknown guidance laws is achieved.

[0065] II. Methods for Decomposing the Relative Motion Information Signals Between Defensive Missiles and Aircraft

[0066] When defensive missiles use different guidance laws to intercept our maneuvering combat aircraft, the line-of-sight angular velocity... and distance change rate The signals are different. This invention uses Empirical Mode Decomposition (EMD) to decompose them and extract the energy features of the signals.

[0067] 2.1 Decomposition of line-of-sight angular velocity and distance rate of change signals based on Empirical Mode Decomposition (EMD)

[0068] Empirical Mode Decomposition (EMD) is a signal analysis and processing method proposed in 1998 by Norden E. Huang, a Chinese-American academician of the National Academy of Engineering. It differs from signal processing methods based on the traditional Fourier transform principle.

[0069] EMD can process complex time-domain signals containing multiple frequency components. and The signal is decomposed into multiple intrinsic mode function (IMF) components in the time domain, ranging from high to low frequency, and a residual. Conversely, the signal can also be reconstructed by superimposing the IMF components and the residual, as follows:

[0070]

[0071] It is important to note that the intrinsic mode function (IMF) components must satisfy the following two conditions:

[0072] (1) The number of extreme points and zero crossings of the signal sequence are the same or at most differ by one over the entire time axis.

[0073] (2) At any point in time, the average value of the upper and lower envelopes formed by the local maxima and local minima of the signal sequence must be 0, that is, the waveform of the signal sequence must be locally symmetrical.

[0074] Using line-of-sight angular velocity signal For example, the decomposition process of EMD is given as follows:

[0075] Step 1: Find the signal For all extreme points, the upper and lower envelopes e are fitted using cubic spline interpolation. max and e min .

[0076] Step 2: Calculate the mean value of the upper and lower envelopes as m(t), then...

[0077]

[0078] Step 3: Send the signal Subtracting the mean of its upper and lower envelopes m(t) yields the sequence c(t).

[0079]

[0080] Step 4: Check if the sequence c(t) satisfies the two conditions of the IMF function. If it does, c(t) will be separated as an IMF component, yielding the remaining sequence r(t), i.e. If not, the above steps are repeated with sequence c(t) as a new signal until sequence c(t) satisfies the IMF condition.

[0081] Step 5: Using the r(t) obtained in the first four steps as the new signal, repeat the above steps to extract all IMF components in sequence. Finally, a finite number of IMF components and one residual component (residual or average trend) are obtained, represented as:

[0082]

[0083] To illustrate the EMD signal decomposition method more intuitively, let's assume the line-of-sight angular velocity signals of the defensive missile and the aircraft under a complex relative motion relationship are as follows:

[0084]

[0085] The sampling frequency is set to 1kHz and the sampling time is 2s. From equation (12), it can be seen that the line-of-sight angular velocity signal at this time has three frequency components: 5Hz, 15Hz, and 45Hz. After decomposition in Steps 1 to 5, the obtained signal is as follows: Figure 2 As shown.

[0086] The signal is decomposed into IMF1 to IMF3 components and the residual res. The frequencies of IMF1 to IMF3 are arranged from high to low according to 45Hz, 15Hz, and 5Hz, and their amplitudes also correspond to the original signal. According to the EMD algorithm, the mean of the upper and lower envelopes of the signal needs to be continuously subtracted, causing the most densely distributed peaks and troughs in the signal to continuously converge towards the time axis. If the necessary conditions of IMF are met, separating it yields the highest frequency time-domain component of the signal, namely the IMF1 component. Repeating the above steps yields the IMF2 and IMF3 components with frequencies from high to low. IMF4 is a spurious component caused by calculation errors in the EMD process. Figure 2 The magnitude of the IMF component relative to The amplitude of the signal frequency components has a small error, and these small errors eventually converge into the IMF4 component. Therefore, the amplitude of the IMF4 component is significantly smaller than that of the other IMF components.

[0087] 2.2 Endpoint Effect Suppression Method for Relative Motion Information Signal Decomposition Based on EMD

[0088] In the EMD method described in section 2.1, cubic spline interpolation, using extreme points as interpolation points, is generally used to fit the upper and lower envelopes of the signal. However, due to... and The two ends of a signal are not necessarily extreme points, causing the upper and lower envelopes at the two ends to shift outward or inward, thus distorting the decomposed IMF components. This distortion continues to shift into the data sequence during the decomposition and filtering process, eventually affecting the entire data sequence; this phenomenon is called the endpoint effect.

[0089] This invention uses the concept of mirror extension to suppress the endpoint effect. That is, a mirror is placed near each of the signal endpoints to symmetrically extend the original signal into a closed loop signal. This loop signal has no endpoints, and its upper and lower envelopes are completely determined by the inside of the signal.

[0090] certain After the signal is mirrored and extended, the changes in its upper and lower envelopes are as follows: Figure 3 As shown.

[0091] Figure 3 The left end of the unextended lower envelope and the right end of the upper envelope both exhibit a clear tendency to shift inwards. This is because the extreme points are not at the endpoints and are relatively far from them. The left and right ends of the signal are mirror-symmetric about the vertical axis, yielding two maxima and minima outside the endpoints, respectively. Mirror extension increases the number of extreme points needed for cubic spline interpolation to calculate the envelope, making... The signal envelope more closely matches the original trend of the signal, reducing the degree of offset of the envelope near the endpoints, thereby suppressing the endpoint effect, such as... Figure 3 As shown by the red curve in the middle.

[0092] The signal is processed through EMD algorithm step 3 to obtain the unextended and extended c(t) sequences, as follows: Figure 4 As shown, there is a significant offset near the endpoints, and the sequence itself is also affected. The EMD algorithm needs to continuously calculate the envelope and filter the IMF step by step. If mirror extension is not used to suppress the endpoint effect, the offset distortion of the IMF will be even more severe.

[0093] The mirror continuation method can suppress the endpoint effect and ensure accurate extraction of the energy characteristics of the line-of-sight angular velocity and distance change rate signals.

[0094] 2.3 Method for Extracting Energy Features of Relative Motion Information

[0095] Extracting energy features from relative motion information is a deep processing method for sample data in guidance law identification using machine learning. The following section uses wavelet packet energy feature extraction as a framework, combining unscented Kalman filtering (UKF) and EMD to extract the feature energy of relative motion information obtained from radar detection. The specific steps are as follows:

[0096] (1) respectively for and The signal is processed by EMD to obtain the corresponding IMF components and residuals res.

[0097] (2) Calculation and The energy of each IMF component of the signal and the residual res is calculated using the following formula:

[0098]

[0099] In the formula, c i r represents the value of each IMF component at time i; i This represents the value of the residual at time i.

[0100] (3) and signal q m and R m The energy band T of the feature vector constructed by the combination of energy features for the guidance law is:

[0101]

[0102] When constructing the characteristic energy band of the guidance law as described above, the following should be noted:

[0103] (1) Each IMF represents an energy characteristic, and under different guidance laws and The number of IMF components obtained from signal decomposition is not necessarily the same. Therefore, zero features are added after the lowest frequency IMF to ensure that the sample data length is consistent in the subsequent guidance law identification stage based on machine learning.

[0104] (2) and The energy characteristics of the signals differ significantly in magnitude and need to be normalized separately.

[0105] The characteristic energy bands of different guidance laws obtained so far will serve as sample data for the subsequent training and identification of the guidance law identification network based on support vector machines.

[0106] III. Guidance Law Identification Based on Support Vector Machine

[0107] The guidance law identification of this invention essentially uses machine learning classification methods to classify sample data, thereby achieving the identification effect. By using the feature energy bands of different guidance laws as machine learning sample inputs for classification, it is possible to identify different guidance laws.

[0108] Support Vector Machines (SVMs) achieve optimal classification of samples by finding an optimal decision hyperplane that maximizes the distance between the nearest sample data on both sides of the hyperplane.

[0109] For a binary classification problem, assuming we need to identify two guidance laws, and extract N guidance law feature energy bands as training samples to form a training set X:

[0110] X={(x i ,y i )|x i ∈R n ,y i ∈{-1,+1}} (15)

[0111] In the formula, i = 1, 2, ..., N; x i Let T be the characteristic energy band of the guidance law, and n be the number of energy characteristics in T, i.e., n = q. m +R m ;y i This is a label for the guidance law category.

[0112] Arbitrary guidance law feature energy band samples x in training set X i =(E1,E2,E3…E n The distance from the hyperplane ωx+b=0 is:

[0113]

[0114] in

[0115] The characteristic energy band samples of the positive and negative guidance laws on both sides of the hyperplane are given by the following formulas:

[0116]

[0117] Where, d SV The distance from the support vector to the hyperplane is the distance between the support vector and the hyperplane. The support vector is the sample that is closest to the hyperplane.

[0118] The hyperplane satisfies the following constraints:

[0119] y i (ωx i +b)≥1,i=1,2,…,N (18)

[0120] The classification margin of the guidance law samples is 2 / ||ω|. When the value of ||ω| is minimized, the classification margin is maximized, which makes the two types of guidance law samples more accurately classified.

[0121] Furthermore, when a small number of outliers in the sample make it impossible to completely linearly separate the two types of guidance laws, a non-slack variable ξ can be introduced. i Let i = 1, 2, ..., N, such that a small number of samples are not accurately separated by the hyperplane during the classification process. Combining this with the above equation, it can be transformed into a constrained quadratic optimization problem:

[0122]

[0123] In the formula, C is the penalty function. The larger C is, the stricter the classification and the more severe the penalty for misclassification.

[0124] When solving the optimization problem, the Lagrange multiplier method is used to obtain the optimal decision function as follows:

[0125]

[0126] In the formula, SV represents support vectors, and a i It is a Lagrange multiplier operator.

[0127] Furthermore, the amplitude and number of IMF components differ depending on the guidance law, making it difficult to linearly separate the guidance law feature energy band samples. Therefore, a kernel function needs to be introduced for nonlinear SVM. The kernel function can map the features of nonlinear sample data from a relatively low dimension to a higher dimension without adding new features. Through the mapping of the kernel function, SVM can classify nonlinear samples in a high-dimensional space.

[0128] Define a kernel function K(x) i ,x j If the Mercer condition (positive definite eigenvalues) is satisfied, then:

[0129] K(x i ,x j )=Φ(x i )·Φ(x j ) (twenty one)

[0130] Where Φ represents a certain mapping. This invention uses a Gaussian kernel function, expressed as:

[0131]

[0132] The optimal decision function for a nonlinear SVM:

[0133]

[0134] The SVM method described above can identify two guidance laws. When it is necessary to identify multiple guidance laws, multiple sets of binary classification SVMs are combined to construct a "one-to-one" multi-classification SVM.

[0135] A "one-to-one" multi-class SVM involves building a binary SVM from any two of the n classes, requiring the design of k binary SVMs. When classifying an unknown guidance law sample, each binary SVM's classification result is counted as one vote, and the guidance law class with the most votes is the class of the unknown sample. The structure of a "one-to-one" multi-class SVM model is as follows: Figure 5 As shown.

[0136] In summary, the entire process of the guidance law identification method based on empirical mode decomposition is as follows: Figure 6 As shown.

[0137] Example:

[0138] The following is a verification of the defense missile guidance law identification method based on signal decomposition.

[0139] Assume our combat aircraft's initial position is (15000, 15000) m, and its speed is V. A = 400m / s, initial trajectory inclination angle θ A =180°, and in order to penetrate defenses, combat aircraft perform serpentine maneuvers.

[0140] The enemy's defensive missile has an initial position of (0,0) and a velocity of V. M =500m / s, initial launch angle θ M =90°, intercepting the aircraft using PPN, TPN, IPN, and APN respectively, with the proportional coefficient K in all four guidance laws being 4. The flight trajectories of the aircraft under the four guidance laws and and like Figure 7-9 As shown.

[0141] Assuming the time interval ΔT = 4 seconds after the start of the confrontation... and The signal is the signal to be identified.

[0142] The relative motion information energy feature extraction method in Section 2.3 was used to analyze the first 4 seconds of four guidance laws. and Energy is extracted from the signal.

[0143] Four guidance laws and The IMF components and residuals after signal decomposition are as follows: Figure 10-17 As shown.

[0144] Will and The energy of each component after signal decomposition is calculated and normalized to obtain the one-dimensional guidance law feature energy band, which is then used as a sample for the subsequent SVM classification model. The feature energy bands of the four guidance laws are shown in Table 1. Energy features 1 to 9 in the energy band come from... The signal, with energy characteristics of 10 to 15, comes from... Signal.

[0145] Table 1. Characteristic energy bands under various guidance laws.

[0146]

[0147] Table 2 Optimization parameters for "One-to-One" multi-class SVM model

[0148]

[0149] SVM-based guidance law identification requires a certain number of samples to train the classification model. Taking the initial position (x0, y0) of our combat aircraft as the center, D... r Within a region of radius I, randomly select I locations to obtain the defensive missiles. and The signal is ultimately used to obtain the guidance law. and Signal.

[0150] Using the method in 2.3, extract and The energy characteristics of the signal are used to construct I sets of guidance law feature energy bands. This process is repeated to obtain m sets of m guidance laws, which serve as the sample set for a "one-to-one" multi-class SVM model.

[0151] Following the steps described above, 100 feature energy bands were obtained for each of the four different guidance laws. Each guidance law feature energy band was randomly divided into a training set of 80 groups and a test set of 20 groups, resulting in a total of 320 training sets and 80 test sets. The 320 training sets were used as input to a "one-to-one" multi-class SVM model to train the optimal multi-class SVM model. The 80 test sets were used to evaluate the optimal multi-class SVM model. After inputting the optimal model, the guidance law identification accuracy was output by calculating the percentage of samples correctly identified in each guidance law category.

[0152] In D r With a value of 500, the verification accuracy is 98.75%, demonstrating high identification accuracy. The optimal classification model parameters for identifying guidance laws are shown in Table 2 below.

[0153] By training the model with 320 sets of samples, the optimal Gaussian kernel function σ and penalty function C for each binary SVM in the multi-class classification model were determined. Each optimal binary SVM combination constitutes a "one-to-one" multi-class SVM model, realizing the classification and identification of different guidance laws.

[0154] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for guidance law identification based on signal decomposition and support vector machines, characterized by, include: Step 1: Simulate the line-of-sight angular velocity of defensive missiles intercepting maneuvering combat aircraft using different guidance laws. and distance change rate Signal; Step 2: Based on the Empirical Mode Decomposition (EMD) method, analyze the line-of-sight angular velocity under different guidance laws. and distance change rate The two signals are decomposed and extracted to obtain all IMF components and a residual res; Step 3: Calculate the line-of-sight angular velocity Energy of each IMF component and residual res, and distance change rate The energy of each IMF component and the residual res is arranged into a vector to form the characteristic vector energy band T corresponding to each guidance law. The guidance law category label is labeled for each characteristic vector energy band T. Step 4: Traverse the pairwise combinations of guidance law categories, construct a binary classification support vector machine (SVM) for each combination, and train the SVM using the feature vector energy band T corresponding to the two guidance laws. Step 5: Line-of-sight angular velocity of the defensive missile to be identified. and distance change rate First, the Empirical Mode Decomposition (EMD) method is used to decompose the signal, and then the corresponding feature vector energy band T is obtained. This T is then input into each trained SVM. The recognition result of each binary SVM is counted as one vote. Finally, the guidance law category with the most votes is the category of the signal to be identified.

2. The guidance law identification method based on signal decomposition and support vector machine as described in claim 1, characterized in that, The specific method for step 2 is as follows: Step 1: Find the line-of-sight angular velocity Or the rate of change of distance For all extreme points, the upper and lower envelopes e are fitted using cubic spline interpolation. max and e min ; Step 2: Calculate the mean value of the upper and lower envelopes as m(t); Step 3: Set the line-of-sight angular velocity Or the rate of change of distance Subtracting m(t) yields the sequence c(t); Step 4: Check whether the sequence c(t) meets the set conditions: If the condition is met, c(t) is separated as an IMF component, yielding the remaining sequence r(t), i.e. or If the conditions are not met, the sequence c(t) is used as a new signal and Step 1 to Step 3 are repeated until the sequence c(t) meets the set conditions. Then, all IMF components and a residual of the signal are extracted. The set conditions are: on the entire time axis, the number of extreme points and zero crossings of the signal sequence are the same or differ by at most one, and at any time point, the average value of the upper envelope and lower envelope formed by the local maxima and local minima of the signal sequence must be 0, that is, the waveform of the signal sequence must be locally symmetrical.

3. The guidance law identification method based on signal decomposition and support vector machine as described in claim 1 or 2, characterized in that, In step 2, regarding the line-of-sight angular velocity Or the rate of change of distance The data is mirrored at both ends of the signal to symmetrically extend the original signal into a closed loop signal, and then the decomposition is performed.

4. The guidance law identification method based on signal decomposition and support vector machine as described in claim 1, characterized in that, In step 3, when the number of T elements in the energy band of the feature vector corresponding to different guidance laws is different, zero features are added after the lowest frequency IMF to make the length of the sample data in the subsequent guidance law identification process based on machine learning consistent.

5. The guidance law identification method based on signal decomposition and support vector machine as described in claim 1, characterized in that, In step 3, the energy band T elements of the feature vector are normalized.

6. The guidance law identification method based on signal decomposition and support vector machine as described in claim 1, characterized in that, SVM uses a Gaussian kernel function.

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