FIR-IAA target Doppler frequency estimation method based on whitening in interference environment

Abstract

The invention discloses a whitening-based FIR-IAA target Doppler frequency estimation method in an interference environment, and the method comprises the steps: carrying out the inversion of the sum of a covariance matrix and a unit matrix of false target interference, obtaining an FIR-MTD Doppler filter group according to the inversion matrix and a DFT-MTD filter group, constructing an initial dimension reduction conversion matrix, and carrying out the calculation of the FIR-IAA target Doppler frequency. And after whitening processing is carried out on the initial dimension reduction matrix, target Doppler frequency estimation is carried out by using IAA. While the Doppler frequency estimation precision and accuracy are ensured, the dimensionality of algorithm operation is reduced by using the dimensionality reduction conversion matrix to process the data, the defects of large calculation amount and high complexity during Doppler estimation are overcome, the problems of main lobe broadening and pseudo spectrum peak brought by the prior art are avoided by whitening processing, and the accuracy of Doppler frequency estimation is improved. According to the invention, the FIR-MTD filter improves the anti-interference capability of target Doppler frequency estimation.

Description

Technical Field

[0001] This invention belongs to the field of radar technology, and more specifically relates to a target Doppler frequency estimation method based on a whitening-based finite impulse response filter iterative adaptive algorithm (FIR-IAA) in the field of radar parameter estimation technology under interference conditions. This invention can be used for target Doppler frequency estimation after whitening and dimensionality reduction processing of pulse Doppler radar received signals under false target interference conditions. Background Technology

[0002] Doppler frequency estimation technology obtains the radial velocity information of a target by analyzing the frequency shift in radar echo signals. Common methods include traditional estimation based on Fast Fourier Transform, high-resolution spectral estimation using subspace classes, maximum likelihood methods, and IAA super-resolution methods. In radar, Doppler frequency estimation is used not only for velocity measurement but also for target separation, anti-jamming, and high-resolution imaging, making it a crucial link in the signal processing chain.

[0003] Shandong University disclosed a method and system for detecting low-speed, slow-moving, and small multi-target targets based on passive radar in its patent application "A Method and System for Detecting Low-Speed, Slow-Moving, and Small Targets Based on Passive Radar" (application date: June 9, 2022, application number CN202210651990.X, publication number: CN115061109A). This method utilizes the ROOT-MUSIC high-resolution algorithm to estimate the target's Doppler frequency, effectively improving the target's velocity resolution. However, a drawback of this patent is that the Root-MUSIC algorithm requires eigenvalue decomposition of the covariance matrix of the received signal, resulting in high computational complexity and poor real-time performance in practical engineering applications.

[0004] Xi'an University of Electronic Science and Technology disclosed a target Doppler frequency estimation method based on a transform iterative adaptive algorithm in its patent application "Target Doppler Frequency Estimation Method Based on T-IAA" (application date: August 15, 2022, application number CN202210975721.9, publication number: CN116106834A). This method sets a transformation matrix, transforms the received signal and pilot vector set, and then uses an iterative adaptive algorithm to estimate the target Doppler frequency. This method solves the problem of high computational complexity in IAA, but its drawback is that it does not perform whitening processing during the transformation process, which can lead to main lobe expansion and spurious spectral peaks, thus reducing the accuracy of Doppler frequency estimation.

[0005] Xi'an University of Electronic Science and Technology disclosed a target Doppler frequency estimation method based on a transform-iterative adaptive algorithm in its patent application "Target Doppler Frequency Estimation Method Based on FIR-IAA in Clutter Environment" (application date: August 15, 2022, application number: CN202210973420.2, publication number: CN115308698A). This method designs an FIR filter bank to filter the received signal and pilot vector set, and then uses an iterative adaptive algorithm to estimate the target Doppler frequency. The method has a drawback: the lack of whitening processing during the design of the FIR filter bank may lead to main lobe broadening and the generation of spurious spectral peaks, thus affecting the accuracy of Doppler frequency estimation. Furthermore, the presence of spurious target interference during dimensionality reduction processing (IAA) makes spectral peak identification difficult, causing deviations in the Doppler frequency estimation results. If the scanning frequency covers the Doppler frequency of spurious target interference, the computational load increases, failing to achieve the goal of reducing computational load. Summary of the Invention

[0006] The purpose of this invention is to address the shortcomings of the existing technologies by proposing a whitening-based FIR-IAA target Doppler frequency estimation method under interference environments. This method solves the problems in existing technologies, such as the Root-MUSIC algorithm requiring eigenvalue decomposition of the covariance matrix when processing received signals, which leads to a decrease in target Doppler frequency estimation performance due to its large computational load and complexity; the T-IAA algorithm being prone to main lobe broadening and pseudo-spectral peaks, reducing the accuracy of Doppler frequency estimation; and the inability of clutter FIR-IAA to estimate Doppler frequencies in environments with false target interference.

[0007] To achieve the above objectives, the present invention is based on the following approach: The covariance matrix of the false target interference is designed. The sum of the covariance matrix and the identity matrix is ​​inverted. The covariance matrix of the false target interference contains Doppler information of the interference. Through inversion calculation, nulls are formed at the Doppler frequencies of the false target interference, which are used to filter out the interference. An FIR-MTD Doppler filter bank is obtained based on the inverted matrix and the DFT-MTD filter bank. The radar received echo signal is preprocessed using the DFT-MTD filter bank to obtain the approximate range of the Doppler frequency main lobe of the preprocessed data. Based on the approximate range of the Doppler frequency main lobe of the preprocessed data, initial dimensionality reduction transformation matrices for the radar received echo signal and initial dimensionality reduction transformation matrices for the pilot vector set are constructed using the FIR-MTD and DFT-MTD filter banks, respectively. The two initial dimensionality reduction matrices are then whitened to obtain the final dimensionality reduction transformation matrix. The principle of whitening is to normalize the projected noise covariance matrix to an identity matrix through a linear transformation, thereby ensuring that the noise remains white noise. Dimensionally reduced filtering data was obtained using a dimension reduction transformation matrix, and finally, IAA super-resolution was performed on the filtered data. Since the dimension of the dimension reduction transformation matrix is ​​less than the number of pulses in the radar received echo signal, the dimension of the inverse matrix required in traditional iterative adaptive algorithms is effectively reduced, thereby reducing computational load and system complexity. This solves the problems of high computational load and complexity in the Root-MUSIC algorithm, making it easier to implement in engineering. This invention whitens the initial dimension reduction transformation matrix, thus avoiding the problems of main lobe broadening and pseudo-spectral peaks, and low Doppler frequency estimation accuracy that easily occur in T-IAA. Because the FIR-MTD filter of this invention forms nulls at false target interference points, it can filter out false target interference in the received signal. During dimension reduction, it effectively reduces pseudo-peaks in the IAA power spectrum, enhancing the anti-interference capability of target Doppler frequency estimation.

[0008] To achieve the above objectives, the technical solution of the present invention includes the following steps:

[0009] Step 1: Construct the covariance matrix of the false target interference;

[0010] Step 2: Based on the DFT-MTD filter bank and the inverse matrix, obtain the FIR-MTD Doppler filter bank in which nulls appear at the Doppler frequency of the false target interference.

[0011] Step 3: Construct the initial dimension reduction transformation matrix of the radar received echo signal based on the approximate range of the Doppler frequency main lobe of the preprocessed data and the FIR-MTD filter bank.

[0012] Step 4: Construct the initial dimension reduction transformation matrix of the pilot vector set based on the approximate range of the Doppler frequency main lobe of the preprocessed data and the DFT-MTD filter bank.

[0013] Step 5: Whiten the initial dimension reduction transformation matrix of the radar received echo signal and the initial dimension reduction transformation matrix of the pilot vector set, respectively.

[0014] Step 6: Perform dimensionality reduction processing on the radar received echo signal and pilot vector set respectively;

[0015] Step 7: Apply IAA to estimate the target Doppler frequency of the dimension-reduced filtered data and the dimension-reduced pilot vector set.

[0016] Furthermore, the covariance matrix of the false target interference is a U-row, V-column matrix, where the values ​​of U and V are both equal to the number of pulses of the radar-received echo signal. The element value in the u-th row and v-th column of the covariance matrix is: Where, δ 2 e represents the power intensity value of the false target interference. [] This represents an exponential operation with the natural constant e as the base, π represents pi, and σ represents the mathematical constant π. 2 The variance of the power spectrum of the false target interference is represented by j, which represents the sign of the imaginary unit. d,I T represents the Doppler frequency of the decoy interference signal. r =1 / f r f represents the pulse repetition period in the echo signal. r This indicates the pulse repetition frequency.

[0017] Furthermore, the DFT-MTD filter bank is: W = [w1, w2, ..., w m ,…w M ], where w m =[1,e j2 π(m-1) / M ,…,e j2π(n-1)(m-1) / M ,…,e j2π(N-1)(m-1) / M ] T Let m represent the m-th filter in the DFT-MTD filter bank, where m = 1, 2, ..., M, M represents the total number of filters in the DFT-MTD filter bank, and n = 1, 2, ..., N, N represents the total number of pulses in the radar echo signal received. T This indicates the transpose operation.

[0018] Furthermore, the FIR-MTD Doppler filter bank is constructed using the inverse matrix (Ri). I +I) -1 The result is obtained by multiplying it by each filter in the DFT-MTD filter bank, where R I Let I represent the covariance matrix of the false target interference, and let I denote the identity matrix. -1 This indicates the inversion operation; the expression for the FIR-MTD Doppler filter bank is: W notch =[w notch，1 ,w notch，2,…,w notch，m ,…,w notch，M ], FIR-MTD filter bank, where w notch，m This represents the m-th filter in the FIR-MTD filter bank. The covariance matrix of the false target interference contains the Doppler frequency information of the false target interference. By combining the covariance matrix of the false target interference with the inversion of the identity matrix, the null at the Doppler frequency of the false target interference is obtained. The position of the null varies with the Doppler frequency of the false target interference. The depth and width of the null shape at the Doppler frequency of the false target interference are respectively equal to δ in the covariance matrix of the false target interference. 2 and σ 2 .

[0019] Furthermore, the approximate range of the Doppler frequency main lobe of the preprocessed data refers to the preprocessed data obtained by preprocessing the radar echo signal through a DFT-MTD filter bank, where z = W H x, where [·] H This indicates the conjugate transpose operation, where x represents the radar received echo signal. The range of the Doppler frequency channel covered by the main lobe of the preprocessed data is taken as the approximate range of the main lobe of the preprocessed data.

[0020] Furthermore, the initial dimension-reduction transformation matrix of the radar received echo signal is: T notch =[w notch，a ,…,w notch，b ], where a and b represent the minimum FIR-MTD filter number and the maximum FIR-MTD filter number, respectively, for the approximate range of the main lobe of the Doppler frequency in the preprocessed data. notch，a w notch，b Let T represent the initial dimension reduction transformation matrix T of the radar received echo signal for the a-th and b-th FIR-MTD filters, respectively. notch There are a total of B filters, where B is less than the number of radar echo signal pulses received.

[0021] Furthermore, the initial dimension reduction transformation matrix of the pilot vector set is: T = [w a' ,…,w b' ], where a' and b' represent the minimum DFT-MTD filter number and the maximum DFT-MTD filter number, respectively, for the approximate range of the main lobe of the Doppler frequency in the preprocessed data. a' w b'Let a' and b' be the a'-th DFT-MTD filter and b' be the b'-th DFT-MTD filter, respectively. The initial dimensionality reduction transformation matrix T of the pilot vector set contains a total of B' filters, where B' is less than the number of radar echo signal pulses. The value of a' is equal to a, the value of b' is equal to b, and the value of B' is equal to B.

[0022] Furthermore, the whitening process involves the following steps:

[0023] The first step is to follow the formula: T notch，orth =T notch (T notch H T notch ) -1 / 2 An orthogonal transformation is performed on the initial dimension-reduced transformation matrix of the radar received echo signal to obtain the final dimension-reduced transformation matrix of the radar received echo signal.

[0024] The second step is to follow the formula: T orth =T(T) H T) -1 / 2 The initial dimension reduction transformation matrix of the pilot vector set is orthogonally transformed to obtain the final dimension reduction transformation matrix of the pilot vector set.

[0025] Furthermore, the steps for dimensionality reduction processing of the radar received echo signal and pilot vector set are as follows:

[0026] The first step is to follow the formula: y = T notch，orth H x, calculate the dimension-reduced filtered data y after the radar received echo signal is processed by the final dimension-reduced transformation matrix of the radar received echo signal;

[0027] The second step is to follow the formula: B(f) = T orth H A(f)=[b(f1),b(f2),…,b(f k ),…,b(f K ]] Calculate the dimension-reduced pilot vector set B(f) after dimension reduction processing of the pilot vector set using the final dimension reduction transformation matrix of the pilot vector set, where A(f) represents the pilot vector set, f represents the scanning frequency, and b(f) represents the dimension reduction vector set. k Let f represent the reduced-dimensional pilot vector corresponding to the k-th scanning frequency of B(f), where f is the pilot vector. k This represents the k-th scan frequency, where k = 1, 2, ..., K, and K represents the total number of scan frequencies.

[0028] Furthermore, the steps for applying IAA to estimate the target Doppler frequency of the dimension-reduced filtered data and the dimension-reduced pilot vector set are as follows:

[0029] First step, according to the formula Calculate the initial power value corresponding to the k'-th scan frequency, where || represents the modulo operation, [·] (0) Indicates the initial value; the obtained K' power values ​​form the initial power vector: k' = 1, 2, ..., K', where the value of k' is equal to k, and the value of K' is equal to K;

[0030] The second step is to calculate the echo signal covariance matrix of the current loop. in,[·] (q) This indicates the qth iteration;

[0031] The third step is to follow the formula. Calculate the power value corresponding to the scanning frequency at the k'-th scan point in the q-th cycle, and construct the power vector of the q-th cycle from the obtained K' power values. Then perform the operation q = q + 1;

[0032] Fourth step: Determine whether the power vector of the current iteration meets the termination condition. If so, use the power vector of the qth iteration as the IAA power vector and then execute the fifth step. Otherwise, execute the second step.

[0033] The termination condition refers to the situation where either of the following two conditions is met:

[0034] 1. The power vectors of two adjacent cycles satisfy the following formula: ||p (q) -p (q-1) ||2<ε, where p (q-1) Let [·] represent the power vector in the (q-1)th cycle. (q-1) represents the previous iteration of the q-th iteration, ||·||2 represents the 2-norm operation, and ε is a threshold adaptively set according to the noise level and estimation accuracy requirements;

[0035] 2. q ≥ Q, where Q is the maximum number of iterations set.

[0036] The fifth step is to use the Doppler frequency corresponding to the peak value of the IAA power vector as the estimated value of the target Doppler frequency.

[0037] Compared with the prior art, the present invention has the following advantages:

[0038] First, this invention designs a dimension-reduction transformation matrix based on the FIR-MTD filter bank. Since the dimension of the dimension-reduction transformation matrix is ​​less than the number of radar echo signal pulses, the dimension of the inverse matrix required in the traditional iterative adaptive algorithm is effectively reduced, thereby reducing the amount of computation and system complexity. This overcomes the shortcomings of the Root-MUSIC algorithm in Doppler estimation, which has a large amount of computation and high complexity, and reduces the requirements for hardware computing power. While ensuring the accuracy of Doppler frequency estimation, it also improves real-time processing performance, making this invention beneficial for engineering applications.

[0039] Secondly, this invention whitens the dimensionality reduction transformation matrix to ensure that the noise remains white noise, avoiding the main lobe broadening and pseudo-spectral peaks problems present in existing technologies, and overcoming the issues of large Doppler frequency estimation errors and decreased accuracy. This results in a significant improvement in Doppler frequency estimation accuracy, enabling high-resolution Doppler frequency performance.

[0040] Third, the FIR-MTD filter bank of this invention takes into account the impact of false target interference on target resolution, so that its amplitude frequency response has a deep null near the Doppler frequency of false target interference, which can suppress false target interference and effectively reduce the spurious peaks of the IAA power spectrum of the prior art. This not only improves the anti-interference capability of target Doppler frequency estimation, but also enhances the clarity and reliability of Doppler frequency spectrum peak resolution, so that it can still maintain high estimation accuracy and stability in the electromagnetic environment of false target interference, providing better performance guarantee for engineering applications. Attached Figure Description

[0041] Figure 1 This is a flowchart of the present invention;

[0042] Figure 2 This is a simulation diagram of simulation experiment 1 of the present invention;

[0043] Figure 3 This is a simulation diagram of simulation experiment 2 of the present invention;

[0044] Figure 4 This is a simulation diagram of simulation experiment 3 of the present invention. Detailed Implementation

[0045] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0046] Reference Figure 1 The specific implementation steps of the embodiments of the present invention will be further described below.

[0047] Step 1: Construct the covariance matrix of the false target interference.

[0048] The covariance matrix R of the false target interference in this embodiment of the invention IThis is a U-row, V-column matrix. The values ​​of U and V are both equal to the number of pulses N of the radar echo signal received. In this embodiment of the invention, the number of radar echo signal pulses N = 64, and the element in the u-th row and v-th column is... u, v = 1, 2, ..., 64. Each element of the matrix corresponds to the correlation between two pulses caused by false target interference. The u-th row represents the correlation between the u-th pulse and all 64 pulses, and the v-th column represents the correlation between the v-th pulse and all 64 pulses. δ 2 The depth of the null trap caused by the false target interference is determined by σ. 2 The width of the null trap for false target interference is determined, and in the embodiments of the present invention, f r =500Hz.

[0049] Step 2: Based on the DFT-MTD filter bank and the inverse matrix, obtain the FIR-MTD Doppler filter bank in which nulls appear at the Doppler frequency of the false target interference.

[0050] Step 2.1: In this embodiment of the invention, there are a total of 128 DFT-MTD filter banks and 128 FIR-MTD filter banks. The DFT-MTD filter bank is W = [w1, w2, ..., w...]. m ,…w 128 ], w m =[1,e j2π(m-1) / 128 ,…,e j2 π(n-1)(m-1) / 128 ,…,e j2π63(m-1) / 128 ] T It is the m-th filter of the DFT-MTD filter, where m = 1, 2, ..., 128 and n = 1, 2, ..., 64.

[0051] Step 2.2, according to the formula: w notch，m =(R I +I) -1 w m Using the inverse matrix (R) I +I) -1 Multiplying by each filter in the DFT-MTD filter bank yields the FIR-MTD filter bank W. notch =[w notch，1 ,w notch，2 ,…,w notch，m ,…w notch，128 ]. Among them, w notch，m It is the m-th filter in the FIR-MTD filter bank, and I is a 64×64-dimensional identity matrix. The covariance matrix of the false target interference contains the Doppler frequency of the false target interference. By calculating the inverse of the covariance matrix and the identity matrix, a null will appear at the Doppler frequency of the false target interference.

[0052] Step 3: Construct the initial dimension reduction transformation matrix of the radar received echo signal based on the approximate range of the Doppler frequency main lobe of the preprocessed data and the FIR-MTD filter bank.

[0053] Step 3.1: Multiply the echo signal x by the conjugate of the DFT-MTD filter W to obtain the preprocessed data z = W. H x. The range of Doppler frequency channels covered by the main lobe of the preprocessed data in this embodiment is the 47th to the 57th channel out of 128 filters, a total of 11 channels.

[0054] Step 3.2: Extract the 47th to 57th FIR-MTD filters from the 128 filters (the total number of extracted filters, 11, is less than the number of echo signal pulses received by the radar, 64, thus achieving dimensionality reduction), and construct the initial dimensionality reduction transformation matrix T of the radar received echo signal. notch =[w notch，47 ,…,w notch，57 ].

[0055] Step 4: Construct the initial dimension reduction transformation matrix of the pilot vector set based on the approximate range of the Doppler frequency main lobe of the preprocessed data and the DFT-MTD filter bank.

[0056] Extract the 47th to 57th DFT-MTD filters from the 128 filters in the DFT-MTD dataset, and construct the initial dimension-reduction transformation matrix T = [w 47 ,…,w 57 ].

[0057] Step 5: Whiten the initial dimension reduction transformation matrix of the radar received echo signal and the initial dimension reduction transformation matrix of the pilot vector set, respectively.

[0058] According to the formula: T notch，orth =T notch (T notch H T notch ) -1 / 2 An orthogonal transformation is performed on the initial dimension-reduced transformation matrix of the radar received echo signal to obtain the final dimension-reduced transformation matrix of the radar received echo signal. According to the formula: T orth =T(T) H T) -1 / 2 The initial dimension reduction transformation matrix of the pilot vector set is orthogonally transformed to obtain the final dimension reduction transformation matrix of the pilot vector set.

[0059] Step 6: Perform dimensionality reduction processing on the radar received echo signal and pilot vector set respectively.

[0060] Step 6.1, according to the formula: y = T notch，orthH x, calculate the dimension-reduced filtered data y after the radar received echo signal is processed by the final dimension-reduced transformation matrix of the radar received echo signal.

[0061] Step 6.2, according to the formula: B(f)=T orth H A(f)=[b(f1),b(f2),…,b(f k ),…,b(f K ]] Calculate the dimension-reduced pilot vector set B(f) after dimension reduction processing of the pilot vector set using the final dimension reduction transformation matrix of the pilot vector set, where A(f) represents the pilot vector set, f represents the scanning frequency, and in this embodiment, K = 25 represents the total number of scanning frequencies, b(f k Let f represent the reduced-dimensional pilot vector corresponding to the k-th scanning frequency of B(f), where f is the pilot vector. k This represents the k-th scan frequency, where k = 1, 2, ..., 25.

[0062] Step 7: Apply IAA to estimate the target Doppler frequency of the dimension-reduced filtered data and the dimension-reduced pilot vector set.

[0063] First step, according to the formula Calculate the initial power value corresponding to the k'-th scan frequency, where || represents the modulo operation, [·] (0) Indicates the initial value; the 25 power values ​​obtained constitute the initial power vector: k' = 1, 2, ..., 25.

[0064] The second step is to calculate the echo signal covariance matrix of the current loop. in,[·] (q) This indicates the qth iteration;

[0065] The third step is to follow the formula. Calculate the power value corresponding to the scanning frequency at the k'-th scan point in the q-th cycle, and construct the power vector for the q-th cycle from the 25 obtained power values. Then perform the operation q = q + 1.

[0066] Fourth step: Determine whether the power vector of the current iteration meets the termination condition. If so, use the power vector of the qth iteration as the IAA power vector and then execute the fifth step. Otherwise, execute the second step.

[0067] The termination condition refers to the situation where either of the following two conditions is met:

[0068] 1. The power vectors of two adjacent cycles satisfy the following formula: ||p (q) -p (q-1) ||2<10 -6, where p (q-1) Let [·] represent the power vector in the (q-1)th cycle. (q-1) This represents the previous iteration of the q-th iteration, ||·||2 represents the 2-norm operation, and 10 -6 The threshold is set adaptively based on the noise level and estimation accuracy requirements.

[0069] 2. q≥100, where 100 is the maximum number of iterations set;

[0070] The fifth step is to use the Doppler frequency corresponding to the peak value of the IAA power vector as the estimated value of the target Doppler frequency.

[0071] The present invention will be further described in detail below with reference to specific embodiments:

[0072] 1. Simulation experimental conditions.

[0073] The hardware platform for the simulation experiment of this invention is as follows: the processor is a 13th Gen Intel(R) Core(TM) i9-13980HX with a main frequency of 2.20GHz, and the memory is 32GB.

[0074] The software platform for the simulation experiment of this invention is: Windows 11 operating system and Matlab R2024b.

[0075] 2. Simulation content and result analysis.

[0076] The present invention includes three simulation experiments. Simulation experiment 1 is a comparative simulation of the time taken before and after dimensionality reduction and the Doppler resolution capability. Simulation experiment 2 is a comparative simulation of whitening and non-whitening treatment. Simulation experiment 3 is a comparative simulation of the presence or absence of false target interference.

[0077] Simulation Experiment 1 of this invention employs the method of this invention and a prior art IAA. Under conditions of 64 radar echo pulses, a pulse repetition period of 500Hz, 128 FIR-MTD filters, and 128 DFT-MTD filters, and with Doppler frequencies of 200Hz for target 1 and 204Hz for target 2, and without false target interference, Monte Carlo experiments were conducted with the signal-to-noise ratio (SNR) increasing by 2dB to 16dB sequentially. 500 Monte Carlo experiments were performed for each SNR, and the number of times the Doppler frequency was successfully resolved in each of the 500 Monte Carlo experiments for each SNR was counted. The resulting curve is shown below. Figure 2 As shown.

[0078] In simulation experiment 1, the prior art IAA refers to the paper "Improving the Doppler Resolution of Ground-Based Surveillance Radar for Drone Detection" published in December 2019 in the journal IEEE Transactions on Aerospace and Electronic Systems by H. Sun, B.-S. Oh, X. Guo and Z. Lin, doi:10.1109 / TAES.2019.2895585.

[0079] Simulation Experiment 2 of this invention employs the method of this invention and a prior art. Under conditions of 64 pulses received by the radar echo, a pulse repetition period of 500Hz, 128 FIR-MTD filters, and 128 DFT-MTD filters, with a Doppler frequency of 200Hz for target 1 and 204Hz for target 2, a signal-to-noise ratio of 10dB, and no false target interference, the IAA normalized power vector diagrams obtained after whitening and without whitening processing are shown below. Figure 3 As shown.

[0080] In simulation experiment 2, the prior art refers to a target Doppler frequency estimation method based on a transformation iterative adaptive algorithm disclosed by Xi'an University of Electronic Science and Technology in its patent application document "Target Doppler Frequency Estimation Method Based on T-IAA" (application date: 2022.08.15, application number CN202210975721.9, application publication number: CN116106834A).

[0081] Simulation Experiment 3 of this invention employs the method of this invention and a prior art. The radar receives 64 pulses of echo signal with a pulse repetition period of 500Hz and uses 128 MTD filters. The Doppler frequency of target 1 is 200Hz, the Doppler frequency of target 2 is 204Hz, the signal-to-noise ratio is 10dB, and the Doppler frequency of the false target interference is 240Hz with a signal-to-noise ratio of 10dB. σ 2 =0.01 and δ 2 =10 10 Under the condition of not filtering false target interference, and after filtering false target interference, the IAA normalized power vector map is as follows: Figure 4 As shown.

[0082] In simulation experiment 3, the prior art refers to a target Doppler frequency estimation method based on a transform iterative adaptive algorithm disclosed by Xi'an University of Electronic Science and Technology in its patent application document "Target Doppler Frequency Estimation Method Based on FIR-IAA in Clutter Environment" (application date: 2022.08.15, application number: CN202210973420.2, application publication number: CN115308698A).

[0083] The following is combined with Figure 2 , Figure 3 , Figure 4 The simulation results further illustrate the effects of the present invention.

[0084] Figure 2 The horizontal axis in the graph represents the signal-to-noise ratio (SNR) in dB, and the vertical axis represents the probability of successful resolution. Figure 2 The black dashed curve represents the curve plotted using only IAA to statistically analyze the success probability of two targets at each signal-to-noise ratio, while the black solid curve represents the curve plotted using the method of this invention to statistically analyze the success probability of two targets at each signal-to-noise ratio.

[0085] from Figure 2 As can be seen, the data of the two curves from -6dB to 16dB are very close. The values ​​of the solid and dashed lines at each signal-to-noise ratio are as follows: 0.318 and 0.332 at -6dB, 0.392 and 0.39 at -4dB, 0.432 and 0.464 at -2dB, 0.508 and 0.602 at 0dB, 0.636 and 0.672 at 2dB, 0.68 and 0.748 at 4dB, 0.772 and 0.85 at 6dB, 0.834 and 0.882 at 8dB, 0.878 and 0.956 at 10dB, 0.916 and 0.956 at 12dB, 0.93 and 0.978 at 14dB, and 0.956 and 0.988 at 16dB. The data above shows that the success rate of the proposed technology is slightly lower than that of the IAA algorithm. However, under the simulation conditions, the IAA algorithm took 1326.8 seconds to run in the MATLAB program, while the proposed technology took only 4.07 seconds. The computation time was significantly reduced, which lowered the requirements for hardware computing power. While ensuring the accuracy of Doppler frequency estimation, the proposed technology significantly improved the performance of real-time processing.

[0086] Figure 3 Figures (a) and (b) are spectrum curves plotted using the existing T-IAA-based target Doppler frequency estimation method and the method of this invention, respectively, under the same simulation conditions. Figure 3In Figures (a) and (b), the horizontal axis represents frequency in Hz, and the vertical axis represents the IAA normalized power vector diagram, which is dimensionless linear power. Figure 3 The curve in the figure is an amplitude curve plotted from the normalized power values ​​corresponding to each scanning frequency.

[0087] from Figure 3 As shown in Figure (a), the existing T-IAA-based target Doppler frequency estimation method does not perform whitening processing, resulting in peaks at 193Hz and 196Hz, which are not the target's Doppler frequencies, thus exhibiting spurious spectral peaks. The true Doppler frequencies of the target are 200Hz and 204Hz. However, main lobe broadening occurs near 200Hz and 204Hz, leading to large errors in the measured target Doppler frequency, which reduces the accuracy of the target Doppler frequency estimation.

[0088] from Figure 3 As shown in Figure (b), only two distinct peaks are formed at 200Hz and 204Hz on the target, accurately measuring the target's Doppler frequency. This proves that the present invention solves the problem of large Doppler frequency estimation error and decreased accuracy in the prior art through whitening processing.

[0089] Figure 4 Figure (a) in the middle Figure 4 Figure (b) shows the spectrum curves plotted using the FIR-IAA-based target Doppler frequency estimation method and the existing IAA power vector obtained under clutter conditions with false target interference. Figure 4 (a) Figure 4 In (b), the horizontal axis represents frequency in Hz, and the vertical axis represents the IAA normalized power vector diagram, which is dimensionless linear power.

[0090] from Figure 4 As shown in (a), three peaks appear at 201Hz, 205Hz, and 210Hz, while the true Doppler frequencies of the target are 200Hz and 204Hz. This indicates that under the interference of false targets, the power spectrum using existing technology shows a spurious peak at 210Hz, the estimated number of target Doppler frequencies is inaccurate, the anti-interference capability of the estimated target Doppler frequencies is weak, and the accuracy of the estimated target Doppler frequencies is poor.

[0091] from Figure 4 As shown in Figure (b), two distinct peaks are formed only at 200Hz and 204Hz on the target, accurately determining the target's Doppler frequency. Figure 4Compared with the previous technology, Figure (a) in the present invention effectively reduces the number of spurious peaks, proving that the method of the present invention improves the anti-interference capability of target Doppler frequency estimation, enhances the clarity and reliability of Doppler frequency spectrum peak resolution, and can maintain high estimation accuracy even in the electromagnetic environment of false target interference.

[0092] In summary, the method of this invention designs a dimension-reduction transformation matrix to convert echo data to the Doppler channel dimension, overcoming the shortcomings of IAA and Root-MUSIC algorithms in Doppler estimation, which involve high computational cost and complexity. This reduces the hardware computing power requirements and improves the system's performance in real-time processing of target Doppler frequencies. The dimension-reduction transformation matrix obtained through whitening processing solves the problems of main lobe broadening and pseudo-spectral peaks in existing technologies, while also addressing the issues of large Doppler frequency estimation errors and decreased accuracy. Clearly, the anti-interference filter designed using FIR in this invention effectively reduces pseudo-peaks in existing technologies, improves the anti-interference capability and estimation accuracy of target Doppler frequency estimation, and enhances the resolution of Doppler frequency spectral peaks. It is a very practical Doppler frequency estimation method.

Claims

1. A whitening-based FIR-IAA target Doppler frequency estimation method under interference conditions, characterized in that, The steps of this method include the following: Step 1: Construct the covariance matrix of the false target interference; Step 2: Based on the DFT-MTD filter bank and the inverse matrix, obtain the FIR-MTD Doppler filter bank in which nulls appear at the Doppler frequency of the false target interference. Step 3: Construct the initial dimension reduction transformation matrix of the radar received echo signal based on the approximate range of the Doppler frequency main lobe of the preprocessed data and the FIR-MTD filter bank. Step 4: Construct the initial dimension reduction transformation matrix of the pilot vector set based on the approximate range of the Doppler frequency main lobe of the preprocessed data and the DFT-MTD filter bank. Step 5: Perform whitening processing on the initial dimension reduction transformation matrix of the radar received echo signal and the initial dimension reduction transformation matrix of the pilot vector set, respectively. Step 6: Perform dimensionality reduction processing on the radar received echo signal and pilot vector set respectively; Step 7: Apply IAA to estimate the target Doppler frequency of the dimension-reduced filtered data and the dimension-reduced pilot vector set.

2. The estimation method according to claim 1, characterized in that: The covariance matrix of the false target interference mentioned in step 1 is a matrix of U rows and V columns, where the values ​​of U and V are both equal to the number of pulses of the echo signal received by the radar. The element value in the u-th row and v-th column of the covariance matrix is: Where, δ 2 e represents the power intensity value of the false target interference. [] σ represents an exponential operation with the natural constant e as the base, π represents pi, and σ represents the mathematical constant π. 2 The variance of the power spectrum of the false target interference is represented by j, which indicates the sign of the imaginary unit. d,I T represents the Doppler frequency of the decoy interference signal. r =1 / f r f represents the pulse repetition period in the echo signal. r This indicates the pulse repetition frequency.

3. The estimation method according to claim 2, characterized in that: The DFT-MTD filter bank mentioned in step 2 is: W = [w1, w2, ..., w m ,…w M ], where w m =[1,e j2π(m-1) / M ,…,e j2π(n-1)(m-1) / M ,…,e j2π(N-1)(m-1) / M ] T Let m represent the m-th filter in the DFT-MTD filter bank, where m = 1, 2, ..., M, M represents the total number of filters in the DFT-MTD filter bank, and n = 1, 2, ..., N, N represents the total number of pulses in the radar echo signal received. T This indicates the transpose operation.

4. The estimation method according to claim 4, characterized in that: The FIR-MTD Doppler filter bank described in step 2 is obtained by inverting the matrix (R... I +I) -1 The result is obtained by multiplying it by each filter in the DFT-MTD filter bank, where R I Let I represent the covariance matrix of the false target interference, and let I denote the identity matrix. -1 This indicates the inversion operation; the expression for the FIR-MTD Doppler filter bank is: W notch =[w notch，1 ,w notch，2 ,…,w notch，m ,…w notch，M ], FIR-MTD filter bank, where w notch，m This represents the m-th filter in the FIR-MTD filter bank. The covariance matrix of the false target interference contains the Doppler frequency of the false target interference. The null at the Doppler frequency of the interference is obtained by combining the covariance matrix of the false target interference with the inversion of the identity matrix. The null position varies with the Doppler frequency of the false target interference. The depth and width of the null shape at the Doppler frequency of the false target interference are equal to the values ​​of δ in the covariance matrix of the false target interference. 2 and σ 2 .

5. The estimation method according to claim 4, characterized in that: The approximate range of the Doppler frequency main lobe mentioned in step 3 refers to the preprocessed data obtained by preprocessing the radar echo signal through a DFT-MTD filter bank, resulting in: z = W H x, where [·] H This indicates the conjugate transpose operation, where x represents the radar received echo signal. The range of the Doppler frequency channel covered by the main lobe of the preprocessed data is taken as the approximate range of the main lobe of the preprocessed data.

6. The estimation method according to claim 5, characterized in that: The initial dimension reduction transformation matrix of the radar received echo signal in step 3 is: T notch =[w notch，a ,…,w notch，b ], where a and b represent the minimum FIR-MTD filter number and the maximum FIR-MTD filter number, respectively, for the approximate range of the Doppler frequency main lobe of the preprocessed data. notch，a w notch，b Let T represent the initial dimension reduction transformation matrix T of the radar received echo signal for the a-th and b-th FIR-MTD filters, respectively. notch There are a total of B filters, where B is less than the number of echo signal pulses received by the radar.

7. The estimation method according to claim 6, characterized in that: The initial dimension reduction transformation matrix of the pilot vector set mentioned in step 4 is: T = [w a' ,…,w b' ], where a' and b' represent the minimum DFT-MTD filter number and the maximum DFT-MTD filter number, respectively, for the approximate range of the main lobe of the Doppler frequency in the preprocessed data. a' w b' Let a' and b' be the a'-th DFT-MTD filter and b' be the b'-th DFT-MTD filter, respectively. The initial dimensionality reduction transformation matrix T of the pilot vector set contains a total of B' filters, where B' is less than the number of radar echo signal pulses. The value of a' is equal to a, the value of b' is equal to b, and the value of B' is equal to B.

8. The estimation method according to claim 7, characterized in that: The whitening process described in step 5 is as follows: The first step is to follow the formula: T notch，orth =T notch (T notch H T notch ) -1 / 2 An orthogonal transformation is performed on the initial dimension-reduced transformation matrix of the radar received echo signal to obtain the final dimension-reduced transformation matrix of the radar received echo signal. The second step is to follow the formula: T orth =T(T) H T) -1 / 2 The initial dimension reduction transformation matrix of the pilot vector set is orthogonally transformed to obtain the final dimension reduction transformation matrix of the pilot vector set.

9. The estimation method according to claim 8, characterized in that: The steps described in step 6 for dimensionality reduction processing of the radar received echo signal and pilot vector set are as follows: The first step is to follow the formula: y = T notch，orth H x, calculate the dimension-reduced filtered data y after the radar received echo signal is processed by the final dimension-reduced transformation matrix of the radar received echo signal; The second step is to follow the formula: B(f) = T orth H A(f)=[b(f1),b(f2),…,b(f k ),…,b(f K ]] Calculate the dimension-reduced pilot vector set B(f) after dimension reduction processing of the pilot vector set using the final dimension reduction transformation matrix of the pilot vector set, where A(f) represents the pilot vector set, f represents the scanning frequency, and b(f) represents the dimension reduction vector set. k Let f represent the reduced-dimensional pilot vector corresponding to the k-th scanning frequency of B(f), where f is the pilot vector. k This represents the k-th scan frequency, where k = 1, 2, ..., K, and K represents the total number of scan frequencies.

10. The estimation method according to claim 9, characterized in that: The steps in step 7 for applying IAA to estimate the target Doppler frequency of the dimension-reduced filtered data and the dimension-reduced pilot vector set are as follows: First step, according to the formula Calculate the initial power value corresponding to the k'-th scan frequency, where || denotes the modulo operation, [·] (0) Indicates the initial value; the obtained K' power values ​​form the initial power vector: Where k' takes the value of k, and K' takes the value of K; The second step is to calculate the echo signal covariance matrix of the current loop. in,[·] (q) This indicates the qth iteration; The third step is to follow the formula. Calculate the power value corresponding to the scanning frequency at the k'-th scan point in the q-th cycle, and construct the power vector of the q-th cycle from the obtained K' power values. Then perform the operation q = q + 1; Fourth step: Determine whether the power vector of the current iteration meets the termination condition. If so, use the power vector of the qth iteration as the IAA power vector and then execute the fifth step. Otherwise, execute the second step. The termination condition refers to the situation where either of the following two conditions is met:

1. The power vectors of two adjacent cycles satisfy the following formula: ||p (q) -p (q-1) ||2<ε, where p (q-1) Let [·] represent the power vector in the (q-1)th cycle. (q-1) represents the previous iteration of the q-th iteration, ||·||2 represents the 2-norm operation, and ε is a threshold adaptively set according to the noise level and estimation accuracy requirements; 2. q ≥ Q, where Q is the maximum number of iterations set; The fifth step is to use the Doppler frequency corresponding to the peak value of the IAA power vector as the estimated value of the target Doppler frequency.

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