A high-speed maneuvering target coherent accumulation method based on scale correction time reversal transform

Abstract

The application relates to a high-speed maneuvering target coherent accumulation method based on a scale correction time reversal transform, and relates to the technical field of radar signal processing.The application is used for solving the problem that the existing motion target coherent accumulation method cannot meet the real-time requirement of target identification due to low efficiency.The application comprises the following steps: obtaining the distance frequency dimension of echo signals; constructing a scale matching filter by using a speed search parameter, so as to obtain a pulse compression result; obtaining the time domain form of the pulse compression result after time reversal by using the pulse compression result; constructing a phase compensation function based on the speed search parameter and an acceleration search parameter; obtaining an inter-pulse accumulation result by using the phase compensation function and the time domain form of the pulse compression result after time reversal, so as to obtain a speed value, a distance value and an acceleration value; and obtaining an accurate estimation value of target jerk by using the speed value, the distance value and the acceleration value.The application is used for target coherent accumulation.

Description

Technical Field

[0001] This invention relates to the field of radar signal processing technology, and in particular to a method for coherent accumulation of high-speed maneuvering targets based on scale-corrected time-reversal transform. Background Technology

[0002] With the continuous development of stealth technology, hypersonic aircraft have begun to emerge in large numbers and are being applied in various fields. These aircraft targets have characteristics such as low signal-to-noise ratio, low signal-to-clutter ratio, high flight speed, and small radar cross-section (RCS), making the detection of such weak targets very difficult. Therefore, those skilled in the art employ coherent accumulation to improve the system's signal-to-noise ratio and enhance the ability to detect weak radar targets.

[0003] Traditional coherent accumulation methods heavily rely on the "stop-and-go" assumption. However, this assumption no longer holds when the target is maneuvering at high speed with significant intra-pulse motion, leading to significant scaling effects, manifested as envelope distortion and intra-pulse Doppler modulation. This disrupts pulse compression matching conditions and severely impacts long-term coherent accumulation performance. To improve coherent accumulation performance, this field has focused on compensating for the coherent accumulation results. Existing compensation methods typically employ high-dimensional joint search to simultaneously correct velocity, acceleration, and jerk. However, this computational complexity is extremely high, resulting in low efficiency of coherent accumulation and failing to meet the real-time requirements of target recognition. Summary of the Invention

[0004] The purpose of this invention is to address the problem that existing coherent accumulation methods for moving targets are inefficient and cannot meet the real-time requirements of target recognition. Therefore, this invention proposes a coherent accumulation method for high-speed moving targets based on scale-corrected time-reversal transform.

[0005] A coherent accumulation method for high-speed maneuvering targets based on scale-corrected time-reversal transform is as follows:

[0006] Step 1: Obtain the echo signal, derive the echo signal time delay expression to rewrite the echo signal, and process the echo signal in a fast time. Perform a Fourier transform to obtain the range-frequency dimension of the echo signal. ;

[0007] Step 2: Set speed search parameters Distance search parameters Acceleration search parameters The search area and search step size are determined using speed search parameters. Constructing scale-matched filters Then, pulse compression is performed based on a scale-matched filter to obtain the pulse compression result. ;

[0008] Step 3: Utilize the pulse compression results Constructing a slow time reversal function Using a slow-time reversal function Pulse compression results Perform a time-reversal transformation to obtain the pulse compression result after time reversal. And obtain the time-domain form of the pulse compression result after time reversal. ;

[0009] Step 4: Search parameters based on speed and acceleration search parameters Constructing a phase compensation function The time-domain form of the pulse compression result using the phase compensation function and time reversal is obtained. Obtain interpulse accumulation results And obtain the velocity value corresponding to the maximum value of the inter-pulse accumulation result. Distance value and acceleration value ;

[0010] Step 5: Utilize the speed value Distance value and acceleration value Construct the target energy accumulation function ,use Obtain an accurate estimate of the target jerk. .

[0011] Furthermore, in step one, the echo signal is acquired, and the echo signal time delay expression is derived to rewrite the echo signal, and the echo signal is processed in a fast time. Perform a Fourier transform to obtain the range-frequency dimension of the echo signal. Specifically:

[0012] Step 11: Acquire the echo signal Specifically:

[0013]

[0014]

[0015] in, It is the time delay of the echo signal. It is the amplitude of the echo signal. It is an echo signal. This represents the unit rectangular window function. The pulse width. For carrier frequency, For frequency modulation slope, For signal bandwidth, It is the imaginary unit. For fast time variables, For slow-time variables;

[0016] Steps one and two: Derive the echo signal time delay expression and rewrite the echo signal based on the echo signal time delay expression, specifically as follows:

[0017] First, retaining only the intra-pulse velocity term, the instantaneous distance between the radar and the target is obtained, specifically:

[0018]

[0019]

[0020]

[0021] in, , , and These represent the target distance, radial velocity, acceleration, and jerk at a midpoint of a coherent accumulation time, respectively. It's the speed of light. It is the pulse repetition interval. It is a range The number in It is the number of pulses;

[0022] Then, based on the instantaneous distance between the radar and the target, the time delay expression of the echo signal is obtained:

[0023]

[0024]

[0025]

[0026]

[0027] in, , , It is an intermediate variable;

[0028] Finally, based on the time delay expression of the echo signal, the echo signal is rewritten as:

[0029]

[0030]

[0031]

[0032]

[0033] in, , It is an intermediate variable;

[0034] Step 13: Perform a fast-time Fourier transform on the echo signal obtained in Step 12 to obtain the distance-frequency dimension of the echo signal. .

[0035] Furthermore, in step one and three, the echo signal obtained in step one and two is subjected to a Fourier transform along fast time to obtain the distance-frequency dimension of the echo signal. Specifically:

[0036]

[0037] in, It is a frequency variable. For signal amplitude, It is the distance-frequency dimension of the echo signal.

[0038] Furthermore, in step two, the speed search parameters are set. Distance search parameters Acceleration search parameters The search area and search step size are determined using speed search parameters. Constructing scale-matched filters Then, pulse compression is performed based on a scale-matched filter to obtain the pulse compression result. Specifically:

[0039] Step 21: Set speed search parameters Distance search parameters Acceleration search parameters Search area and search step size:

[0040] set up , , ;set up The search step size is , The search step size is , The search step size is ;

[0041] in, It is the minimum distance. It is the maximum distance. It is the minimum acceleration. It is the maximum acceleration. It is the minimum speed. It is the maximum speed;

[0042] Step 22: Using speed to search for parameters Constructing scale-matched filters Specifically:

[0043]

[0044]

[0045]

[0046] in, , It is an intermediate variable;

[0047] Steps 2 and 3: Based on scale-matched filters Distance-frequency dimension of the echo signal Obtain pulse compression results .

[0048] Furthermore, the scale-matched filter in steps two and three... Distance-frequency dimension of the echo signal Obtain pulse compression results Specifically:

[0049] First, the pulse compression process is constructed, specifically as follows:

[0050]

[0051] Then, when , , At that time, the pulse compression result is:

[0052]

[0053] in, It is the signal amplitude after pulse compression.

[0054] Furthermore, the pulse compression result in step three... Constructing a slow time reversal function Using a slow-time reversal function Pulse compression results Perform a time-reversal transformation to obtain the pulse compression result after time reversal. And obtain the time-domain form of the pulse compression result after time reversal. Specifically:

[0055] Step 31: Utilizing the pulse compression results Constructing a slow time reversal function Specifically:

[0056]

[0057] Step 3.2: Utilize the slow-time reversal function Pulse compression results Perform a time-reversal transformation to obtain the pulse compression result after time reversal. Specifically:

[0058]

[0059] in, It is the signal amplitude after the time reversal operation;

[0060] Step 33: Regarding distance frequency... By applying the inverse Fourier transform, the time-domain form of the pulse compression result after time reversal is obtained. .

[0061] Furthermore, in step three, the distance frequency is... By applying the inverse Fourier transform, the time-domain form of the pulse compression result after time reversal is obtained. Specifically:

[0062]

[0063] in, This represents the signal amplitude after transformation to the time domain.

[0064] Furthermore, the speed-based search parameters in step four... and acceleration search parameters Constructing a phase compensation function The time-domain form of the pulse compression result using the phase compensation function and time reversal is obtained. Obtain interpulse accumulation results And obtain the velocity value corresponding to the maximum value of the inter-pulse accumulation result. Distance value and acceleration value Specifically:

[0065] Step 41: Search parameters based on speed and acceleration search parameters Constructing a phase compensation function Specifically:

[0066]

[0067] Step 42: Utilizing the phase compensation function The time-domain form of the pulse compression result after time reversal Obtain interpulse accumulation results Specifically:

[0068]

[0069] in, It is the coherent accumulation time;

[0070] Step 4.3: According to the search step size , and In respectively , and Get search parameters within range , and Get the value The value of each search parameter corresponding to the maximum value , , ;

[0071] in, It's a speed value. It's a distance value. It is the acceleration value.

[0072] Furthermore, in step five, the speed value is utilized. Distance value and acceleration value Construct the target energy accumulation function ,use Obtain an accurate estimate of the target jerk. Specifically:

[0073] Step 51, Utilize , , and each accelerometer candidate value Build a parametric mesh and set ;set up The search step size is For each candidate value in the parameter grid , combined , and Calculate the target energy accumulation function:

[0074]

[0075]

[0076] in, It is an intermediate variable. It is the result of pulse compression;

[0077] Step 52: Maximize the target energy accumulation function to obtain an accurate estimate of the target jerk. .

[0078] Furthermore, in step five-two, the target energy accumulation function is maximized to obtain an accurate estimate of the target jerk. Specifically:

[0079]

[0080] in, It is a precise estimate of the target's jerk.

[0081] The beneficial effects of this invention are as follows:

[0082] This invention proposes an efficient coherent accumulation method based on Scale Corrected Time Reversal Transform (SCTRT). First, a scale-matched filter is used to compensate for intra-pulse scale effects. Then, a time reversal transform is used to suppress range walk (RM) and Doppler modulation (DFM). Finally, a phase compensation function is introduced to suppress residual inter-pulse mismatch and achieve multi-pulse coherent accumulation. Then, a grid search strategy with jerk is used to further improve parameter estimation capabilities. This invention effectively compensates for inter-pulse range walk, Doppler modulation, and intra-pulse scale mismatch while reducing the search dimensionality, improving the accuracy of parameter estimation. Furthermore, this invention has low computational complexity, thereby improving the efficiency of coherent accumulation. This invention can meet the real-time requirements of target recognition. Attached Figure Description

[0083] Figure 1 This is a geometric model of the radar's motion relative to the target;

[0084] Figure 2(a) shows the simulation results of scale-matched filtering;

[0085] Figure 2(b) shows the simulation results of the time reversal transformation;

[0086] Figure 2(c) shows the simulation results in the acceleration-distance plane;

[0087] Figure 2(d) shows the simulation results of the accumulation on the velocity-jerk plane;

[0088] Figure 3 This is a comparison chart of target detection probabilities;

[0089] Figure 4(a) is a comparison chart of distance RMSE curves;

[0090] Figure 4(b) is a comparison of the velocity RMSE curves;

[0091] Figure 4(c) is a comparison of acceleration RMSE curves;

[0092] Figure 4(d) Comparison of accelerometer RMSE curves;

[0093] Figure 5 This is a flowchart of the present invention;

[0094] Figure 6 The figure shows a comparison of the computational complexity of the four algorithms in the example under different pulse number conditions. Detailed Implementation

[0095] Specific implementation method one: as follows Figure 5 As shown, the specific process of a coherent accumulation method for high-speed maneuvering targets based on scale-corrected time-reversal transform in this embodiment is as follows:

[0096] Step 1: Acquire echo signal The echo signal time delay expression is derived to rewrite the echo signal, and the echo signal is processed in a fast time. Perform a Fourier transform to obtain the range-frequency dimension of the echo signal. Specifically:

[0097] Step 11: Acquire the echo signal Specifically:

[0098] First, assume the radar transmitted signal is an LFM pulse signal, whose mathematical expression is:

[0099]

[0100]

[0101] in, This represents the unit rectangular window function. The pulse width. For carrier frequency, For frequency modulation slope, For signal bandwidth, It is the imaginary unit. It is transmitting a signal. For fast time variables;

[0102] Then, the received echo signal is obtained by utilizing the time delay between the transmitted signal and the echo signal, specifically as follows:

[0103]

[0104] in, It is the time delay of the echo signal. It is the amplitude of the echo signal. It is an echo signal. For slow-time variables;

[0105] Steps one and two: Derive the echo signal time delay expression and rewrite the echo signal based on the echo signal time delay expression, specifically as follows:

[0106] First, if only the intra-pulse velocity term is retained, the instantaneous distance between the radar and the target can be expressed as:

[0107]

[0108]

[0109]

[0110] in, , , and These represent the target distance, radial velocity, acceleration, and jerk at a midpoint of a coherent accumulation time, respectively. For fast time variables, For slow time variables, It is the time delay of the echo signal. It's the speed of light. It is the pulse repetition interval. It is a range The number in It is the number of pulses;

[0111] Then, the time delay expression of the echo signal is obtained:

[0112]

[0113]

[0114]

[0115]

[0116] in, , , It is an intermediate variable;

[0117] Finally, based on the time delay expression of the echo signal, the echo signal is rewritten as:

[0118]

[0119]

[0120]

[0121]

[0122] in, , It is an intermediate variable.

[0123] Step 13: According to the Standing Phase Theorem (PSP), perform a Fourier transform on the echo signal along the fast time path to obtain the range-frequency dimension of the echo signal. Specifically:

[0124]

[0125] in, It is a frequency variable. For signal amplitude, It is the distance-frequency dimension of the echo signal.

[0126] In this step, in real-world scenarios, the scaling effect is primarily caused by the target's velocity, while acceleration and jerk have a relatively weak impact on the intra-pulse signal structure. Therefore, under high-speed, high-order motion conditions, the intra-pulse delay can consider only the velocity term, while the inter-pulse delay needs to consider velocity, acceleration, and jerk simultaneously. The geometric model of the radar's motion relative to the target is as follows: Figure 1 As shown.

[0127] Step 2: Set velocity search parameters based on prior information from radar and the target. Distance search parameters Acceleration search parameters The search area and search step size are determined using speed search parameters. Constructing scale-matched filters Then, pulse compression is performed based on a scale-matched filter to obtain the pulse compression result. Specifically:

[0128] Step 21: Set speed search parameters Distance search parameters Acceleration search parameters Search area and search step size:

[0129] set up , , ;set up The search step size is , The search step size is , The search step size is ;

[0130] in, It is the minimum distance. It is the maximum distance. It is the minimum acceleration. It is the maximum acceleration. It is the minimum speed. It is the maximum speed;

[0131] Step 22: Using speed to search for parameters Constructing scale-matched filters Specifically:

[0132]

[0133]

[0134]

[0135] in, , It is an intermediate variable;

[0136] Steps two and three: Based on the scale-matched filter and the distance-frequency dimension of the echo signal Obtain pulse compression results Specifically:

[0137] First, the pulse compression process is constructed, specifically as follows:

[0138]

[0139] in, It is the result of pulse compression;

[0140] Then, the scale-matched filter obtained in step two-two... The distance-frequency dimension of the echo signal obtained in step one Substitute the values ​​into the pulse compression process to obtain the pulse compression result. Specifically:

[0141]

[0142] When search speed , , At this point, the echo signal and the matched filter are perfectly matched. In this case, the pulse compression result can be rewritten as:

[0143]

[0144] in, It is the signal amplitude after pulse compression.

[0145] This step utilizes a scale-matched filter to achieve effective intra-pulse energy accumulation. This invention organically combines target scale matching, time-reversal transform, and phase compensation to construct a three-stage coherent accumulation structure.

[0146] Step 3: Utilize the pulse compression results Constructing a slow time reversal function Using a slow-time reversal function Pulse compression results Perform a time-reversal transformation to obtain the pulse compression result after time reversal. And obtain the time-domain form of the pulse compression result after time reversal. Specifically:

[0147] Step 31: Utilizing the pulse compression results Constructing a slow time reversal function Specifically:

[0148]

[0149] Even after intrapulse compression, the signal still exhibits distance travel (RM) and Doppler modulation (DFM) between pulses. Therefore, this step introduces a time reversal function.

[0150] Step 3.2: Utilize the slow-time reversal function Pulse compression results Perform a time-reversal transformation to obtain the pulse compression result after time reversal. Specifically:

[0151]

[0152] in, It is the signal amplitude after the time reversal operation;

[0153] Step 33: Regarding distance frequency... By applying the inverse Fourier transform, the time-domain form of the pulse compression result after time reversal is obtained. Specifically:

[0154]

[0155] in, This represents the signal amplitude after transformation to the time domain.

[0156] After time reversal transformation and The coupling with the range frequency has been eliminated, but it still exists. Coupled with the distance frequency, this can still cause RM and DFM. Therefore, in step four of this invention, a phase compensation function is designed to correct these issues and complete the multi-pulse coherent accumulation.

[0157] Step 4: Search parameters based on speed and acceleration search parameters Constructing a phase compensation function The time-domain form of the pulse compression result using the phase compensation function and time reversal is obtained. Obtain interpulse accumulation results And obtain the velocity value corresponding to the maximum value of the inter-pulse accumulation result. Distance value and acceleration value Specifically:

[0158] Step 41: Search parameters based on speed and acceleration search parameters Constructing a phase compensation function Specifically:

[0159]

[0160] Step 42: Utilizing the phase compensation function The time-domain form of the pulse compression result after time reversal Obtain interpulse accumulation results Specifically:

[0161]

[0162] in, It is the coherent accumulation time;

[0163] Step 4.3: According to the search step size , and In respectively , and Get search parameters within range , and Get the value The value of each search parameter corresponding to the maximum value , , ;

[0164] in, It's a speed value. It's a distance value. It is the acceleration value.

[0165] Step 5: Utilize the speed value Distance value and acceleration value Construct the target energy accumulation function ,use Obtain an accurate estimate of the target jerk. Specifically:

[0166] Step 51, Utilize , , and each accelerometer candidate value Build a parametric mesh and set ;set up The search step size is For each candidate value in the parameter grid Combined with known precise values , and Calculate the target energy accumulation function:

[0167]

[0168]

[0169] in, It is an intermediate variable. It is the result of pulse compression;

[0170] Step 52: Maximize the target energy accumulation function to obtain an accurate estimate of the target jerk. Specifically:

[0171]

[0172] in, It is a precise estimate of the target's jerk.

[0173] Example: To verify the beneficial effects of the present invention, a simulation experiment was conducted in this example:

[0174] To quantitatively evaluate the target detection capability and motion parameter estimation performance of the algorithm, the radar parameters involved in the simulation experiment included: carrier frequency of 0.5 GHz, signal bandwidth of 100 MHz, sampling frequency of 200 MHz, pulse repetition frequency of 500 Hz, and pulse duration of 1 ms. The target was located at a distance of 67.5 km from the radar, with a radial velocity of 5000 m / s and an acceleration of 50 m / s². 2 The jerk is 30 m / s². 3 .

[0175] First, the entire process of the SCTRT algorithm (this invention) under noise-free conditions was simulated. The simulation results are shown in Figures 2(a)-2(d). Figure 2(a) shows the result after scale-matched filtering. The energy is well focused within a single period, but it still shows a slanted peak distribution on the slow time axis, indicating that distance travel has not been completely eliminated. Figure 2(b) shows the result of time reversal transformation. The peak travel is significantly reduced, but due to the presence of... The coupling between the term and the range frequency results in a hyperbolic signal. Figure 2(c) shows the accumulation results of the SCTRT algorithm on the range-acceleration plane, with the target energy focused into a clear main peak. Figure 2(d) shows the accumulation results on the velocity-acceleration plane after applying the grid search strategy.

[0176] This embodiment compares and analyzes the performance of four algorithms—NU-SCGRFT, SCTRT, SCRFT, and TRT-SKT-LVD—through a large-scale Monte Carlo simulation experiment. In the simulation settings, the signal-to-noise ratio ranged from -65 dB to -15 dB, the step size was 1 dB, and the false alarm probability was PFA = 10⁻³. Figure 3 As shown, NU-SCGRFT exhibits the best detection capability due to its search space encompassing the joint effects of all major motion parameters, serving as a benchmark for performance limits. SCTRT demonstrates excellent robustness and practicality, achieving stable detection even at -28 dB. SCRFT's detection probability is close to that of SCTRT. TRT-SKT-LVD shows the worst detection performance, with its detection probability approaching 1 after -23 dB. Figures 4(a)–4(d) show the RMSE curves of different algorithms for estimating the four types of motion parameters. NU-SCGRFT, as a benchmark for performance limits, demonstrates the best estimation accuracy for all four types of parameters. SCTRT takes into account the estimation of all four types of parameters and outputs stable estimation results near -29 dB, exhibiting good estimation capability. SCRFT only has a coarse estimation capability for distance and velocity. Although the RMSE shows a decreasing trend after -48 dB, the estimation error always exists, making it difficult to effectively accumulate the target's principal energy. Furthermore, SCRFT cannot estimate acceleration and jerk. TRT-SKT-LVD has the worst estimation performance, unable to output velocity and jerk estimates, only able to estimate acceleration relatively well, and its distance estimation always has a systematic bias due to the lack of consideration of scale effects.

[0177] Figure 6This paper presents a comparison of the computational complexity of four algorithms—SCTRT, NU-SCGRFT, SCRFT, and TRT-SKT-LVD—under different pulse count conditions. SCTRT optimizes the search strategy through structural design, decomposing the original high-dimensional parameter search task into a three-dimensional + one-dimensional search, effectively reducing the overall computational burden. From the complexity curves, SCRFT and TRT-SKT-LVD have lower overall complexity, but they fail to consider higher-order motion factors, making them difficult to adapt to the changing characteristics of high-speed maneuvering targets, resulting in significant performance limitations. NU-SCGRFT incorporates the target's higher-order motion parameters (velocity, acceleration, jerk) into a joint search framework, achieving the best detection and estimation performance, but its 4-dimensional search structure introduces extremely high computational complexity, posing a significant challenge to the processing capabilities of practical engineering systems.

[0178] Comprehensive analysis shows that SCTRT exhibits high stability across multiple performance dimensions. It not only demonstrates excellent target detection capabilities at low to medium signal-to-noise ratios, but also provides usable outputs for estimating four types of parameters: distance, velocity, acceleration, and jerk. Its strong robustness and broad adaptability achieve a better balance between target detection capability and computational complexity, making it suitable for widespread application in various practical environments.

Claims

1. A method for coherent accumulation of high-speed maneuvering targets based on scale-corrected time-reversal transform, characterized in that... The specific process of the method is as follows: Step 1: Obtain the echo signal, derive the echo signal time delay expression to rewrite the echo signal, and process the echo signal in a fast time. Perform a Fourier transform to obtain the range-frequency dimension of the echo signal. ; Step 2: Set distance search parameters Speed ​​search parameters Acceleration search parameters The search area and search step size are determined using speed search parameters. Constructing scale-matched filters Then, pulse compression is performed based on a scale-matched filter to obtain the pulse compression result. Specifically: Step 2: Set distance search parameters Speed ​​search parameters Acceleration search parameters Search area and search step size: set up , , ; set up The search step size is , The search step size is , The search step size is ; in, It is the minimum speed. That is the maximum speed. It is the minimum acceleration. It is the maximum acceleration. It is the minimum distance. It is the maximum distance; Step 22: Using speed to search for parameters Constructing scale-matched filters Specifically: in, , It is an intermediate variable. For signal bandwidth, For carrier frequency, It is the imaginary unit. For frequency modulation slope, It's the speed of light. It is a frequency variable; Steps 2 and 3: Based on scale-matched filters Distance-frequency dimension of the echo signal Obtain pulse compression results ; Step 3: Utilize the pulse compression results Constructing a slow time reversal function Using a slow-time reversal function Pulse compression results Perform a time-reversal transformation to obtain the pulse compression result after time reversal. And obtain the time-domain form of the pulse compression result after time reversal. Specifically: Step 31: Utilizing the pulse compression results Constructing a slow time reversal function Specifically: in, For slow time variables, It is the signal amplitude after pulse compression. It is an intermediate variable. , , and These represent the target distance, velocity, acceleration, and jerk at a midpoint of a coherent accumulation time; Step 3.2: Utilize the slow-time reversal function Pulse compression results Perform a time-reversal transformation to obtain the pulse compression result after time reversal. Specifically: in, It is the signal amplitude after the time reversal operation; Step 33: Regarding the distance frequency... By applying the inverse Fourier transform, the time-domain form of the pulse compression result after time reversal is obtained. ; Step 4: Search parameters based on distance and acceleration search parameters Constructing a phase compensation function The time-domain form of the pulse compression result using the phase compensation function and time reversal is obtained. Obtain interpulse accumulation results When the inter-pulse accumulation result is at its maximum, the target distance at the midpoint of the coherent accumulation time is obtained. ,speed acceleration Specifically: Step 41: Search parameters based on distance and acceleration search parameters Constructing a phase compensation function Specifically: Step 42: Utilizing the phase compensation function The time-domain form of the pulse compression result after time reversal Obtain interpulse accumulation results Specifically: in, It is the coherent accumulation time. For fast time variables; Step 4.3: According to the search step size , and In respectively , and Get search parameters within range , and Get the value The value of each search parameter corresponding to the maximum value , , ; in, , , These represent the target distance, velocity, and acceleration at the midpoint of the coherent accumulation time, respectively. Step 5: Utilize coherent accumulation of the target distance at the midpoint of time. ,speed and acceleration Construct the target energy accumulation function ,use Obtain an accurate estimate of the target jerk. .

2. The method for coherent accumulation of high-speed maneuvering targets based on scale-corrected time-reversal transform according to claim 1, characterized in that: In step one, the echo signal is acquired, the echo signal time delay expression is derived to rewrite the echo signal, and the echo signal is processed in a fast time. Perform a Fourier transform to obtain the range-frequency dimension of the echo signal. Specifically: Step 11: Acquire the echo signal Specifically: in, It is the time delay of the echo signal. It is the amplitude of the echo signal. It is an echo signal. This represents the unit rectangular window function. The pulse width. For carrier frequency, For frequency modulation slope, For signal bandwidth, It is the imaginary unit. For fast time variables, For slow-time variables; Steps one and two: Derive the echo signal time delay expression and rewrite the echo signal based on the echo signal time delay expression, specifically as follows: First, retaining only the intra-pulse velocity term, the instantaneous distance between the radar and the target is obtained, specifically: in, , , and These represent the target distance, velocity, acceleration, and jerk at a midpoint of a coherent accumulation time, respectively. It's the speed of light. It is the pulse repetition interval. It is a range The number in It is the number of pulses; Then, based on the instantaneous distance between the radar and the target, the time delay expression of the echo signal is obtained: in, , , It is an intermediate variable; Finally, based on the time delay expression of the echo signal, the echo signal is rewritten as: in, , It is an intermediate variable; Step 13: Perform a fast-time Fourier transform on the echo signal obtained in Step 12 to obtain the distance-frequency dimension of the echo signal. .

3. The method for coherent accumulation of high-speed maneuvering targets based on scale-corrected time-reversal transform according to claim 2, characterized in that: In step one and three, the echo signal obtained in step one and two is subjected to a fast-time Fourier transform to obtain the distance-frequency dimension of the echo signal. Specifically: in, It is a frequency variable. For signal amplitude, It is the distance-frequency dimension of the echo signal.

4. The method for coherent accumulation of high-speed maneuvering targets based on scale-corrected time-reversal transform according to claim 3, characterized in that: The scale-matched filter in steps two and three Distance-frequency dimension of the echo signal Obtain pulse compression results Specifically: First, the pulse compression process is constructed, specifically as follows: Then, when , , At that time, the pulse compression result is: in, It is the signal amplitude after pulse compression.

5. The method for coherent accumulation of high-speed maneuvering targets based on scale-corrected time-reversal transform according to claim 4, characterized in that: In step three, the distance frequency is... By applying the inverse Fourier transform, the time-domain form of the pulse compression result after time reversal is obtained. Specifically: in, This represents the signal amplitude after transformation to the time domain.

6. The method for coherent accumulation of high-speed maneuvering targets based on scale-corrected time-reversal transform according to claim 5, characterized in that: Step five involves using the target distance at the midpoint of the coherent accumulation time. ,speed and acceleration Construct the target energy accumulation function ,use Obtain an accurate estimate of the target jerk. Specifically: Step 51, Utilize , , and each accelerometer candidate value Build a parametric mesh and set ;set up The search step size is For each candidate value in the parameter grid , combined , and Calculate the target energy accumulation function: in, It is an intermediate variable. It is the result of pulse compression; Step 52: Maximize the target energy accumulation function to obtain an accurate estimate of the target jerk. .

7. The method for coherent accumulation of high-speed maneuvering targets based on scale-corrected time-reversal transform according to claim 6, characterized in that: In step five-two, the target energy accumulation function is maximized to obtain an accurate estimate of the target jerk. Specifically: in, It is a precise estimate of the target's jerk.

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