Method for acquiring high-resolution one-dimensional range profile (HRRP) of high-speed moving target of frequency agile radar based on sparse processing

Abstract

The invention belongs to the field of radar signal processing, discloses a method for acquiring a one-dimensional range profile of a high-speed moving target by sub-pulse linear frequency modulation emission and inter-pulse frequency agility radar, and realizes frequency agility waveform echo high-speed target detection and correction based on sparse representation. In the prior art, distance and Doppler parameter estimation of target echoes can be generally realized by adopting sparse representation and sparse processing, and orthogonal matching pursuit (OMP) is one of common solution algorithms. The carrier frequency of a frequency agility radar jumps randomly between pulses, and the acquisition of a one-dimensional range profile of a high-speed moving target not only needs to correct inter-pulse range migration, but also needs to compensate intra-pulse range-Doppler coupling generated by the change of the carrier frequency. According to the method, firstly, compensation of intra-pulse distance-Doppler coupling is carried out, then distance migration correction is carried out on each frequency agility pulse based on a KeyStone method, sparse processing is carried out on a corrected echo signal by adopting an orthogonal matching pursuit algorithm, and a high-resolution one-dimensional distance image of a target is obtained. Experimental results show that the one-dimensional range profile processing method for performing inter-pulse range migration correction through the KeyStone algorithm is beneficial to target detection in high-speed motion.

Description

Technical Field

[0001] This invention belongs to the field of radar signal processing, specifically relating to a method for acquiring high-resolution one-dimensional range profiles of high-speed moving targets in frequency-agile radar based on sparse processing. Technical Background

[0002] Frequency-agile radar possesses excellent low-interception and anti-jamming performance. Renowned for its outstanding low-interception characteristics and anti-jamming capabilities, frequency-agile radar has been widely researched and applied in the radar field. The frequency-agile waveform is academically referred to as a random step-frequency waveform, characterized by rapid and random jumps in the carrier frequency of the radar pulse. Target range migration refers to the phenomenon where, during long-term accumulation of radar signals, the observed target echo envelope may cross multiple range gates. This phenomenon becomes more pronounced with increasing target velocity and longer accumulation time, and is typically corrected using the Keystone method for inter-pulse range migration. The Keystone transform is a classic radar target range migration correction tool. Its core concept is to establish a virtual slow time to decouple the fast-time frequency from the slow-time frequency. When target velocity ambiguity exists, ambiguity number estimation is performed for phase compensation. This process primarily addresses cases where the target only has radial velocity. However, if the target has higher-order terms such as acceleration or jerk, higher-order KT methods need to be considered, with the core concept remaining the same. In high-speed target detection, combining linear frequency modulation (LFM) signals with Keystone transform is a suitable option. Summary of the Invention

[0003] The purpose of this invention is to overcome the shortcomings of the prior art and propose a method for acquiring high-resolution one-dimensional range profiles of high-speed moving targets using frequency agile radar based on sparse processing. This method improves existing target detection algorithms based on sparse processing. The algorithm establishes a frequency agile radar echo signal after KeyStone transformation for high-speed moving targets, constructs a sparse processing model based on the target echo after KeyStone transformation, and then uses the OMP algorithm for iterative calculation to obtain sparse solutions, thereby realizing sparse reconstruction of high-speed targets.

[0004] To achieve the above objectives, the present invention employs the following technical methods.

[0005] A method for acquiring high-resolution one-dimensional range images of high-speed moving targets using frequency-agile radar based on sparse processing includes the following steps:

[0006] Step 1: Establish a signal model x where the transmitted signal is a frequency-agile waveform. T(t) The obtained radar echo signal is pulse compressed and then intra-pulse Doppler compensation is performed to obtain the target echo signal model x after pulse compression. m (t);

[0007] Step 2: Perform KeyStone transform on the pulse-compressed target echo signal to compensate for the range migration in the coarse-resolution dimension caused by high-speed motion, and establish the target echo signal model X after inter-pulse Doppler compensation. final-Keystone (f, t) k );

[0008] Step 3: Calculate the range resolution and velocity resolution, as well as the high-resolution range and high-resolution velocity, corresponding to the radar echo signal after pulse compression processing, and divide the signal into high-resolution range grids and high-resolution velocity grids. Based on sparse signal processing theory, construct the high-resolution range-velocity dictionary matrix ψ under different coarse-resolution range units to complete target detection in sparse frequency agile waveform scenarios.

[0009] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0010] (1) The KeyStone algorithm was introduced to obtain the one-dimensional range image of a high-speed moving target, which overcomes the difficulty of obtaining the one-dimensional range image of the target due to the distance migration of the high-speed moving target and effectively corrects the true position of the target.

[0011] (2) When processing the frequency-agile waveform echo signal, the sparse reconstruction theory is introduced to overcome the difficulties of the traditional fast Fourier transform Doppler processing method and effectively obtain the one-dimensional range image of the target. Attached Figure Description

[0012] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0013] Figure 1 It is a method for acquiring high-resolution one-dimensional range images of high-speed moving targets in frequency-agile radar based on sparse processing.

[0014] Figure 2 This is a simulation of a range gate detection image on the Matlab platform after range migration correction without KeyStone transformation.

[0015] Figure 3 This is a simulation on the Matlab platform of a high-resolution distance-velocity detection planar image based on the OMP algorithm without KeyStone transformation.

[0016] Figure 4 This is a distance gate detection image after distance migration correction using KeyStone transform, simulated on the Matlab platform.

[0017] Figure 5 This is a high-resolution distance-velocity detection planar image based on the OMP algorithm after KeyStone transformation simulation on the Matlab platform. Detailed Implementation

[0018] The present invention will be further described below with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and should not be used to limit the scope of protection of the present invention.

[0019] like Figure 1 As shown, the frequency-agile waveform target detection method based on the RNC-OMP algorithm includes the following steps:

[0020] Step 1: Establish the LFM echo signal model under frequency agility conditions. T (t) The obtained radar echo signal is pulse compressed, and then the echo model x is established after compensating for the intra-pulse range-Doppler coupling term. m (t);

[0021] Specifically, step 1 includes the following sub-steps:

[0022] Sub-step 1.1: The radar transmits M pulses in one frame. The carrier frequency of the m-th pulse can be expressed as:

[0023] f m =f0+a m Δf,m=0,1,…,M-1 (1)

[0024] The transmitted signal of the m-th pulse can be represented as:

[0025] x T (t)=x(t)exp(j2πf m t) (2)

[0026] Regarding the symbols appearing in the above formula, f0 represents the initial carrier frequency of the radar, and a m Let t be a randomly varying integer sequence, Δf be the minimum frequency hopping interval, and A be the number of frequency hopping. k +t m Representing the total time, x(t) is the baseband waveform, T r The pulse repetition period is t, where j is the imaginary unit and t is the pulse repetition period. k t represents fast time. m =mT r It indicates a slow time.

[0027] Assuming the radar transmits pulse signals using a linear frequency modulated (LFM) signal pattern, the m-th pulse transmitted by the radar can be expressed as:

[0028]

[0029] In the formula, μ is the linear frequency modulation, T p The transmitted signal pulse width is μ = B / T p B is the transmission signal bandwidth, and the lth k The distance corresponding to each distance gate is l k When = 0, the corresponding distance is R0, and the target distance is . This corresponds to the distance traveled in a fast time, and the corresponding number of doors is... ΔR is a single distance gate, ΔR = c / 2f s Let the radial velocity of the target be vm / s, and the distance of the target on the m-th pulse be: The corresponding distance gate is:

[0030] Sub-step 1.2 involves down-converting and pulse compression of the initial radar echo signal. The compressed radar echo signal can then be expressed as:

[0031]

[0032] By sampling the signal, the fast and slow time matrix of the m-th pulse can be obtained as follows:

[0033]

[0034] In the formula, A door that indicates the distance traveled in slow time.

[0035] Step 2: Perform a fast Fourier transform on the obtained frequency-agile radar echo model in the fast time dimension. In the frequency domain, use the sinc function interpolation method and the KeyStone algorithm to correct the inter-pulse range migration caused by high-speed motion in the frequency-agile radar echo, and establish the echo model X after KeyStone transform compensation for inter-pulse Doppler. final-Keystone (f, t) k ).

[0036] Specifically, step 2 includes the following sub-steps:

[0037] Sub-step 2.1 involves performing range migration correction using the KeyStone algorithm on the radar echo signal after pulse compression processing. Firstly, due to the inter-pulse variation of the carrier frequency in the frequency-agile waveform, intra-pulse Doppler occurs. The resulting range-Doppler coupling varies, leading to detection errors. Therefore, compensating for intra-pulse Doppler yields:

[0038]

[0039] Ideally, the fast-time-slow-time matrix, ignoring inter-pulse distance migration, is:

[0040]

[0041] Performing an FFT on the fast time yields:

[0042]

[0043] The frequency-agile radar echo signal after pulse-Doppler compensation is as follows:

[0044]

[0045] Sub-step 2.2, performing an FFT on the frequency-agile radar echo signal after pulse Doppler compensation yields:

[0046]

[0047] Comparison X ideal (f, m) and X real It can be observed that, ideally, f and v have no overlapping terms. In this case, the KeyStone transform is used to eliminate the overlapping terms of f and v to correct for distance migration caused by inter-pulse Doppler. The KeyStone transform corrects distance migration through a slow-time coordinate transformation. The slow-time term in the case of distance migration occurs at time t. m =mT r Sampling of the signal, X real (f, m) can be rewritten as:

[0048]

[0049] Define a virtual time t k Make We can obtain:

[0050]

[0051] Using Sink interpolation to implement the Keystone transform, the echo model X after inter-pulse Doppler compensation can be obtained. final-Keystone (f, t) k ):

[0052]

[0053] Step 3: Calculate the range resolution and velocity resolution, as well as the high-resolution range and high-resolution velocity, corresponding to the radar echo signal after pulse compression processing, and divide the signal into high-resolution range grids and high-resolution velocity grids. Based on sparse signal processing theory, construct the high-resolution range-velocity dictionary matrix ψ for different coarse-resolution range units; use the OMP algorithm to sparsely reconstruct the echo signal under the coarse-resolution range unit, obtain the high-resolution range-velocity measurement results under that coarse-resolution range unit, and save the results, thus completing target detection in a frequency-agile waveform sparse scene.

[0054] Specifically, step 3 includes the following sub-steps:

[0055] Sub-step 3.1: Based on sparse signal processing theory, construct the high-resolution range-velocity dictionary matrix ψ for different coarse-resolution range-velocity units. Divide a coarse-resolution range unit into P high-resolution range units, and divide the velocity range into Q velocity grid points. Let R be the distance corresponding to the p-th (p = 1, 2, ..., P) range grid point. p The velocity magnitude corresponding to the q-th (q = 1, 2, ..., Q) velocity grid point is v. q To facilitate sparsity handling, new variables are defined as follows:

[0056]

[0057] Where θ is the target scattering coefficient at the p-th range grid point and the q-th velocity grid point. For distance, This is the velocity term. When the target distance satisfies R0 = R p The target velocity satisfies v = v q hour, Includes distance information to the target. It contains the target's velocity information. The echo signal can then be represented as:

[0058]

[0059] This allows us to construct a dictionary matrix, where each atom contains distance and velocity information of the possible location of the target. The submatrix element corresponding to the i-th distance grid point is:

[0060]

[0061] Matrix ψ p The dimension is P×Q. Then the matrix ψ can be used. p Representing the dictionary matrix Ω:

[0062] Ω=[ψ1 ψ2 … ψ P (17)

[0063] The dictionary matrix Ω has dimensions M×PQ, where M is the number of emitted pulses. Using the above definitions of symbols and formulas, the sparse representation model can be expressed as:

[0064] Y=Ωθ+ε (18)

[0065] In the formula, Y is the observation vector, θ is the scattering coefficient, and ε is the noise. The observation vector Y is the echo signal after KeyStone transformation.

[0066] Sub-step 3.2 introduces the Orthogonal Matching Pursuit (OMP) algorithm, and the iterative steps of the OMP algorithm are given below:

[0067] Input: Observation data vector Y, dictionary matrix Ω.

[0068] Step 1 of iteration: Define the initial residual e0 = Y; set of atomic indices. The number of iterations z = 1, and the number of iterations for the initial residual z = 0. 。

[0069] The second step of the iteration is to calculate the inner product between each atom in the dictionary Ω and the residual, that is, to find the atom in the dictionary matrix Ω that best matches the residual (with the largest absolute value of the inner product), and store the position of this atom as λ. (z) Update the location of the atom and the set of atoms: Λ (z) =Λ (z-1) ∪λ (z) ,

[0070] Iteration step 3: Update residual e z =e z-1 -ρ (z) e z-1 =(I-ρ (z) )e z-1 , where ρ (z) Defined as Ω (z) orthogonal projection operator ρ of column space (z) =Ω (z) [(Ω (z) ) T Ω (z) ] -1 (Ω (z) ) T Then iterate through the residuals and perform steps two and three;

[0071] Fourth step of iteration: Calculate the sparse solution

[0072] Fifth iteration: If z = z max If the residual is less than the threshold, stop the iteration; otherwise, increment the iteration count k by 1 and jump to step (2).max The number of iterations is preset to estimate the target sparsity.

[0073] Output: Sparse solution vector θ.

[0074] Table 1 Simulation parameter settings

[0075] Parameter name Parameter size <![CDATA[Initial carrier frequency f0]]> 3GHz Minimum frequency hopping interval Δf 5MHz Number of frequency points K 40 Number of transmitted pulses M 40 <![CDATA[Pulse repetition period T r > 1ms <![CDATA[Pulse width T of the LFM signal p > 50us <![CDATA[LFM signal bandwidth B p > 5MHz

[0076] Four scattering points are set up in the radar observation scenario. The distances of these scattering points from the radar are 99988m, 99991.8m, 100000m, and 100006m, respectively. The moving speed of the four scattering points is 2500m / s.

[0077] Figure 2 and Figure 4 The figures show the range gate migration of a high-speed moving target before and after KeyStone transformation. It is clear from the figures that before KeyStone transformation to compensate for inter-pulse range migration, the result after pulse compression is a diagonal line, indicating that the target crosses multiple range gates. After KeyStone transformation to correct inter-pulse range migration... Figure 2 The "slashes" in the text have been corrected to "straight lines".

[0078] Figure 3 and Figure 5 The images show the sparse reconstruction of the target detection plane before and after the KeyStone transform. Before KeyStone transform to compensate for inter-pulse range migration, sparse processing cannot reconstruct the one-dimensional range image of the target. This is because the input observation vector moves across multiple range gates, causing a decrease in the matching performance of atoms in the dictionary matrix. After the KeyStone transform, sparse processing accurately reconstructs the range and velocity of the four target scattering points. This is because the position of the input observation vector is corrected to the range gate where the first pulse is located, improving the matching degree between atoms in the dictionary matrix and the observation vector, thus leading to an improvement in the dilution reconstruction performance.

[0079] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for acquiring high-resolution one-dimensional range profiles (HRRP) of high-speed moving targets using frequency-agile radar based on sparse processing, characterized in that... Includes the following steps: Step 1: Establish the LFM echo signal model under frequency agility conditions. T (t) The obtained radar echo signal is pulse compressed, and then the echo model x is established after compensating for the intra-pulse range-Doppler coupling term. m (t); Step 2: Perform a fast Fourier transform on the obtained frequency-agile radar echo model in the fast time dimension. In the frequency domain, use the sinc function interpolation method and the KeyStone algorithm to correct the inter-pulse range migration caused by high-speed motion in the frequency-agile radar echo, and establish the echo model X after KeyStone transform compensation for inter-pulse Doppler. final-Keystone (f, t) k ). Step 3: Calculate the range resolution and velocity resolution, as well as the high-resolution range and high-resolution velocity, corresponding to the radar echo signal after pulse compression processing, and divide the signal into high-resolution range grids and high-resolution velocity grids. Based on sparse signal processing theory, construct the high-resolution range-velocity dictionary matrix ψ for different coarse-resolution range units; use the OMP algorithm to sparsely reconstruct the echo signal under the coarse-resolution range unit, obtain the high-resolution range-velocity measurement results under that coarse-resolution range unit, and save the results, thus completing target detection in a frequency-agile waveform sparse scene.

2. The method for acquiring high-resolution one-dimensional range profiles (HRRP) of high-speed moving targets using frequency-agile radar based on sparse processing according to claim 1, characterized in that, Step 1 includes the following sub-steps: Sub-step 1.1: The radar transmits M pulses within one frame, with the carrier frequency of the transmitted pulses randomly varying within a certain synthetic bandwidth. The carrier frequency of the m-th pulse can be expressed as: R m =f0+a m Δf,m=0,1,...,M-1 The transmitted signal of the m-th pulse can be represented as: x T (t)=x(t)exp(j2πf m t) Regarding the symbols appearing in the above formula, f0 represents the initial carrier frequency of the radar, and a m Let t be a randomly varying integer sequence, Δf be the minimum frequency hopping interval, and A be the number of frequency hopping. k +t m Representing the total time, x(t) is the baseband waveform, T r The pulse repetition period is t, where j is the imaginary unit and t is the pulse repetition period. k t represents fast time. m =mT r It indicates a slow time. Assuming the radar transmits pulse signals using a linear frequency modulated (LFM) signal pattern, the m-th pulse transmitted by the radar can be expressed as: In the formula, μ is the linear frequency modulation, T p The transmitted signal pulse width is μ = B / T p B is the transmission signal bandwidth, and the lth k The distance corresponding to each distance gate is l k When = 0, the corresponding distance is R0, and the target distance is . This corresponds to the distance traveled in a fast time, and the corresponding number of doors is... ΔR is a single distance gate, ΔR = c / 2f s Let the radial velocity of the target be vm / s, and the distance of the target on the m-th pulse be: The corresponding distance gate is: Sub-step 1.2 involves down-converting and pulse compression of the initial radar echo signal. The compressed radar echo signal can then be expressed as: By sampling the signal, the fast and slow time matrix of the m-th pulse can be obtained as follows: In the formula, A door that indicates the distance traveled in slow time.

3. The method for acquiring high-resolution one-dimensional range profiles (HRRP) of high-speed moving targets using frequency-agile radar based on sparse processing according to claim 2, characterized in that, Step 2 includes the following sub-steps: Sub-step 2.1 involves performing range migration correction using the KeyStone algorithm on the radar echo signal after pulse compression processing. Firstly, due to the inter-pulse variation of the carrier frequency in the frequency-agile waveform, intra-pulse Doppler occurs. The resulting range-Doppler coupling varies, leading to detection errors. Therefore, compensating for intra-pulse Doppler yields: Ideally, the fast-time-slow-time matrix, ignoring inter-pulse distance migration, is: Performing an FFT on the fast time yields: The frequency-agile radar echo signal after pulse-Doppler compensation is as follows: Sub-step 2.2: Performing an FFT on the frequency-agile radar echo signal after pulse Doppler compensation yields the following results: Comparison X ideal (f, m) and X real It can be observed that, ideally, f and v have no overlapping terms. In this case, the KeyStone transform is used to eliminate the overlapping terms of f and v to correct for distance migration caused by inter-pulse Doppler. The KeyStone transform corrects distance migration through a slow-time coordinate transformation. The slow-time term in the case of distance migration occurs at time t. m =mT r Sampling of the signal, X real (f, m) can be rewritten as: Define a virtual time t k Make , can be obtained Using Sink interpolation to implement the Keystone transform, the echo model X after inter-pulse Doppler compensation can be obtained. final-Keystone (f, t) k ):

4. The method for acquiring high-resolution one-dimensional range profiles (HRRP) of high-speed moving targets using frequency-agile radar based on sparse processing according to claim 3, characterized in that, Step 3 includes the following sub-steps: Sub-step 3.1: Based on sparse signal processing theory, construct the high-resolution range-velocity dictionary matrix ψ for different coarse-resolution range-velocity units. Divide a coarse-resolution range unit into P high-resolution range units, and divide the velocity range into Q velocity grid points. Let R be the distance corresponding to the p-th (p = 1, 2, ..., P) range grid point. p The velocity magnitude corresponding to the q-th (q = 1, 2, ..., Q) velocity grid point is v. q To facilitate sparsity handling, new variables are defined as follows: Where θ is the target scattering coefficient at the p-th range grid point and the q-th velocity grid point. For distance, This is the velocity term. When the target distance satisfies R0 = R p The target velocity satisfies v = v q hour, Includes distance information to the target. It contains the target's velocity information. The echo signal can then be represented as: This allows us to construct a dictionary matrix, where each atom contains distance and velocity information of the possible location of the target. The submatrix element corresponding to the i-th distance grid point is: Matrix ψ p The dimension is P×Q. Then the matrix ψ can be used. p Representing the dictionary matrix Ω: Ω=[ψ1 ψ2 … ψ P ] The dictionary matrix Ω has dimensions M×PQ, where M is the number of emitted pulses. Using the above definitions of symbols and formulas, the sparse representation model can be expressed as: Y = Ωθ + ε In the formula, Y is the observation vector, θ is the scattering coefficient, and ε is the noise. The observation vector Y is the echo signal after KeyStone transformation. Sub-step 3.2 introduces the Orthogonal Matching Pursuit (OMP) algorithm, and the iterative steps of the OMP algorithm are given below: Input: Observation data vector Y, dictionary matrix Ω. Step 1 of iteration: Define the initial residual e0 = Y; set of atomic indices. The number of iterations z = 1, and the number of iterations for the initial residual z = 0. The second step of the iteration is to calculate the inner product between each atom in the dictionary Ω and the residual, that is, to find the atom in the dictionary matrix Ω that best matches the residual (with the largest absolute value of the inner product), and store the position of this atom as λ. (z) Update the location of the atom and the set of atoms: Λ (z) =Λ (z-1) ∪λ (z) , Iteration step 3: Update residual e z =e z-1 -ρ (z) e z-1 =(I-ρ (z) )e z-1 , where ρ (z) Defined as Ω (z) orthogonal projection operator ρ of column space (z) =Ω (z) [(Ω (z) ) T Ω (z) ] -1 (Ω (z) ) T Then iterate over the residuals and perform steps (2) and (3); Fourth step of iteration: Calculate the sparse solution Fifth iteration: If z = z max If the residual is less than the threshold, stop the iteration; otherwise, increment the iteration count k by 1 and jump to step (2). max The number of iterations is preset to estimate the target sparsity. Output: Sparse solution vector θ.

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