Vehicle-mounted millimeter wave radar signal reconstruction method in tunnel scene

Abstract

The invention discloses a vehicle-mounted millimeter wave radar signal reconstruction method in a tunnel scene, and relates to the technical field of signal processing and radar, and the method comprises the steps: firstly introducing a multi-modal measurement matrix phi adaptive to different radar scene characteristics, so as to enhance the sparse projection expression capability; secondly, based on a reconstruction error dynamic adjustment sparse level estimation method, the adaptability of the algorithm to the actual sparsity of the signal is improved; analyzing the cross stability of the support set in the multi-iteration process; meanwhile, a regularization residual feedback mechanism is introduced, and recognition and compensation of weak components are enhanced in each round of iteration; and finally, the reconstruction precision and robustness are further improved through integration of a final office reconstruction optimization strategy. Experimental results show that the method has better detection rate, lower error and stronger generalization ability under different sparse levels, signal-to-noise ratios and sampling rates, and is particularly suitable for vehicle-mounted radar system signal processing in a resource-constrained environment.

Description

Technical Field

[0001] This invention relates to the fields of signal processing and radar technology, and in particular to a method for reconstructing vehicle-mounted millimeter-wave radar signals in tunnel scenarios. Background Technology

[0002] With the rapid development of autonomous driving and intelligent transportation, vehicle-mounted millimeter-wave radar, due to its high resolution, strong anti-interference capabilities, and all-weather operation, is gradually becoming an important sensor for vehicle environmental perception. In tunnel scenarios, due to the enclosed space and smooth walls, radar signals are highly susceptible to strong multipath effects. Multipath interference not only causes false targets and energy diffusion but also leads to a decrease in signal sparsity, thereby affecting the reliability of target detection and tracking.

[0003] In terms of signal acquisition, traditional millimeter-wave radar signal acquisition is usually based on the Nyquist sampling theorem, which requires sampling at a rate much higher than the signal bandwidth. This leads to problems such as high sampling rate, large data volume, long processing latency, and high hardware cost. These problems are particularly prominent in resource-constrained embedded automotive scenarios due to limitations in computing resources and energy consumption, severely restricting the deployment and application of high-resolution radar systems.

[0004] In recent years, Compressed Sensing (CS) technology has provided a new solution for radar signal acquisition and reconstruction. This method is based on the sparsity of the signal in a certain domain. By designing an appropriate measurement matrix Φ, it acquires observations with a sampling number far lower than the Nyquist rate, and then uses reconstruction algorithms to recover the original signal.

[0005] In terms of reconstruction algorithms, mainstream methods include greedy algorithms (such as Orthogonal Matching Pursuit (OMP) and Compressed Sample Matching Pursuit (CoSaMP), convex optimization methods (such as Basic Pursuit (BP) and L1 minimization), and thresholding iterative algorithms (such as Iterative Hard Thresholding (IHT) and Alternating Direction Multiplier Method (ADMM). Among these, CoSaMP has high practical value in engineering implementation due to its relatively fast reconstruction speed and moderate accuracy. However, these algorithms generally rely on preset sparsity level parameters and lack the ability to adaptively adjust to the sparsity of the actual signal, affecting their adaptability and robustness in complex dynamic scenarios.

[0006] In the context of vehicle-mounted millimeter-wave radar, some studies have applied compressed sensing to tasks such as target detection, range-Doppler spectrum estimation, and moving target recognition. For example, some researchers have introduced compressed sensing into FMCW radar systems for sparse echo reconstruction, significantly reducing the number of sampling points while preserving key target information; other studies have combined multi-channel sparse reconstruction methods to jointly process target echoes, thereby improving multi-target resolution.

[0007] Despite the positive progress made so far, the following problems still exist: most algorithms have fixed sparsity levels, which cannot adapt to changing signal sparsity characteristics, resulting in decreased recovery performance in strong multipath or resource-constrained scenarios; during iterative reconstruction, the support set often oscillates and fluctuates, and there is a lack of judgment and feedback mechanisms based on support set stability metrics, affecting the overall reconstruction effect; there is a lack of feedback optimization mechanisms that integrate multi-dimensional criteria, making it difficult to perform dynamic corrections based on residual distribution; existing research is mostly based on static radar scenarios, lacking customized optimization designs for vehicle-mounted dynamic multi-target environments. Summary of the Invention

[0008] To address the above technical problems, this invention provides a method for reconstructing vehicle-mounted millimeter-wave radar signals in tunnel scenarios, comprising the following steps: S1. Radar echo signal preprocessing and multi-dimensional feature extraction: After acquiring the raw echo signal from the vehicle-mounted millimeter-wave radar, preprocessing operations are performed on the signal. S2. Measurement Matrix Construction and Selection: Based on the number of multipath interferences, compression ratio, hardware resource utilization, and target radial velocity, different measurement matrix construction strategies are selected. S3. Compressed sensing observation: The measurement matrix constructed in step S2 is used to subsample the preprocessed radar echo signal; S4. Initial sparsity level estimation and pruning: Estimate the initial sparsity level of the signal based on the proportion of projected energy, and screen the initial support set to remove candidates with low confidence; optimize and update the sparsity level based on the correlation peak ratio, the concentration of projected energy, and the energy distribution entropy. S5. Support set extraction and stability judgment: Based on the estimated sparsity level and compressed observations, the support set of the signal is extracted using an iterative algorithm, and its stability is judged. If the requirements are met, step S7 is executed; otherwise, step S6 is executed. S6. Re-estimation and update of unstable support set: The estimated value is adaptively widened or tightened according to the change of support set, the measurement weight or residual is adjusted, and the support set extraction process is re-entered, that is, the process returns to step S4. S7. Regularized residual feedback update: After the support set is stable, a regularized residual feedback mechanism is introduced to update the signal residual; S8. Error Judgment and Loop Feedback: Determine whether the current reconstructed signal meets the error threshold. If it does, proceed to step S9; otherwise, go to step S4. S9. Final Reconstruction and Tuning Output and Reconstruction Signal Output: Under the premise of meeting the error requirements, the final reconstruction and tuning steps are executed to generate the final estimated signal.

[0009] The technical solution further defined in this invention is: Furthermore, in step S1, the target radial velocity is estimated during preprocessing using the radar range-Doppler spectrum, assuming the original radar echo signal is... N represents the length of the sparse signal to be recovered. The following is represented as: Where s represents the sparse coefficient vector; The number of non-zero components in vector s is represented by K, and the sparsity level of the signal is represented by K. The sparse basis Ψ is used to transform the original signal x into an orthogonal or incomplete basis of the sparse representation s.

[0010] As described above, in the method for reconstructing vehicle-mounted millimeter-wave radar signals in a tunnel scenario, the measurement matrix construction strategy in step S2 is as follows: When the number of multipath interferences is ≤4 and the hardware resource utilization rate is ≤60%, the Gaussian-Fourier mixture mode is selected, and the Gaussian random matrix is... With partial Fourier matrices Perform dimensional stitching: Where M1 represents the number of compressed observations taken in Gaussian measurement mode, M2 represents the number of compressed observations taken in Fourier measurement mode, and M1+M2=M; N represents the length of the original signal, that is, the length of the sparse signal to be recovered. When the number of multipath interferences is ≥5 and the hardware resource utilization rate is ≤50%, multimodal weighted fusion is adopted, and the weight α is dynamically adjusted to improve robustness. The weighting coefficients α1, α2, and α3 are dynamically adjusted based on the signal-to-noise ratio, sampling rate, and ambient noise level, where α1 + α2 + α3 = 1, and α i ≥0.2, α1, α2, and α3 are dynamically updated based on the real-time acquired signal-to-noise ratio and compression ratio, with the update period consistent with the radar signal frame period: α1=max(0.2,0.5×(SNR / SNR_max)) α2=max(0.2,0.3×(1-CR)) α3 = 1 - α1 - α2 Wherein, α1 represents the correlation threshold adjustment factor, used to control how many strongly correlated elements are retained in the support set extraction; SNR represents the real-time signal-to-noise ratio; SNR_max represents the maximum acceptable signal-to-noise ratio of the radar system; when SNR≥10dB, α1≥0.25; α2 represents the stability judgment adjustment factor, used to judge the consistency of the support set in multiple iterations; CR represents the compression ratio; when CR≤0.5, α2≥0.15; α3 represents the sparsity level estimation update adjustment factor, used to control whether the new sparsity level, i.e., the K-value estimate, is adjusted up or down, and α3≥0.2; When hardware resource utilization exceeds 70%, the Gaussian matrix Φ is dynamically selected based on the compression ratio. G Or Hartley matrix Φ H : Where M represents the number of rows in the measurement matrix Φ, and γ represents the threshold parameter that controls the selection of the measurement matrix.

[0011] As described above, in a method for reconstructing vehicle-mounted millimeter-wave radar signals in a tunnel scenario, step S3 involves compressed sensing measurement, and a compressed observation model is constructed as follows: y=Φx+n=ΦΨs+n in, This represents a compressed observation vector. The equivalent sensing matrix is ​​represented by N, where N represents the length of the original signal, and n represents Gaussian white noise of length M, with the same dimension as the compressed observation vector y; n~N0(0,σ 2 I), N0(0,σ 2 I) represents a multidimensional Gaussian distribution, where the mean vector is 0 and the covariance matrix is ​​σ. 2 I and σ represent the standard deviation calculated based on the set signal-to-noise ratio, and I represents the identity matrix with a size of M×M.

[0012] As described above, in a method for reconstructing vehicle-mounted millimeter-wave radar signals in a tunnel scenario, step S4 involves an adaptive hierarchical coupled multi-index sparse level determination mechanism based on multipath environment characteristics to perform sparse level estimation and dynamic update. This process includes the following sub-steps: S4.1 Residual Initialization and Correlation Calculation: Before the 0th iteration, there is no estimate of x, therefore let... Therefore, the initial residual value is set to r. (0) =y; the residuals thereafter are expressed as ; Calculate the correlation vector between the current residual and the columns of the measurement matrix: u = Φ T r (0) ;in, Φ represents the reconstruction importance of each position. TThis represents the transpose of the measurement matrix Φ, used for inverse projection onto the signal dimension to obtain a measure of the importance of each signal component to the current residual; S4.2 Projected Energy Calculation and Ranking: Let... If the i-th column is the measurement matrix Φ, then we have ; Calculate the observation residual r (t) The correlation vector u=Φ with the sensing matrix Φ T r (t) ; Calculate the projected energy e of each atom i The square of the projection value at the i-th position is Sort them in descending order: e (1) ≥e (2) ≥...≥e (N) S4.3 Adaptive Sparsity Level Estimation Based on Energy Coverage: Calculate the cumulative energy ratio of the top k largest energies. : Based on the target characteristics in a multipath tunnel environment, an adaptive energy coverage threshold ρ is selected, and the minimum value k is found such that the first k maximum energies cover the proportion of the total energy ρ, as shown in the following formula: K init =min{k:E k ≥ρ}, ρ∈[0.6,0.9] Where ρ represents the energy coverage threshold, when the number of multipaths n mp When ρ ≤ 2, the radar signal exhibits single-target echo characteristics, and when the proportion of non-zero components is ≤ 10%, ρ is taken as 0.6-0.7; when 3 ≤ n mp When n ≤ 4, the radar signal exhibits multi-target echo characteristics, and when the proportion of non-zero components is 10%-30%, ρ is taken as 0.7-0.8; when n mp When the radar signal has a value of ≥5, it exhibits characteristics of weak targets, and when the proportion of non-zero components is >30%, ρ is taken as 0.8-0.9. Prune according to amplitude, taking the top [value]. The index corresponding to the maximum amplitude is used as the initial support set. ; S4.4 Calculate the correlation peak ratio: Among them, u i This represents the i-th element in the correlation vector, i.e., the correlation value between the residual vector and the i-th column of the measurement matrix; u jThe j-th element in the correlation vector is used to calculate the average level of the correlation amplitude of the entire signal; N represents the length of the original signal, i.e., the total number of elements in the correlation vector u; CPR represents the peak correlation ratio, which measures the sparsity. The more prominent the peak, the sparser the signal. S4.5 Calculate the energy distribution entropy: This involves converting the current residual correlation vector u... (t) Normalized to a probability distribution: To introduce energy concentration discrimination, the normalized entropy of the support set amplitude is defined as follows: Where ϵ represents avoiding small amounts of log0; H (t) The larger the value of H, the more uniform the residual distribution, indicating that the uncaptured signal is dispersed, increasing the sparsity level; conversely, the smaller the value of H, the more uniform the residual distribution. (t) The smaller the value, the lower the sparsity level; S4.6 Couple candidate spectra and calculate ΔK: Let the current estimated sparsity level be K. (t) The step size is ΔK (t) ,but: Where CPR(t) represents the peak correlation ratio in the t-th iteration, P target Indicates the expected peak ratio; v (t) The projected energy concentration of the candidate set is defined as: Among them, c i (t) represents the projected energy of the residual for the i-th column of atoms: The average energy is: Among them, T t τ represents the set of candidate atoms selected in the t-th iteration. v H represents the stability threshold. (t) The energy entropy of the support set, log2k (t) β1 represents the sparsity level scaling factor; β2 and β3 represent the peak ratio adjustment weight, residual projection energy distribution weight, and information entropy normalization adjustment weight, respectively. Update sparsity level: Where, sign(ΔK) (t) ) represents the sign function, used to determine the direction of sparsity level adjustment: +1 indicates increasing the sparsity level, -1 indicates decreasing the sparsity level, and 0 indicates no adjustment; ΔK maxThis represents the maximum allowed value for adjusting the sparsity level in each iteration, set to 10%-20% of the current sparsity level. The updated sparsity level K is used as the input for the next round. The residual, peak ratio, and information entropy are repeatedly calculated and the sparsity level is updated to form an adaptive optimization closed loop, thereby realizing the dynamic adjustment of the signal sparsity level.

[0013] As described above, in the method for reconstructing vehicle-mounted millimeter-wave radar signals in a tunnel scenario, step S5 introduces a concentration index of the projected energy distribution of the candidate set during the support set determination and update process. This index is used to weight the stability of the support set and drive the closed-loop update. Specifically, this includes: Let the sliding window size be 3, and let the support set within the window be S. t-2 S t-1 and S t t represents the current iteration number, and the basic threshold is denoted as J. thresh =0.85; Calculate Jaccard similarity: Among them, S i Let S represent the support set obtained in the i-th iteration. j This represents the support set obtained in the j-th iteration; The stability metric for the sliding window is set as the mean Jaccard similarity of all adjacent support sets within the window: The supporting set energy entropy weights are: The residual descent rate is: v(t) represents the concentration of the candidate spectrum; If Stab(t) ≥ 0.85, the support set is determined to be stable, and step S7 is executed to enter the final reconstruction stage; if Stab(t) < 0.85, the support set is determined to be unstable, and step S6 is executed to enter the candidate expansion step.

[0014] As described above, in the method for reconstructing vehicle-mounted millimeter-wave radar signals in a tunnel scenario, in step S6, during the candidate expansion stage, a candidate support set is constructed based on the residual projection score. , where current k This indicates the size of the currently estimated support set; a scores mechanism is introduced, where in the t-th iteration, a score is calculated for each column based on the residuals to evaluate the contribution of each basis vector to the residuals; combining the projection strength and matrix column norm, the candidate index with the highest score outside the current support set is selected: Among them, C i Represents the correlation projection coefficient; r (t-1)a represents the residual energy from the previous iteration; j,i This represents the element in the j-th row and i-th column of the measurement matrix Φ; ε represents a small positive number to prevent the denominator from being 0. Excluding elements from the current support set, calculate the score for all unselected atoms, and then select the atoms with the highest scores (L) to form a candidate set T, where L is a function of the current sparse estimate K. Therefore: Wherein, min(3K) (t) ,·) indicates the first level of restriction. This represents the second-level correction term, and incorporates historical feedback from the support set; the candidate set T is then merged with the current support set S to form an extended support set. Furthermore, an orthogonal-upper triangular decomposition is performed on the extended support set, that is, a matrix is ​​decomposed into the product of an orthogonal matrix and an upper triangular matrix, which serves as the input for subsequent least squares estimation.

[0015] As described above in the method for reconstructing vehicle-mounted millimeter-wave radar signals in a tunnel scenario, in step S6, a screening threshold is constructed based on the median and mean absolute deviation to eliminate outliers; the screening threshold is... Retain the support set corresponding to coefficients exceeding the threshold, and update the support set. The reconstructed signal is θ represents the signal amplitude estimate obtained by fitting the observation y with the support set column matrix, MAD represents the mean absolute deviation, and σ represents the standard deviation calculated based on the set signal-to-noise ratio.

[0016] As described above, in a method for reconstructing vehicle-mounted millimeter-wave radar signals in a tunnel scenario, step S7 involves regularizing the feedback update of the residual, with the feedback weight λ. (t) Dynamically adjusts according to an exponential decay law with the number of iterations: Calculate the basic residual Starting from the 6th iteration, a regularization feedback term is embedded in the residual update to enhance robustness. , where λ (t) The exponential decay regularity coefficient representing the iteration correlation is defined as: Where λ0=0.05×σ represents the initial coefficient, and τ=5 represents the attenuation factor; Update residuals: otherwise: Determine if the residual norm satisfies the following formula: Stop iteration if the residual does not decrease as shown in the following formula: in, This indicates the threshold for the percentage decrease in residuals; when the percentage decrease in residuals is less than... Stop the iteration early.

[0017] As described above, in a method for reconstructing vehicle-mounted millimeter-wave radar signals in a tunnel scenario, step S9 records the support set S of the three most recent iterations. (t) S (t-1) and S (t-2) By calculating the average Jaccard similarity, it can be determined whether the support sets have reached a stable state. The Jaccard similarity is obtained by calculating the ratio of the intersection size to the union size of the two sets. Where T represents the total number of iterations, t represents the current iteration index, and S (t) Let represent the support set for the t-th iteration; When J avg When the value is less than 0.85, it is determined that the support set has not yet reached a stable state. Final support set optimization is then performed, dynamically adjusting the support set size based on the signal amplitude, and resolving the least squares problem to obtain the final reconstruction result. Among them, A S This represents the column submatrix corresponding to the support set S in the measurement matrix. Represents the column submatrix A S The transpose of , where y represents the observation vector. Denotes the optimal solution on the support set; Solving for coefficients on the support set S using the least squares method Then embed it into a sparse vector x of length N. * In the middle, the coefficients of the support set outside positions are set to zero, resulting in the final complete sparse coefficient vector x. * Based on this, the final reconstructed signal can be recovered. : .

[0018] The beneficial effects of this invention are: (1) In this invention, an adaptive multimodal measurement matrix selection mechanism is proposed by combining a Gaussian random matrix with a Fourier matrix and taking into account environmental constraints such as hardware resource utilization, number of multipaths in the tunnel environment and compression ratio. When there is little multipath interference and the hardware load is moderate, a Gaussian and Fourier mixed matrix is ​​used to balance randomness and sparsity to ensure accurate signal recovery. When the multipath is complex or the noise is severe, a weighted fusion strategy is introduced to dynamically adjust the weight of each mode according to the real-time signal-to-noise ratio and compression ratio to improve the robustness of the system in a strong interference environment. When hardware resources are scarce, the system automatically switches to a lightweight matrix to reduce computational overhead and ensure the real-time performance of the vehicle system. This mechanism can maintain better reconstruction accuracy and computational efficiency in tunnel scenarios with different complexities, overcomes the problem of poor adaptability of traditional algorithms under fixed matrix conditions, and greatly enhances the practicality of this method in resource-constrained environments. (2) In this invention, a hierarchical coupling judgment mechanism based on correlation peak ratio, energy concentration and energy distribution entropy is proposed, which can adaptively estimate and dynamically adjust sparsity in each iteration, effectively avoiding reconstruction distortion caused by excessive or insufficient sparsity; at the same time, this invention introduces a support set stability analysis method in the iteration process, comprehensively considering Jaccard similarity, residual decrease rate and energy concentration to judge the convergence of the support set; when the support set is detected to be unstable, the system will trigger a candidate expansion and robust threshold screening mechanism to automatically remove false atoms caused by tunnel reflection, thereby ensuring the reliability of the support set; this design significantly reduces the false alarm rate, improves precision, recall and F1 score, and achieves robust adaptation to complex multipath environments; (3) In the iterative update stage, the present invention introduces a residual-gradient hybrid regularization feedback mechanism, which uses exponentially decaying dynamic weights to enhance the identification and compensation of weak target components, and can still maintain high detection sensitivity under tunnel multipath interference. In the final stage, the present invention further introduces weighted least squares tuning based on amplitude weights to perform amplitude weighted correction on the coefficients on the support set, which significantly improves the accuracy of amplitude estimation and the overall signal fidelity. Through comparative experiments with OMP and CoSaMP, the present invention can achieve lower mean square error (MSE) and higher reconstruction signal-to-noise ratio (RSNR) under the same conditions, while maintaining a faster convergence speed. This design not only improves the algorithm's ability to recover weak targets, but also ensures the advantages of the final reconstructed signal in terms of accuracy and stability, and has significant engineering application value. Attached Figure Description

[0019] Figure 1 This is a schematic diagram of the overall process of the present invention; Figure 2 This is a schematic diagram of the measurement matrix construction strategy in an embodiment of the present invention; Figure 3 This is a schematic diagram of the sparsity estimation process in an embodiment of the present invention. Detailed Implementation

[0020] This embodiment provides a method for reconstructing vehicle-mounted millimeter-wave radar signals in a tunnel scenario, such as... Figure 1 As shown, it includes the following steps: S1. Radar echo signal preprocessing and multi-dimensional feature extraction: After acquiring the raw echo signal from the vehicle-mounted millimeter-wave radar, preprocessing operations are performed on the signal.

[0021] During preprocessing, the target's radial velocity is estimated using the radar range-Doppler spectrum. Let the original radar echo signal be... N represents the length of the sparse signal to be recovered. The following is represented as: Where s represents the sparse coefficient vector; The number of non-zero components in vector s is represented by K, and the sparsity level of the signal is represented by K. The sparse basis Ψ is used to transform the original signal x into an orthogonal or incomplete basis of the sparse representation s.

[0022] S2. Measurement Matrix Construction and Selection: Based on the number of multipath interferences, compression ratio, hardware resource utilization, and target radial velocity, different measurement matrix construction strategies are selected.

[0023] like Figure 2 As shown, when the number of multipath interferences is small (≤4) and the hardware resource utilization rate is ≤60%, the number of interference targets is not large. Randomness (Gaussian) + frequency domain sparsity (Fourier) can guarantee the signal recovery accuracy, and the computational cost is low. Therefore, the Gaussian-Fourier mixture mode is selected, and the Gaussian random matrix is ​​used to... With partial Fourier matrices Perform dimensional stitching: Where M1 represents the number of compressed observations taken in Gaussian measurement mode, which is much smaller than N; M2 represents the number of compressed observations taken in Fourier measurement mode, which is much smaller than N, and M1+M2=M; N represents the length of the original signal, that is, the length of the sparse signal to be recovered.

[0024] When the number of multipath interferences is large (≥5) and the hardware resource utilization rate is ≤50%, there are too many interference sources, and the robustness of a single matrix combination is insufficient. It is necessary to increase matrix diversity through weighted fusion to suppress multipath noise. Multimodal weighted fusion is adopted, and the weight α is dynamically adjusted to improve robustness. The weighting coefficients α1, α2, and α3 are dynamically adjusted based on the signal-to-noise ratio, sampling rate, and ambient noise level, where α1 + α2 + α3 = 1, and α i ≥0.2, α1, α2, and α3 are dynamically updated based on the real-time acquired signal-to-noise ratio and compression ratio, with the update period consistent with the radar signal frame period: α1=max(0.2,0.5×(SNR / SNR_max)) α2=max(0.2,0.3×(1-CR)) α3 = 1 - α1 - α2 Wherein, α1 represents the correlation threshold adjustment factor, which controls how many strongly correlated elements are retained in the support set extraction; SNR represents the real-time signal-to-noise ratio; SNR_max represents the maximum acceptable signal-to-noise ratio of the radar system; when SNR≥10dB, α1≥0.25; α2 represents the stability judgment adjustment factor, which is used to judge the consistency of the support set in multiple iterations; CR represents the compression ratio; when CR≤0.5, α2≥0.15; α3 represents the sparsity level estimation update adjustment factor, which controls whether the new sparsity level, i.e., the K-value estimate, is adjusted up or down, and α3≥0.2.

[0025] When hardware resources are scarce (utilization > 70%), real-time performance and computational load are guaranteed, and the Gaussian matrix Φ is dynamically selected based on the compression ratio. G Or Hartley matrix Φ H : Where M represents the number of rows in the measurement matrix Φ, and γ represents the threshold parameter for controlling the selection of the measurement matrix, which can be set according to the specific application scenario.

[0026] S3. Compressed sensing observation: The measurement matrix constructed in step S2 is used to subsample the preprocessed radar echo signal.

[0027] Based on the multimodal measurement matrix Φ constructed in step S2 that matches the multipath environment of the tunnel, the preprocessed radar echo signal x is linearly projected to construct the compressed observation model as follows: y=Φx+n=ΦΨs+n in, This represents a compressed observation vector. The equivalent sensing matrix is ​​represented by N, where N represents the length of the original signal, and n represents Gaussian white noise of length M, with the same dimension as the compressed observation vector y; n~N0(0,σ 2 I), N0(0,σ 2 I) represents a multidimensional Gaussian distribution, where the mean vector is 0 and the Cov (covariance) is σ. 2I and σ represent the standard deviation calculated based on the set signal-to-noise ratio, and I represents the identity matrix with a size of M×M.

[0028] S4. Initial sparsity level estimation and pruning: Estimate the initial sparsity level of the signal based on the proportion of projected energy, and screen the initial support set to remove candidates with low confidence; optimize and update the sparsity level based on the correlation peak ratio, the concentration of projected energy, and the energy distribution entropy.

[0029] Based on the characteristics of multipath environments, an adaptive hierarchical coupled multi-index sparsity level determination mechanism is adopted for sparsity level estimation and dynamic update. Figure 3 As shown, the specific steps include the following: S4.1 Residual Initialization and Correlation Calculation: Before the 0th iteration, there is no estimate of x, therefore let... Therefore, the initial residual value is set to r. (0) =y; the residuals thereafter are expressed as ; Calculate the correlation vector between the current residual and the columns of the measurement matrix: u = Φ T r (0) ;in, Φ represents the reconstruction importance of each position. T This represents the transpose of the measurement matrix Φ, used for inverse projection onto the signal dimension to obtain a measure of the importance of each signal component to the current residual.

[0030] S4.2 Projected Energy Calculation and Ranking: Let... If the i-th column is the measurement matrix Φ, then we have ; Calculate the observation residual r (t) The correlation vector u=Φ with the sensing matrix Φ T r (t) ; Calculate the projected energy e for each atom (column of the measurement matrix). i The square of the projection value at the i-th position is Sort them in descending order: e (1) ≥e (2) ≥...≥e (N) .

[0031] S4.3 Adaptive Sparsity Level Estimation Based on Energy Coverage: Calculate the cumulative energy ratio of the top k largest energies. : Based on the target characteristics in a multipath tunnel environment, an adaptive energy coverage threshold ρ is selected, and the minimum value k is found such that the first k maximum energies cover the proportion of the total energy ρ, as shown in the following formula: Kinit =min{k:E k ≥ρ}, ρ∈[0.6,0.9] Where ρ represents the energy coverage threshold, when the environment is simple (number of multipaths n) mp When the radar signal exhibits single-target echo characteristics and the proportion of non-zero components is ≤10%, ρ is taken as 0.6-0.7; when the environment is moderate (multipath number 3≤n) mp When the radar signal is ≤4), it exhibits multi-target echo characteristics, and the proportion of non-zero components is 10%-30%, ρ is taken as 0.7-0.8; when the environment is complex (multipath number n) mp When the radar signal exhibits characteristics of weak targets and the proportion of non-zero components is greater than 30%, ρ is taken as 0.8-0.9. Prune according to amplitude, taking the top [value]. The index corresponding to the maximum amplitude is used as the initial support set. .

[0032] S4.4 Calculate the correlation peak ratio, which is used to measure the sparsity of the signal: Among them, u i This represents the i-th element in the correlation vector, i.e., the correlation value between the residual vector and the i-th column of the measurement matrix; u j The j-th element in the correlation vector is used to calculate the average level of the correlation amplitude of the entire signal; N represents the length of the original signal, i.e., the total number of elements in the correlation vector u; CPR represents the peak correlation ratio, which measures the sparsity. The more prominent the peak, the sparser the signal.

[0033] S4.5 Calculate the energy distribution entropy: This involves converting the current residual correlation vector u... (t) Normalized to a probability distribution: To introduce energy concentration discrimination, the normalized entropy of the support set amplitude is defined as follows: Where ϵ represents avoiding small amounts of log0; H (t) The larger the H value, the more uniform the residual distribution, indicating that the uncaptured signal is dispersed, which is suitable for increasing the sparsity level; conversely, the smaller the H value, the more uniform the residual distribution. (t) The smaller the value, the more concentrated the residuals are in a few elements, and the sparsity level may be too high, requiring a reduction in the sparsity level.

[0034] S4.6 Calculate ΔK (coupled candidate spectrum): Let the current estimated sparsity level be K. (t) The step size is ΔK (t) ,but: Where CPR(t) represents the correlation peak ratio in the t-th iteration, reflecting the contrast between the strongest atom and the average level; P target The desired peak-to-peak ratio (P / P) can be obtained by statistically analyzing the P / P distribution of real radar signals in a tunnel environment. In tunnels with multipath propagation, the signal is more dispersed. target ∈[3.5,4.5], take 4 more.

[0035] v (t) The projected energy concentration of the candidate set is defined as: Among them, c i (t) represents the projected energy of the residual for the i-th column of atoms: The average energy is: Among them, T t τ represents the set of candidate atoms selected in the t-th iteration; v To represent the stability threshold, τ is taken in the tunnel environment. v ∈[2,2.5], to balance the interference of strong targets and multipath spurious peaks; H (t) The energy entropy of the support set measures the uncertainty of energy distribution; log2k (t) This represents the sparsity level scaling factor, used for normalization to prevent the entropy term from becoming too large.

[0036] β1, β2, and β3 represent weighting coefficients used to control the contribution of the two indicators; Peak ratio adjustment weight: β1∈[0.5-0.6], ensuring that peak ratio dominates sparsity level adjustment, serving as the core driver; Residual projection energy distribution weight: β2∈[0.3,0.8], avoiding excessive increase in sparsity level due to multipath virtual atoms, serving as an auxiliary adjustment; Information entropy normalization adjustment weight: β3∈[0.2,0.3], suppressing excessive expansion of sparsity level, serving as a safety valve.

[0037] Update sparsity level: Where, sign(ΔK) (t) ) represents the sign function, used to determine the direction of sparsity level adjustment: +1 indicates increasing the sparsity level, -1 indicates decreasing the sparsity level, and 0 indicates no adjustment; ΔK max This represents the maximum allowable value for adjusting the sparsity level in each iteration, used to avoid excessive jumps that could cause the reconstruction to diverge. It is set to 10%-20% of the current sparsity level.

[0038] The updated sparsity level K is used as the input for the next round. The residual, peak ratio, and information entropy are repeatedly calculated and the sparsity level is updated to form an adaptive optimization closed loop, thereby realizing the dynamic adjustment of the signal sparsity level.

[0039] S5. Support set extraction and stability judgment: Based on the estimated sparsity level and compressed observations, the support set of the signal is extracted using an iterative algorithm, and its stability is judged. If the requirements are met, step S7 is executed; otherwise, step S6 is executed.

[0040] In the process of supporting set determination and updating, a concentration index of the projected energy distribution of candidate sets is introduced to weight the stability of the supporting sets and drive closed-loop updates. Specifically, this includes: Let the sliding window size be 3, and let the support set within the window be S. t-2 S t-1 and S t t represents the current iteration number, and the basic threshold is denoted as J. thresh =0.85; Calculate Jaccard similarity: Among them, S i Let S represent the support set obtained in the i-th iteration. j Let represent the support set obtained in the j-th iteration.

[0041] The stability metric for the sliding window is set as the mean Jaccard similarity of all adjacent support sets within the window: The supporting set energy entropy weights are: The residual descent rate is: v(t) represents the concentration of the candidate spectrum; if Stab(t) ≥ 0.85, the support set is determined to be stable, and step S7 is executed to enter the final reconstruction stage; if Stab(t) < 0.85, the support set is determined to be unstable, and step S6 is executed to enter the candidate expansion step.

[0042] S6. Re-estimation and update of unstable support set: Adaptively loosen or tighten the estimated value according to the change of the support set, adjust the measurement weight or residuals, and re-enter the support set extraction process, i.e. return to step S4.

[0043] In the candidate expansion phase, a candidate support set is constructed based on the residual projection score. , where current kThis indicates the size of the currently estimated support set. To overcome the interference of multipath false targets in the tunnel environment on the construction of the candidate set, a scoring mechanism is introduced. In the t-th iteration, the score of each column is calculated based on the residuals to evaluate the contribution of each basis vector to the residuals. Combining the projection intensity and the matrix column norm, the candidate index with the highest score outside the current support set is selected. Among them, C i Represents the correlation projection coefficient; r (t-1) a represents the residual energy from the previous iteration; j,i ε represents the element in the j-th row and i-th column of the measurement matrix Φ; ε represents a small positive number to prevent the denominator from being 0.

[0044] Excluding elements from the current support set, calculate the score for all unselected atoms, and then select the atoms with the highest scores (L) to form a candidate set T, where L is a function of the current sparse estimate K. Therefore: Wherein, min(3K) (t) ,·) indicates the first level of restriction. This represents the second-level correction term, and incorporates historical feedback from the support set; the candidate set T is then merged with the current support set S to form an extended support set. Furthermore, an orthogonal-upper triangular decomposition is performed on the extended support set, that is, a matrix is ​​decomposed into the product of an orthogonal matrix and an upper triangular matrix, which serves as the input for subsequent least squares estimation.

[0045] To suppress spurious atom interference caused by multipath effects in the tunnel environment, robust threshold screening based on median and mean absolute deviation (MAD) is introduced on the extended support set to remove outliers; the screening threshold is... Retain the support set corresponding to coefficients exceeding the threshold, and update the support set. The reconstructed signal is θ represents the signal amplitude estimate obtained by fitting the observation y with the support set column matrix, MAD represents the mean absolute deviation, and σ represents the standard deviation calculated based on the set signal-to-noise ratio.

[0046] S7. Regularized Residual Feedback Update: After the support set stabilizes, a regularized residual feedback mechanism is introduced to update the signal residuals; the residuals are updated using regularized feedback, with feedback weight λ. (t) It is dynamically adjusted according to an exponential decay law with the number of iterations.

[0047] Calculate the basic residual Starting from the 6th iteration, a regularization feedback term is embedded in the residual update to enhance robustness. , where λ (t)The exponential decay regularity coefficient representing the iteration correlation is defined as: Where λ0=0.05×σ represents the initial coefficient, and τ=5 represents the attenuation factor.

[0048] Update residuals: otherwise: Determine if the residual norm satisfies the following formula: Stop iteration if the residual does not decrease as shown in the following formula: in, This indicates the threshold for the percentage decrease in residuals; when the percentage decrease in residuals is less than... Stop the iteration early.

[0049] S8. Error Judgment and Loop Feedback: Determine whether the current reconstructed signal meets the error threshold. If it does, proceed to step S9; otherwise, go to step S4.

[0050] S9. Final Reconstruction and Tuning Output and Reconstruction Signal Output: Under the premise of meeting the error requirements, the final reconstruction and tuning steps are executed to generate the final estimated signal.

[0051] Record the support set S of the last three iterations (t) S (t-1) and S (t-2) By calculating the average Jaccard similarity, it can be determined whether the support sets have reached a stable state. The Jaccard similarity is obtained by calculating the ratio of the intersection size to the union size of the two sets. Where T represents the total number of iterations, t represents the current iteration index (from 1 to T), and S (t) Let represent the support set for the t-th iteration.

[0052] When J avg When the value is less than 0.85, it is determined that the support set has not yet reached a stable state. Final support set optimization is then performed, dynamically adjusting the support set size based on the signal amplitude, and resolving the least squares problem to obtain the final reconstruction result. Among them, A S This represents the column submatrix corresponding to the support set S in the measurement matrix. Represents the column submatrix A SThe transpose of , where y represents the observation vector. This represents the optimal solution on the support set (in the least squares sense).

[0053] Solving for coefficients on the support set S using the least squares method Then embed it into a sparse vector x of length N. * In the middle, the coefficients of the support set outside positions are set to zero, resulting in the final complete sparse coefficient vector x. * Based on this, the final reconstructed signal can be recovered. : .

[0054] This embodiment first introduces a multimodal measurement matrix Φ adapted to different radar scenario characteristics to enhance the sparse projection representation capability. Second, a sparse level estimation method based on dynamic adjustment of reconstruction error improves the algorithm's adaptability to the actual sparsity of the signal. Then, it combines the cross-stability analysis of the support set in the multi-iteration process. Simultaneously, a regularized residual feedback mechanism is introduced to strengthen the identification and compensation of weak components in each iteration. Finally, through the integration of final reconstruction optimization strategies, the reconstruction accuracy and robustness are further improved. Experimental results show that the method of this invention has better detection rate, lower error, and stronger generalization ability under different sparsity levels, signal-to-noise ratios, and sampling rates, making it particularly suitable for signal processing of vehicle-mounted radar systems in resource-constrained environments.

[0055] In addition to the embodiments described above, the present invention may have other implementations. All technical solutions formed by equivalent substitution or equivalent transformation fall within the protection scope claimed by the present invention.

Claims

1. A method for reconstructing vehicle-mounted millimeter-wave radar signals in a tunnel scenario, characterized in that: Includes the following steps: S1. Radar echo signal preprocessing and multi-dimensional feature extraction: After acquiring the raw echo signal from the vehicle-mounted millimeter-wave radar, preprocessing operations are performed on the signal. S2. Measurement Matrix Construction and Selection: Based on the number of multipath interferences, compression ratio, hardware resource utilization, and target radial velocity, different measurement matrix construction strategies are selected. S3. Compressed sensing observation: The measurement matrix constructed in step S2 is used to subsample the preprocessed radar echo signal; S4. Initial sparsity level estimation and pruning: Estimate the initial sparsity level of the signal based on the proportion of projected energy, and screen the initial support set to remove candidates with low confidence; optimize and update the sparsity level based on the correlation peak ratio, the concentration of projected energy, and the energy distribution entropy. S5. Support set extraction and stability judgment: Based on the estimated sparsity level and compressed observations, the support set of the signal is extracted using an iterative algorithm, and its stability is judged. If the requirements are met, step S7 is executed; otherwise, step S6 is executed. S6. Re-estimation and update of unstable support set: The estimated value is adaptively widened or tightened according to the change of support set, the measurement weight or residual is adjusted, and the support set extraction process is re-entered, that is, the process returns to step S4. S7. Regularized residual feedback update: After the support set is stable, a regularized residual feedback mechanism is introduced to update the signal residual; S8. Error Judgment and Loop Feedback: Determine whether the current reconstructed signal meets the error threshold. If it does, proceed to step S9; otherwise, go to step S4. S9. Final Reconstruction and Tuning Output and Reconstruction Signal Output: Under the premise of meeting the error requirements, the final reconstruction and tuning steps are executed to generate the final estimated signal.

2. The method for reconstructing vehicle-mounted millimeter-wave radar signals in a tunnel scenario according to claim 1, characterized in that: In step S1, the target radial velocity is estimated using the radar range-Doppler spectrum during preprocessing. Let the original radar echo signal be... N represents the length of the sparse signal to be recovered. Representing the set of real numbers, in The following is represented as: Where s represents the sparse coefficient vector; The number of non-zero components in vector s is represented by K, and the sparsity level of the signal is represented by K. The sparse basis Ψ is used to transform the original signal x into an orthogonal or incomplete basis of the sparse representation s.

3. The method for reconstructing vehicle-mounted millimeter-wave radar signals in a tunnel scenario according to claim 1, characterized in that: In step S2, the measurement matrix construction strategy is specifically as follows: When the number of multipath interferences is ≤4 and the hardware resource utilization rate is ≤60%, the Gaussian-Fourier mixture mode is selected, and the Gaussian random matrix is... With partial Fourier matrices Perform dimensional stitching: Where M1 represents the number of compressed observations taken in Gaussian measurement mode, M2 represents the number of compressed observations taken in Fourier measurement mode, and M1 + M2 = M; N represents the length of the original signal, i.e., the length of the sparse signal to be recovered. Represents the set of real numbers; When the number of multipath interferences is ≥5 and the hardware resource utilization rate is ≤50%, multimodal weighted fusion is adopted, and the weight α is dynamically adjusted to improve robustness. The weighting coefficients α1, α2, and α3 are dynamically adjusted based on the signal-to-noise ratio, sampling rate, and ambient noise level, where α1 + α2 + α3 = 1, and α i ≥0.2, α1, α2, and α3 are dynamically updated based on the real-time acquired signal-to-noise ratio and compression ratio, with the update period consistent with the radar signal frame period: α1=max(0.2,0.5×(SNR / SNR_max)) α2=max(0.2,0.3×(1-CR)) α3=1-α1-α2 Wherein, α1 represents the correlation threshold adjustment factor, used to control how many strongly correlated elements are retained in the support set extraction; SNR represents the real-time signal-to-noise ratio; SNR_max represents the maximum acceptable signal-to-noise ratio of the radar system; when SNR≥10dB, α1≥0.25; α2 represents the stability judgment adjustment factor, used to judge the consistency of the support set in multiple iterations; CR represents the compression ratio; when CR≤0.5, α2≥0.15; α3 represents the sparsity level estimation update adjustment factor, used to control whether the new sparsity level, i.e., the K-value estimate, is adjusted up or down, and α3≥0.2; When hardware resource utilization exceeds 70%, the Gaussian matrix Φ is dynamically selected based on the compression ratio. G Or Hartley matrix Φ H : Where M represents the number of rows in the measurement matrix Φ, and γ represents the threshold parameter that controls the selection of the measurement matrix.

4. The method for reconstructing vehicle-mounted millimeter-wave radar signals in a tunnel scenario according to claim 1, characterized in that: In step S3, compressed sensing measurement is performed, and a compressed observation model is constructed as follows: y=Φx+n=ΦΨs+n Where Φ represents the selected measurement matrix, x represents the echo signal, s represents the sparse coefficient vector, and Ψ represents the sparse basis; This represents a compressed observation vector. Represents the equivalent sensing matrix. Let N represent the set of real numbers, and let n represent the length of the original signal; n represents Gaussian white noise of length M, with the same dimension as the compressed observation vector y; n ~ N0(0,σ 2 I), N0(0,σ 2 I) represents a multidimensional Gaussian distribution, where the mean vector is 0 and the covariance matrix is ​​σ. 2 I and σ represent the standard deviation calculated based on the set signal-to-noise ratio, and I represents the identity matrix with a size of M×M.

5. The method for reconstructing vehicle-mounted millimeter-wave radar signals in a tunnel scenario according to claim 1, characterized in that: In step S4, an adaptive hierarchical coupled multi-index sparsity level determination mechanism is used to perform sparsity level estimation and dynamic update based on the characteristics of the multipath environment. It includes the following steps: S4.1 Residual Initialization and Correlation Calculation: Before the 0th iteration, there is no estimate of x, therefore let... Therefore, the initial residual value is set to r. (0) =y; the residuals thereafter are expressed as Where y represents the compressed observation vector, This represents the echo signal at time t=0, i.e., the initial, unestimated signal; Calculate the correlation vector between the current residual and the columns of the measurement matrix: u = Φ T r (0) ;in, This indicates the importance of the reconstruction at each location. Let N represent the set of real numbers, and Φ represent the signal length. T This represents the transpose of the measurement matrix Φ, used for inverse projection onto the signal dimension to obtain a measure of the importance of each signal component to the current residual; S4.2 Projected Energy Calculation and Ranking: Let... If the i-th column is the measurement matrix Φ, then we have u i express The inner product of y and y, i.e., the correlation between the two; calculate the observed residual r. (t) The correlation vector u=Φ with the sensing matrix Φ T r (t) ; Calculate the projected energy e of each atom i The square of the projection value at the i-th position is Sort them in descending order: and (1) ≥e (2) ≥...≥e (N) Among them, e (N) This represents the projected energy of the atom at position N; S4.3 Adaptive Sparsity Level Estimation Based on Energy Coverage: Calculate the cumulative energy ratio of the top k largest energies. : Among them, e (i) This represents the projected energy of the atom at position i. Based on the target characteristics in a multipath tunnel environment, an adaptive energy coverage threshold ρ is selected, and the minimum value k is found such that the first k maximum energies cover the proportion of the total energy ρ, as shown in the following formula: K init =min{k:E k ≥ρ},ρ∈[0.6,0.9] Among them, K init The initial value of the sparsity level K is represented by ρ, which represents the energy coverage threshold when the number of multipaths n mp When ρ ≤ 2, the radar signal exhibits single-target echo characteristics, and when the proportion of non-zero components is ≤ 10%, ρ is taken as 0.6-0.7; when 3 ≤ n mp When n ≤ 4, the radar signal exhibits multi-target echo characteristics, and when the proportion of non-zero components is 10%-30%, ρ is taken as 0.7-0.8; when n mp When the radar signal has a value of ≥5, it exhibits characteristics of weak targets, and when the proportion of non-zero components is >30%, ρ is taken as 0.8-0.

9. Prune according to amplitude, taking the top [value]. The index corresponding to the maximum amplitude is used as the initial support set Ω = argTopK i∈{1,...,N} (|u i |,K i ), K i This represents the value of K after the i-th iteration. An estimate representing the sparsity level; S4.4 Calculate the peak correlation ratio: Among them, u i This represents the i-th element in the correlation vector, i.e., the correlation value between the residual vector and the i-th column of the measurement matrix; u j The j-th element in the correlation vector is used to calculate the average level of the correlation amplitude of the entire signal; N represents the length of the original signal, i.e., the total number of elements in the correlation vector u; CPR represents the peak correlation ratio, which measures the sparsity. The more prominent the peak, the sparser the signal. S4.5 Calculate the energy distribution entropy: This involves converting the current residual correlation vector u... (t) Normalized to a probability distribution: Wherein, the numerator represents the current residual correlation vector u. (t) The absolute value of the i-th element reflects the magnitude of the i-th component in the residual correlation; the denominator represents the residual correlation vector u. (t) The sum of the absolute values ​​of all elements serves as a normalization function. To introduce energy concentration discrimination, the normalized entropy of the support set amplitude is defined as follows: Where ϵ represents avoiding small amounts of log0; H (t) The larger the value of H, the more uniform the residual distribution, indicating that the uncaptured signal is dispersed, increasing the sparsity level; conversely, the smaller the value of H, the more uniform the residual distribution. (t) The smaller the value, the lower the sparsity level; S4.6 Couple candidate spectra and calculate ΔK: Let the current estimated sparsity level be K. (t) The step size is ΔK (t) ,but: Where CPR(t) represents the peak correlation ratio in the t-th iteration, P target Indicates the expected peak ratio; v (t) The projected energy concentration of the candidate set is defined as: Among them, c i (t) represents the projected energy of the residual for the i-th column of atoms: The average energy is: Among them, T t τ represents the set of candidate atoms selected in the t-th iteration. v H represents the stability threshold. (t) The energy entropy of the support set, log2k (t) β1 represents the sparsity level scaling factor; β2 and β3 represent the peak ratio adjustment weight, residual projection energy distribution weight, and information entropy normalization adjustment weight, respectively. Update the sparsity level. The value of the sparsity level after the (t+1)th iteration is: Where, sign(ΔK) (t) ) represents the sign function, used to determine the direction of sparsity level adjustment: +1 indicates increasing the sparsity level, -1 indicates decreasing the sparsity level, and 0 indicates no adjustment; ΔK max This represents the maximum allowed value for adjusting the sparsity level in each iteration, set to 10%-20% of the current sparsity level. The updated sparsity level K is used as the input for the next round. The residual, peak ratio, and information entropy are repeatedly calculated and the sparsity level is updated to form an adaptive optimization closed loop, thereby realizing the dynamic adjustment of the signal sparsity level.

6. The method for reconstructing vehicle-mounted millimeter-wave radar signals in a tunnel scenario according to claim 1, characterized in that: In step S5, during the support set determination and update process, a concentration index of the projected energy distribution of the candidate set is introduced to perform a weighted determination of the support set stability and drive the closed-loop update. Specifically, this includes: Let the sliding window size be 3, and let the support set within the window be S. t-2 S t-1 and S t t represents the current iteration number, S t-2 S t-1 and S t Let J represent the support sets obtained after the (t-2), (t-1), and (t)th iterations, respectively; the basic threshold is denoted as J. thresh =0.85; Calculate Jaccard similarity: Among them, S i Let S represent the support set obtained in the i-th iteration. j This represents the support set obtained in the j-th iteration; The stability metric for the sliding window is set as the mean Jaccard similarity of all adjacent support sets within the window: The supporting set energy entropy weights are: k (t) H represents the sparsity level after the t-th iteration. (t) The energy entropy of the support set after the t-th iteration is: The residual descent rate is: r (t-1) Let r represent the residual value after the (t-1)th iteration. (t) Let represent the residual value after the t-th iteration; v(t) represents the concentration of the candidate spectrum; ω(t-1) and γ(t-1) represent the support set energy entropy weight and the residual decrease rate at the (t-1)-th iteration, respectively; If Stab(t) ≥ 0.85, the support set is determined to be stable, and step S7 is executed to enter the final reconstruction stage; if Stab(t) < 0.85, the support set is determined to be unstable, and step S6 is executed to enter the candidate expansion step.

7. The method for reconstructing vehicle-mounted millimeter-wave radar signals in a tunnel scenario according to claim 1, characterized in that: In step S6, during the candidate expansion stage, a candidate support set is constructed based on the residual projection score. ,in, The current value represents the estimate of the sparsity level. k This indicates the size of the currently estimated support set; a scores mechanism is introduced, where in the t-th iteration, a score is calculated for each column based on the residuals to evaluate the contribution of each basis vector to the residuals; combining the projection strength and matrix column norm, the candidate index with the highest score outside the current support set is selected: Where M represents the number of rows in the measurement matrix Φ, c i Represents the correlation projection coefficient; r (t-1) a represents the residual energy from the previous iteration; j,i This represents the element in the j-th row and i-th column of the measurement matrix Φ; ε represents a small positive number to prevent the denominator from being 0. Excluding elements from the current support set, calculate the score for all unselected atoms, and then select the atoms with the highest scores (L) to form a candidate set T, where L is a function of the current sparse estimate K. Therefore: Among them, K (t) S represents the sparsity level after the t-th iteration. (t-1) Let represent the support set obtained after the (t-1)th iteration, min(3K) (t) ,·) indicates the first level of restriction. This represents the second-level correction term, and incorporates historical feedback from the support set; the candidate set T is then merged with the current support set S to form an extended support set. Furthermore, an orthogonal-upper triangular decomposition is performed on the extended support set, that is, a matrix is ​​decomposed into the product of an orthogonal matrix and an upper triangular matrix, which serves as the input for subsequent least squares estimation.

8. The method for reconstructing vehicle-mounted millimeter-wave radar signals in a tunnel scenario according to claim 7, characterized in that: In step S6, a screening threshold is constructed by setting coefficients based on the median and mean absolute deviation to eliminate outliers; the screening threshold is... Retain the support set corresponding to coefficients exceeding the threshold, and update the support set. The reconstructed signal is θ represents the signal amplitude estimate obtained by fitting the observation y with the support set column matrix, MAD represents the mean absolute deviation, σ represents the standard deviation calculated based on the set signal-to-noise ratio, and i represents the index used to identify the i-th element. This represents the candidate support set, which contains a set of indices that may belong to the valid signal support set; Indicates the reconstructed signal The i-th component; τ (t) This represents the filtering threshold at the t-th iteration.

9. The method for reconstructing vehicle-mounted millimeter-wave radar signals in a tunnel scenario according to claim 1, characterized in that: In step S7, the residuals are updated using regularized feedback, with feedback weight λ. (t) Dynamically adjusts according to an exponential decay law with the number of iterations: Calculate the basic residual Starting from the 6th iteration, a regularization feedback term is embedded in the residual update to enhance robustness. Where y represents the compressed observation vector, r (t) Let A represent the residual value after the t-th iteration, and let A represent the complete compressed observation matrix. This represents the submatrix corresponding to the current support set; This indicates that the support set s is at the t-th iteration. (t) The corresponding reconstructed signal component; s (t) Let A represent the support set after the t-th iteration; A represents the complete compressed observation matrix. λ represents the reconstructed signal at the (t-1)th iteration; (t) The exponential decay regularity coefficient representing the iteration correlation is defined as: Where λ0=0.05×σ represents the initial coefficient, and τ=5 represents the attenuation factor; Update residuals: otherwise: Determine if the residual norm satisfies the following formula: Stop iteration if the residual does not decrease as shown in the following formula: in, This represents the initial residual at the t-th iteration. This indicates the threshold for the percentage decrease in residuals; when the percentage decrease in residuals is less than... Stop the iteration early.

10. The method for reconstructing vehicle-mounted millimeter-wave radar signals in a tunnel scenario according to claim 1, characterized in that: In step S9, the support set S of the three most recent iterations is recorded. (t) S (t-1) and S (t-2) By calculating the average Jaccard similarity, it can be determined whether the support sets have reached a stable state. The Jaccard similarity is obtained by calculating the ratio of the intersection size to the union size of the two sets. Where T represents the total number of iterations, t represents the current iteration index, and S (t) Let S represent the support set for the t-th iteration. (t-1) Let S represent the support set for the (t-1)th iteration. (t-2) Let represent the support set for the (t-2)th iteration; When J avg When the value is less than 0.85, it is determined that the support set has not yet reached a stable state. Final support set optimization is then performed, dynamically adjusting the support set size based on the signal amplitude, and resolving the least squares problem to obtain the final reconstruction result. in, Indicates the final reconstructed signal, A S Let u represent the column submatrix corresponding to the support set S in the measurement matrix, s represent the sparse coefficient vector, and Ψ represent the sparse basis. Represents the column submatrix A S The transpose of , where y represents the observation vector. Denotes the optimal solution on the support set; Solving the coefficient vector on the support set S using the least squares method Then embed it into a sparse vector x of length N. * In the middle, the coefficients of the support set outside positions are set to zero, resulting in the final complete sparse coefficient vector x. * Based on this, the final reconstructed signal can be recovered. : 。

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