A method for ballistic midcourse target recognition using HRRP sequence at low data rate

Abstract

The application provides a method for trajectory midcourse target recognition based on a low-data-rate HRRP sequence, and relates to the technical field of radar signal processing.The method obtains target signals through steps one and two, and inputs the HRRP sequence obtained by observing the target through a radar sensor as sample data; the method extracts features of the target through steps three and four: the method establishes a precession model by taking a cone-cylinder target as an example, uses the periodicity of scattering center points in the HRRP sequence to perform time-frequency analysis, and realizes one-dimensional feature distribution of energy strength by using a projection method, so as to extract a precession frequency; and the method extracts target structure features, entropy value features and period features; the method performs signal feature fusion processing through step five, classifies the features by performing feature importance analysis and using a Random Forest algorithm, obtains the category of a target to be recognized, and outputs a final fusion result.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of radar signal processing, and particularly relates to a method for trajectory midcourse target recognition by using HRRP sequence under low data rate. BACKGROUND

[0002] As a main means of missile defense system early warning detector, wideband radar plays an important role in practical application, which is to identify warheads, decoys or fragments. How to identify real warheads from the target group released in the trajectory midcourse and intercept them is an important problem in the trajectory defense system. The trajectory missile defense interception mainly includes tracking, identification and interception. The basic approach of radar target recognition is to extract the structural features and motion features of the target from the target back electromagnetic scattering, and then to identify the true and false according to certain prior information. The structural features include the size, shape and material of the target, which are the intuitive properties of distinguishing true and false targets. The motion features include macro trajectory characteristics and micro motion characteristics, which reflect the essential properties of the target from different aspects. The early rough target feature recognition can be realized at low resolution, such as obtaining the RCS amplitude signal of the echo, etc. However, due to the limitation of signal bandwidth, it is difficult to realize steps such as scattering center distribution feature extraction and radial length information extraction in low resolution radar echo signal. In high resolution radar, SAR and ISAR use the distance and azimuth information between radar and target to image, but the imaging process needs relatively complicated compensation and takes a long time. High resolution range profile (HRRP) is the vector sum of the subecho of the target scattering point projected on the radar ray, which provides the distribution information of the target scattering point along the distance direction. When the distance resolution of the radar is much smaller than the size of the target, the HRRP can be obtained according to the radar echo, which contains information about the structure, size and shape of the target. Compared with SAR and ISAR images, HRRP has more advantages in processing. It is very important to effectively obtain and use these information in the field of trajectory target recognition.

[0003] Most of the current research based on the characteristics of HRRP sequence mainly uses radar to transmit pulses with medium and high repetition frequency to achieve high-precision target parameter measurement. In the research of extracting target motion characteristics from HRRP sequence, there are various feature extraction methods, for example, the literature (Chalin, Chen Daqing, Wu Peng. Space precession target parameter estimation method based on HRRP sequence, Radar Science and Technology, 2020) uses the extreme value information of the radial length sequence of the warhead target to estimate the coupling results of the precession parameters and shape parameters, and then constructs an auxiliary function according to the radial length sequence to realize the decoupling of the precession parameters and shape parameters, and finally uses the extracted parameter information for target recognition. The literature (Wang Yang, Sang Yujie. Extracting missile target micro-motion characteristics using one-dimensional range profile sequence [J]. Modern Radar, 2014) proposes a method of calculating the maximum sliding correlation coefficient change of the range profile sequence to extract the period and frequency. The literature (Zhou Daiying, Zhang Ying, Feng Jian, Estimate target precession frequency using one-dimensional image sequence time difference [J]. Acta Aeronautica et Astronautica, 2018) reduces other frequency components by calculating the difference between adjacent one-dimensional range images to enhance the precession frequency component and avoid estimation errors caused by changes in the target scattering point distribution model. The literature (Zhu Yupeng, Wang Hongqiang, Li Xiang, et al. Space ballistic target micro-motion feature extraction based on one-dimensional range image sequence [J]. Journal of Aerospace Power, 2009) uses the scattering center position transformation rule to estimate the precession frequency and other micro-motion parameters of the space ballistic target based on the generalized Radon transform.

[0004] For long-range radars, the radar needs to transmit wide pulses to ensure sufficient radiation energy to obtain effective target information, and the corresponding radar pulse repetition frequency will be reduced. At present, there is a lack of research on feature extraction and identification of HRRP sequence under low data rate. SUMMARY

[0005] The purpose of the present application is to solve the problems in the prior art, and to provide a method for identifying ballistic midcourse targets based on low-data-rate HRRP sequence. The present application takes the HRRP sequence obtained by a low-repetition-frequency wideband radar as the research object, studies the precession feature extraction method and joint multi-feature ballistic midcourse target recognition, and considers the differences in size, shape and micro-motion model of different targets. The characteristics of the warhead, heavy decoy, light decoy and fragment targets in the ballistic missile midcourse flight scene are simulated. Combined with the simulation data, the precession features and structural features of the target are extracted using the HRRP sequence under low data rate, and the importance of each feature is evaluated using the Random Forest algorithm. The multi-feature fusion technology is used to combine the various features of the radar target to identify the ballistic target, thereby improving the recognition performance of the radar target.

[0006] Technical content: A method for identifying ballistic midcourse targets based on low-data-rate HRRP sequence, comprising the following steps:

[0007] Step one, analyze the target motion characteristics of the middle section of the trajectory, establish the target precession model, get the change rule of the target attitude angle with time and the target HRRP;

[0008] Step two, combine the STK simulated missile trajectory, the target attitude angle at each sampling time and the corresponding electromagnetic calculation results to obtain the wideband echo signal; finally, superimpose the Gaussian white noise and the theoretical radar echo signal to obtain the radar observation echo signal, and obtain the target HRRP sequence under low data rate from it;

[0009] Step three, taking the target one-dimensional range image sequence as the research object, the image projection method is used to extract the precession frequency of the target low data rate HRRP sequence;

[0010] Step four, extract the target structure features, entropy features and periodic features from the target low data rate HRRP sequence;

[0011] Step five, the features obtained in steps three and four are fused into a long vector by splicing, the Random Forest algorithm is used for feature screening and evaluation based on feature importance, and is put into the classifier for classification training to obtain the category of the target to be identified.

[0012] Further, when the target is a precession cone-shaped warhead, the calculation method of the target attitude angle and the target HRRP in step one is as follows:

[0013] 1) Establish a precession model, assume that the reference coordinate system OXYZ is established with the target mass center O as the origin, the spin angular velocity of the target rotating around the symmetry axis OA is set as ω Z , the motion of the target rotating around the precession axis OZ is called cone spin, and the cone spin angular velocity of the target is set as ω p ; the angle between OZ and OA is θ, which is called precession angle; assuming that the radar line of sight RLOS direction is located in the plane, the angle α between YOZ and OZ is the radar line of sight angle, and the angle ρ between the radar line of sight RLOS and the OA axis is called the attitude angle;

[0014] 2) Assuming that at t=0, the initial azimuth angle of the spin axis in the YOZ plane is , then the change formula of the attitude angle ρ with time is:

[0015]

[0016] In the above formula, the change of the radar line of sight angle α in a precession period can be ignored, so α can be regarded as a constant value;

[0017] 3) The HRRP of the target can be obtained by inverse Fourier transform of the target frequency, which can be written as:

[0018]

[0019] where f is the frequency, c is the speed of light, k is the number of scattering points on the target, B k and R k are the amplitude of the kth scattering point and the distance between the kth scattering point and the radar at a certain time, respectively, and X(f) represents the high-resolution range profile of the target.

[0020] Further, the specific content of the step three is: 1) assuming that the wideband radar transmits a frequency stepping signal, when the PRF value is too low, the time-frequency curve is blurred, the periodicity of the scattering center points in the HRRP sequence is utilized, time-frequency analysis is carried out, and projection method is used to realize vertical projection of the energy strength, and one-dimensional feature distribution is completed; 2) the micro-motion frequency of the scattering center is extracted, and the mean value of the micro-motion frequencies of multiple scattering centers is taken as the precession frequency of the target.

[0021] Further, in step three, the image projection method is used to extract the precession frequency of the target low-data-rate HRRP sequence, and the specific algorithm implementation steps are:

[0022] Step 3.1, first, the received N p frame target HRRP is subjected to micro-motion period extraction, and a to-be-processed one-dimensional image data matrix is established as:

[0023]

[0024] wherein N s represents the number of distance cells in each range image, and N p represents the number of received target HRRP frames;

[0025] Step 3.2, zero padding interpolation is performed on the N p frame HRRP sequence in the slow time domain, assuming that the sampling rate of the original HRRP sequence is f s , the sampling rate after interpolation is f d , and the interpolated matrix is and the following relationship exists:

[0026] f d =Mf s

[0027]

[0028] wherein M is the zero padding interpolation number, is the interpolated matrix (n=MN p );

[0029] Step 3.3, non-coherent accumulation is performed on each distance cell, and Further, the step four, the target structure features include the number of scattering points, skewness, target length, SVD, irregularity, and the periodic features include the change period of the target length and the period change of the amplitude, echo power. r sk Further, the step four, the target structure features include the number of scattering points, skewness, target length, SVD, irregularity, and the periodic features include the change period of the target length and the period change of the amplitude, echo power.

[0030] Step 3.4, the formula for vertical projection of the time-frequency diagram is as follows:

[0031]

[0032] t is the time sequence length of the time-frequency diagram; S f (t,ω) represents the N sk strong scattering center units in Y d (t,ω) are sequentially subjected to short-time Fourier transform (STFT) to obtain the time-frequency distribution diagram of the scattering points, Y (t,ω) represents the N sk strong scattering center units in Y d (t,ω) are sequentially subjected to short-time Fourier transform (STFT) to obtain the time-frequency distribution diagram of the scattering points, Y

[0033] Step 3.5, FFT is performed on Y d to obtain the frequency spectrum F of the time-frequency curve, and the frequency domain peak value of F is taken to obtain the precession frequency value at the current scattering point is represented as follows:

[0034] F=FFT(Y d )

[0035]

[0036] wherein F represents the frequency spectrum of the estimated time-frequency curve, is the precession frequency estimation value;

[0037] Step 3.6, assuming that N sk strong scattering center units are extracted from the HRRP sequence, steps 3.4-3.5 are repeated for each strong scattering center unit to obtain N sk precession frequency estimation values, and the average of the precession frequency estimation values is taken to obtain the final frequency estimation value.

[0038] Further, in the step four, the target structure features include the number of scattering points, skewness, target length, SVD, irregularity, and the periodic features include the change period of the target length and the period change of the amplitude, echo power.

[0039] Further, the specific operation steps of the step five are as follows:

[0040] Step 5.1, selecting a suitable feature subset according to the contribution degree of different features on each decision tree in the data forest;

[0041] Step 5.2 sequentially ranks the feature importance according to the importance of each feature; the ranking result from high to low is: micro-motion frequency, number of scattering points, target length, skewness, irregularity, target length period, SVD, entropy value, length variation amplitude, echo power;

[0042] Step 5.3 performs a traversal search, and in each iteration process, one feature with low importance is deleted from the feature subset;

[0043] Step 5.4 performs screening successively;

[0044] Step 5.5 finally selects the corresponding feature with the highest classification accuracy as the selection result;

[0045] Step 5.6 according to the importance ranking result of each feature, 10 feature subsets are formed by different target features to identify the warhead target.

[0046] Compared with the prior art, the beneficial effects of the present application are:

[0047] 1) The present method uses image projection method and multi-feature fusion technology under low data rate to solve the phenomenon of periodic blur of time-frequency curve caused by too low original sampling rate of HRRP and the problem of low target recognition accuracy caused by single feature, and through multiple Monte Carlo experiments and method comparison, the precession frequency of the midcourse target can be accurately estimated in the low PRF range of 10Hz to 100Hz, and the result has good stability.

[0048] 2) After the target micro-motion feature and multiple target structure features are fused and processed and classified by the feature classifier, the purpose of improving the recognition accuracy of various targets is finally achieved. BRIEF DESCRIPTION OF DRAWINGS

[0049] Figure 1 It is a precession model diagram of the midcourse target of the present application;

[0050] Figure 2 It is a simulated trajectory diagram of the ballistic missile of the present application;

[0051] Figure 3 It is a time-frequency diagram under different PRF values of the present application;

[0052] Figure 4 It is a time-frequency Figure 1 projection curve comparison diagram of the present application;

[0053] Figure 5 It is an amplitude-frequency diagram of the vertical projection sequence;

[0054] Figure 6 It is the mean value of the precession frequency estimated by the method of the present application and the comparative example under the PRF value of 10-100Hz;

[0055] Figure 7 The mean square error curves of the precession frequency estimated by the method of the application and the method of the comparative example for the target in the examples at the PRF value of 10-100 Hz are shown in the following table. DETAILED DESCRIPTION

[0056] The technical solutions of the application will be described in detail below with reference to the drawings and specific implementation cases.

[0057] The method for ballistic midcourse target recognition based on a low-data-rate HRRP sequence, which is used to improve the recognition performance of radar targets in the midcourse ballistic at a low data rate, comprises the following steps:

[0058] Step one, analyzing the motion characteristics of the target in the midcourse ballistic, establishing a precession model of the target, and obtaining the variation law of the attitude angle of the target with time and the HRRP of the target;

[0059] The midcourse ballistic provides a long time for the anti-missile system to recognize the target, and the successful recognition in this section will greatly improve the interception probability of the entire anti-missile system, so the target recognition in the midcourse ballistic becomes the focus of the entire ballistic target recognition.

[0060] The target in the midcourse ballistic includes a warhead and decoys, and the decoys are composed of light decoys, heavy decoys, fragments, etc., and the shapes of the decoys are relatively special, among which the rotating symmetrical bodies are the most common, which are generally composed of cones, columns, frustums, and spherical caps.

[0061] When the target is a precession cone-shaped warhead, the calculation method of the attitude angle of the target and the HRRP of the target in step one is as follows:

[0062] 1) establishing a precession model, Figure 1 which is a typical precession model of a micro-motion of a cone-shaped warhead in the midcourse flight process; and Figure 1 taking the precession model shown in FIG. 1 as an example, a reference coordinate system OXYZ is established with the mass center O of the target as the origin. The spin angular velocity of the target rotating around the symmetry axis OA of the target is set as ω Z ; the motion of the target rotating around the precession axis OZ is called cone rotation, and the cone rotation angular velocity of the target is set as ω p ; the angle between OZ and OA is θ, which is called the precession angle. It is assumed that the direction of the radar line of sight (RLOS) is in the plane, the angle α between YOZ and OZ is the radar line of sight angle, and the angle ρ between the RLOS and the OA axis is called the attitude angle;

[0063] 2) assuming that the initial azimuth angle of the spin axis in the YOZ plane at t = 0 is , the variation formula of the attitude angle ρ with time is:

[0064]

[0065] In the above formula, the radar line-of-sight angle a changes with the flight time of the ballistic target. The flight time of the midcourse of the ballistic missile is generally several minutes, while the precession period is in seconds, and the change of a in a precession period is almost negligible, so a can be regarded as a constant value.

[0066] 3) The HRRP (High Range Resolution Profile) of the target can be obtained by inverse Fourier transform of the frequency of the target, which can be written as:

[0067]

[0068] where f is the frequency, c is the speed of light, k is the number of scattering points on the target, B k and R k are the amplitude of the kth scattering point and the distance between the kth scattering point and the observation radar at a certain time, respectively, and X(f) represents the high range resolution profile of the target.

[0069] Step two, the wideband echo signal is obtained by combining the STK simulated missile trajectory (distance, speed), the target attitude angle at each sampling time, and the corresponding electromagnetic calculation results. Finally, the Gaussian white noise is superimposed with the theoretical radar echo signal to obtain the radar observation echo signal, from which the HRRP sequence of the target under low data rate and high repetition frequency is obtained.

[0070] As shown in Figure 2 , according to the flight trajectory of the ballistic missile simulated by STK, the target is launched at 0 seconds and flies to the radar observation section in the range of 540 seconds to 820 seconds, and the observation line-of-sight angle of the radar in this interval is in the range of [55°-85°].

[0071] According to practical experience, the precession angle of the warhead is generally small due to attitude control, and the precession axis is often the reentry direction. On the contrary, the precession angle of the decoy is relatively large, and the debris usually shows a tumbling motion. Therefore, according to the motion characteristics of the ballistic target, eight simulated targets with different sizes and different micro-motion parameters are set as four categories of warhead, heavy decoy, light decoy and debris, and the specific parameters are shown in Table 1.

[0072] Table 1 Micro-motion parameters of simulated targets

[0073]

[0074] The target micro-motion parameters and the radar line-of-sight angle obtained by STK simulation are substituted into the attitude angle formula to obtain the target attitude angle at each sampling time. The radar scattering amplitude and phase obtained by FEKO simulation are looked up using the target attitude angle.

[0075] The missile trajectory simulated by STK and the target attitude angle obtained at each sampling time are combined with the corresponding electromagnetic calculation results to obtain a wideband echo signal. Finally, the theoretical radar echo signal is superimposed with Gaussian white noise to obtain the radar observation echo signal. The target flight time in the observation area is 280 seconds, and the echo signal of each radar is sliced to form a signal sample within this range. For each target, 224 signal windows are randomly selected as the training data set, and the remaining 56 signal windows are used for the test data set.

[0076] Step three, taking the target one-dimensional range image sequence as the research object, the image projection method is used to extract the precession frequency of the target low data rate HRRP sequence;

[0077] Specifically, assuming that the wideband radar transmits frequency stepped signals, when the PRF value is too low, the time-frequency curve is blurred, the periodicity of the scattering center point in the HRRP sequence is used for time-frequency analysis, and the projection method is used to realize the vertical projection of the energy strength, and the one-dimensional feature distribution is completed; the micro-motion frequency of the scattering center is extracted, and the mean value of the micro-motion frequencies of multiple scattering centers is taken as the precession frequency of the target.

[0078] Taking the cone-cylinder model of Figure 1 as the experimental object for analysis, assuming that the wideband radar transmits frequency stepped signals, the radar center frequency f0 is set to 9.5 GHz, the frequency step Δf is set to 15.625 MHz, and the frequency stepping number N is set to 64. During the movement of the target, when the radar line-of-sight angle is 50°, the radar pulse repetition frequency (PRF) is set to 500 Hz, 200 Hz, 50 Hz and 10 Hz, respectively. Figure 3 The radar echo HRRP sequence is shown in Figure 3 .

[0079] As shown in Figure 3 , it can be seen that under high PRF (500 Hz), the time-frequency curve in the time-frequency diagram has obvious sinusoidal oscillation, and when the PRF is 200 Hz and 50 Hz, the time-frequency curve characteristics are weakened, but the time-frequency curve of the HRRP sequence generated by the echo still has obvious periodic characteristics. At low frequency 10 Hz, the time-frequency diagram has serious frequency domain blurring and overlapping phenomenon, and the curve characteristics cannot be obtained intuitively. Therefore, from Figure 3The precession characteristics of the target can be analyzed from the time-frequency graph under different PRF, which can cause the time-frequency curve of each scattering point to present a periodic form similar to a sine function. However, this intuitive periodicity is only applicable to high PRF. When the PRF value is too low, the time-frequency curve will appear blurred in the frequency domain. However, by observing the time-frequency distribution graph, it can be found that the energy strength of the strong scattering center will periodically change in time. Based on this characteristic, the energy strength distribution characteristics in the time-frequency graph can be changed into one-dimensional characteristics by vertical projection.

[0080] The HRRP sequence is interpolated in the slow time domain, and the sampling rate after interpolation is 500 Hz. The strong scattering unit is extracted and STFT processing is performed to obtain a time-frequency graph. The time-frequency and projection graphs before and after interpolation are shown in Figure 4 .

[0081] As can be seen from the vertical projection graph in Figure 4 , compared with the graph before interpolation Figure 4 (a), the amplitude strength of the scattering points in the graph after interpolation Figure 4 (b) presents a more obvious and fine sinusoidal periodic change in the time axis. As shown in the figure, when the time window length is 4 seconds, there are 8 peak points in the vertical projection graph, so the precession frequency is about 2 Hz.

[0082] In order to more accurately obtain the relationship between the frequency and the amplitude value, the vertical projection sequence is subjected to fast Fourier transform to convert from the time domain to the frequency domain, so as to obtain the amplitude characteristics of the waveform under the frequency. The frequency value corresponding to the amplitude peak value is taken as the final estimation result. The amplitude-frequency graph of the vertical projection sequence is shown in Figure 5 , and the frequency at the peak value thereof is obtained as 2.0508 Hz, which has a small error with the true value 2 Hz. Thus, the micro-motion frequency of the scattering center is extracted, and the frequency is the precession frequency of the target.

[0083] The image projection method is used to extract the precession frequency of the target low-data-rate HRRP sequence, and the specific algorithm implementation steps are as follows:

[0084] Step 3.1, first, the micro-motion period of the received N p frame target HRRP is extracted, and a one-dimensional image data matrix to be processed is established as follows:

[0085]

[0086] Wherein, N s represents the number of distance units in each range image, and N p represents the number of received target HRRP frames.

[0087] Step 3.2, the N pThe HRRP sequence is zero-padded in the slow time domain, assuming the original HRRP sequence has a sampling rate of f. s The interpolated sampling rate is f d The interpolated matrix is And the following relationships exist:

[0088] f d =Mf s

[0089]

[0090] Where M is the number of zero-padding interpolations, The interpolated matrix (n = MN) p ).

[0091] Step 3.3, for Incoherent accumulation is performed on each distance cell to obtain Then through y r Perform constant false alarm rate (CFAR) detection and extract the N value of the target HRRP. sk A strong scattering center location.

[0092] Step 3.4, the formula for the vertical projection of the time-frequency graph is:

[0093]

[0094] t is the time series length of the time-frequency diagram; S f (t,ω) represents the pair of... N in sk The time-frequency distribution map of the scattering points is obtained by sequentially performing Short Time Fourier Transform (STFT) processing on the strong scattering center elements, Y. d It represents the amplitude after time-frequency projection.

[0095] Step 3.5, for Y d Performing an FFT transform yields the spectrum F of the time-frequency curve. Taking the peak value in the frequency domain from F gives the precession frequency at the current scattering point. It is expressed as follows:

[0096] F = FFT(Y) d )

[0097]

[0098] Where F represents the spectrum of the estimated time-frequency curve, This is an estimated value for the precession frequency;

[0099] Step 3.6: Assume that N is extracted from the HRRP sequence. ska strong scattering center unit, repeating steps 3.4-3.5 for each strong scattering center unit to obtain N sk precession frequency estimates, averaging them to obtain a final frequency estimate.

[0100] Step four: extracting target structure features, entropy value features, and periodicity features from the target low-data-rate HRRP sequence;

[0101] Because the light and heavy decoys and warheads have similar precession characteristics, multiple target features need to be extracted for joint identification to improve the target recognition accuracy in the low-data-rate HRRP sequence. Therefore, in addition to the precession frequency feature extraction in step two, target structure features, entropy value features, and periodicity features are extracted from the low-data-rate HRRP sequence.

[0102] The target structure features specifically include the number of scattering points, skewness, target length, SVD, and irregularity, and the periodicity features include the change period of the target length and the periodic change of the amplitude and echo power.

[0103] The detailed calculation method is shown in Table 2:

[0104] Table 2 Radar Feature Table

[0105]

[0106]

[0107] Step five: fusing the features obtained in steps three and four into a long vector using a splicing method, screening and evaluating the features based on feature importance using the Random Forest algorithm, and inputting them into the classifier for classification training to obtain the class of the target to be identified.

[0108] Through feature importance analysis of the HRRP sample test data, the data are input into the classifier for classification and recognition according to the training results, and the final output result is obtained.

[0109] The specific operation steps of step five are as follows:

[0110] Step 5.1 selecting a suitable feature subset according to the contribution of different features to each decision tree in the data forest;

[0111] Step 5.2 sequentially sorting the feature importance according to the importance measure of each feature;

[0112] The sorting results from high to low are: micro-motion frequency, number of scattering points, target length, skewness, irregularity, target length period, SVD, entropy value, length change amplitude, and echo power;

[0113] Step 5.3 performs a traversal search, and in each iteration, a feature with low importance is deleted from the feature subset;

[0114] Step 5.4 performs screening in sequence;

[0115] Step 5.5 finally selects the corresponding feature with the highest classification accuracy as the selection result;

[0116] Step 5.6 according to the importance ranking result of each feature, different target features are used to form 10 feature subsets to identify the warhead target; and finally the target recognition accuracy is improved.

[0117] The application analyzes the cone-cylinder model of the middle trajectory, and studies the extraction of target micro-motion features and structural features by using the low data rate HRRP sequence in combination with simulation data. The target micro-motion features are extracted by using the periodic characteristics of the scattering center points in the HRRP sequence, performing time-frequency analysis, and realizing one-dimensional feature distribution of energy strength by using the projection method. Then, the features are fused, the importance of the features is analyzed, the target is classified and recognized by using the feature classifier, and the final result is obtained. The experimental results show that the method solves the problems of periodic ambiguity of the time-frequency curve caused by the too low original sampling rate of the HRRP and the low target recognition accuracy caused by the single feature by using the image projection method and the multi-feature fusion technology under the low data rate. Through multiple Monte Carlo tests and method comparison, the precession frequency of the middle target can be accurately estimated in the low PRF range of 10Hz to 100Hz, and the result has good stability. After the target micro-motion features and various target structural features are fused and classified by using the feature classifier, the purpose of improving the target recognition accuracy is achieved.

[0118] The cone-cylinder model of Figure 1 is taken as the experimental object for analysis, a wideband radar transmitting frequency stepping signal is assumed, the radar center frequency f0 is set to 9.5GHz, the frequency step Δf is set to 15.625MHz, and the frequency stepping number N is set to 64. In the process of target motion, when the radar line of sight angle is 50°, the echo statistical window length is 4 seconds, the PRF is 10-100Hz, and the interval is 1Hz, the performance of the method is compared with the method of generalized Radon used in the comparative example (Zhu Yupeng, Wang Hongqiang, Li Xiang, etc. Micro-motion feature extraction of spatial trajectory target based on one-dimensional range profile sequence [J]. Journal of Spacecraft Technology, 2009.). Figure 6 、 7 The estimated average value and mean square error value obtained after 50 Monte Carlo experiments are shown in

[0119] Figure 6The mean precession frequency estimated by the method of the present application and the comparative example at PRF values in the range of 10-100 Hz; Figure 6 It is shown that when the echo statistical window length is 4 seconds, the precession frequency estimated by the method of the present application at PRF values in the range of 10-100 Hz is 2 Hz and tends to be stable, while the precession frequency estimated by the comparative example method fluctuates greatly in this range, and fluctuates more obviously at lower PRF values in the range of 10-50 Hz, and from Figure 7 It can be seen from the precession frequency estimation mean square error curves at different echo statistical window lengths that the error value of the present algorithm is lower and more stable than that of the generalized Radon method. Therefore, considering the time cost and test effect comprehensively, we finally select PRF of 10 Hz to extract the precession frequency feature of the HRRP sequence. It can be obtained from the comparison of experimental results that the frequency value estimated by the generalized Radon transform method used in the comparative example (Zhu Yupeng, Wang Hongqiang, Li Xiang, et al. Micro-motion feature extraction of space ballistic target based on one-dimensional range profile sequence [J]. Journal of Spacecraft Technology, 2009) has a large deviation in the case of low data rate and multiple scattering points. The experiment proves that the method proposed in the present application has better estimation accuracy and stability in the case of low data rate and complex model. Therefore, the method of the present application has more advantages in estimating frequency at low PRF.

[0120] Based on the extraction of the precession frequency described above, in combination with various target structure features, according to the importance ranking of each feature, 10 feature subsets are formed by different target features to identify the warhead target, and the identification accuracy of each target under different feature level fusion methods is shown in Table 3. It can be seen from Table 3 that when only the micro-motion frequency feature is used, the identification accuracy is 68.33%, and the identification effect is poor. With the increase of the number of features in the feature subset, the identification accuracy of the target shows a gradually rising trend, and when the number of features reaches 6, the feature set is {micro-motion frequency, number of scattering points, target length, skewness, irregularity, target length period}, and the accuracy reaches 96% and tends to be stable.

[0121] Table 3 Identification accuracy of each target under different feature level fusion methods

[0122]

[0123]

Claims

1. A method for mid-course ballistic target identification based on low data rate (HRRP) sequences, characterized in that, Includes the following steps: Step 1: Analyze the target motion characteristics in the mid-course phase of the trajectory, establish the target precession model, and obtain the change law of the target's attitude angle over time and the target's HRRP; Step 2: Combine the missile trajectory simulated by STK, the target attitude angle at each sampling time, and the corresponding electromagnetic calculation results to obtain the broadband echo signal; finally, superimpose Gaussian white noise with the theoretical radar echo signal to obtain the radar observation echo signal, from which the target's HRRP sequence at low data rate is obtained; Step 3: Taking the target's one-dimensional range image sequence as the research object, the precession frequency of the target's low data rate HRRP sequence is extracted using the image projection method; Step 4: Extract target structural features, entropy features, and periodic features from the low data rate HRRP sequence of the target; Step 5: Combine the features obtained in Steps 3 and 4 into a long vector using a concatenation method. Use the RandomForest algorithm to filter and evaluate features based on their importance, and then feed them into a classifier for classification training to obtain the category of the target to be identified.

2. The method for mid-course ballistic target identification based on a low data rate (HRRP) sequence according to claim 1, characterized in that, When the target is a precessing cone-shaped warhead, the calculation methods for the target's attitude angle and HRRP in step one are as follows: 1) Establish a precession model, assuming the target centroid is at the center of mass. Establish a reference coordinate system for the origin. The target revolves around its own axis of symmetry. The spin angular velocity of rotation is set to The target revolves around the precession axis Rotational motion is called conical rotation, and the target conical rotation angular velocity is set as... ; and The included angle is This is called the precession angle; assuming the radar line-of-sight (RLOS) direction is in the plane, then... and The included angle For radar line-of-sight angle, radar line-of-sight RLOS and Angle between axes This is called the attitude angle; 2) Assume that at t=0, the spin axis is at... The initial azimuth angle of the plane is Then the attitude angle The formula for its change over time is: ； In the above formula, the radar line-of-sight angle Changes within one precession period are ignored, so Treat it as a fixed value; 3) The target's HRRP is obtained by performing an inverse Fourier transform on the target's frequency, expressed as the formula: ； in For frequency, At the speed of light, The number of scattering points on the target. and These represent the amplitude of the k-th scattering point and the distance between the k-th scattering point and the observation radar over a certain period of time, respectively. Represents a high-resolution range image of the target.

3. The method for mid-course ballistic target identification based on a low data rate (HRRP) sequence according to claim 1, characterized in that, The specific content of step three is as follows: 1) Assuming that the broadband radar transmits a frequency step signal, when the PRF value is too low, the time-frequency curve is blurred. Utilize the periodic characteristics of the scattering center point in the HRRP sequence to perform time-frequency analysis and use the projection method to vertically project the energy intensity to complete the one-dimensional feature distribution. 2) Extract the micro-motion frequency of the scattering center, and take the average of the micro-motion frequencies of multiple scattering centers as the precession frequency of the target.

4. The method for mid-course ballistic target identification based on a low data rate (HRRP) sequence according to claim 1, characterized in that, In step three, the precession frequency of the low data rate HRRP sequence of the target is extracted using the image projection method. The specific algorithm implementation steps are as follows: Step 3.1: First, process the received data... HRRP is used to extract the micro-motion period of the frame target, and the one-dimensional image data matrix to be processed is established as follows: ； In the matrix This represents the number of distance units within each distance image. This represents the number of target HRRP frames received; Step 3.2, for The HRRP sequence is zero-padded in the slow time domain, assuming the original HRRP sequence has a sampling rate of 100%. The interpolated sampling rate is The interpolated matrix is And they have the following relationship: ； ； Where M is the number of zero-padding interpolations, This is the interpolated matrix. ; Step 3.3, for Incoherent accumulation is performed on each distance cell to obtain ; and then through the Perform constant false alarm rate (CFAR) detection and extract the target HRRP. The location of a strong scattering center; Step 3.4, the formula for the vertical projection of the time-frequency graph is: ； The time series length of the time-frequency diagram; Representative to In The time-frequency distribution map of the scattering points is obtained by sequentially performing Short-Time Fourier Transform (STFT) processing on the strong scattering center elements. Represents the amplitude after time-frequency projection; Indicates the radar center frequency; Step 3.5, for Perform an FFT transform to obtain the spectrum of the time-frequency curve. And then By taking the peak value in the frequency domain, the precession frequency value at the current scattering point can be obtained. , It is expressed as follows: ； ； in, The spectrum representing the estimated time-frequency curve. This is an estimated value for the precession frequency; Step 3.6: Assuming that the following is extracted from the HRRP sequence... For each strong scattering central element, repeat steps 3.4-3.5 to obtain... The average of the estimated precession frequencies is calculated to obtain the final frequency estimate.

5. The method for mid-course ballistic target identification based on a low data rate HRRP sequence according to claim 1, characterized in that, In step four, the target structural features include the number of scattering points, skewness, target length, SVD, and irregularity; the periodic features include the period of change of the target length and the periodic change of the amplitude, and the echo power.

6. The method for mid-course ballistic target identification based on a low data rate (HRRP) sequence according to claim 5, characterized in that, The specific steps for step five are as follows: Step 5.1 Select a suitable subset of features based on their contribution to each decision tree in the data forest; Step 5.2 Sort the features according to their importance measures; the sorting results from high to low are: micro-motion frequency, number of scattering points, target length, skewness, irregularity, target length period, SVD, entropy value, length change amplitude, and echo power. Step 5.3 Perform a traversal search, removing a low-importance feature from the feature subset during each iteration; Step 5.4 Perform the filtering process sequentially; Step 5.5 Finally, select the feature with the highest classification accuracy as the selection result; Step 5.6 Based on the above ranking of the importance of each feature, the different target features are divided into 10 feature subsets for identification of the warhead target.

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