Weak target long-time accumulation detection method and system based on SoKT-NuFFT

Abstract

The invention discloses a weak target long-time accumulation detection method based on second-order keystone transform-non-uniform fast Fourier transform (SoKT-NuFFT). Comprising the following steps: S1, carrying out distance pulse pressure and distance fast Fourier transform (FFT) on a received radar original echo signal; step S2, executing second-order keystone transform (SoKT) in a range frequency-slow time domain so as to correct second-order range migration generated by the radial acceleration of the target; s3, constructing a speed matching filter bank in a distance frequency-slow time domain, and eliminating a residual radial speed item through one-dimensional search; and S4, performing distance fast inverse Fourier transform (IFFT) and slow time non-uniform fast Fourier transform (NuFFT) in sequence to complete coherent accumulation of target energy. Through a peak detection technology, estimation of target motion parameters is realized. According to the method, searching of speed fuzzy numbers is not needed, and compared with classical generalized Radon Fourier transform, the accumulation performance is similar, but the calculation complexity is remarkably reduced.

Description

Technical Field

[0001] The present invention relates to the field of radar technology, and in particular to a weak target long-term accumulation detection method and system based on second-order keystone transform-non-uniform fast Fourier transform (SoKT-NuFFT). Background Art

[0002] In recent years, with the rapid development of science and technology, the influence of aerial targets in modern warfare has been increasing day by day. UAVs, jet fighters, supersonic aircraft and adjacent space aircraft have brought unprecedented threats and challenges to traditional radars. These targets have the characteristics of "long distance, low observation and high maneuverability". Long-term coherent accumulation, as an effective means to improve the signal-to-noise ratio of weak target echoes, is hindered by the range migration and Doppler migration of target echoes under long-term observation, which greatly reduces the performance of traditional moving target detection methods (MTD).

[0003] For the range and Doppler migration problems, the traditional Radon Fourier transform method (RFT), axis rotation MTD method (AR-MTD), scaled IFFT (SCIFT) method can only deal with the linear range migration caused by velocity, but are powerless against the second-order range migration and Doppler frequency migration caused by acceleration. Although the generalized Radon Fourier transform (GRFT), Radon fractional Fourier transform (RFRFT), and Radon Lübeck distribution variation (RLVD) based on Radon class have emerged, they involve multi-dimensional parameter grid search and complex calculations, making them difficult to apply in engineering real-time processing.

[0004] Although the two-dimensional frequency domain matched filter method based on the stationary phase point method has been proposed to reduce the computational complexity, it is only applicable to targets with extremely large time bandwidth. Although the method based on keystone-matched filtering (KT-MF) has reduced the computational complexity to a certain extent and is conducive to engineering processing, it still needs to search for velocity fuzzy numbers and acceleration when facing fast-moving targets, and the computational complexity is still high.

[0005] Although methods such as improved axis rotation-fractional Fourier transform (IAR-FRFT), improved axis rotation-LV transform (MART-LVT), improved position rotation transform and improved discrete chirp Fourier transform (MLRT-IDCFT) reduce the computational complexity by ignoring the second-order range migration caused by the target radial acceleration, they sacrifice accuracy.

[0006] In addition, although nonlinear methods such as adjacent cross-correlation function (ACCF), time-frequency distribution-based, time-flip transform-based, and distance-frequency flip-based methods can separate target motion parameters through nonlinear transformation and thus significantly reduce the amount of calculation, their performance significantly decreases in a multi-target low signal-to-noise ratio environment, and the cross-terms increase the probability of false alarms, making them unsuitable for engineering processing.

[0007] Through searching patent documents, it was found that the invention patent with publication number CN109633622B discloses a radar maneuvering target cross-unit accumulation method based on time-reversed second-order Keystone transform. First, the radar data after pulse compression is Fourier transformed along the fast time to obtain echo distance frequency slow time two-dimensional data; secondly, the slow time dimension data is time-reversed; then, the slow time dimension is subjected to second-order Keystone transform to complete high-order distance movement compensation; finally, the distance frequency dimension is subjected to inverse Fourier transform, and the slow time dimension is subjected to second-order matching Fourier transform to complete cross-unit coherent accumulation. This patent does not involve performance under low SNR, and cannot reflect good detection performance at low SNR and avoid velocity fuzzy number search, which limits its application in complex environments or fast moving target detection.

[0008] In summary, in response to the above-mentioned problems of the prior art, studying a weak target long-term accumulation detection method and system based on second-order keystone transform-non-uniform fast Fourier transform (SoKT-NuFFT) has become a key task that needs to be solved urgently. Summary of the invention

[0009] In view of the defects in the prior art, the purpose of the present invention is to provide a weak target long-term accumulation detection method and system based on second-order keystone transform-non-uniform fast Fourier transform.

[0010] According to the present invention, a weak target long-term accumulation detection method based on second-order keystone transform-non-uniform fast Fourier transform includes the following steps:

[0011] Step S1, receiving the original radar echo signal and down-converting it to obtain the baseband echo signal s r (t,t m ), where t represents the fast time variable, t m represents a slow time variable;

[0012] Step S2: baseband echo signal s r (t,t m ) Perform range pulse pressure and range fast Fourier transform to obtain the echo signal S in the range frequency-slow time domain c (f,t m ), where f represents the distance frequency variable;

[0013] Step S3, the signal S c (f,t m ) Apply the second-order keystone transform to eliminate the second-order range migration caused by the target radial acceleration and obtain the echo signal S c (f,t n ), where t n is the transformed slow time variable;

[0014] Step S4, constructing a velocity matching filter group H(f,t n ; V res ), V res is the target residual radial velocity after SoKT. The residual radial velocity term is eliminated by one-dimensional search to obtain the echo signal S MF (f,t n );

[0015] Step S5: MF (f,t n ) Perform the distance fast inverse Fourier transform and slow time non-uniform fast Fourier transform in sequence to achieve target energy focusing and obtain the signal

[0016] Step S6, based on the echo signal S c (f,t n ) and velocity matching filter bank H(f,t n ; V res ), through the peak detection technique, we can obtain The peak information of the target can be obtained to estimate the radial acceleration and radial velocity of the target.

[0017] Preferably, in step S1, the radar receives a weak maneuvering target echo of a linear frequency modulation pulse, and the mathematical expression of the linear frequency modulation pulse signal is as follows:

[0018]

[0019] Where t is the fast time variable; T p is the pulse width; f c is the carrier frequency; μ is the modulation frequency; rect(·) is the rectangular window function;

[0020] The instantaneous slant range between the radar and a target with constant radial acceleration is:

[0021]

[0022] Where r0 is the target initial slant distance; v is the target radial velocity; a is the target radial acceleration; t m =m / PRF

[0023] (m=0,1,…,M-1) is the slow time; PRF is the pulse repetition frequency.

[0024] After down-converting the target original echo signal, the target received baseband echo signal is expressed as:

[0025]

[0026] Among them, σ0 is the target scattering coefficient; c is the speed of light; λ is the wavelength.

[0027] Preferably, in step S2, a matched filter associated with the transmitted signal is used to perform range pulse compression on the baseband signal, and a range fast Fourier transform is performed to obtain an echo signal in the range frequency-slow time domain, and the mathematical expression is:

[0028]

[0029] Among them, * and represent complex conjugate operation and convolution operation respectively, σ1 is the signal amplitude in the range frequency-slow time domain; f is the range frequency variable; B is the range bandwidth; N amb is the velocity fuzzy number; It is blind speed; is the target baseband velocity, and considering the target velocity ambiguity, its radial velocity is written as:

[0030] v=N amb v amb +v base .

[0031] Preferably, in step S3, the second-order keystone expression is as follows:

[0032]

[0033] Among them, f c is the radar carrier frequency, t n is the new slow time variable.

[0034] Preferably, in step S3, after the second-order keystone transformation, the echo signal S c (f,t n ) is as follows:

[0035]

[0036] In the formula, is the residual radial velocity; N amb is the velocity fuzzy number; It is blind speed; is the baseband speed; c is the speed of light; λ is the wavelength.

[0037] Preferably, in step S4, the velocity matching filter group H(f,t n ; V res ) is as follows:

[0038]

[0039] Among them, v base =2[V res -round(V res / v amb )v amb ], round(·) is the rounding operation.

[0040] Preferably, in step S4, the echo signal S after matching filtering MF (f,t n ) is obtained as follows:

[0041]

[0042] Preferably, in step S5, the target energy focusing is achieved by the following mathematical expression:

[0043]

[0044] Where σ3 is the complex amplitude after the target is focused; For The corresponding frequency variables are sinc(·) for the Sigmund function and δ(·) for the Dirac delta function. is the slow-time non-uniform fast Fourier transform, IFFT f is the fast inverse Fourier transform of distance.

[0045] Preferably, in step S6, the peak value is retrieved to obtain the motion parameter estimation value in the following manner:

[0046]

[0047] Among them, the echo signal S c (f,t n ) is the signal obtained in step S3, H(f,t n ; V res ) is the velocity matched filter bank constructed in step S4;

[0048] Radial acceleration estimate The formula is:

[0049]

[0050] Therefore, the estimation formula of the target radial velocity is as follows:

[0051]

[0052] In the formula, is the estimated radial residual velocity; is the estimated radial velocity, is the estimated value of baseband speed.

[0053] The present invention also provides a weak target long-time accumulation detection system based on second-order keystone transform-non-uniform fast Fourier transform, comprising:

[0054] Module M1 receives the original radar echo signal and down-converts it to obtain the baseband echo signal s r (t,t m ), where t represents the fast time variable, t m represents a slow time variable;

[0055] Module M2, baseband echo signal s r (t,t m ) Perform range pulse pressure and range fast Fourier transform to obtain the echo signal S in the range frequency-slow time domain c (f,t m ), where f represents the distance frequency variable;

[0056] Module M3, for signal S c (f,t m ) Apply the second-order keystone transform to eliminate the second-order range migration caused by the target radial acceleration and obtain the echo signal S c (f,t n ), where t n is the transformed slow time variable;

[0057] Module M4, constructs a velocity matching filter bank H(f,t n ; V res ), V res is the target residual radial velocity after SoKT. The residual radial velocity term is eliminated by one-dimensional search to obtain the echo signal S MF (f,t n );

[0058] Module M5, for the echo signal S MF (f,t n ) Perform the distance fast inverse Fourier transform and slow time non-uniform fast Fourier transform in sequence to achieve target energy focusing and obtain the signal

[0059] Module M6, based on the echo signal S c (f,t n ) and velocity matching filter bank H(f,t n; V res ), through the peak detection technique, we can obtain The peak information of the target can be obtained to estimate the radial acceleration and radial velocity of the target.

[0060] Compared with the prior art, the present invention has the following beneficial effects:

[0061] 1. The present invention effectively solves the energy defocusing problem caused by second-order range migration and Doppler phase diffusion, ensures that the target echo energy can be effectively focused, and improves the accuracy and reliability of detection.

[0062] 2. Due to the linear transformation characteristics, the present invention can effectively avoid cross-term interference when processing multi-target scenes, accurately detect and analyze each target, and ensure the detection accuracy and stability in a multi-target detection environment.

[0063] 3. For fast-moving targets, the present invention does not need to perform velocity fuzzy number search, but only needs to perform one-dimensional grid search, which reduces the computational complexity. Moreover, even under low signal-to-noise ratio (SNR) conditions, the present invention still maintains good target detection performance, has excellent robustness and efficiency, and has more advantages in engineering applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] Other features, objects and advantages of the present invention will become more apparent from the detailed description of non-limiting embodiments made with reference to the following drawings:

[0065] Figure 1 It is a flow chart of a weak target long-time accumulation detection method based on second-order keystone transform-non-uniform fast Fourier transform in the implementation of the present invention;

[0066] Figure 2 It is the motion trajectory of the moving target after passing through the range pulse pressure in Experiment 1 of the embodiment of the present invention;

[0067] Figure 3 It is the range-Doppler spectrum of the echo signal in Experiment 1 of the embodiment of the present invention;

[0068] Figure 4 It is the radial residual velocity result of the echo signal in Experiment 1 of the embodiment of the present invention after the second-order keystone and velocity matching filter search;

[0069] Figure 5 It is the coherent accumulation result of the target T1 in Experiment 1 of the embodiment of the present invention after adopting the method of the present invention;

[0070] Figure 6 It is the coherent accumulation result of the target T2 in Experiment 1 of the embodiment of the present invention after adopting the method of the present invention;

[0071] Figure 7 is the range Doppler spectrum before clutter suppression in Experiment 2 of the embodiment of the present invention;

[0072] Figure 8 is the range Doppler spectrum after clutter suppression in Experiment 2 of the embodiment of the present invention;

[0073] Fig. 9 It is the motion trajectory of the target in Experiment 2 of the embodiment of the present invention;

[0074] Fig.10 It is the radial residual velocity result of the echo signal after the second-order keystone and velocity matching filter search in Experiment 2 of the embodiment of the present invention;

[0075] Fig.11 This is the coherent accumulation result of the target signal in Experiment 2 of the embodiment of the present invention after adopting the method of the present invention. DETAILED DESCRIPTION

[0076] The present invention is described in detail below in conjunction with specific embodiments. The following embodiments will help those skilled in the art to further understand the present invention, but are not intended to limit the present invention in any form. It should be noted that, for those of ordinary skill in the art, several changes and improvements can also be made without departing from the concept of the present invention. These all belong to the protection scope of the present invention.

[0077] The present invention is suitable for engineering processing of second-order motion models in low signal-to-noise ratio environments, and aims to achieve target energy focusing with high efficiency in low signal-to-noise ratio environments.

[0078] Embodiment 1:

[0079] Figure 1 The present invention is a flowchart of a weak target long-term accumulation detection method based on second-order keystone transform-non-uniform fast Fourier transform in the implementation of the present invention.

[0080] like Figure 1 As shown, this embodiment provides a weak target long-term accumulation detection method based on second-order keystone transform-non-uniform fast Fourier transform, including the following steps:

[0081] Step S1, receiving the original radar echo signal and down-converting it to obtain the baseband echo signal s r (t,t m ), where t represents the fast time variable, t m Represents a slow time variable.

[0082] Specifically, the radar receives a linear frequency modulated pulse of a weak maneuvering target echo. The mathematical expression of the linear frequency modulated pulse signal is as follows:

[0083]

[0084] Where t is the fast time variable; T p is the pulse width; f c is the carrier frequency; μ is the modulation frequency; rect(·) is the rectangular window function.

[0085] Specifically, ignoring the effects of high-order components and phase noise, the instantaneous slant range between the radar and the target with constant radial acceleration is:

[0086]

[0087] Where r0 is the target initial slant distance; v is the target radial velocity; a is the target radial acceleration; t m =m / PRF (m=0,1,…,M-1) is the slow time; PRF is the pulse repetition frequency.

[0088] After down-converting the target original echo signal, the target received baseband echo signal is expressed as:

[0089]

[0090] Where σ0 is the target scattering coefficient; c is the speed of light; λ is the wavelength.

[0091] Step S2: baseband echo signal s r (t,t m ) Perform range pulse pressure and range fast Fourier transform to obtain the echo signal S in the range frequency-slow time domain c (f,t m ), where f represents the distance frequency variable.

[0092] Specifically, a matched filter related to the transmitted signal is used to perform range pulse compression on the baseband signal, and a range fast Fourier transform is performed to obtain an echo signal in the range frequency-slow time domain. The mathematical expression is:

[0093]

[0094] In the formula, * and represent complex conjugate operation and convolution operation respectively, σ1 is the signal amplitude in the range frequency-slow time domain; f is the range frequency variable; B is the range bandwidth; N amb is the velocity fuzzy number; It is blind speed; is the target baseband velocity, and considering the target velocity ambiguity, its radial velocity is written as:

[0095] v=N amb v amb +v base .

[0096] Step S3, the signal S c (f,t m ) applies the second-order keystone (SoKT) transform to eliminate the second-order range migration caused by the target radial acceleration and obtain the echo signal S c (f,t n ), where t n is the slow time variable after SoKT transformation.

[0097] Specifically, the expression of the second-order keystone (SoKT) is as follows:

[0098]

[0099] In the formula, f c is the radar carrier frequency, t n is the new slow time variable.

[0100] Specifically, after the second-order keystone transform, the echo signal S c (f,t n ) is as follows:

[0101]

[0102] For narrowband radar, since f≈f c , there is the following approximation:

[0103]

[0104] Therefore, the simplified echo signal S c (f,t n ) is expressed as follows:

[0105]

[0106] In the formula, is the residual radial velocity; N amb is the velocity fuzzy number; It is blind speed; is the baseband speed; c is the speed of light; λ is the wavelength.

[0107] Step S4, constructing a velocity matching filter group H(f,t n ; V res ), V res is the target residual radial velocity after SoKT. The residual radial velocity term is eliminated by one-dimensional search to obtain the echo signal S MF (f,t n ).

[0108] Specifically, the velocity matched filter group H(f,t n ; V res ) is as follows:

[0109]

[0110] In the formula, v base =2[V res -round(V res / v amb )v amb ], round(·) is the rounding operation.

[0111] Specifically, the echo signal S after matched filtering MF (f,t n ) is obtained as follows:

[0112]

[0113] Step S5: MF (f,t n ) sequentially performs distance fast inverse Fourier transform (IFFT) and slow time non-uniform fast Fourier transform (NuFFT) to achieve target energy focusing and obtain signal

[0114] Specifically, the target energy focusing is achieved through the following mathematical expression:

[0115]

[0116] Where σ3 is the complex amplitude after the target is focused; For The corresponding frequency variables are sinc(·) for the Sigmund function and δ(·) for the Dirac delta function. is the slow-time non-uniform fast Fourier transform, IFFT f is the fast inverse Fourier transform of distance.

[0117] Step S6, based on the echo signal S c (f,t n ) and velocity matching filter bank H(f,t n ; V res ), through the peak detection technique, we can obtain The peak information of the target can be obtained to estimate the radial acceleration and radial velocity of the target.

[0118] Specifically, the peak value is retrieved to obtain the motion parameter estimation value in the following manner:

[0119]

[0120] In the formula, the echo signal S c (f,t n ) is the signal obtained in step S3, H(f,t n ; V res ) is the velocity matching filter group constructed in step S4.

[0121] Radial acceleration estimate The formula is:

[0122]

[0123] Therefore, the estimation formula of the target radial velocity is as follows:

[0124]

[0125] In the formula, is the estimated radial residual velocity; is the estimated radial velocity, is the estimated value of baseband speed.

[0126] Through the above processing flow, the method based on SoKT-NuFFT can reduce a two-dimensional motion parameter search process to a one-dimensional motion parameter search. This processing flow can be executed regardless of whether the target speed is blurred, that is, for speed blurred targets, there is no need to add additional fuzzy number searches. Therefore, the computational complexity of the method of the present invention is greatly reduced, and excellent detection performance can be achieved under low signal-to-noise ratio (SNR) conditions.

[0127] The technical solution of the present invention is further described below in conjunction with embodiments.

[0128] Embodiment 2:

[0129] The radar system simulation parameters of the experiment in this embodiment are as follows: carrier frequency is 2 GHz, range bandwidth is 40 MHz, range sampling frequency is 60 MHz, pulse repetition frequency is 1000 Hz, and pulse width is 1 μs.

[0130] This embodiment provides two targets with different motion parameters, which are denoted as T1 and T2. The radial velocity, radial acceleration and signal-to-noise ratio after range pulse compression of T1 are set to 310 m / s and -15 m / s respectively. 2 The radial velocity, radial acceleration and signal-to-noise ratio after range pulse compression of T2 are set to -245m / s, 10m / s 2 and 4dB.

[0131] Figure 2 It is the motion trajectory of the moving target after passing through the range pulse pressure in Experiment 1 of the embodiment of the present invention; Figure 3It is the range-Doppler spectrum of the echo signal in Experiment 1 of the embodiment of the present invention.

[0132] like Figure 2 The trajectories of the two moving targets are shown in Figure 1. Both targets have experienced serious range migration. Figure 3 As shown, the two targets experience energy diffusion due to the coupling of distance frequency and slow time.

[0133] Figure 4 This is the radial residual velocity result of the echo signal in Experiment 1 of the embodiment of the present invention after the second-order keystone and velocity matching filter search.

[0134] Using the method of the present invention, Figure 4 As shown, the estimated radial residual velocities of T1 and T2 are 305 m / s and -235 m / s respectively. Based on this, the radial velocities of the two targets can be obtained to be 310 m / s and -245 m / s respectively.

[0135] Figure 5 It is the coherent accumulation result of the target T1 in Experiment 1 of the embodiment of the present invention after adopting the method of the present invention; Figure 6 This is the coherent accumulation result of the target T2 in Experiment 1 of the embodiment of the present invention after adopting the method of the present invention.

[0136] like Figure 5 As shown, from its peak position, its radial acceleration can be estimated to be -15m / s 2 .like Figure 6 As shown, from its peak position, its radial acceleration can be estimated to be 9.975m / s 2 .

[0137] Embodiment 3:

[0138] The experiment of this embodiment verifies the effectiveness of the present invention by using actual measured data of airborne X-band SAR.

[0139] The measured data was collected by a three-channel airborne radar in Shaanxi. The main system parameters are as follows: carrier frequency is 8.85GHz, range bandwidth is 40MHz, range sampling frequency is 60MHz, pulse repetition frequency is 1000Hz, pulse width is 10μs, and platform speed is 120m / s.

[0140] Figure 7 is the range Doppler spectrum before clutter suppression in Experiment 2 of the embodiment of the present invention; Figure 8 is the range Doppler spectrum after clutter suppression in Experiment 2 of the embodiment of the present invention; Fig. 9 1 is the trajectory of the moving target in Experiment 2 of the embodiment of the present invention.

[0141] like Figure 7The clutter range-Doppler spectrum of the first receiving channel is shown, and it can be seen that the target signal is submerged by the clutter. Figure 8 The result after clutter cancellation is shown in the figure, from which we can see the range-Doppler spectrum of the moving target signal. Fig. 9 The trajectory of the moving target shown shows that the target has migrated over a distance.

[0142] Fig.10 It is the radial residual velocity result of the echo signal after the second-order keystone and velocity matching filter search in Experiment 2 of the embodiment of the present invention; Fig.11 This is the coherent accumulation result of the target signal in Experiment 2 of the embodiment of the present invention after adopting the method of the present invention.

[0143] Using the method of the present invention, Fig.10 The search results of the radial residual velocity of the target are shown in the figure. From the peak position in the figure, it can be estimated that the radial residual velocity of the target is about 15.8m / s. According to the radar system parameters, it can be estimated that the velocity ambiguity number of the target is 1, and the baseband velocity is about -2.2983m / s. Therefore, the radial velocity of the target is about 14.6508m / s.

[0144] like Fig.11 As shown in the figure, the radial acceleration of the target can be estimated to be about 0.8552m / s from the peak position in the figure 2 .

[0145] From the above analysis, it can be seen that the method of the present invention is suitable for processing measured data.

[0146] Embodiment 4:

[0147] The present invention also provides a weak target long-time accumulation detection system based on second-order keystone transform-non-uniform fast Fourier transform. The weak target long-time accumulation detection system based on second-order keystone transform-non-uniform fast Fourier transform can be realized by executing the process steps of the weak target long-time accumulation detection method based on second-order keystone transform-non-uniform fast Fourier transform, that is, those skilled in the art can understand the weak target long-time accumulation detection method based on second-order keystone transform-non-uniform fast Fourier transform as a preferred implementation of the weak target long-time accumulation detection system based on second-order keystone transform-non-uniform fast Fourier transform.

[0148] The weak target long-term accumulation detection system includes:

[0149] Module M1 receives the original radar echo signal and down-converts it to obtain the baseband echo signal s r (t,t m ), where t represents the fast time variable, t m represents a slow time variable;

[0150] Module M2, baseband echo signal s r (t,t m ) Perform range pulse pressure and range fast Fourier transform to obtain the echo signal S in the range frequency-slow time domain c (f,t m ), where f represents the distance frequency variable;

[0151] Module M3, for signal S c (f,t m ) Apply the second-order keystone transform to eliminate the second-order range migration caused by the target radial acceleration and obtain the echo signal S c (f,t n ), where t n is the transformed slow time variable;

[0152] Module M4, constructs a velocity matching filter bank H(f,t n ; V res ), V res is the target residual radial velocity after SoKT. The residual radial velocity term is eliminated by one-dimensional search to obtain the echo signal S MF (f,t n );

[0153] Module M5, for the echo signal S MF (f,t n ) Perform the distance fast inverse Fourier transform and slow time non-uniform fast Fourier transform in sequence to achieve target energy focusing and obtain the signal

[0154] Module M6, based on the echo signal S c (f,t n ) and velocity matching filter bank H(f,t n ; V res ), through the peak detection technique, we can obtain The peak information of the target can be obtained to estimate the radial acceleration and radial velocity of the target.

[0155] Those skilled in the art know that, in addition to realizing the system and its various devices, modules, and units provided by the present invention in a purely computer-readable program code, it is entirely possible to realize the same functions in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers by logically programming the method steps. Therefore, the system and its various devices, modules, and units provided by the present invention can be considered as a hardware component, and the devices, modules, and units included therein for realizing various functions can also be regarded as structures within the hardware component; the devices, modules, and units for realizing various functions can also be regarded as both software modules for realizing the method and structures within the hardware component.

[0156] The above describes the specific embodiments of the present invention. It should be understood that the present invention is not limited to the above specific embodiments, and those skilled in the art can make various changes or modifications within the scope of the claims, which does not affect the essence of the present invention. In the absence of conflict, the embodiments of the present application and the features in the embodiments can be combined with each other arbitrarily.

Claims

1. A weak target long-term accumulation detection method based on second-order keystone transform-non-uniform fast Fourier transform, characterized in that: The following steps are involved: Step S1, receiving the original radar echo signal and down-converting it to obtain the baseband echo signal s r (t,t m ), where t represents the fast time variable, t m represents a slow time variable; Step S2, the baseband echo signal s r (t,t m ) Perform range pulse pressure and range fast Fourier transform to obtain the echo signal S in the range frequency-slow time domain c (f,t m ), where f represents the distance frequency variable; Step S3, the signal S c (f,t m ) Apply the second-order keystone transform to eliminate the second-order range migration caused by the target radial acceleration and obtain the echo signal S c (f,t n ), where t n is the transformed slow time variable; Step S4, constructing a velocity matching filter group H(f,t n ; V res ), V res is the target residual radial velocity after SoKT. The residual radial velocity term is eliminated by one-dimensional search to obtain the echo signal S MF (f,t n ); Step S5: MF (f,t n ) Perform the distance fast inverse Fourier transform and slow time non-uniform fast Fourier transform in sequence to achieve target energy focusing and obtain the signal Step S6, based on the echo signal S c (f,t n ) and the velocity matching filter bank H(f,t n ; V res ), through the peak detection technique, we obtain The peak information of the target can be obtained to estimate the radial acceleration and radial velocity of the target.

2. According to claim 1, a weak target long-term accumulation detection method based on second-order keystone transform-non-uniform fast Fourier transform is characterized in that: In step S1, the radar receives a weak maneuvering target echo of a linear frequency modulation pulse, and the mathematical expression of the linear frequency modulation pulse signal is as follows: Where t is the fast time variable; T p is the pulse width; f c is the carrier frequency; μ is the modulation frequency; rect(·) is the rectangular window function; The instantaneous slant range between the radar and a target with constant radial acceleration is: Where r0 is the target initial slant distance; v is the target radial velocity; a is the target radial acceleration; t m =m / PRF (m=0,1,…,M-1) is the slow time; PRF is the pulse repetition frequency, After down-converting the target original echo signal, the target received baseband echo signal is expressed as: Where σ0 is the target scattering coefficient; c is the speed of light; λ is the wavelength.

3. According to claim 1, a weak target long-term accumulation detection method based on second-order keystone transform-non-uniform fast Fourier transform is characterized in that: In step S2, a matched filter associated with the transmitted signal is used to perform range pulse compression on the baseband signal, and a range fast Fourier transform is performed to obtain an echo signal in the range frequency-slow time domain. The mathematical expression is: In the formula, * and represent complex conjugate operation and convolution operation respectively, σ1 is the signal amplitude in the range frequency-slow time domain; f is the range frequency variable; B is the range bandwidth; N amb is the velocity fuzzy number; It is blind speed; is the target baseband velocity, and considering the target velocity ambiguity, its radial velocity is written as: v=N amb v amb +v base 。 4. According to claim 1, a weak target long-term accumulation detection method based on second-order keystone transform-non-uniform fast Fourier transform is characterized in that: In step S3, the second-order keystone expression is as follows: In the formula, f c is the radar carrier frequency, t n is the new slow time variable.

5. According to claim 1, a weak target long-term accumulation detection method based on second-order keystone transform-non-uniform fast Fourier transform is characterized in that: In step S3, after the second-order keystone transformation, the echo signal S c (f,t n ) is as follows: In the formula, is the residual radial velocity; N amb is the velocity fuzzy number; It is blind speed; is the baseband speed; c is the speed of light; λ is the wavelength.

6. According to claim 1, a weak target long-term accumulation detection method based on second-order keystone transform-non-uniform fast Fourier transform is characterized in that: In step S4, the velocity matching filter group H(f,t n ; V res ) is as follows: In the formula, v base =2[V res -round(V res / v amb )v amb ], round(·) is the rounding operation.

7. According to claim 1, a weak target long-term accumulation detection method based on second-order keystone transform-non-uniform fast Fourier transform is characterized in that: In step S4, the echo signal S after matching filtering is MF (f,t n ) is obtained as follows:

8. According to claim 1, a weak target long-term accumulation detection method based on second-order keystone transform-non-uniform fast Fourier transform is characterized in that: In step S5, the target energy focusing is achieved by the following mathematical expression: Where σ3 is the complex amplitude after the target is focused; For The corresponding frequency variables are sinc(·) for the Sigmund function and δ(·) for the Dirac delta function. is the slow-time non-uniform fast Fourier transform, IFFT f is the fast inverse Fourier transform of distance.

9. According to claim 1, a weak target long-term accumulation detection method based on second-order keystone transform-non-uniform fast Fourier transform is characterized in that: In step S6, the peak value is retrieved to obtain the motion parameter estimation value in the following manner: In the formula, the echo signal S c (f,t n ) is the signal obtained in step S3, H(f,t n ; V res ) is the velocity matched filter bank constructed in step S4; Radial acceleration estimate The formula is: Therefore, the estimation formula of the target radial velocity is as follows: In the formula, is the estimated radial residual velocity; is the estimated radial velocity, is the estimated value of baseband speed.

10. A weak target long-term accumulation detection system based on second-order keystone transform-non-uniform fast Fourier transform, characterized in that: include: Module M1 receives the original radar echo signal and down-converts it to obtain the baseband echo signal s r (t,t m ), where t represents the fast time variable, t m represents a slow time variable; Module M2, for the baseband echo signal s r (t,t m ) Perform range pulse pressure and range fast Fourier transform to obtain the echo signal S in the range frequency-slow time domain c (f,t m ), where f represents the distance frequency variable; Module M3, for signal S c (f,t m ) Apply the second-order keystone transform to eliminate the second-order range migration caused by the target radial acceleration and obtain the echo signal S c (f,t n ), where t n is the transformed slow time variable; Module M4, constructs the velocity matching filter bank H(f,t n ; V res ), V res is the target residual radial velocity after SoKT. The residual radial velocity term is eliminated by one-dimensional search to obtain the echo signal S MF (f,t n ); Module M5, for the echo signal S MF (f,t n ) Perform the distance fast inverse Fourier transform and slow time non-uniform fast Fourier transform in sequence to achieve target energy focusing and obtain the signal Module M6, based on the echo signal S c (f,t n ) and the velocity matching filter bank H(f,t n ; V res ), through the peak detection technique, we obtain The peak information of the target can be obtained to estimate the radial acceleration and radial velocity of the target.

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