Fast Detection and Parameter Estimation Methods for Hypersonic Acceleration Targets in Broadband Radar

Abstract

This invention relates to a rapid detection and parameter estimation method for hypersonic acceleration targets using broadband radar, and addresses the issue of low detection accuracy in existing technologies for uniformly accelerating targets. This application utilizes Time Reversal Theory (TRT) to effectively separate different motion parameters, resulting in two matrices, O and E. Based on the TRT results, VPRT is then used to specifically search for velocity parameters using information from the velocity correlation matrix O, enabling accurate identification of the velocity characteristics of uniformly accelerating targets and thus enhancing the accuracy of uniformly accelerating target detection.

Description

Technical Field

[0001] This invention relates to the field of radar detection technology, specifically a method for rapid detection and parameter estimation of hypersonic acceleration targets using broadband radar. Background Technology

[0002] In the early days, radar range resolution was low. Therefore, within the coherent processing interval, it could be assumed that the target was located in a single range-resolved cell, and the echoes of its different pulses only differed in phase without envelope changes, i.e., there was no so-called "range movement." Based on this assumption, the earliest moving target detection (MTD) method was proposed. However, in practical applications, targets may also exhibit range movement.

[0003] To address the challenge of multi-pulse joint processing in cases of target range movement, the Hough Transform (HT) was initially proposed. This non-coherent accumulation method utilizes only the amplitude information of the target echo, neglecting phase information. Subsequently, the Keystone Transform (KT) was introduced as a coherent accumulation technique, simultaneously utilizing amplitude and phase information, effectively improving radar detection performance. However, KT requires complex interpolation calculations and suffers from Doppler ambiguity. To address this, the Radon-Fourier Transform (RFT), based on the Radon and Fourier transforms, was proposed. By jointly searching for the target's range and velocity parameters and performing coherent accumulation along the corresponding trajectory, RFT can effectively handle uniformly moving targets. Nevertheless, the performance of both KT and RFT is affected when the target's acceleration is non-zero. Therefore, existing technologies suffer from low detection accuracy for uniformly accelerating targets. Summary of the Invention

[0004] The purpose of this invention is to address the problem of low detection accuracy in existing technologies for uniformly accelerating targets by providing a method for rapid detection and parameter estimation of hypersonic acceleration targets using broadband radar.

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

[0006] A method for rapid detection and parameter estimation of hypersonic acceleration targets using broadband radar, comprising the following steps:

[0007] Step 1: Acquire multiple radar pulse echo sampling data, and construct a time-domain echo matrix Z using the radar pulse echo sampling data. The time-domain echo matrix Z is an MxN matrix, where M represents the number of pulses and N represents the number of sampling points per pulse.

[0008] Step 2: Obtain the target distance range, velocity range, and acceleration range, and divide the target distance range, velocity range, and acceleration value range into equal intervals. Sort the distance, velocity, and acceleration values ​​obtained from the equal intervals in ascending order.

[0009] Step 3: Perform a Fast Fourier Transform on each row of the time-domain echo matrix Z to convert the time-domain echo matrix Z into a frequency-domain echo matrix Z. f ;

[0010] Step 4: For the frequency domain echo matrix Z f Perform a time-reversal transformation to obtain the reference matrix.

[0011] Step 5: Based on the frequency domain echo matrix Z f and reference matrix Constructing a matrix sum matrix

[0012] in, Representation matrix The conjugate of , ⊙ denotes element-wise matrix multiplication, O denotes a matrix that depends only on velocity parameters, and E denotes a matrix that depends only on distance and acceleration parameters;

[0013] Step 6: Perform a Fast Fourier Transform on each column of matrix O to obtain matrix O1;

[0014] Step 7: Calculate the VPRT output for each velocity in the sorting based on matrix O1;

[0015] Step 8: Based on the results of Step 7, select the maximum value of the VPRT output and determine whether the maximum value exceeds the threshold. If it does, a target exists, and the maximum value is used as the target's velocity estimate. Continue to step 9; otherwise, if no target exists, the process ends.

[0016] Step 9: Use the target's velocity estimate Constructing the velocity matched filter matrix

[0017] Step 10: Using matrix E and matrix Construct matrix E1, which is represented as

[0018] Step 11: Based on matrix E1, obtain the DMT output for each distance in the distance sorting obtained in Step 2. The distance corresponding to the maximum DMT output is the estimated distance to the target.

[0019] Based on matrix E1, obtain the DMT output for each acceleration in the acceleration sorting obtained in step 2. The acceleration corresponding to the maximum DMT output is the estimated acceleration value of the target.

[0020] Furthermore, the time-domain echo matrix Z is expressed as:

[0021] Z = αS θ +N

[0022] Where α represents the target echo amplitude, S θ Let θ represent the target echo matrix, N represent the received noise matrix, and θ represent the target's motion parameters, θ = [r, v, a], where r represents the target's initial distance, v represents the target's velocity, and a represents the target's acceleration.

[0023] Furthermore, the frequency domain echo matrix Z f Represented as:

[0024] Z f =FFT r (Z)

[0025] Among them, FFT r (·) indicates that a fast Fourier transform is performed on each row of the matrix.

[0026] Furthermore, the reference matrix Represented as:

[0027]

[0028] Here, flip means to flip the matrix vertically.

[0029] Furthermore, the matrix O1 is represented as:

[0030] O1 = FFT c (O)

[0031] Among them, FFT c (·) indicates that a fast Fourier transform is performed on each column of the matrix.

[0032] Furthermore, the VPRT output is represented as:

[0033]

[0034] ρ xΔv =1-λ xΔv

[0035] Where Δf represents the fast time frequency interval, Δf = f s / N,f sThe sampling frequency is represented by N, the number of sampling points per pulse is represented by Δv, the velocity search interval is represented by x, and the velocity value is represented by u. xΔv l xΔv , λ xΔv and ρ xΔv f represents an intermediate variable. c B represents the radar carrier frequency, C represents the radar bandwidth, [·] represents the speed of light, and |·| represents the modulus of the complex number. n,x The subscript x represents the x-th velocity value, and n represents the n-th fast time frequency, corresponding to the n-th column of matrix O1. Different columns of matrix O1 correspond to different fast time frequencies. The fast time frequency corresponding to the n-th column is represented by f. n This indicates that the fast time frequencies corresponding to columns 1 to N are as follows:

[0036]

[0037] Different rows of matrix O1 correspond to different slow time frequencies, and the fast time frequency corresponding to the m-th row is represented by f. m This indicates that the slow time frequencies corresponding to rows 1 to M are as follows:

[0038]

[0039] Where M represents the number of pulses, f r Indicates the pulse repetition frequency;

[0040] Calculate the following linear equation based on the x-th velocity value:

[0041]

[0042] in, These represent the slow time frequency and the fast time frequency on the trajectory, respectively;

[0043] o n,x The rules for determining the value are as follows:

[0044] make f n For the fast time frequency corresponding to the nth column of matrix O1, calculate... If with The closest slow time frequency is the m-th slow time frequency f. m Then o n,x It equals the element in the m-th row and n-th column of matrix O1, i.e., o n,x =O1(m,n), where O1(m,n) represents the element in the m-th row and n-th column of matrix O1.

[0045] Furthermore, the velocity estimate of the target Represented as:

[0046]

[0047] in, This represents an estimated value of x.

[0048] Furthermore, the velocity matched filter matrix Represented as:

[0049]

[0050] in, Representation matrix The element in the m-th row and n-th column, rect(·) is a rectangular window function, exp(·) is an exponential function, t m T represents the slow time corresponding to the m-th pulse. c Indicates the radar coherent processing time. The imaginary unit is represented by π, the mathematical constant pi is represented by π, and K is represented by the radar frequency modulation. and Indicates an intermediate variable.

[0051] Furthermore, the DMT output is obtained through the following steps:

[0052] Acceleration DMT output:

[0053] Step 1.1: In the acceleration sorting, select the first acceleration;

[0054] Step 1.2: Based on the selected acceleration, calculate the matching acceleration output of each column of matrix E1, and denote the result as DMT(y,n), where y represents the y-th acceleration and n represents the n-th column of matrix E1;

[0055] Step 1.3: Repeat steps 1.1 and 1.2 until all accelerations in the acceleration sort are obtained, corresponding to DMT(y,n);

[0056] DMT(y,n) is represented as:

[0057]

[0058] Among them, e n ∈C M×1 The nth column of matrix E1 represents the number of pulses, Δa represents the acceleration search interval, and u y,n Indicates intermediate variables;

[0059] Distance to DMT output:

[0060] Step 2.1: In the distance sorting, select the first distance;

[0061] Step 2.2: Based on the selected distance, calculate the matching distance output for each column of matrix E1, and denote the result as DMT(y,z), where y represents the y-th distance and z represents the z-th distance parameter value;

[0062] Step 2.3: Repeat steps 2.1 and 2.2 until all distances in the distance sort are obtained for the corresponding DMT(y,z);

[0063] DMT(y,z) is represented as:

[0064] DMT(y,z)=d y v y,z

[0065] Where, d y Let v represent the y-th row of matrix DMT(y,n). y,z (n) = exp(j2πnΔf(zΔr)), where Δr represents the distance search interval, v y,z Indicates an intermediate variable.

[0066] Furthermore, the distance estimate of the target and target acceleration estimates Represented as:

[0067]

[0068]

[0069] The beneficial effects of this invention are:

[0070] This application effectively separates different motion parameters by performing a time-reversal operation on the echo signal using TRT, resulting in the separation of two matrices, O and E. Then, based on the results of TRT, VPRT is used to utilize the information of the velocity correlation matrix O to perform a targeted search for velocity parameters, which can accurately identify the velocity characteristics of uniformly accelerated targets, thereby enhancing the accuracy of uniformly accelerated target detection. Attached Figure Description

[0071] Figure 1 This is the overall flowchart of this application;

[0072] Figure 2 This is a schematic diagram of matrix O1;

[0073] Figure 3 This is a schematic diagram of VPRT output;

[0074] Figure 4 This is a schematic diagram of DMT output;

[0075] Figure 5 This is a schematic diagram of the DMT output along the distance profile.

[0076] Figure 6 This is a schematic diagram of the DMT output along the acceleration profile. Detailed Implementation

[0077] It should be noted that, where there is no conflict, the various embodiments disclosed in this application can be combined with each other.

[0078] Specific Implementation Method 1: The broadband radar hypersonic acceleration target rapid detection and parameter estimation method described in this implementation method includes the following steps:

[0079] Step 1: Acquire multiple radar pulse echo sampling data, and construct a time-domain echo matrix Z using the radar pulse echo sampling data. The time-domain echo matrix Z is an MxN matrix, where M represents the number of pulses and N represents the number of sampling points per pulse.

[0080] Step 2: Obtain the target distance range, velocity range, and acceleration range, and divide the target distance range, velocity range, and acceleration value range into equal intervals. Sort the distance, velocity, and acceleration values ​​obtained from the equal intervals in ascending order.

[0081] Step 3: Perform a Fast Fourier Transform on each row of the time-domain echo matrix Z to convert the time-domain echo matrix Z into a frequency-domain echo matrix Z. f ;

[0082] Step 4: For the frequency domain echo matrix Z f Perform a time-reversal transformation to obtain the reference matrix.

[0083] Step 5: Based on the frequency domain echo matrix Z f and reference matrix Construct matrices O and E, where matrix O is represented as:

[0084]

[0085] Matrix E is represented as:

[0086]

[0087] in, Representation matrix The conjugate of , ⊙ denotes element-wise matrix multiplication, O denotes a matrix that depends only on velocity parameters, and E denotes a matrix that depends only on distance and acceleration parameters;

[0088] Step 6: Perform a Fast Fourier Transform on each column of matrix O to obtain matrix O1; as shown Figure 2 As shown.

[0089] Step 7: Calculate the VPRT output for each velocity in the sorted sequence based on matrix O1; for example... Figure 3 As shown.

[0090] Step 8: Based on the results of Step 7, select the maximum value of the VPRT output and determine whether the maximum value exceeds the threshold. If it does, a target exists, and the maximum value is used as the target's velocity estimate. Continue to step 9; otherwise, if no target exists, the process ends.

[0091] Step 9: Use the target's velocity estimate Constructing the velocity matched filter matrix

[0092] Step 10: Using matrix E and matrix Construct matrix E1, which is represented as

[0093] Step 11: Obtain the DMT output for each distance in the distance sorting obtained in Step 2 based on matrix E1. The maximum value of the DMT output is the estimated distance to the target. like Figure 4 , Figure 5 as well as Figure 6 As shown.

[0094] Step 12: Obtain the DMT output for each acceleration in the sorted matrix E1. The maximum value of the DMT output is the estimated acceleration of the target.

[0095] Step 1: Assuming the target is undergoing uniform acceleration motion, acquire time-domain sampling data of multiple radar pulse echoes. Each pulse echo sampling data is arranged as a row vector, and the echo data of different pulses are arranged as an echo matrix Z. The first row of the matrix represents the first pulse echo sampling data, and so on. Assume the discrete sampling data received by the radar is as follows:

[0096] Z = αS θ +N

[0097] Where α represents the target echo amplitude, S θ Let θ represent the target echo matrix, N represent the received noise matrix, θ = [r, v, a] represent the target's motion parameters, r represent the target's initial distance, v represent the target's velocity, and a represent the target's acceleration. The possible distance, velocity, and acceleration values ​​of the target are divided into equally spaced parameters, resulting in a series of different distance, velocity, and acceleration values. These values ​​are then arranged in ascending order, with the first value corresponding to the minimum distance, velocity, and acceleration value.

[0098] Step 2: Perform a Fast Fourier Transform on each row of the echo matrix to transform the time-domain echo matrix into a frequency-domain echo matrix Z. f This can be expressed as a formula:

[0099] Z f =FFT r (Z)

[0100] FFT r (·) indicates that a fast Fourier transform is performed on each row of the matrix.

[0101] Step 3: For matrix Z f Perform a time-reversal transform (TRT), which involves constructing a reference matrix based on the frequency domain echo matrix. It is the frequency domain echo matrix Z f Flip it up or down, that is The first row corresponds to the last pulse, and so on. This can be expressed by the formula:

[0102]

[0103] Here, flip means to flip the matrix vertically.

[0104] Step 4: Based on the frequency domain echo matrix Z f and reference matrix Calculate matrices O and E, expressed by the formula:

[0105]

[0106] in Representation matrix The conjugate of , ⊙ denotes element-wise matrix multiplication, O represents a matrix that depends only on velocity parameters, and E represents a matrix that depends only on distance and acceleration parameters. This step separates the target parameters, enabling individual parameter estimation and avoiding coupling.

[0107] Step 5: Perform a Fast Fourier Transform on each column of matrix O, and denote the result as matrix O1. This can be expressed by the formula:

[0108] O1 = FFT c (O)

[0109] FFT c (·) indicates that a fast Fourier transform is performed on each column of the matrix.

[0110] Step 6: Calculate the VPRT output for each velocity value based on matrix O1. This step consists of the following sub-steps:

[0111] (1) Select the first speed parameter value;

[0112] (2) Calculate the VPRT output of the selected speed parameter;

[0113] (3) Select the next speed parameter value in sequence and repeat step (2) to obtain the VPRT output of all parameter values;

[0114] The VPRT output for the x-th velocity value is represented as:

[0115]

[0116] Where Δf=f s / N represents the fast time frequency interval, f s This represents the sampling frequency, and N represents the number of sampling points per pulse. Δv represents the velocity search interval, and the search velocity v s It can be represented as v s =xΔv. f c Indicates the radar carrier frequency. ρ xΔv =1-λ xΔv B represents radar bandwidth, c represents the speed of light, and o n,x Represents the discrete trajectory corresponding to the search velocity The data above, where f m The m-th row represents the fast time frequency, the symbol [·] represents the rounding operation, and |·| represents the modulus of the complex number.

[0117] Step 7: Based on the results of Step 6, calculate the maximum value of the VPRT output, compare this maximum value with the threshold, and if it exceeds the threshold, the corresponding parameter point is identified as a target. Record this parameter value as the target's velocity estimate. Continue to step eight; otherwise, determine that the target does not exist and end the algorithm. The estimated target velocity is expressed as follows:

[0118]

[0119] in This represents the speed estimate. The existence of a target can be determined using the following formula:

[0120]

[0121] Where T represents the detection threshold.

[0122] Step 8: Estimate the velocity parameters based on Step 7. Constructing a matrix The formula is expressed as follows:

[0123]

[0124] in Representation matrix The element in the m-th row and n-th column, rect(·) is a rectangular window function, exp(·) is an exponential function, t m T represents the slow time corresponding to the m-th pulse. c Indicates the radar coherent processing time. The symbol represents the imaginary unit, π represents the mathematical constant pi, and K represents the radar frequency modulation.

[0125] Step 9: Based on matrix E from step 4 and matrix E from step 8 The matrix E1 is calculated using the following formula:

[0126]

[0127] Step 10: Calculate the DMT output for each distance and acceleration value based on matrix E1. This step consists of the following sub-steps:

[0128] Matching acceleration steps:

[0129] (1-1) Select the first acceleration parameter value;

[0130] (1-2) Based on the selected velocity parameter values, calculate the matching acceleration output of different columns of matrix E1, and denote the result as DMT(y,n), where y represents the y-th acceleration parameter value, here y=1, and n represents the n-th column of matrix E1;

[0131] (1-3) Select the next acceleration parameter value in sequence and repeat step (1-2) until all acceleration parameter values ​​are calculated.

[0132] DMT(y,n) can be expressed by the following formula:

[0133]

[0134] Where e n ∈C M×1 Let M represent the nth column of matrix E1, and M represent the number of pulses. Δa is the acceleration search interval, and the search acceleration can be expressed as a. s =yΔa.

[0135] Matching distance steps:

[0136] (2-1) Select the first distance parameter value;

[0137] (2-2) Based on the selected distance parameter values, calculate the matching distance output of different rows of DMT(y,n) and record the result as DMT(y,z), where y represents the y-th row of DMT(y,n) and corresponds to the y acceleration parameter values, and z represents the z-th distance parameter value, where z = 1;

[0138] (2-3) Select the next distance parameter value in sequence and repeat step (2-2) until all distance parameter values ​​are calculated.

[0139] DMT(y,z) is expressed by the following formula:

[0140] DMT(y,z)=d y v y,z

[0141] Where d y Let v represent the y-th row of matrix DMT(y,n). y,z (n) = exp(j2πnΔf(zΔr)), where Δr represents the distance search interval, and the search distance can be expressed as r s =zΔr.

[0142] Step 11: Based on the results of step 10, calculate the maximum value of the DMT(y,z) output, and use the parameter values ​​corresponding to the maximum value to estimate the target's distance and acceleration. This can be expressed by the formula:

[0143]

[0144] in This represents the estimated acceleration value. This represents the distance estimate.

[0145] Where Δf represents the fast time frequency interval, Δf = f s / N,f s The sampling frequency is represented by N, the number of sampling points per pulse is represented by Δv, the velocity search interval is represented by x, and the velocity value is represented by u. xΔv l xΔv , λ xΔv and ρ xΔv f is an intermediate variable. c B represents the radar carrier frequency, C represents the radar bandwidth, [·] represents the speed of light, and |·| represents the modulus of the complex number.

[0146] o n,x The subscript 'x' represents the x-th velocity value, and 'n' represents the n-th fast time frequency, corresponding to the n-th column of matrix O1. Different columns of matrix O1 correspond to different fast time frequencies, and the fast time frequency corresponding to the n-th column is denoted by 'f'. n This indicates that the fast time frequencies corresponding to columns 1 to N are as follows:

[0147]

[0148] Different rows of matrix O1 correspond to different slow time frequencies, and the fast time frequency corresponding to the nth column is represented by f. m This indicates that the slow time frequencies corresponding to rows 1 to M are as follows:

[0149]

[0150] Where M represents the number of pulses, f r This indicates the pulse repetition frequency.

[0151] Calculate the following linear equation based on the x-th velocity value:

[0152]

[0153] in These represent the slow time frequency and the fast time frequency on the trajectory, respectively. n,x The rules for determining the value of are as follows: Let f n For the fast time frequency corresponding to the nth column of matrix O1, calculate... Judgment and The closest slow time frequency, let's assume it's the m-th slow time frequency f. m Then o n,x It equals the element in the m-th row and n-th column of matrix O1, i.e., o n,x =O1(m,n), where O1(m,n) represents the element in the m-th row and n-th column of matrix O1.

[0154] Estimating target range and acceleration using DMT (Dual Matched Transform of Range and Acceleration): After velocity estimation, this step focuses on accurate estimation of range and acceleration. DMT consists of two sub-steps:

[0155] (a) Matching Acceleration (MA): First, the acceleration of the target is matched to ensure the accuracy of the acceleration parameters.

[0156] (b) Matching distance (MR): Subsequently, the distance parameters of the target are matched to achieve high-precision distance estimation.

[0157] This step-by-step processing method not only ensures the independence and accuracy of each parameter estimate, effectively solving the problems of high computational complexity and difficulty in real-time processing in traditional methods, but also improves computational efficiency by precisely processing different types of parameters in stages.

[0158] It should be noted that the specific embodiments are merely explanations and illustrations of the technical solution of the present invention and should not be used to limit the scope of protection. Any modifications made in accordance with the claims and specification of the present invention that are only partial should still fall within the protection scope of the present invention.

Claims

1. A method for rapid detection and parameter estimation of hypersonic acceleration targets using broadband radar, characterized in that... Includes the following steps: Step 1: Acquire multiple radar pulse echo sampling data and construct a time-domain echo matrix using the radar pulse echo sampling data. The time-domain echo matrix It is an M x N matrix, where M represents the number of pulses and N represents the number of sampling points per pulse; Step 2: Obtain the target distance range, velocity range, and acceleration range, and divide the target distance range, velocity range, and acceleration value range into equal intervals. Sort the distance, velocity, and acceleration values ​​obtained from the equal intervals in ascending order. Step 3: Analyze the time-domain echo matrix Perform a Fast Fourier Transform on each row to transform the time-domain echo matrix. Convert to frequency domain echo matrix ; Step 4: Perform frequency domain echo matrix analysis. Perform a time-reversal transformation to obtain the reference matrix. ; Step 5: Based on the frequency domain echo matrix and reference matrix Constructing a matrix sum matrix , in, Representation matrix conjugate, This represents element-wise matrix multiplication. This represents a matrix that depends only on the velocity parameter. This represents a matrix that depends only on the distance and acceleration parameters; Step 6: For the matrix Perform a Fast Fourier Transform on each column to obtain a matrix. ; Step 7: Based on the matrix Calculate the VPRT output for each velocity in the sorting; Step 8: Based on the results of Step 7, select the maximum value of the VPRT output and determine whether the maximum value exceeds the threshold. If it does, a target exists, and the maximum value is used as the target's velocity estimate. Continue to step 9; otherwise, if no target is found, the process ends. Step 9: Use the target's velocity estimate Construct the velocity matched filter matrix ; Step 10: Using the matrix sum matrix Constructing a matrix ,matrix Represented as ; Step 11: Based on the matrix Obtain the DMT output for each distance in the distance sorting obtained in step 2. The distance corresponding to the maximum DMT output is the estimated distance to the target. ; According to the matrix Obtain the DMT output for each acceleration from the acceleration sorting obtained in step 2. The acceleration corresponding to the maximum DMT output is the estimated acceleration value of the target. ; Where DMT is a dual-matched transformation of distance and acceleration; The VPRT output is represented as follows: in, Indicates a fast time frequency interval. , Indicates the sampling frequency. This indicates the number of sampling points for each pulse. Indicates the speed search interval. Indicates the first A speed value, , , as well as Indicates intermediate variables. Indicates the radar carrier frequency. Indicates radar bandwidth. Represents the speed of light. This indicates the rounding operation. Represents the modulus of a complex number. Subscript Indicates the first A speed value, Indicates the first Each fast time frequency corresponds to a matrix. The Columns, matrices Different columns correspond to different fast time frequencies, the first The corresponding fast time frequency of the column is used This indicates that from column 1 to column 2... The corresponding fast time frequencies for each column are: matrix Different rows correspond to different slow time frequencies, the first The corresponding fast time frequency of the row This indicates that from the first row to the... The corresponding slow time frequencies for each row are: in, Indicates the number of pulses. Indicates the pulse repetition frequency; According to the The equation for the following straight line is calculated based on the given velocity values: in, , These represent the slow time frequency and the fast time frequency on the trajectory, respectively; The rules for determining the value are as follows: make , For matrix No. Calculate the fast time frequency corresponding to the column. If with The closest slow time frequency is the th slow time frequency ,but equal matrix The Line 1 The elements of the column, i.e. , Representation matrix The Line 1 The elements of the column.

2. The method for rapid detection and parameter estimation of broadband radar hypersonic acceleration targets according to claim 1, characterized in that... The time-domain echo matrix Represented as: in, Indicates the target echo amplitude. Represents the target echo matrix. This represents the received noise matrix. Represents the motion parameters of the target. , Indicates the initial distance to the target. Indicates the speed of the target. This indicates the target's acceleration.

3. The method for rapid detection and parameter estimation of broadband radar hypersonic acceleration targets according to claim 2, characterized in that... The frequency domain echo matrix Represented as: in, This indicates that a Fast Fourier Transform is performed on each row of the matrix.

4. The method for rapid detection and parameter estimation of broadband radar hypersonic acceleration targets according to claim 3, characterized in that... The reference matrix Represented as: in, This indicates that the matrix is ​​flipped vertically.

5. The method for rapid detection and parameter estimation of broadband radar hypersonic acceleration targets according to claim 4, characterized in that... The matrix Represented as: in, This indicates that a Fast Fourier Transform is performed on each column of the matrix.

6. The method for rapid detection and parameter estimation of broadband radar hypersonic acceleration targets according to claim 5, characterized in that... The velocity estimate of the target Represented as: in, express The estimated value.

7. The method for rapid detection and parameter estimation of broadband radar hypersonic acceleration targets according to claim 6, characterized in that... The velocity matching filter matrix Represented as: in, Representation matrix No. Okay, number Column elements, For rectangular window functions, It is an exponential function. Indicates the first The slow time corresponding to each pulse Indicates the radar coherent processing time. Represents the imaginary unit. Represents pi (π). Indicates radar frequency modulation. , , and Indicates an intermediate variable.

8. The method for rapid detection and parameter estimation of broadband radar hypersonic acceleration targets according to claim 7, characterized in that... The DMT output is obtained through the following steps: Acceleration DMT output: Step 1.1: In the acceleration sorting, select the first acceleration; Step 1.2: Calculate the matrix based on the selected acceleration. The matched acceleration output for each column is denoted as . ,in Indicates the first An acceleration, Representation matrix No. List; Step 1.3: Repeat steps 1.1 and 1.2 until all accelerations in the acceleration sort are obtained. ; Represented as: in, Representation matrix The List, Indicates the number of pulses. Indicates the acceleration search interval. Indicates intermediate variables; Distance to DMT output: Step 2.1: In the distance sorting, select the first distance; Step 2.2: Calculate the matrix based on the selected distance. The matching distance for each column is output, and this result is denoted as... ,in Indicates the first A distance, Indicates the first One distance parameter value; Step 2.3: Repeat steps 2.1 and 2.2 until all distances corresponding to the distances in the distance sort are obtained. ; Represented as: in, Representation matrix The OK, , Indicates the distance to the search interval. Indicates an intermediate variable.

9. The method for rapid detection and parameter estimation of broadband radar hypersonic acceleration targets according to claim 8, characterized in that... The distance estimate of the target and target acceleration estimates Represented as: 。

Images