Range super-resolution method of pulse pressure radar based on SBL algorithm

Abstract

This invention discloses a range-dimensional super-resolution method for pulse-compression radar based on the Sparse Bayesian Learning (SBL) algorithm. The implementation steps are as follows: pulse compression of the radar echo signal; construction of a dictionary matrix after pulse compression to establish a sparse reconstruction model; processing of the pulse-compressed echo signal using the SBL algorithm to obtain the time delay positions of the radar signals for multiple targets; and conversion of the time delay information of different targets into actual range information to obtain a one-dimensional range profile. This invention combines target echo delay and pulse-compressed waveform characteristics to construct a dictionary matrix and uses the SBL algorithm for super-resolution processing, achieving a resolution effect more than double that of traditional range resolution. This invention avoids the shortcomings of traditional methods that require known sparsity and can be used for range-dimensional super-resolution processing when the number of targets is unknown.

Description

Technical Field

[0001] This invention belongs to the field of radar technology, and more specifically relates to a radar range super-resolution method based on the Sparse Bayesian Learning (SBL) algorithm in pulse compression radar, within the field of radar target detection technology. This invention can achieve range super-resolution capability that breaks the Rayleigh limit under limited radar bandwidth resources, realizing range super-resolution in pulse compression radar. Background Technology

[0002] In modern radar systems, most radars utilize pulse compression. Modern radars employ high range resolution to improve their ability to distinguish multiple targets, and enhance target identification performance and achieve high-resolution radar imaging through high-resolution one-dimensional range images. Conventionally, high range resolution is primarily achieved by increasing the bandwidth of the transmitted signal; however, this increase undoubtedly places higher demands on hardware processing power and spectrum resources. The essence of range-dimensional super-resolution in radar systems is to overcome the Rayleigh limit through novel signal processing methods, achieving resolution exceeding range resolution. Common methods include deconvolution, linear prediction, and feature-based methods. These methods utilize all spectral information beyond the signal bandwidth to extrapolate the signal bandwidth, thereby improving range resolution. However, they are significantly affected by factors such as sampling frequency, noise model, signal-to-noise ratio, and signal model errors, making them impractical for real-world systems.

[0003] The University of Electronic Science and Technology of China (UESTC) proposed a range super-resolution method based on frequency domain deskewing and sparse Bayesian algorithms in its patent application, "A Radar Range Super-Resolution Calculation Method Based on Sparse Bayesian Learning Algorithm" (Application No. 202110674717.4, Publication No.: CN 113406575 A). The implementation steps are as follows: First, pulse compression is performed on the radar echo signal, and frequency domain deskewing is performed on the target radar signal segment. Second, a range-dimensional mathematical model of multiple targets is constructed, a complete dictionary matrix is ​​built using frequency domain deskewing steering vectors, and a sparse Bayesian learning algorithm is used to perform super-resolution processing on the single-frequency signal. This yields the frequency points of the group target radar signals, thus obtaining the super-resolution range image, ultimately achieving radar range super-resolution. However, a drawback of this method is that because it uses frequency domain deskewing steering vectors to build a complete dictionary matrix, it can only achieve range super-resolution in deskewing radar systems and is not applicable to pulse compression radar systems without deskewing processing.

[0004] Xi'an University of Electronic Science and Technology disclosed a sparse recovery-based pulse compression radar range super-resolution method in its patent application "A Sparse Recovery-Based Pulse Compression Radar Range Super-Resolution Method" (Application No.: 202211033518.6, Application Date: 2022.08.26, Publication No.: CN 115343708A). The implementation steps of this method are: performing windowless pulse compression processing on the radar echo data; constructing a subdivided time matrix using radar parameter information; obtaining a simulated pulse compression data matrix through the subdivided time matrix; extracting data from both sides of the pulse compression peak to obtain a peak data matrix; constructing a peak-matching sparse dictionary matrix; processing the pulse-compressed echo data using an orthogonal matching tracking algorithm to obtain a recovery matrix; extracting target information from the recovery matrix to obtain a one-dimensional super-resolution range image of the radar. This method addresses the problems of existing methods being unsuitable for pulse compression radar and having excessive computational load. However, the method still has shortcomings. It uses an orthogonal matching pursuit algorithm to achieve super-resolution, but the algorithm has poor resolution performance when the signal-to-noise ratio is low. Furthermore, the algorithm is related to the sparsity of the observed signal and requires prior knowledge of the number of targets, which is difficult to meet in practical applications. Summary of the Invention

[0005] The purpose of this invention is to address the shortcomings of the prior art by proposing a radar range super-resolution method based on a sparse Bayesian learning algorithm for pulse compression systems. This method aims to solve the problems that existing deslant range super-resolution methods are not suitable for pulse compression systems, and that orthogonal matching tracking processing methods require a known number of targets and suffer from performance degradation under low signal-to-noise ratio conditions.

[0006] To achieve the above objectives, the present invention proposes the following approach: Construct a subdivided time matrix based on the time delays corresponding to different target distances; utilize the waveform characteristics of the radar pulse compression echo signal to obtain simulated pulse compression data; arrange the data into a complete dictionary matrix according to different time delays; and then use a sparse Bayesian learning algorithm to reconstruct the signal, obtaining the range information of different targets. Existing de-skewing-based range super-resolution methods use a dictionary matrix constructed from de-skewing steering vectors, which is therefore unsuitable for pulse compression radar systems. The orthogonal matching pursuit algorithm selects the most relevant atom in each iteration, which reduces computational load to some extent, but its resolution is poor under low signal-to-noise ratio conditions, failing to effectively distinguish target positions, and requires a known number of targets. This invention uses a complete dictionary matrix constructed from simulated pulse compression data as the dictionary matrix in the sparse Bayesian learning algorithm. It employs the sparse Bayesian learning algorithm to sparsely reconstruct the radar pulse compression echo signal to obtain a one-dimensional range profile of the target. This eliminates the need for prior knowledge of the number of targets and effectively distinguishes targets even under low signal-to-noise ratio conditions, achieving a super-resolution effect more than double that of traditional range resolution.

[0007] To achieve the above objectives, the technical solution adopted by the present invention includes the following steps:

[0008] Step 1: Perform pulse compression on the radar echo signal to obtain the pulse-compressed echo signal;

[0009] Step 2: Based on the echo delay of different targets and the waveform characteristics of the echo signal after pulse compression, construct a complete dictionary matrix after pulse compression.

[0010] Step 3: Use the sparse Bayesian learning algorithm to process the pulse compression echo signal to obtain the time delay position of the group target radar signal.

[0011] Step 4: Convert the time delay information of different targets into the actual distance information of the targets to obtain a one-dimensional distance profile.

[0012] Furthermore, the step of pulse compression of the radar echo signal is as follows:

[0013] If a linear frequency modulated (LFM) signal is used as the radar's transmitted signal, then ideally the echo signal s r The expression for (t) is:

[0014]

[0015] Where a1 represents the echo signal amplitude, rect(·) represents the rectangular function, t represents the fast time, T represents the pulse width of the LFM signal, exp represents the exponential operation with the natural constant e as the base, j represents the imaginary unit sign, π represents pi, u represents the frequency modulation slope of the linear frequency modulation signal, u=B / T, B represents the signal bandwidth, and t1 represents the time elapsed from transmission to reception.

[0016] After multiplying the radar echo signal and the pulse compression coefficient in the frequency domain, an inverse Fourier transform is performed on the frequency domain signal. Without considering the target Doppler frequency, the pulse-compressed time-domain signal y1(t) is obtained:

[0017]

[0018] Where a2 represents the amplitude of the output signal after pulse compression, and sin(·) represents the sine function.

[0019] Furthermore, the steps for constructing the complete dictionary matrix after pulse compression are as follows:

[0020] The radar pulse width is divided into K grids, each grid representing a different time delay, and the target time delay is arranged into a subdivided time matrix.

[0021] Calculate the simulated pulse pressure value for each element in each column of the complete dictionary matrix, and arrange the simulated pulse pressure data according to time delay into the following matrix:

[0022]

[0023] Where A represents the complete dictionary matrix after pulse compression, y1(t) represents the time-domain signal after pulse compression in the ideal case, and τ k This represents the target latency in the k-th column of the corresponding complete dictionary matrix. k = 1, 2, ..., K, where K represents the total number of radar time-width subdivisions and L represents the number of rows in the complete dictionary matrix.

[0024] Furthermore, the conversion of the time delay information of different targets into the actual distance information of the targets means that by searching the final mean vector spectrum peaks, the number of grid points corresponding to multiple maximum peaks can be obtained, and the location of the grid points can be converted into the distance of the target.

[0025] Furthermore, the steps of the sparse Bayesian learning algorithm are as follows:

[0026] The first step is to determine the power σ of the noise vector based on the complete dictionary matrix. 2 The variance parameter γ of the compressible signal z is initialized and the initialization result is then used in the iteration process.

[0027] The second step is to calculate the posterior covariance matrix Σ and the posterior mean vector μ of the compressible signal z based on the prior parameters obtained from the current iteration.

[0028] The third step is to update the power σ of the noise vector. 2 And the prior variance parameter γ of the compressible signal z;

[0029] The fourth step is to determine the power (σ) of the updated noise vector. 2 ) new The prior variance parameter γ of the compressible signal z new If the convergence condition is met, the iterative update ends, and the grid point position corresponding to the element with the largest modulus in the posterior mean vector μ is converted into the time delay position of the group target radar signal; otherwise, the second step is executed.

[0030] Furthermore, the expressions for the mean vector μ and covariance matrix Σ of the compressible signal are:

[0031] μ = σ -2 ΣA H y

[0032] Σ=(σ -2 A H A+Γ -1 ) -1

[0033] Where y = [y1(1), y1(2), ... y1(L)] T, representing the observed signal vector, (·) T Indicates matrix transpose. diag(γ) represents a diagonal matrix with γ as its diagonal element, γ = [γ1, γ2, ... γ K ] T σ represents the prior variance of the compressible signal z. 2 Let H represent the variance of the noise signal n, and H represent the conjugate transpose operation.

[0034] The updated parameter γ i (new) and σ 2(new) The expression is:

[0035] γ i (new) =Ε(z) i 2 )=Σ i,i +μ i 2

[0036]

[0037] Where, γ i Let Σ represent the i-th element of γ, E(·) represent the expectation, and Σ i,i μ represents the element in the i-th row and i-th column of the covariance matrix Σ. i Denotes the i-th element of the mean vector μ, ||·|| 2 The expression represents the l2 norm operation, and Tr(·) represents the trace of the matrix.

[0038] The convergence condition refers to the condition when ε i The algorithm is considered to have converged when the maximum value is less than a set threshold or when the maximum number of iterations is reached.

[0039]

[0040] Where, ε i The criteria for determining convergence are given, i = 1, 2, ..., K, and γ. t+1 Let σ represent the posterior variance of the compressible signal z after the t-th iteration update. t+1 Let represent the variance of the noise signal after the t-th iteration update.

[0041] Compared with the prior art, the present invention has the following advantages:

[0042] First, in the model building stage, this invention utilizes the radar's own parameter information and combines it with different time delays to construct a complete dictionary matrix containing pulse-compressed waveform information and the position information of different targets. This overcomes the shortcomings of existing deslant range super-resolution methods that cannot be applied to pulse-compressed radar, enabling this invention to be applied to pulse-compressed radar and achieving range-dimensional super-resolution for pulse-compressed radar.

[0043] Secondly, this invention addresses the problem that the range resolution capability of conventional pulse compression is limited by signal bandwidth, making target identification difficult. Under the current measurement accuracy of radar, it proposes a pulse compression radar range super-resolution algorithm based on sparse Bayesian learning. The algorithm converts the radar target range information into time delay information, then uses a Bayesian learning algorithm to perform super-resolution, analyzes the target time delay estimate, converts it into a target range estimate, and finally distinguishes each target. This overcomes the shortcomings of orthogonal matching pursuit algorithms, which require known target numbers and suffer from performance degradation at low signal-to-noise ratios. Therefore, this invention's pulse compression radar range super-resolution algorithm based on sparse Bayesian learning can effectively achieve more than one times the super-resolution effect of traditional range resolution in low signal-to-noise ratio environments, even without knowing the number of targets. Attached Figure Description

[0044] Figure 1 This is a flowchart of an embodiment of the present invention;

[0045] Figure 2 This is a diagram showing the traditional pulse compression processing result when the distance between two targets is less than the distance resolution in simulation experiment 1 of this invention;

[0046] Figure 3 This is a diagram showing the result of processing the pulse-compressed radar echo data in simulation experiment 2 of this invention.

[0047] Figure 4 This is a statistical graph showing the resolution probability of the method of the present invention under different signal-to-noise ratios in simulation experiment 3 of the present invention. Detailed Implementation

[0048] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0049] Reference Figure 1 The implementation steps of the embodiments of the present invention will be described in further detail below.

[0050] Step 1: Establish the radar multi-target echo model of this embodiment of the invention, and use the pulse compression coefficient without windowing to compress the echo signal.

[0051] Step 1.1, the radar transmits a linear frequency modulated signal, represented as:

[0052]

[0053] Where s(t) represents the radar transmitted signal, rect(·) is a rectangular function, t represents fast time, T is the pulse width of the LFM signal, exp(·) is an exponential function with base e, j represents the imaginary number, π is pi, u is the frequency modulation slope of the linear frequency modulated signal u = B / T, and B is the signal bandwidth. Then the radar echo signal can be expressed as:

[0054]

[0055] Where a1 represents the amplitude of the echo signal, and t1 is the time elapsed from transmission to reception.

[0056] Constructing a windowless matched filter for radar transmitted signals:

[0057] h(t) = s * (t0-t)

[0058] in,(·) * Indicates conjugate.

[0059] Step 1.2, convolving the radar echo data with the pulse compression coefficient is equivalent to multiplying in the frequency domain. Without considering the target Doppler frequency, the frequency domain expression of the pulse-compressed echo data can be obtained, as shown below:

[0060]

[0061] Where H(f) represents the frequency domain expression of h(t), S r (f) represents s r The frequency domain expression of (t). The time domain output is obtained by performing an inverse Fourier transform on the pulse-compressed output signal, as shown in the formula:

[0062]

[0063] Where a2 is the amplitude of the output signal after pulse compression, and sin(·) represents the sine function. The main lobe width of this signal in the time domain is 1 / B. When the Doppler frequency shift of the signal is 0, the waveform envelope of the LFM signal after matched filtering takes the form of a singer function. Assuming there are M targets in the range direction, the pulse compression of the so-target echo signal can be written as:

[0064]

[0065] Where y(t) represents the post-pulse compression echo signal, z m and δ m Let be the scattering complex coefficients and propagation delay corresponding to the m-th target, respectively, and n(t) be the noise signal.

[0066] In the case of discrete sampling, the echo signal in the above equation can be:

[0067]

[0068] Among them, f s Indicates the sampling frequency.

[0069] Step 2: Based on the echo delay of different targets and the waveform characteristics of the echo signal after pulse compression, construct a complete dictionary matrix after pulse compression and establish a sparse reconstruction model.

[0070] As shown in step 1, the LFM signal waveform after matched filtering exhibits a sinc function shape, and the main lobe width in the time domain is 1 / B. Therefore, when the time delay difference corresponding to multiple target distances is less than the main lobe width, multiple targets will overlap into a single target, making them difficult to distinguish. Typically, for a given radar detection wave position, only a few targets exist within the range of interest; that is, they can only be detected at a few distance points (corresponding to time delays (δ1, δ2, ..., δ...)). M The target exists on the surface, and its distribution is sparse.

[0071] Based on different target delays, the complete dictionary matrix is ​​constructed as follows:

[0072] Step 2.1: Calculate the delay of each column in the subdivision time matrix according to the following formula. The delay expression corresponding to the k-th column of the dictionary matrix is:

[0073]

[0074] Where k = 1, 2, ..., K, K represents the total number of subdivisions of the radar pulse width. The total number L of the subdivision time matrix rows is equal to the total length of the discrete sequence after compression of the radar transmitted signal pulse.

[0075] Step 2.2: Calculate the simulated pulse pressure data for each column of the discretized dictionary matrix according to the following formula. The expression for calculating the simulated pulse pressure data in the k-th column of the dictionary matrix is:

[0076]

[0077] The simulated pulse compression data are arranged according to time delay into the following matrix:

[0078]

[0079] Where A is the constructed complete dictionary matrix, and L represents the number of rows in the dictionary matrix. Furthermore, the echo signal is written as:

[0080]

[0081] In the above formula, A contains the time delay information of different targets, [z(1),z(2),z(3),…,z(K)] T The values ​​are non-zero only at a limited number of positions, corresponding to information about the true target, indicating sparsity in the target's properties. Its matrix form can be written as:

[0082] y = Az + n

[0083] Where y represents the observed signal vector, z represents the compressible signal, and n represents the noise vector.

[0084] Step 3: Process the pulse-compressed echo signal using the sparse Bayesian learning algorithm to obtain the time delay location of the group target radar signal.

[0085] Based on the complete dictionary matrix established in the previous step, the following sparse Bayesian algorithm is used for processing. The specific steps include:

[0086] Step 3.1, based on the complete dictionary matrix, calculate the noise power σ of the noise vector n. 2 The variance parameter γ of the compressible signal z is initialized.

[0087] In an embodiment of the present invention, a Gaussian prior distribution y is introduced for y. i ~N(0,γ) i ): That is, assuming each component of y is y i y is a set of independent Gaussian random variables with zero mean, where y i ~N(0,γ) i ) represents y i Follows the γ with a mean of 0 i The variance is a Gaussian distribution. That is, the prior distribution of the entire sparse vector is... Where γ = [γ1, γ2, ... γ K In the embodiments of the present invention, the prior variance of the compressible signal z is 100.

[0088] For a noise vector n, assume that each component of n has a mean of 0 and a variance of σ. 2 The Gaussian distribution, i.e., n i ~N(0,σ 2 The components are independent of each other. In this invention example, it is assumed that the variance of the noise vector n is 1.

[0089] Step 3.2: Based on the current prior variance, calculate the posterior covariance matrix Σ and the posterior mean vector μ of the compressible signal z.

[0090] For a fixed value of the hyperparameter controlling the prior, the posterior probability density of z can be expressed as:

[0091]

[0092] The expressions for the mean vector μ and covariance matrix Σ of the compressible signal are:

[0093] μ = σ -2 ΣA H y

[0094] Σ=(σ -2 A H A+Γ -1 ) -1

[0095] in, Let σ represent a diagonal matrix with γ as its diagonal element, where γ represents the prior variance of the compressible signal z, and σ represents the prior variance of the signal z. 2 Let represent the variance of the noise signal n, and H represent the conjugate transpose. During the iteration process, the variance of z increases, indicating that the corresponding mean vector decreases. From the above equation, we can see that γ, σ 2 Given that the value of the sparse signal z is μ, the value can be estimated by the maximum a posteriori probability.

[0096] Step 3.3, update the noise power σ of the noise vector n. 2 And the prior variance parameter γ of the compressible signal z.

[0097] In an embodiment of the present invention, the hyperparameters are updated using the Expectation-Maximization (EM) algorithm: z is considered as a latent variable, and the parameter to be estimated is γ. The expected likelihood function is then:

[0098]

[0099] Among them, E z {·} represents the posterior expectation corresponding to Z, ln(·) represents the logarithmic function with base e, and p represents the likelihood function.

[0100] Find the γ that maximizes the above expression. i The updated parameter γ i (new) The expression is:

[0101] γ i (new) =Ε(z) i 2 )=Σ i,i +μ i 2

[0102] Where E(·) represents the expectation, Σ i,i Let μ represent the (i,i)th element of the covariance matrix Σ. i This represents the i-th element of the mean vector μ.

[0103] Similarly, we obtain σ 2 Update σ 2(new) The expression is:

[0104]

[0105] Among them, ||·|| 2 Let represent the l2 norm, Tr(·) represent the trace of the matrix, and L represent the number of rows in the dictionary matrix.

[0106] In summary, the posterior probability of z can be obtained iteratively, and the mean μ of the posterior probability can be used as an estimate of z. The K elements with the largest modulus in z are then identified, and the positions of these K elements correspond to the positions of the actual time delays of the K targets.

[0107] Step 3.4, determine the noise power (σ) of the updated noise vector n. 2 ) new And the prior variance parameter γ of the compressible signal z new If the convergence condition is met, the iteration update ends, and the grid point position corresponding to the element with the largest modulus in the posterior mean vector μ is converted into the time delay position of the group target radar signal. Otherwise, return to step 3.2.

[0108] Let ε be the criterion for judging the convergence of the algorithm:

[0109]

[0110] Where, γ t+1 Let γ represent the posterior variance of the compressible signal z after the t-th iteration update. t Let represent the posterior variance of the compressible signal z at the start of the t-th iteration.

[0111] When max(ε) i If the value is less than 0.01 or the maximum number of iterations is reached, the algorithm is considered to have converged.

[0112] Step 4: Convert the time delay information of different targets into the actual distance information of the targets to obtain a one-dimensional distance profile.

[0113] As shown in step 3, the mean value μ of the posterior probability is used as the estimated value of z. When the algorithm convergence condition or the number of iterations is reached, the final z is obtained. By searching its spectral peaks, the number of grid points corresponding to the M largest peaks can be obtained. The location of the grid points is converted into the distance to the target, and a one-dimensional distance image is obtained.

[0114] The effects of this invention will be further illustrated below with simulation experiments:

[0115] 1. Simulation experimental conditions:

[0116] The hardware platform for the simulation experiment of this invention is: Intel(R) Core(TM) i9-14900HX CPU with a main frequency of 3.60GHz and 16.00GB of memory.

[0117] The software platform for the simulation experiments of this invention is: Windows 11 operating system and MATLAB R2023b.

[0118] The simulation data for this invention are as follows: the time width T of the LFM signal transmitted by the radar is 50 × 10. -6 s, bandwidth B = 6 × 10 6 Hz, sampling frequency f s =6×10 6 The range resolution of conventional pulse compression is Δr = c / 2B = 50m. The radar echo signal includes the target signal and Gaussian white noise signal. The detection signal-to-noise ratios of the two targets are SNR1 = 20dB and SNR2 = 20dB, respectively. Each sampling unit is divided into 5 parts. Target 1 is located in range unit 61.2 and target 2 is located in range unit 61.8. The distance between the two targets is d = 30m. In the experiment, the distance interval between the two targets is 0.6 times the theoretical resolution of conventional pulse compression processing. The targets are both stationary. When the statistical detection probability changes with the signal-to-noise ratio, the signal-to-noise ratio changes from -4dB to 10dB. The distance between the two targets remains constant.

[0119] 2. Simulation content and result analysis.

[0120] There are three simulation experiments in this invention.

[0121] Simulation Experiment 1: Under the above simulation conditions, the radar received echo signal is processed using the existing windowless pulse compression coefficient to obtain a one-dimensional range image of the target in the out-of-dimension dimension, such as... Figure 2 As shown. Figure 2 In the graph, the horizontal axis represents the distance unit, the vertical axis represents the normalized amplitude value, and the curve represents a one-dimensional range profile of the target distribution along the range dimension. Figure 2 As can be seen from the curves shown, the existing pulse compression technology processes the radar received echo signal, resulting in aliasing and forming only one peak, making it impossible to detect the two targets in the echo signal separately.

[0122] Simulation Experiment 2: Under the conditions described in the above simulation experiment, the pulse compression radar range super-resolution method based on the sparse Bayesian learning algorithm of this invention is used to process the radar pulse-compressed echo data to obtain a super-resolution range image representing the target distribution in the range dimension, as shown below. Figure 3 As shown. Figure 3 In the diagram, the horizontal axis represents the distance unit, the vertical axis represents the amplitude value, and the peak represents the spectral peak value of the target distribution in the distance dimension.

[0123] from Figure 3 As can be seen, obvious spikes appear near the range cells 61 where the two targets are located in the super-resolution range image, achieving the resolution of two targets with a range interval close to 0.5 times that of the theoretical resolution of traditional pulse compression processing. Therefore, the range super-resolution method based on sparse recovery in this invention outperforms traditional pulse compression processing by more than 1 times in resolution performance.

[0124] Simulation Experiment 3: Under the condition of keeping the positions of the two targets constant, the resolution probability of the algorithm of this invention was statistically analyzed as a function of signal-to-noise ratio (SNR). 500 Monte Carlo experiments were conducted for each SNR. The condition for successful resolution was the appearance of two significant peaks at the actual target's location within a distance cell, with amplitudes considerably higher than the peaks at other distance cells. The number of grid cells corresponding to the two peaks was converted to a distance less than 0.2 distance cells from the actual target distance, which was used to determine whether the resolution was successful. The statistical results are as follows: Figure 4 As shown.

[0125] Depend on Figure 4 It can be seen that, with the distance between the two targets remaining constant, the resolution performance of the proposed method is significantly enhanced as the signal-to-noise ratio increases. When the signal-to-noise ratio is higher than 0 dB, the success rate of resolution can reach more than 50%, indicating that the proposed method effectively improves the distance resolution.

Claims

1. A range super-resolution method for pulse compression radar based on the SBL algorithm, characterized in that, A complete dictionary matrix is ​​constructed after pulse compression, and the echo signal after pulse compression is processed based on a sparse Bayesian learning algorithm. The specific steps of this super-resolution method are as follows: Step 1: Perform pulse compression on the radar echo signal to obtain the pulse-compressed echo signal; Step 2: Based on the echo delay of different targets and the waveform characteristics of the pulse-compressed echo signal, construct a complete dictionary matrix for pulse compression; the steps are as follows: The first step is to calculate the latency of each column in the subdivided time matrix according to the following formula: ； in, Represents the first element of the dictionary matrix. The corresponding delay is listed below. , This indicates the total number of subdivisions in the radar pulse. Indicates the pulse width of the LFM signal; The second step is to calculate the simulated pulse compression data for each column of the discretized dictionary matrix according to the following formula. The expression for calculating the simulated pulse pressure data of the column is: ； in, This indicates the amplitude of the output signal after pulse compression. Represents the sine function. Represents pi (π). Indicates signal bandwidth. Indicates the sampling frequency. , Indicates the number of rows in a complete dictionary matrix; The simulated pulse compression data are arranged according to time delay into the following matrix: ； in, This represents the complete dictionary matrix after pulse compression. This represents the time-domain signal after pulse compression. Step 3: Use the sparse Bayesian learning algorithm to process the pulse compression echo signal to obtain the time delay position of the group target radar signal. Step 4: Convert the time delay information of different targets into the actual distance information of the targets to obtain a one-dimensional distance profile.

2. The super-resolution method according to claim 1, characterized in that, The pulse compression steps for the radar echo signal described in step 1 are as follows: The first step is the radar echo signal. for: ； in, Indicates the amplitude of the echo signal. Represents a rectangle function. exp represents fast time, expressed in terms of the natural constant. An exponential function with base 0. The symbol representing the imaginary unit. This represents the frequency modulation slope of a linear frequency modulated signal. , This indicates the time elapsed from signal transmission to reception; The second step involves multiplying the radar echo data and pulse compression coefficient in the frequency domain, and then performing an inverse Fourier transform on the frequency domain signal according to the following formula: ； in, This represents the pulse compression time-domain signal without considering the target Doppler effect.

3. The super-resolution method according to claim 1, characterized in that: Step 4, which involves converting the time delay information of different targets into the actual distance information of the targets, refers to obtaining this information through a search of the final mean vector spectral peaks. The number of grid points corresponding to the maximum peak value is used to convert the location of the grid point into the distance to the target.

4. The super-resolution method according to claim 3, characterized in that, The steps of the sparse Bayesian learning algorithm described in step 3 are as follows: The first step is to process the noise vector based on the complete dictionary matrix. noise power and compressible signals variance parameter Perform initialization assignment and input the initialization results into the iteration process; The second step is to calculate the compressible signal based on the prior variance obtained from the current iteration. posterior covariance matrix and posterior mean vector ; The third step is to update the noise vector. noise power and compressible signals Prior variance parameter ; The fourth step is to determine the updated noise vector. noise power With compressible signals Prior variance parameter Check if the convergence condition is met. If it is, end the iterative update and update the posterior mean vector. The grid point position corresponding to the largest element in the medium model is converted into the time delay position of the group target radar signal; otherwise, proceed to step two.

5. The super-resolution method according to claim 4, characterized in that, The mean vector of the compressible signal Covariance Matrix The expression is: ； in, , representing the observed signal vector, Indicates matrix transpose. , Indicates A diagonal matrix with diagonal elements. , indicating a compressible signal The prior variance, Indicates noise signal variance This indicates the conjugate transpose operation.

6. The super-resolution method according to claim 5, characterized in that, The updated parameters and The expression is: ； ； in, express The One element, Expressing expectations, Represents the covariance matrix The The first line List the elements, Represents the mean vector The One element, express Norm operations Represents the trace of a matrix.

7. The super-resolution method according to claim 6, characterized in that, The convergence condition refers to the condition when... The algorithm is considered to have converged when the maximum value is less than a set threshold or when the maximum number of iterations is reached. ； in, This indicates the criteria for judging convergence. , Indicates the first The compressible signal after the next iteration update The posterior variance, Indicates the first The variance of the noise signal after the next iteration.

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