Hypersonic maneuvering target robust detection method and system based on short-time TRT-VRFT

Abstract

The invention discloses a hypersonic maneuvering target robust detection method and system based on short-time TRT-VRFT, relates to the technical field of radar detection, and aims to solve the problem of low detection accuracy of a complex moving target in the existing method. According to the technical scheme of the invention, short-time sliding window processing is carried out in a slow time, so that the influence of target maneuverability on detection performance is reduced, and the detection accuracy of the hypersonic maneuvering target is improved. Echo data in each sliding window is processed through TRT-VRFT, the TRT-VRFT can cope with the scale effect, range walk and Doppler walk problems caused by the hypersonic velocity and acceleration of a target at the same time, the search dimension is reduced through parameter separation, and compared with an existing traversal search method, the calculation complexity is lower, and the search efficiency is improved. And therefore, the calculation requirements are greatly reduced. And through short-time sliding window processing, adaptive change is carried out on the target motion parameters, so that the detection accuracy of the complex moving target is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of radar detection, and specifically to a robust detection method and system for hypersonic maneuvering targets based on short-time TRT-VRFT transform. Background Art

[0002] A radar detects by transmitting electromagnetic waves and receiving echoes from targets. Due to the relative motion between the target and the radar, the received echoes exhibit diversity. To enhance the detection performance of the radar, modern radar systems usually jointly process the echoes of multiple pulses, and the time required for this processing method is called the coherent processing interval. Compared with processing a single pulse alone, joint processing of multiple pulses can significantly improve the signal-to-noise ratio of the target echo, thereby increasing the probability of target detection and enhancing the overall detection ability of the radar.

[0003] Existing methods are all based on the narrowband assumption, that is, the displacement of the target within one pulse duration is less than the range resolution of the radar. However, for wideband radars or hypersonic targets, this assumption no longer holds, because the high speed of the target at this time will cause scale effects in the echo, making the above methods unable to achieve the best performance. To solve this problem, the Scale-Constrained Radon-Fourier Transform (SCRFT) and the Scale-Constrained Generalized Radon-Fourier Transform (SCGRFT) that consider scale effects have emerged. They construct a matched filter according to the search speed, thus overcoming the challenges brought by scale effects. However, existing methods all assume that the motion model parameters of the target remain fixed during the coherent processing time, and due to the complexity of target motion, this is usually not true for highly maneuvering targets or long accumulation times. Therefore, existing methods have the problem of low detection accuracy for targets with complex motions. Summary of the Invention

[0004] The purpose of the present invention is to provide a robust detection method and system for hypersonic maneuvering targets based on short-time TRT-VRFT transform, aiming at the problem that existing methods have low detection accuracy for targets with complex motions.

[0005] The technical solution adopted by the present invention to solve the above technical problems is as follows:

[0006] A robust detection method for hypersonic maneuvering targets based on short-time TRT-VRFT transform, comprising the following steps:

[0007] Step 1: Obtain multiple radar pulse echo sampling data, and construct a time-domain echo matrix Y using the radar pulse echo sampling data. The time-domain echo matrix Y is a matrix of PxN, where P represents the number of pulses and N represents the number of sampling points for each pulse;

[0008] Step 2: Obtain the target speed parameter range, then equally divide the target speed parameter range and sort the equal division results;

[0009] Step 3: Perform a fast Fourier transform on each row of the time-domain echo matrix Y to convert the time-domain echo matrix Y into a frequency-domain echo matrix Y f ;

[0010] Step 4: Set the width and step size of the short-time sliding window. The width of the short-time sliding window is the total number of pulses, and the step size of the short-time sliding window is the number of pulses between the starting pulses of adjacent sliding windows;

[0011] Step 5: Use the short-time sliding window to extract the frequency-domain echo matrix Y f to obtain the sub-frequency-domain echo matrix Z within each short-time sliding window f , and perform the TRT-VRFT transform on each sub-frequency-domain echo matrix Z f to obtain a complex vector;

[0012] The steps of the TRT-VRFT transform are as follows:

[0013] Step 5.1: Perform a time reversal transform on the sub-frequency-domain echo matrix Z f to obtain a reference matrix

[0014] Step 5.2: Use the sub-frequency-domain echo matrix Z f and the reference matrix to obtain the matrix O, where represents the conjugate of the matrix , ⊙ represents element-by-element multiplication of matrices, and O represents a matrix that depends only on the speed parameter;

[0015] Step 5.3: Perform an inverse fast Fourier transform on each row of the matrix O to obtain the matrix O1;

[0016] Step 5.4: Calculate the VRFT output for each speed in the sorting according to the matrix O1;

[0017] Step 5.5: Arrange the VRFT output for each speed into a one-dimensional vector, i.e., a complex vector;

[0018] Step 6: Stack the complex vectors obtained from different sub-frequency-domain echo matrices to obtain a complex matrix, and take the real part of the complex matrix to obtain a real part matrix;

[0019] Step 7: Based on the real part matrix, use the dynamic programming algorithm to accumulate the target energy to obtain an accumulation output;

[0020] Step 8: Compare the accumulated output with a preset threshold. If it exceeds the threshold, it is determined that the target exists; otherwise, it is determined that the target does not exist.

[0021] Further, the time-domain echo matrix Y is expressed as:

[0022] Y = αS + N

[0023] where α represents the target echo amplitude, S represents the target echo matrix, and N represents the received noise matrix.

[0024] Further, the frequency-domain echo matrix Y f is expressed as:

[0025] Y f = FFT r (Y)

[0026] where FFT r (·) represents performing a fast Fourier transform on each row of the matrix.

[0027] Further, the VPRT output is expressed as:

[0028]

[0029] where M represents the number of pulses contained in matrix O1, i.e., the number of rows of matrix O1, f c represents the radar carrier frequency, v s represents the selected speed parameter value, exp(·) represents the exponential function, π represents the pi, c represents the speed of light, represents the imaginary unit, o m represents an intermediate variable;

[0030] o m The value-taking rule of o is as follows: Matrix O1 has M rows and N columns. The fast time corresponding to each column is:

[0031]

[0032] where t s represents the sampling interval, N represents the number of columns of matrix O1, represents rounding to the nearest integer, and the slow time corresponding to the m-th row is t m = mT r where T r represents the pulse repetition period;

[0033] Obtain the column closest to the fast time and i.e., the n-th m column of matrix O1. o m is equal to the element in the m-th row and n-th m column of matrix O1, i.e., om = O1(m,n m ).

[0034] Furthermore, the accumulated output is expressed as:

[0035]

[0036] where J(k, j k ) represents the cost function of different speed values of the k-th short-time sliding window, 2 ≤ k ≤ K, K represents the number of short-time sliding windows, and j k represents the j k -th speed value of the k-th short-time sliding window, j k-1 represents the j k-1 -th speed value of the (k - 1)-th short-time sliding window, R(k, j k ) represents the real part of the VRFT output corresponding to the j k -th speed value of the k-th short-time sliding window, represents the set of values that can be transferred to j k , k-1 and represents the set of integers.

[0037] A robust detection system for hypersonic maneuvering targets based on short-time TRT-VRFT transformation, the system includes: a radar pulse echo sampling module, a parameter range division module, a TRT-VRFT transformation module, and a dynamic programming module;

[0038] The radar pulse echo sampling module is used to obtain multiple radar pulse echo sampling data, and construct a time-domain echo matrix Y using the radar pulse echo sampling data. The time-domain echo matrix Y is a PxN matrix, where P represents the number of pulses and N represents the number of sampling points per pulse;

[0039] The parameter range division module is used to obtain the target speed parameter range, then equally spaced divide the target speed parameter range, and sort the equally spaced division results;

[0040] The TRT-VRFT transformation module performs the following steps:

[0041] Step 1: Perform a fast Fourier transform on each row of the time-domain echo matrix Y to convert the time-domain echo matrix Y into a frequency-domain echo matrix Y f ;

[0042] Step 2: Set the width and step size of the short-time sliding window. The width of the short-time sliding window is the total number of pulses, and the step size of the short-time sliding window is the number of pulses between the start pulses of adjacent sliding windows;

[0043] Step 3: Use the short-time sliding window to process the frequency-domain echo matrix Y f ​Extract to obtain the sub-frequency domain echo matrix Z within each short-time sliding window f , and for each sub-frequency domain echo matrix Z f perform the TRT-VRFT transform to obtain a complex vector;

[0044] The steps of the TRT-VRFT transform are as follows:

[0045] Step 3.1: Perform a time reversal transform on the sub-frequency domain echo matrix Z f to obtain a reference matrix

[0046] Step 3.2: Use the sub-frequency domain echo matrix Z f and the reference matrix to obtain matrix O, where represents the conjugate of matrix , ⊙ represents element-wise multiplication of matrices, and O represents a matrix that depends only on the velocity parameter;

[0047] Step 3.3: Perform an inverse fast Fourier transform on each row of matrix O to obtain matrix O1;

[0048] Step 3.4: Calculate the VRFT output for each velocity in the sorting based on matrix O1;

[0049] Step 3.5: Arrange the VRFT output for each velocity as a one-dimensional vector, i.e., a complex vector;

[0050] Step 4: Stack the complex vectors obtained from different sub-frequency domain echo matrices to obtain a complex matrix, and take the real part of the complex matrix to obtain a real part matrix;

[0051] The dynamic programming module is based on the real part matrix and uses the dynamic programming algorithm to accumulate the target energy to obtain an accumulated output. Then, the accumulated output is compared with a pre-set threshold. If it exceeds the threshold, it is determined that the target exists; otherwise, it is determined that the target does not exist.

[0052] Furthermore, the time domain echo matrix Y is expressed as:

[0053] Y = αS + N

[0054] where α represents the target echo amplitude, S represents the target echo matrix, and N represents the received noise matrix.

[0055] Furthermore, the frequency domain echo matrix Y f is expressed as:

[0056] Y f = FFT r (Y)

[0057] Among them, FFT r (·) represents performing a fast Fourier transform on each row of the matrix.

[0058] Furthermore, the VPRT output is expressed as:

[0059]

[0060] Among them, M represents the number of pulses contained in matrix O1, that is, the number of rows of matrix O1, f c represents the radar carrier frequency, v s represents the selected speed parameter value, exp(·) represents the exponential function, π represents the pi, c represents the speed of light, represents the imaginary unit, o m represents an intermediate variable;

[0061] o m The value-taking rule of o is as follows: Matrix O1 has M rows and N columns, and the fast time corresponding to each column is:

[0062]

[0063] Among them, t s represents the sampling interval, N represents the number of columns of matrix O1, represents rounding to the nearest integer, and the slow time corresponding to the m-th row is t m = mT r , T r represents the pulse repetition period;

[0064] Obtain the column closest to the fast time and that is, the n m -th column of matrix O1, o m is equal to the element in the m-th row and n m -th column of matrix O1, that is, o m = O1(m, n m ).

[0065] Furthermore, the accumulation output is expressed as:

[0066]

[0067] Among them, J(k, j k ) represents the cost function of different speed values in the k-th short-time sliding window, 2 ≤ k ≤ K, K represents the number of short-time sliding windows, j k represents the j k -th speed value in the k-th short-time sliding window, j k-1 represents the j k-1 -th speed value in the (k - 1)-th short-time sliding window, R(k, j k ) represents the corresponding jk The real part of the VRFT output of a speed value, indicating a possible transfer to j k of j k-1 value set, indicating the set of integers.

[0068] The beneficial effects of the present invention are:

[0069] The technical solution of this application reduces the influence of target maneuverability on detection performance by performing short-time sliding window processing in slow time. For the echo data within each sliding window, the TRT-VRFT transform is used for processing. The TRT-VRFT transform can simultaneously address the scale effect, range walk, and Doppler walk problems caused by the target's hypersonic speed and acceleration, and reduces the search dimension through parameter separation, with a lower computational complexity compared to the existing exhaustive search method, thus greatly reducing the computational requirements. And through short-time sliding window processing, the target motion parameters are adaptively changed, thereby improving the accuracy of detecting complex moving targets. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 is a schematic diagram of the TRT-VRFT transform:

[0071] Figure 2 is a schematic diagram of the short-time TRT-VRFT transform;

[0072] Figure 3 is a schematic diagram of the real part of the short-time TRT-VRFT output of a uniformly accelerating target;

[0073] Figure 4 is a schematic diagram of the detection probability curve of the proposed method for a uniformly accelerating target;

[0074] Figure 5 is a schematic diagram of the real part of the short-time TRT-VRFT output of a uniformly varying accelerating target;

[0075] Figure 6 is a schematic diagram of the detection probability curve of the proposed method for a uniformly varying accelerating target;

[0076] Figure 7 is a schematic diagram of the real part of the short-time TRT-VRFT output of a target with sudden acceleration change;

[0077] Figure 8 is a schematic diagram of the detection probability curve of the proposed method for a target with sudden acceleration change. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0078] It should be noted that, without conflict, the various embodiments disclosed in this application can be combined with each other.

[0079] Embodiment 1: The robust detection method for hypersonic maneuvering targets based on short-time TRT-VRFT transformation described in this embodiment includes the following steps:

[0080] Step 1: Obtain multiple radar pulse echo sampling data, and use the radar pulse echo sampling data to construct a time-domain echo matrix Y. The time-domain echo matrix Y is a PxN matrix, where P represents the number of pulses and N represents the number of sampling points for each pulse.

[0081] Step 2: Obtain the target speed parameter range, then divide the target speed parameter range at equal intervals, and sort the equal-interval division results.

[0082] Step 3: Perform a fast Fourier transform on each row of the time-domain echo matrix Y to convert the time-domain echo matrix Y into a frequency-domain echo matrix Y f ;

[0083] Step 4: Set the width and step size of the short-time sliding window. The width of the short-time sliding window is the total number of pulses, and the step size of the short-time sliding window is the number of pulses between the starting pulses of adjacent sliding windows.

[0084] Step 5: Use the short-time sliding window to extract the frequency-domain echo matrix Y f to obtain a sub-frequency-domain echo matrix Z within each short-time sliding window f , and perform TRT-VRFT transformation on each sub-frequency-domain echo matrix Z f to obtain a complex vector.

[0085] The steps of the TRT-VRFT transformation are as follows:

[0086] Step 5.1: Perform a time reversal transformation on the sub-frequency-domain echo matrix Z f to obtain a reference matrix

[0087] Step 5.2: Use the sub-frequency-domain echo matrix Z f and the reference matrix to obtain a matrix O, where represents the conjugate of the matrix , ⊙ represents element-wise multiplication of matrices, and O represents a matrix that depends only on the speed parameter;

[0088] Step 5.3: Perform an inverse fast Fourier transform on each row of the matrix O to obtain a matrix O1;

[0089] Step 5.4: Calculate the VRFT output for each speed in the sorting according to the matrix O1;

[0090] Step 5.5: Arrange the VRFT output for each speed into a one-dimensional vector, that is, a complex vector;

[0091] Step 6: Stack the complex vectors obtained from different sub-frequency domain echo matrices to obtain a complex matrix, and take the real part of the complex matrix to obtain a real part matrix;

[0092] Step 7: Based on the real part matrix, use the dynamic programming algorithm to accumulate the target energy to obtain an accumulated output;

[0093] Step 8: Compare the accumulated output with a pre-set threshold. If it exceeds the threshold, determine that the target exists; otherwise, determine that the target does not exist.

[0094] Embodiment

[0095] Step 1: Obtain the time-domain sampling data of multiple radar pulse echoes. The sampling data of each pulse echo is arranged as a row vector, and the echo data of different pulses is arranged as an echo matrix Y. The first row of the matrix represents the sampling data of the first pulse echo, and so on. Assume the received data of the radar is:

[0096] Y = αS + N

[0097] where α represents the target echo amplitude, S represents the target echo matrix, and N represents the received noise matrix.

[0098] Step 2: Perform a fast Fourier transform on each row of the echo matrix to convert the time-domain echo matrix into a frequency-domain echo matrix Y f , which is expressed by the formula:

[0099] Y f = FFT r (Y)

[0100] where FFT r (·) represents performing a fast Fourier transform on each row of the matrix.

[0101] Step 3: Set the width and step size of each short-time sliding window. The width of the short-time sliding window is the corresponding number of pulses, and the step size of the short-time sliding window is the number of pulses between the starting pulses of adjacent sliding windows; equally divide the target speed parameter range to obtain a series of different speed values, arrange the speed values from small to large, and the first speed value corresponds to the minimum speed value.

[0102] Step 4: Extract the frequency-domain echo matrix within each short-time sliding window in sequence, and perform the TRT-VRFT transform on the frequency-domain echo matrix within each sliding window to output a one-dimensional vector that varies with the search speed value.

[0103] (4-1) Denote each sub-frequency domain echo matrix within the short-time sliding window as Z f ;

[0104] (4-2) For the matrix Z fPerform time reversal transformation (TRT), that is, construct a reference matrix according to the frequency-domain echo matrix It is to flip the frequency-domain echo matrix Z f vertically, that is the first row of corresponds to the last pulse in the sliding window, and so on;

[0105] (4-3) Calculate matrix O according to the sub-frequency-domain echo matrix Z f and the reference matrix where where represents the conjugate of matrix ⊙ represents element-by-element multiplication of matrices, and O represents a matrix that depends only on the velocity parameter. Through this step, the target velocity parameter can be separated, so as to realize the separate estimation of the parameter and reduce the problem dimension.

[0106] (4-4) Perform an inverse fast Fourier transform on each row of matrix O, and the result is denoted as matrix O1;

[0107] (4-5) Calculate the VRFT output of each velocity value according to matrix O1, which is specifically divided into the following sub-steps:

[0108] (4-5-1) Select the first velocity parameter value;

[0109] (4-5-2) Calculate the VRFT output of this velocity value according to the selected velocity parameter;

[0110] (4-5-3) Select the next velocity parameter value in turn, and repeat step (2) to obtain the VRFT output of all parameter values;

[0111] (4-6) Arrange the output of (4-5) into a one-dimensional vector that changes with velocity.

[0112] The calculation formula of the VRFT output in (4-5-2) is

[0113]

[0114] where M represents the number of pulses contained in matrix O1, that is, the number of rows of matrix O1, f c represents the radar carrier frequency, v s represents the selected velocity parameter value, exp(·) represents the exponential function, π represents the pi, c represents the speed of light, represents the imaginary unit.

[0115] o m The value-taking rule of is as follows: Assume that matrix O1 has M rows and N columns, and the fast time corresponding to each column is:

[0116]

[0117] where \(t\) s represents the sampling interval, \(N\) represents the number of columns of matrix \(O1\), represents rounding to the nearest integer. The slow time corresponding to the \(m\)-th row is \(t\) m \(= mT\) r , \(T\) r represents the pulse repetition period, calculate to determine the column closest to the corresponding fast time and assuming the closest column is the \(n\)-th m column of matrix \(O1\), then \(o\) m is equal to the element in the \(m\)-th row and \(n\)-th m column of matrix \(O1\), that is, \(o\) m \(= O1(m, n\) m ).

[0118] Step Five: Stack the one-dimensional vectors output by different sliding windows into a matrix.

[0119] Step Six: Take the real part of the matrix obtained in Step Five to get a real-value matrix denoted as \(R\).

[0120] Step Seven: Use the dynamic programming algorithm to accumulate the target energy for the matrix obtained in Step Six. The detailed description of the dynamic programming algorithm is as follows:

[0121] (7-1) Input: \(R\) and \(L\), where \(R\) represents the real-value matrix obtained in Step Six, represents a set of real matrices of size \(K\times V\), \(K\) represents the number of short-time sliding windows, \(V\) represents the number of velocity values obtained in Step Three, and \(L\) represents the maximum transfer range of the target velocity between adjacent short-time sliding windows.

[0122] (7-2) Dynamic programming processing procedure:

[0123] (7-2-1) Initialization: Calculate the cost function for different velocity values of the first short-time sliding window as follows:

[0124] \(J(1, j1) = R(1, j1)\)

[0125] where \(j1\) represents the \(j1\)-th velocity value of the first short-time sliding window, and \(R(1, j1)\) represents the real part of the TRT-VRFT output corresponding to the \(j1\)-th velocity value of the first short-time sliding window.

[0126] (7-2-2) Dynamic programming stage: For \(2\leq k\leq K\), calculate the cost function for different velocity values of the \(k\)-th short-time sliding window as follows:

[0127]

[0128] where \(j\) kDenote the j-th speed value of the k-th short-time sliding window k as, where j k-1 denotes the j-th speed value of the (k - 1)-th short-time sliding window, and R(k, j k-1 ) represents the real part of the output of TRT-VRFT corresponding to the j-th speed value of the k-th short-time sliding window, k k k k-1 denotes the set of j k that may transfer to j k-1 , denotes the set of integers.

[0129] (7 - 3) Output: According to the cost function J(K, j K ) calculated by dynamic programming, the final output of step seven is:

[0130]

[0131] Step eight: Compare the output result of step seven with a pre-set threshold. If it exceeds the threshold, it is determined that the target exists; otherwise, it is determined that the target does not exist. The threshold is obtained through Monte Carlo experiments and can be obtained by looking up a table in actual applications.

[0132] Verify the effectiveness of the algorithm using simulation experiments. Set the radar pulse width T P = 0.3 ms, the bandwidth B = 200 MHz, the sampling frequency f s = 240 MHz, the carrier frequency f c = 1.5 GHz, and the pulse repetition period T r = 1 ms. The data matrix Y received by the radar is modeled as:

[0133] Y = αS + N

[0134] where α represents the target echo amplitude, S represents the target echo matrix, N represents the received noise matrix, and each element of N is a Gaussian random variable with zero mean and variance σ 2 that is independently and identically distributed. Define the signal-to-noise ratio (SNR) as follows:

[0135]

[0136] Set the number of pulses to 400, the short-time sliding window width to 50 pulses, the sliding window step size to 25 pulses, and set the search speed interval to 0.5 m / s; set the dynamic programming input L = 6, corresponding to a maximum transfer speed of 3 m / s for adjacent sliding windows. Set the false alarm rate to 10 -2 , the threshold is obtained through 10 4 Monte Carlo simulation experiments, and the detection probability is calculated through 10 2 Monte Carlo simulation experiments.

[0137] Case 1: Uniformly accelerated moving target, the target distance equation is expressed as:

[0138]

[0139] In this case, the real part of the short-time TRT-VRFT output is given by Figure 3 and the detection probability curve is given by Figure 4 given.

[0140] Case 2: Uniformly variable accelerated moving target, the target distance equation is expressed as:

[0141]

[0142] In this case, the real part of the short-time TRT-VRFT output is given by Figure 5 and the detection probability curve is given by Figure 6 given.

[0143] Case 3: Target with sudden acceleration change, the target distance equation is expressed as:

[0144]

[0145] In this case, the real part of the short-time TRT-VRFT output is given by Figure 7 and the detection probability curve is given by Figure 8 given.

[0146] It can be seen from the experimental results in the three cases that the output of the short-time TRT-VRFT can reflect the instantaneous velocity change of the target, and the detection probability of the proposed method is almost unchanged in the three cases, verifying the robustness of the proposed method.

[0147] It should be noted that the specific implementation manners are only explanations and illustrations of the technical solutions of the present invention, and the scope of the patent protection cannot be limited thereby. Those that are only partial changes made according to the claims and the specification of the present invention should still fall within the protection scope of the present invention.

Claims

1. A robust detection method for hypersonic maneuvering targets based on short-time TRT-VRFT transformation, characterized in that It includes the following steps: Step 1: Obtain multiple radar pulse echo sampling data, and use the radar pulse echo sampling data to construct a time-domain echo matrix Y. The time-domain echo matrix Y is a matrix of PxN, where P represents the number of pulses and N represents the number of sampling points per pulse; Step 2: Obtain the target speed parameter range, then equally divide the target speed parameter range, and sort the equal division results; Step 3: Perform a fast Fourier transform on each row of the time-domain echo matrix Y to convert the time-domain echo matrix Y into a frequency-domain echo matrix Y f ; Step 4: Set the width and step size of the short-time sliding window. The short-time sliding window width is the total number of pulses, and the short-time sliding window step size is the number of pulses between the starting pulses of adjacent sliding windows; Step 5: Use a short-time sliding window to extract the frequency-domain echo matrix Y f to obtain the sub-frequency-domain echo matrix Z within each short-time sliding window f , and perform the TRT-VRFT transform on each sub-frequency-domain echo matrix Z f to obtain a complex vector; The steps of the TRT-VRFT transformation are as follows: Step 5.1: Perform a time reversal transformation on the sub-frequency domain echo matrix Z f to obtain a reference matrix Step 5.2: Utilize the sub-frequency domain echo matrix Z f and the reference matrix to obtain the matrix O, where denotes the conjugate of the matrix , ⊙ represents element-wise multiplication of matrices, and O represents a matrix that depends only on the velocity parameter; Step 5.3: Perform a fast inverse Fourier transform on each row of the matrix O to obtain the matrix O1; Step 5.4: Calculate the VRFT output of each speed in the sorting according to the matrix O1; Step 5.5: Arrange the VRFT output of each speed into a one-dimensional vector, that is, a complex vector; Step 6: Stack the complex vectors obtained from different sub-frequency domain echo matrices to obtain a complex matrix, and perform a real part processing on the complex matrix to obtain a real part matrix; Step 7: Based on the real part matrix, use the dynamic programming algorithm to accumulate the target energy to obtain an accumulation output; Step 8: Compare the accumulation output with a preset threshold. If it exceeds the threshold, it is determined that the target exists; otherwise, it is determined that the target does not exist.

2. The robust detection method for hypersonic maneuvering targets based on short-time TRT-VRFT transform according to claim 1, characterized in that The time-domain echo matrix Y is expressed as: Y = αS + N where α represents the target echo amplitude, S represents the target echo matrix, and N represents the received noise matrix.

3. The robust detection method for hypersonic maneuvering targets based on short-time TRT-VRFT transform according to claim 2, wherein The frequency-domain echo matrix Y f is expressed as: Y f = FFT r (Y) Among them, FFT r (·) represents performing a fast Fourier transform on each row of the matrix.

4. The robust detection method for hypersonic maneuvering targets based on short-time TRT-VRFT transform according to claim 3, characterized in that The VPRT output is expressed as: where M represents the number of pulses contained in matrix O1, i.e., the number of rows of matrix O1, f c represents the radar carrier frequency, v s represents the selected value of the velocity parameter, exp(·) represents the exponential function, π represents the pi, c represents the speed of light, represents the imaginary unit, o m represents the intermediate variable; o m The value-taking rule is as follows: The matrix O1 has M rows and N columns, and the fast time corresponding to each column is: Among them, t s represents the sampling interval, N represents the number of columns of matrix O1, represents rounding to the nearest integer for , the slow time corresponding to the m-th row is t m = mT r , and T r represents the pulse repetition period; Obtain the fast time and the closest column, i.e., the nth m column of matrix O1, o m is equal to the element at the mth row and nth m column of matrix O1, i.e., o m = O1(m, n m ).

5. The robust detection method for hypersonic maneuvering targets based on short-time TRT-VRFT transformation according to claim 4, characterized in that The accumulation output is expressed as: Among them, J(k, j k ) represents the cost function of different speed values in the k-th short-time sliding window, where 2 ≤ k ≤ K, and K represents the number of short-time sliding windows. j k represents the j k -th speed value in the k-th short-time sliding window, and j k-1 represents the j k-1 -th speed value in the (k - 1)-th short-time sliding window. R(k, j k ) represents the real part of the VRFT output corresponding to the j k -th speed value in the k-th short-time sliding window. represents the set of values that can be transferred to j k , and k-1 represents the set of integer values. represents the set of integers.

6. A robust detection system for hypersonic maneuvering targets based on short-time TRT-VRFT transformation, characterized in that The system includes: a radar pulse echo sampling module, a parameter range division module, a TRT-VRFT transformation module, and a dynamic programming module; The radar pulse echo sampling module is used to obtain multiple radar pulse echo sampling data, and use the radar pulse echo sampling data to construct a time-domain echo matrix Y. The time-domain echo matrix Y is a matrix of PxN, where P represents the number of pulses and N represents the number of sampling points per pulse; The parameter range division module is used to obtain the target speed parameter range, then equally divide the target speed parameter range, and sort the equal division results; The TRT-VRFT transformation module performs the following steps: Step 1: Perform a fast Fourier transform on each row of the time-domain echo matrix Y to convert the time-domain echo matrix Y into a frequency-domain echo matrix Y f ; Step: 2: Set the width and step size of the short-time sliding window. The short-time sliding window width is the total number of pulses, and the short-time sliding window step size is the number of pulses between the starting pulses of adjacent sliding windows; Step 3: Use a short-time sliding window to extract the frequency-domain echo matrix Y f to obtain the sub-frequency-domain echo matrix Z within each short-time sliding window f , and perform the TRT-VRFT transform on each sub-frequency-domain echo matrix Z f to obtain a complex vector; The steps of the TRT-VRFT transformation are as follows: Step 3.1: Perform a time reversal transformation on the sub-frequency domain echo matrix Z f to obtain a reference matrix Step 3.2: Utilize the sub-frequency domain echo matrix Z f and the reference matrix to obtain the matrix O, where denotes the conjugate of the matrix , ⊙ represents element-wise matrix multiplication, and O represents a matrix that depends only on the velocity parameter; Step 3.3: Perform a fast inverse Fourier transform on each row of the matrix O to obtain the matrix O1; Step 3.4: Calculate the VRFT output of each speed in the sorting according to the matrix O1; Step 3.5: Arrange the VRFT output of each speed into a one-dimensional vector, that is, a complex vector; Step 4: Stack the complex vectors obtained from different sub-frequency domain echo matrices to obtain a complex matrix, and perform a real part processing on the complex matrix to obtain a real part matrix; The dynamic programming module is based on the real part matrix, and uses the dynamic programming algorithm to accumulate the target energy to obtain an accumulated output. Then, the accumulated output is compared with a preset threshold. If it exceeds the threshold, it is determined that the target exists; otherwise, it is determined that the target does not exist.

7. The robust detection system for hypersonic maneuvering targets based on short-time TRT-VRFT transform according to claim 6, characterized in that The time-domain echo matrix Y is expressed as: Y = αS + N where α represents the target echo amplitude, S represents the target echo matrix, and N represents the received noise matrix.

8. The robust detection system for hypersonic maneuvering targets based on short-time TRT-VRFT transformation according to claim 7, characterized in that The frequency-domain echo matrix Y f is expressed as: Y f = FFT r (Y) Among them, FFT r (·) represents performing a fast Fourier transform on each row of the matrix.

9. The robust detection system for hypersonic maneuvering targets based on short-time TRT-VRFT transformation according to claim 8, characterized in that The VPRT output is expressed as: Among them, M represents the number of pulses contained in matrix O1, that is, the number of rows of matrix O1, f c represents the radar carrier frequency, v s represents the selected speed parameter value, exp(·) represents the exponential function, π represents the pi, c represents the speed of light, represents the imaginary unit, o m represents an intermediate variable; o m The value-taking rule is as follows: The matrix O1 has M rows and N columns, and the fast time corresponding to each column is: where t s represents the sampling interval, N represents the number of columns of matrix O1, represents rounding to the nearest integer, and the slow time corresponding to the m-th row is t m = mT r , where T r represents the pulse repetition period; Obtain the fast time and the closest column, that is, the nth m column of matrix O1, o m is equal to the element in the mth row and nth m column of matrix O1, that is, o m = O1(m, n m ).

10. The robust detection system for hypersonic maneuvering targets based on short-time TRT-VRFT transformation according to claim 9, characterized in that The accumulated output is expressed as: Among them, J(k, j k ) represents the cost function of different speed values in the k-th short-time sliding window, where 2 ≤ k ≤ K, K represents the number of short-time sliding windows, and j k represents the j k -th speed value in the k-th short-time sliding window, j k-1 represents the j k-1 -th speed value in the (k - 1)-th short-time sliding window, R(k, j k ) represents the real part of the VRFT output corresponding to the j k -th speed value in the k-th short-time sliding window, represents the set of values of j k that can be transferred to j k-1 , represents the set of integers.

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