Pulse pressure system radar distance super-resolution method based on SBL algorithm

Abstract

The invention discloses a pulse compression system radar distance dimension super-resolution method based on a sparse Bayesian learning SBL algorithm. The method comprises the following implementation steps: performing pulse compression on radar echo signals; constructing a dictionary matrix after pulse compression, and establishing a sparse reconstruction model; utilizing a sparse Bayesian learning algorithm to process the echo signal after pulse compression to obtain a time delay position of a group target radar signal; and converting the time delay information of different targets into actual distance information of the targets to obtain a one-dimensional distance image. According to the method, the dictionary matrix is constructed in combination with the target echo delay and the post-pulse-compression waveform characteristics, super-resolution processing is performed by using the sparse Bayesian algorithm, and the resolution effect of more than one time of the traditional range resolution is realized. According to the method, the defect that a traditional method needs to take known sparseness as the premise is overcome, and the method can be used for distance dimension super-resolution processing under the condition that the number of targets is unknown.

Description

Technical Field

[0001] The present invention belongs to the field of radar technology, and further relates to a radar distance dimension super-resolution method in a pulse compression system based on a sparse Bayesian learning (SBL) algorithm in the field of radar target detection technology. The present invention can obtain a distance super-resolution capability that breaks through the Rayleigh limit when radar bandwidth resources are limited, and realize the distance dimension super-resolution of a pulse compression system radar. Background Art

[0002] In modern radar systems, most radars use pulse compression systems. Modern radars use high range resolution to improve the radar's ability to resolve group targets, and use high-resolution range one-dimensional images to improve target recognition performance and achieve high-resolution radar imaging. Under conventional processing methods, high range resolution is mainly achieved by increasing the bandwidth of the transmitted signal, but the increase in signal bandwidth undoubtedly puts higher requirements on hardware processing capabilities and occupied spectrum resources. The essence of range-dimensional super-resolution of radar systems is to break through the Rayleigh limit through new signal processing methods and achieve resolution capabilities that exceed range resolution. Common methods include deconvolution, linear prediction, and feature methods. In the process of implementation, these methods all use all spectral information outside the signal bandwidth to realize signal bandwidth extrapolation, thereby improving the range resolution. However, in the processing process, they are greatly affected by factors such as sampling frequency, noise model, signal-to-noise ratio, and signal model error, and cannot be applied in actual systems.

[0003] The University of Electronic Science and Technology of China proposed a distance super-resolution method based on frequency domain de-skewing and sparse Bayesian in its patent document "A radar distance super-resolution calculation method based on sparse Bayesian learning algorithm" (application number 202110674717.4 application publication number: CN 113406575 A). The implementation steps of this method are as follows: first, pulse compression is performed on the echo signal received by the radar, and the target radar signal segment is de-skewed in the frequency domain; secondly, a multi-target range dimension mathematical model is constructed, and a complete dictionary matrix is ​​constructed using the frequency domain de-skewing steering vector, and a sparse Bayesian learning algorithm is used to perform super-resolution processing on the single-frequency signal; then the frequency point position of the group target radar signal is obtained, and the super-resolution range image is obtained, and finally the radar range super-resolution is realized. However, the disadvantage of this method is that since the method uses the frequency domain de-skewing steering vector to construct a complete dictionary matrix, the method can only realize distance super-resolution in de-skewing radars, and cannot be applied to pulse compression radars without de-skewing.

[0004] Xidian University has disclosed a pulse compression radar distance super-resolution method based on sparse recovery in its patent document "Pulse compression radar distance super-resolution method based on sparse recovery" (application number: 202211033518.6 application date: 2022.08.26 application publication number: CN 115343708A). The implementation steps of this method are: pulse compression processing without windowing the radar echo data; constructing a subdivided time matrix using radar parameter information; obtaining a simulated pulse compression data matrix by subdividing the time matrix, intercepting the data on both sides of the pulse compression peak to obtain a peak data matrix, constructing a peak matching sparse dictionary matrix, using an orthogonal matching tracking algorithm to process the echo data after pulse compression to obtain a recovery matrix, extracting the target information of the recovery matrix, and obtaining a one-dimensional super-resolution distance image of the radar. This method solves the problem that the existing methods are not applicable to pulse compression radars and the amount of computation is too large. However, the method still has some shortcomings. The method uses an orthogonal matching pursuit algorithm to achieve super-resolution. The algorithm used has poor resolution performance when the signal-to-noise ratio is low. In addition, the algorithm is related to the sparsity of the observed signal and requires the number of targets to be known in advance. This condition is difficult to meet in practical applications. Summary of the invention

[0005] The purpose of the present invention is to address the deficiencies of the above-mentioned prior art and to propose a radar range dimension super-resolution method based on a sparse Bayesian learning algorithm for use in a pulse compression system, so as to solve the problems that the existing de-slant range super-resolution method is not suitable for the pulse compression system, and the orthogonal matching pursuit processing method requires a known number of targets as a prerequisite, and the resolution performance decreases under low signal-to-noise ratio conditions.

[0006] To achieve the above purpose, the idea of ​​the present invention is: construct the time delay corresponding to different target distances into a subdivided time matrix, and use the waveform characteristics of the radar pulse compression echo signal to obtain simulated pulse compression data. Arrange it into a complete dictionary matrix according to different time delays, and then use the sparse Bayesian learning algorithm to reconstruct the signal to obtain the distance information of different targets. The existing de-slant distance super-resolution method uses a dictionary matrix constructed by de-slant steering vectors, so it cannot be applied to pulse compression radar. The orthogonal matching pursuit algorithm selects a most relevant atom in each iteration process. Although it reduces the amount of calculation to a certain extent, the algorithm has poor resolution effect under low signal-to-noise ratio conditions, cannot effectively distinguish the target position, and requires the known number of targets as a prerequisite. The present invention uses the complete dictionary matrix composed of simulated pulse compression data as the dictionary matrix in the sparse Bayesian learning algorithm, and uses the sparse Bayesian learning algorithm to sparsely reconstruct the radar pulse compression echo signal to obtain a one-dimensional distance image of the target. It does not need to know the number of targets in advance, and can effectively distinguish the targets in a low signal-to-noise ratio environment, effectively achieving a super-resolution effect of more than one times the traditional distance resolution.

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

[0008] Step 1, pulse compressing the radar echo signal to obtain a pulse compressed echo signal;

[0009] Step 2, according to different target echo delays and the waveform characteristics of the echo signal after pulse compression, a complete dictionary matrix after pulse compression is constructed;

[0010] Step 3, using a sparse Bayesian learning algorithm, the pulse compression echo signal is processed 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 range image.

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

[0013] If the linear frequency modulation (LFM) signal is used as the radar transmission signal, then ideally the echo signal s r (t) is expressed as:

[0014]

[0015] Wherein, a1 represents the amplitude of the echo signal, 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 symbol of the imaginary unit, π represents the circumference of the circle, 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 from the signal transmission to the reception;

[0016] After multiplying the radar echo signal and the pulse compression coefficient in the frequency domain, the frequency domain signal is inversely Fourier transformed to obtain the time domain signal y1(t) after pulse compression without considering the target Doppler frequency:

[0017]

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

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

[0020] Divide the radar pulse width into K grids, each grid represents a different time delay, and arrange the target delay into a subdivided time matrix;

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

[0022]

[0023] Among them, A represents the complete dictionary matrix after pulse compression, y1(t) represents the ideal time domain signal after pulse compression, τ k represents the target delay corresponding to the kth column in the complete dictionary matrix, k=1,2,...,K, K represents the total number of subdivisions of the radar time width, and L represents the number of rows of the complete dictionary matrix.

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

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

[0026] The first step is to calculate the power σ of the noise vector according to the complete dictionary matrix. 2 Initialize and assign the variance parameter γ of the compressible signal z, and bring the initialization result into the iterative process;

[0027] The second step is to calculate the posterior covariance matrix Σ and the posterior mean vector μ of the compressible signal z according to the prior parameters obtained by 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 of the updated noise vector (σ 2 ) new and the prior variance parameter γ of the compressible signal z new Whether the convergence condition is met, if so, the iterative update is terminated, 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 of the mean vector μ and the 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, represents the observed signal vector, (·) T represents the matrix transpose, diag(γ) represents a diagonal matrix with γ as the diagonal element, γ=[γ1,γ2,...γ K ] T , represents the prior variance of the compressible signal z, σ 2 represents the variance of the noise signal n, and H represents 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] Among them, γ i represents the i-th element of γ, E(·) represents the expectation, Σ i,i represents the i-th column element of the i-th row of the covariance matrix Σ, μ i represents the i-th element of the mean vector μ, ||·|| 2 represents the l2-norm operation, and Tr(·) represents the trace of the matrix.

[0038] The convergence condition is that when ε i The maximum value of is less than the set threshold or reaches the set maximum number of iterations, the algorithm is considered to have reached convergence:

[0039]

[0040] Among them, ε i represents the criterion for judging convergence, i=1,2,...,K,γ t+1 represents the posterior variance of the compressible signal z after the tth iteration update, σ t+1 Represents the variance of the noise signal after the tth iteration update.

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

[0042] First, the present invention uses the radar's own parameter information in the model building stage, combined with different time delays, to build a complete dictionary matrix containing the waveform information after pulse compression and the location information of different targets. This overcomes the disadvantage that the existing de-slant distance super-resolution method cannot be applied to pulse compression radar, so that the present invention can be applied to pulse compression radar and realizes the distance dimension super-resolution of pulse compression radar.

[0043] Secondly, in order to solve the problem that the distance resolution capability of conventional pulse compression is limited by the signal bandwidth and the target resolution and identification is difficult, the present invention proposes a pulse compression radar distance super-resolution algorithm based on sparse Bayesian learning under the measurement accuracy of existing radars. The distance information of the radar target is converted into time delay information, and then the Bayesian learning algorithm is used to complete the super-resolution. The target delay estimation is analyzed and then converted into the target distance estimation, and finally each target is identified. It overcomes the shortcomings of the orthogonal matching pursuit processing algorithm that the number of targets needs to be known as a prerequisite and the resolution performance decreases under low signal-to-noise ratio. The pulse compression radar distance super-resolution algorithm based on sparse Bayesian learning of the present invention can effectively achieve a super-resolution effect of more than double the traditional distance resolution in a low signal-to-noise ratio environment without knowing the number of targets. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 is a flow chart of an embodiment of the present invention;

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

[0046] Figure 3 This is a result diagram of processing the radar echo data after pulse compression in simulation experiment 2 of the present invention;

[0047] Figure 4 It is a statistical diagram of 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 DESCRIPTION

[0048] The present invention is further described in detail below in conjunction with the accompanying drawings and embodiments.

[0049] Reference Figure 1 , the implementation steps of the embodiment of the present invention are further described in detail.

[0050] Step 1: Establish a radar multi-target echo model according to an embodiment of the present invention, and perform pulse compression on the echo signal using a pulse compression coefficient without adding a window.

[0051] Step 1.1, the radar transmits a linear frequency modulation signal, which is expressed as:

[0052]

[0053] Among them, s(t) represents the radar transmission 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 the real number e as the base, j represents an imaginary number, π is the circumference of pi, u is the frequency modulation slope of the linear frequency modulation signal u=B / T, and B is the signal bandwidth. Then the radar echo signal can be expressed as:

[0054]

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

[0056] Construct an unwindowed matched filter for the radar transmit signal:

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

[0058] in,(·) * Indicates conjugation.

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

[0060]

[0061] Where H(f) represents the frequency domain expression of h(t), S r (f) means s r The frequency domain expression of (t). The inverse Fourier transform of the output signal after pulse compression is used to obtain its time domain output 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 width of the main lobe of the 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 presents a Sinker function shape. Assuming that there are M targets in the range, the multi-target echo signal after pulse compression can be written as:

[0064]

[0065] Among them, y(t) represents the echo signal after pulse compression, z m and δ m are the scattering complex coefficient and propagation delay corresponding to the mth target respectively, and n(t) is the noise signal.

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

[0067]

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

[0069] Step 2: According to different target echo delays and the waveform characteristics of the echo signal after pulse compression, a complete dictionary matrix after pulse compression is constructed to establish a sparse reconstruction model.

[0070] From step 1, we can see that the LFM signal waveform after matched filtering presents a sinc function shape, and the main lobe width of the signal in the time domain is 1 / B. Therefore, when the delay difference corresponding to multiple distances of the target is less than the main lobe width, multiple targets will be aliased into a single target and difficult to distinguish. Usually, for a certain detection wave position of the radar, there are only a few targets within the range of interest, that is, it is only possible to detect targets at a few distance points (corresponding to the delay (δ1,δ2,…,δ M ))There are targets on the network, and their distribution is sparse.

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

[0072] Step 2.1, calculate the delay of each column in the segmented time matrix according to the following formula. The delay expression corresponding to the kth column of the dictionary matrix is:

[0073]

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

[0075] Step 2.2, calculate the simulated pulse pressure data of each column of the discretized dictionary matrix according to the following formula. The calculation expression of the simulated pulse pressure data of the kth column of the dictionary matrix is:

[0076]

[0077] Arrange the simulated pulse pressure data into the following matrix according to time delay:

[0078]

[0079] Among them, A is the constructed complete dictionary matrix, and L represents the number of rows of the dictionary matrix. Further, the echo signal is written as:

[0080]

[0081] In the above formula, A contains the delay information of different targets, [z(1),z(2),z(3),…,z(K)] T Only a limited number of locations have non-zero values, corresponding to the information of the real target, and the target is sparse. Its matrix form can be written as:

[0082] y=Az+n

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

[0084] 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.

[0085] According to 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, according to the complete dictionary matrix, the noise power σ of the noise vector n 2 And 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, assume that each component y i are independent zero-mean Gaussian distributed random variables, where y i ~N(0,γ i ) represents y i Subject to γ ​​with mean 0 i is the Gaussian distribution of variance. That is, the prior distribution of the entire sparse vector is where γ=[γ1,γ2,…γ K ], in the embodiment of the present invention, the prior variance of the assigned compressible signal z is 100.

[0088] For the noise vector n, assume that each component in n has a mean of 0 and a variance of σ 2 Gaussian distribution, that is, n i ~N(0,σ 2 ), and each component is independent of each other. In the example of the present invention, 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 fixed values ​​of the hyperparameters controlling the prior, the posterior probability density of z can be expressed as:

[0091]

[0092] Among them, the expressions of 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, represents a diagonal matrix with γ as the diagonal element, γ represents the prior variance of the compressible signal z, σ 2 represents the variance of the noise signal n, and H represents the conjugate transpose. During the iteration process, the variance of z becomes larger and larger, indicating that the corresponding mean vector becomes smaller and smaller. From the above formula, we can know that γ, σ 2 When it is known, the estimated value of the sparse signal z can be obtained as μ by the maximum a posteriori probability estimation.

[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 expectation maximization algorithm (EM) is used to update the hyperparameters: z is regarded as a latent variable, the parameter to be estimated is γ, and the expected likelihood function is:

[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 equation 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 represents the (i,i)th element of the covariance matrix Σ, μ i represents the i-th element of the mean vector μ.

[0103] Similarly, we get σ 2 The update of σ 2(new) The expression is:

[0104]

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

[0106] In summary, the posterior probability of z can be obtained in an iterative manner, and the mean μ of the posterior probability is used as the estimated value of z. The K elements with the largest modulus value are found in z, and the positions of these K elements correspond to the positions of the actual delays of the K targets.

[0107] Step 3.4, determine the noise power (σ 2 ) new and the prior variance parameter γ of the compressible signal z new Whether the convergence condition is met, if so, the iterative update is terminated, 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] Among them, γ t+1 represents the posterior variance of the compressible signal z after the tth iteration update, γ t represents the posterior variance of the compressible signal z at the beginning of the tth iteration.

[0111] When max(ε i )<0.01 or reaches the set maximum number of iterations, 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 range image.

[0113] According to step 3, the mean 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 spectrum peak, the number of grid points corresponding to the M maximum peaks can be obtained. The position of the grid point is converted into the distance of the target to obtain a one-dimensional range image.

[0114] The effect of the present invention is further described below in conjunction with simulation experiments:

[0115] 1. Simulation experiment conditions:

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

[0117] The software platforms for the simulation experiment of the present invention are: Windows 11 operating system and MATLAB R2023b.

[0118] The simulation experiment data of the present invention is: the time width T of the LFM signal emitted by the radar is 50×10 -6 s, bandwidth B = 6 × 10 6 Hz, sampling frequency f s =6×10 6 Hz, the distance resolution of conventional pulse compression is Δr=c / 2B=50m, the radar echo signal contains the target signal and Gaussian white noise signal, the detection signal-to-noise ratios of the two targets are SNR1=20dB, SNR2=20dB, each sampling unit is divided into 5 parts, target 1 is located at distance unit 61.2, target 2 is located at distance unit 61.8, the distance between the two targets is d=30m, the distance interval between the two targets in the experiment is 0.6 times the theoretical resolution of traditional pulse compression processing, the targets are all in a stationary state, when the statistical detection probability changes with the signal-to-noise ratio, the signal-to-noise ratio changes from -4dB to 10dB, and the distance between the two targets remains fixed.

[0119] 2. Analysis of simulation content and results.

[0120] There are 3 simulation experiments of the present invention.

[0121] Simulation experiment 1, under the above simulation conditions, the radar received echo signal is processed by the pulse compression coefficient without windowing in the prior art to obtain a one-dimensional range image of the target in the distance dimension, such as Figure 2 shown. Figure 2 The horizontal axis in represents the distance unit, the vertical axis represents the normalized amplitude value, and the curve represents the one-dimensional range image of the target distribution in the distance dimension. Figure 2 It can be seen from the curve shown that after the existing pulse compression technology processes the radar received echo signal, the processing result is aliased, only one peak is formed, and the two targets in the echo signal cannot be detected separately.

[0122] Simulation experiment 2, under the conditions of the above simulation experiment, the pulse compression radar range super-resolution method based on the sparse Bayesian learning algorithm of the present invention is used to process the echo data after the radar pulse compression to obtain a super-resolution range image representing the target distribution in the range dimension, such as Figure 3 shown. Figure 3 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 It can be seen that obvious peaks appear near the distance unit 61 where the two targets are located in the super-resolution range image, and the resolution of two targets with a distance interval close to 0.5 times the theoretical resolution of the traditional pulse compression processing is achieved. Therefore, the range super-resolution method based on sparse recovery in the present invention is more than 1 times better than the traditional pulse compression processing in terms of resolution performance.

[0124] Simulation experiment 3, under the condition of keeping the positions of the two targets unchanged, the resolution probability of the algorithm of the present invention is statistically analyzed as the signal-to-noise ratio changes. 500 Monte Carlo experiments are performed for each signal-to-noise ratio. The condition for judging whether the resolution is successful is that two obvious peaks appear at the distance unit where the actual target is located, and the amplitude is much higher than the peaks at other distance units to a certain extent. The number of grids corresponding to the two peaks is converted into a distance less than 0.2 distance units from the actual distance of the target, so as to judge whether the resolution is successful. The statistical results are as follows: Figure 4 shown.

[0125] Depend on Figure 4 It can be seen that when the distance interval between the two targets remains unchanged, with the increase of the signal-to-noise ratio, the resolution performance of the method proposed in the present invention is also significantly enhanced. When the signal-to-noise ratio is higher than 0 dB, the probability of successful resolution can reach more than 50%, indicating that the method proposed in the present invention effectively improves the distance resolution.

Claims

1. A pulse compression radar range super-resolution method based on SBL algorithm, characterized in that: A complete dictionary matrix after pulse compression is constructed, and the echo signal after pulse compression is processed based on a sparse Bayesian learning algorithm; the specific steps of the super-resolution method are as follows: Step 1, pulse compressing the radar echo signal to obtain a pulse compressed echo signal; Step 2, according to different target echo delays and the waveform characteristics of the echo signal after pulse compression, a complete dictionary matrix after pulse compression is constructed; Step 3, using a sparse Bayesian learning algorithm, the pulse compression echo signal is processed 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 range image.

2. The super-resolution method according to claim 1, characterized in that: The steps for pulse compressing the radar echo signal in step 1 are as follows: In the first step, the radar echo signal s1(t) is: Wherein, a1 represents the amplitude of the echo signal, rect(·) represents the rectangular function, t represents the fast time, T represents the pulse width of the LFM signal, exp represents the exponential function with the natural constant e as the base, j represents the symbol of the imaginary unit, π represents the circumference of 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 from the signal transmission to the reception; In the second step, after multiplying the radar echo data by the pulse compression coefficient in the frequency domain, the frequency domain signal is inversely Fourier transformed according to the following formula to obtain the time domain signal y1(t) after pulse compression without considering the target Doppler: Where a2 represents the amplitude of the output signal after pulse compression, and sin(·) represents the sine function.

3. The super-resolution method according to claim 2, characterized in that: The steps for constructing the complete dictionary matrix after pulse compression described in step 2 are as follows: The first step is to calculate the delay of each column in the segmented time matrix according to the following formula. The delay expression corresponding to the kth column of the dictionary matrix is: In the second step, the simulated pulse pressure data of each column of the discretized dictionary matrix is ​​calculated according to the following formula. The calculation expression of the simulated pulse pressure data of the kth column of the dictionary matrix is: Among them, f s Indicates the sampling frequency; Arrange the simulated pulse pressure data into the following matrix according to time delay: Among them, A represents the complete dictionary matrix after pulse compression, y1 represents the time domain signal after pulse compression, K represents the total number of subdivisions of the radar pulse, and L represents the number of rows of the complete dictionary matrix.

4. The super-resolution method according to claim 1, characterized in that: Converting the time delay information of different targets into the actual distance information of the target in step 4 means that the number of grid points corresponding to the M maximum peaks can be obtained by searching the final mean vector spectrum peak, and the position of the grid point is converted into the distance of the target.

5. 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 calculate the noise power σ of the noise vector n according to the complete dictionary matrix. 2 Initialize and assign the variance parameter γ of the compressible signal z, and bring the initialization result into the iterative process; The second step is to calculate the posterior covariance matrix Σ and the posterior mean vector μ of the compressible signal z according to the prior variance obtained by the current iteration; The third step is to update the noise power σ of the noise vector n. 2 and the prior variance parameter γ of the compressible signal z; The fourth step is to determine the noise power (σ 2 ) new and the prior variance parameter γ of the compressible signal z new Whether the convergence condition is met, if so, the iterative update is terminated, 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.

6. The super-resolution method according to claim 5, characterized in that: The expressions of the mean vector μ and covariance matrix Σ of the compressible signal are: μ = σ -2 SA H y S=(s -2 A H A+C -1 ) -1 Where y=[y1(1),y1(2),...y1(L)] T , represents the observed signal vector, (·) T represents the matrix transpose, diag(γ) represents a diagonal matrix with γ as the diagonal element, γ=[γ1,γ2,...γ K ] T , represents the prior variance of the compressible signal z, σ 2 represents the variance of the noise signal n, (·) H Represents the conjugate transpose operation.

7. The super-resolution method according to claim 6, characterized in that: The updated parameter γ i (new) and σ 2(new) The expression is: c i (new) =E(z i 2 )=S i,i +m i 2 Among them, γ i represents the i-th element of γ, E(·) represents the expectation, Σ i,i represents the i-th column element of the i-th row of the covariance matrix Σ, μ i represents the i-th element of the mean vector μ, ||·|| 2 represents the l2-norm operation, and Tr(·) represents the trace of the matrix.

8. The super-resolution method according to claim 5, characterized in that: The convergence condition is that when ε i The maximum value of is less than the set threshold or reaches the set maximum number of iterations, the algorithm is considered to have reached convergence: Among them, ε i represents the criterion for judging convergence, i=1,2,...,K,γ t+1 represents the posterior variance of the compressible signal z after the tth iteration update, σ t+1 Represents the variance of the noise signal after the tth iteration update.

Images