A long-time coherent accumulation method for complex maneuvering targets

Abstract

The application discloses a long-time coherent accumulation method for complex maneuvering targets, and belongs to the technical field of radar signal processing, and comprises the following steps: (1) arranging echo signals received by a radar receiver according to fast time domain-slow time domain, and performing pulse compression processing on the signals in the fast time domain; (2) performing positive-order second-order keystone transformation and inverse-order second-order keystone transformation on the obtained signals respectively by using keystone transformation, multiplying the two signals, realizing decoupling of fast frequency and second-order slow time, and eliminating first-order and third-order range migration; (3) estimating target acceleration by using fractional Fourier transformation, and constructing an acceleration compensation function according to the estimation result to compensate for bending caused by the accelerator; and (4) transforming the signals to the fast time domain by inverse Fourier transformation, performing coherent accumulation, and detecting the accumulation result to extract target information. The application solves the problem of long-time coherent accumulation of radar on maneuvering targets with high-order motion models.

Description

Technical Field

[0001] The present invention belongs to the technical field of radar signal processing, and in particular relates to a long-time coherent integration method for complex maneuvering targets. Background Art

[0002] In recent years, with the development of the low-altitude economy, the number of drones has increased significantly. Low-altitude targets, such as drones, are highly maneuverable and have a small radar cross-section, resulting in a very low signal-to-noise ratio (SNR) in their return signals. According to relevant theory, radar system parameters are timed, and extended coherent integration can improve radar detection performance. However, for highly maneuverable targets, prolonged coherent integration can lead to range and Doppler shifts, preventing effective target energy accumulation. This poses a significant challenge to current low-altitude target monitoring.

[0003] Traditional radar coherent integration methods assume that the target's echo signal is always within a range gate and has a fixed motion model, preventing cross-range gate and Doppler fluctuations. However, for highly maneuverable, faint targets, the target echo signal will cross multiple range gates as the integration time increases. Furthermore, the target's motion model is not fixed in different time periods, resulting in severe range and Doppler fluctuations after coherent integration. Existing solutions typically perform a traversal search on multiple parameters, resulting in a large amount of computation. Furthermore, these solutions only consider the case of targets with uniformly variable speed motion, resulting in poor accumulation performance for targets with complex motion models. Summary of the Invention

[0004] Purpose of the invention: To provide a long-term coherent integration method for complex maneuvering targets, which solves the problem of long-term coherent integration of radar for maneuvering targets with high-order motion models.

[0005] Technical solution: A long-term coherent integration method for complex maneuvering targets, including the following steps:

[0006] Step 1: Arrange the echo signals received by the radar receiver according to the fast time domain-slow time domain to obtain the data matrix s r (τ,t m ), pulse compression processing is performed on the signal in the fast time domain to obtain the data matrix s in the fast frequency domain-slow time domain p (f,t m ), where τ is the fast time, t m is the slow time, and f is the corresponding frequency in the fast time domain;

[0007] Step 2: Use the keystone transformation to transform the data matrix s obtained in step 1 p (f,t m) Perform positive sequence second-order Keystone transform and reverse sequence second-order Keystone transform in the slow time domain to obtain two data matrices s after decoupling the fast frequency and the second-order slow time. p (f,t' m ) and s p (f,-t' m ), multiply the two signals and get the data matrix T(f,t') that eliminates the first-order and third-order range movement. m ), where t' m It is the virtual slow time in the keystone transformation;

[0008] Step 3: Use fractional Fourier transform to estimate the target acceleration a, and construct the acceleration compensation function g(t' m ) to compensate for the bending caused by the accelerator;

[0009] Step 4: Transform the signal into the fast time domain through inverse Fourier transform to obtain the data matrix T c (τ,t' m ), and perform coherent accumulation, and detect the accumulation results to extract the target information.

[0010] Furthermore, the specific operation method of step one is as follows:

[0011] 1) The expression of the radar transmission signal in a single pulse period is:

[0012] s(τ)=u(τ)·exp(j2πf0τ) (1)

[0013] Where τ is the fast time, u(τ) is the waveform emitted by the radar, f0 is the carrier frequency, exp(·) represents the exponential function with the natural logarithm e as the base, and j is the imaginary unit;

[0014] 2) The target is at t m The distance from the radar receiver at the moment is:

[0015]

[0016] Among them, t m is the slow time, R (n) is the nth derivative of the distance, is the nth power of the slow time, n=1,2,3,…. Usually, the coefficients of the fourth and higher order terms are very small and can be ignored. The target distance R(t m ) can be written as:

[0017]

[0018] Wherein, R0 is the distance of the target from the radar receiver at 0 moment, v0 is the radial velocity of the target at 0 moment, a0 is the radial acceleration of the target at 0 moment, j0 is the radial acceleration change rate of the target at 0 moment;

[0019] 3), the radar receiver receives the echo signal and down-converts to obtain the data matrix s arranged according to fast time domain-slow time domain r (τ,t m ):

[0020]

[0021] Wherein, c is the speed of light;

[0022] The pulse compression processing is performed on the signal in the fast time domain to obtain the data matrix s in the fast frequency domain-slow time domain p (f,t m );

[0023]

[0024] Wherein, f is the corresponding frequency in the fast time domain, U(f) is the frequency domain expression of the radar transmission waveform; R(t m ) is substituted into s p (f,t m ):

[0025]

[0026] Further, the specific operation method of the step two is as follows:

[0027] The data matrix s p (f,t m ) obtained in the step one is respectively subjected to the positive order second-order keystone transformation and the inverse order second-order keystone transformation in the slow time domain to obtain s p (f,t' m ) and s p (f,-t' m ):

[0028]

[0029] Wherein, t' m is the virtual time of the signal after the keystone transformation, at this time, the virtual second-order slow time f has been decoupled, the multiplication of the two data matrices s p (f,t' m ) and s p (f,-t' m ) is performed to obtain the data matrix T(f,t'm );

[0030]

[0031] Furthermore, the specific operation method of step three is as follows:

[0032] For the data matrix T(f,t' obtained in step 2 m ) Perform a fractional Fourier transform (FrFT) in the virtual slow time direction:

[0033]

[0034] Formula (10) can be transformed to obtain:

[0035]

[0036] Among them, α is the transformation angle of fractional Fourier transform, u is the domain after fractional Fourier transform, Inside, F α [T(f,t' m )] has an extreme value, at which:

[0037]

[0038] The target acceleration a0 can be obtained by solving formula (12); the acceleration compensation function g(t m ):

[0039]

[0040] For the data matrix T(f,t' m ) to compensate and obtain the compensated data matrix T c (f,t' m ):

[0041]

[0042] Furthermore, the specific operation method of step 4 is as follows:

[0043] The data matrix T is transformed by inverse Fourier transform c (f,t' m ) is transformed into the fast time domain to obtain the data matrix T c (τ,t' m ):

[0044]

[0045] Where u s (τ) is |U(f)| 4The time domain expression after inverse Fourier transform, the data matrix T c (τ,t' m ) is accumulated in phase, a peak will be formed at the point of (τ,f' a ) plane, containing the position and acceleration signal of the target, realizing the phase accumulation of the maneuvering target with high order motion model.

[0046] Beneficial effects: the application solves the problem of difficult accumulation of maneuvering target energy in long time phase accumulation, considers the case of target with high order motion model, estimates the motion parameters of the target, reduces the operation time, and effectively improves the phase accumulation detection ability of radar to the maneuvering target with high order motion model. BRIEF DESCRIPTION OF DRAWINGS

[0047] Figure 1 The flow chart of the application;

[0048] Figure 2 The result schematic diagram of the signal pulse compression processing received by the radar receiver;

[0049] Figure 3 The result schematic diagram of the traditional phase accumulation processing;

[0050] Figure 4 The result schematic diagram of the phase accumulation after the signal multiplication of the positive order and negative order keystone transformation;

[0051] Figure 5 The result schematic diagram of the target acceleration estimation by fractional Fourier transform;

[0052] Figure 6 The result schematic diagram of the phase accumulation after the acceleration bending compensation. DETAILED DESCRIPTION

[0053] The technical solutions of the application will be described in detail below with reference to the drawings, but the protection scope of the application is not limited to the described embodiments.

[0054] As Figure 1 ​As shown, the application provides a long-time coherent accumulation method for complex maneuvering targets. In the first step, the echo signal received by the radar receiver is arranged according to the fast time domain-slow time domain, the signal is pulse compressed in the fast time domain, and a data matrix in the fast frequency domain-slow time domain is obtained. In the second step, the signal obtained in the previous step is subjected to forward-order second-order keystone transformation and reverse-order second-order keystone transformation respectively using keystone transformation, and the two signals are multiplied to realize decoupling of the fast frequency and the second-order slow time, and eliminate the first-order and third-order range migration. In the third step, the fractional Fourier transform is used to estimate the target acceleration, and an acceleration compensation function is constructed according to the estimation result to compensate for the bending caused by the accelerator. In the fourth step, the signal is transformed to the fast time domain through inverse Fourier transform, coherent accumulation is performed, and the accumulation result is detected to extract target information.

[0055] The expression of the radar transmitted signal in a single pulse period is:

[0056] s(τ)=u(τ)·exp(j2πf0τ) (1)

[0057] Wherein, τ is the fast time, u(τ) is the waveform of the radar transmission, f0 is the carrier frequency, exp(·) represents the exponential function with the natural logarithm e as the base, and j is the imaginary unit.

[0058] The distance between the target and the radar receiver at t m is:

[0059]

[0060] Wherein t m is the slow time, R (n) is the n-th derivative of the distance, is the n-th power of the slow time, n=1, 2, 3, …, and in the usual case, the coefficients of the fourth and higher order terms are very small and can be ignored. The target distance R(t m ) can be written as:

[0061]

[0062] Wherein R0 is the distance between the target and the radar receiver at 0 time, v0 is the radial velocity of the target at 0 time, a0 is the radial acceleration of the target at 0 time, and j0 is the radial acceleration change rate of the target at 0 time.

[0063] The radar receiver receives the echo signal and performs frequency down-conversion to obtain a data matrix s r (τ, t m ) arranged according to the fast time domain-slow time domain:

[0064]

[0065] wherein c is the speed of light;

[0066] The signal is pulse compressed in the fast time domain to obtain a data matrix s p (f,t m ) in the fast frequency-slow time domain

[0067]

[0068] wherein f is the corresponding frequency in the fast time domain, and U(f) is the frequency domain expression of the radar transmitted waveform. Substitute R(t m ) into s p (f,t m ):

[0069]

[0070] The data matrix s p (f,t m ) is respectively subjected to a forward second-order keystone transform and an inverse second-order keystone transform in the slow time domain to obtain s p (f,t' m ) and s p (f,-t' m ):

[0071]

[0072] wherein t' m is the virtual time of the signal after the keystone transform, and the virtual second-order slow time f has been decoupled, and the data matrix T(f,t' p ) eliminating the first-order and third-order range migration is obtained by multiplying the two data matrices s m (f,t' p ) and s m (f,-t' m );

[0073]

[0074] The data matrix T(f,t' m ) is subjected to a fractional Fourier transform (FrFT) in the virtual slow time direction:

[0075]

[0076] The formula (10) can be obtained by transformation:

[0077]

[0078] Among them, α is the transformation angle of fractional Fourier transform, u is the domain after fractional Fourier transform, Inside, F α [T(f,t' m )] has an extreme value, at which:

[0079]

[0080] The target acceleration a0 can be obtained by solving formula (12). The acceleration compensation function g(t m ):

[0081]

[0082] For the data matrix T(f,t' m ) to compensate and obtain the compensated data matrix T c (f,t' m ):

[0083]

[0084] The data matrix T is transformed by inverse Fourier transform c (f,t' m ) is transformed into the fast time domain to obtain the data matrix T c (τ,t' m ):

[0085]

[0086] Where u s (τ) is |U(f)| 4 The time domain expression after inverse Fourier transform. c (τ,t' m ) for coherent accumulation, at (τ,f' a ) on the plane A peak will be formed at the point, which contains the position and acceleration signals of the target, realizing the coherent accumulation of the maneuvering target with a high-order motion model.

[0087] Matlab is used to conduct simulation experiments to verify the method proposed in the present invention. The experimental results show the effectiveness of the method proposed in the present invention. The simulation results are described below:

[0088] Simulation parameters: sampling rate 122.88NHz, radar carrier frequency 2.52495GHz, pulse repetition frequency 5000Hz, number of accumulated pulses 10000, target initial distance 500m, target initial velocity 50m / s, target initial acceleration 20m / s 2, target initial acceleration change rate 10 m / s 3 .

[0089] In the first step of the present application, the radar signal received by the radar receiver is pulse compressed to obtain a one-dimensional range profile containing multi-order curvature caused by target motion, as shown in Figure 2 ; the result of coherent accumulation of the data obtained in the first step is shown in Figure 3 ; a large number of range walks and Doppler walks result in ineffective accumulation of target energy; the signal obtained in the first step is subjected to forward second-order keystone transformation and reverse second-order keystone transformation using keystone transformation, and the two signals are multiplied to realize decoupling of fast frequency and second-order slow time, and eliminate first-order and third-order range walks, as shown in Figure 4 ; the result of the second step is shown in Figure 4 ; the result of the second step is shown in Figure 5 ; the result of the third step fractional Fourier transform for target acceleration estimation is shown in the figure, the two dimensions in the figure are the transformation angle of fractional Fourier transform and the domain after fractional Fourier transform, respectively, the target acceleration can be estimated according to the value at the extreme point in the figure, and an acceleration compensation function is constructed according to the estimation result to compensate for the curvature caused by the accelerator; in the fourth step, the signal is transformed to the fast time domain through inverse Fourier transform, and coherent accumulation is performed, as shown in Figure 6 ; the target energy is accumulated at a point, that is, good coherent accumulation effect is achieved. Therefore, the method has good accumulation effect, and compared with the existing method, the operation time is reduced, and the coherent accumulation detection capability of the radar for the maneuvering target with high-order motion model is effectively improved.

[0090] As described above, although the present application has been shown and described with reference to specific preferred embodiments, it is to be understood that the present application is not to be limited to the details of the foregoing illustrated embodiments. Various changes in form and detail can be made without departing from the spirit and scope of the present application.

Claims

1. A long-term coherent integration method for complex maneuvering targets, characterized by: The steps include: Step 1: Arrange the echo signals received by the radar receiver according to the fast time domain-slow time domain to obtain the data matrix , perform pulse compression processing on the signal in the fast time domain to obtain the data matrix in the fast frequency domain-slow time domain ,in, For fast time, For slow time, is the corresponding frequency in the fast time domain; Step 2: Use the keystone transformation to transform the data matrix obtained in step 1 Perform positive sequence second-order Keystone transform and reverse sequence second-order Keystone transform in the slow time domain to obtain two data matrices after decoupling the fast frequency and the second-order slow time. and , multiply the two signals to obtain the data matrix that eliminates the first-order and third-order range movement ,in, It is the virtual slow time in the keystone transformation; Step 3: Estimate the target acceleration using fractional Fourier transform , construct the acceleration compensation function based on the estimation results , to compensate for the bending caused by the accelerator; Step 4: Transform the signal to the fast time domain through inverse Fourier transform to obtain the data matrix , and perform coherent accumulation, and detect the accumulation results to extract target information.

2. The long-term coherent integration method for complex maneuvering targets according to claim 1, characterized in that: The specific operation method of step one is as follows: 1) The expression of the radar transmission signal in a single pulse period is: （1） in, For fast time, is the waveform emitted by the radar, is the carrier frequency, Expressed in natural logarithm The exponential function of base is is an imaginary unit; 2) The goal is The distance from the radar receiver at the moment is: （2） in, For slow time, For distance derivatives, For slow time Power, , target distance for: （3） in, is the distance between the target and the radar receiver at time 0, is the radial velocity of the target at time 0, is the radial acceleration of the target at time 0, is the radial acceleration change rate of the target at time 0; 3) The radar receiver receives the echo signal and performs down-conversion to obtain a data matrix arranged in the fast time domain-slow time domain. : （4） in, is the speed of light; Perform pulse compression processing on the signal in the fast time domain to obtain a data matrix in the fast frequency domain-slow time domain ; （5） in, is the corresponding frequency in the fast time domain, is the frequency domain expression of the radar emission waveform; Substitution middle: （6）。 3. The long-term coherent integration method for complex maneuvering targets according to claim 2, characterized in that: The specific operation method of step 2 is as follows: For the data matrix obtained in step 1 Perform positive sequence second-order Keystone transform and reverse sequence second-order Keystone transform in the slow time domain, and we get and : （7） （8） in, is the virtual time after the signal is keystone transformed. At this time, the virtual second-order slow time With fast frequency Decoupled, the two data matrices and Multiply them together to get the data matrix that eliminates the first-order and third-order distance movement. ; （9）。 4. The long-term coherent integration method for complex maneuvering targets according to claim 3, characterized in that: The specific operation method of step three is as follows: For the data matrix obtained in step 2 Take the fractional Fourier transform in the imaginary slow time direction: （10） Formula (10) can be transformed to obtain: （11） in, is the transformation angle of fractional Fourier transform, is the domain after fractional Fourier transform, Inside, There is an extreme value, at which: （12） Solution formula Target acceleration can be obtained ; Construct acceleration compensation function based on the estimated target acceleration : （13） For the data matrix Perform compensation and obtain the compensated data matrix : （14）。 5. The long-term coherent integration method for complex maneuvering targets according to claim 4, characterized in that: The specific operation method of step 4 is as follows: The data matrix is ​​transformed by inverse Fourier transform Transform to the fast time domain and get the data matrix : （15） In the formula for The time domain expression after inverse Fourier transform is the data matrix Perform coherent accumulation, On the plane A peak will be formed at the point, which contains the position and acceleration signals of the target, realizing the coherent accumulation of the maneuvering target with a high-order motion model.

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