Angle measurement method for dense targets based on IAA beam space whitening in complex environment

Abstract

The application discloses a dense target angle measurement method based on IAA beam space whitening in a complex environment, obtains echo signals received by a radar; converts the echo signals to beam domain data by using a constructed notch dimension reduction beam conversion matrix, performs whitening processing on the beam domain data; converts an array element dimension scanning manifold matrix to a scanning manifold matrix in the beam domain, performs IAA super-resolution processing on the dimension reduction data by using the scanning manifold matrix in the beam domain, searches for a peak value in an iterated power spectrum, and judges the angle of a target. The method reduces the dimension of echo array element data to beam domain data by using a notch whitening dimension reduction conversion matrix, ensures that noise of the dimension reduction data is still white noise, reduces the data dimension, suppresses interference, realizes resolution of dense targets in a complex environment, and has the advantages of reduced super-resolution operation amount and good algorithm robustness.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of radar, and further relates to a method for suppressing interference and converting array element data to a beam domain by constructing a notched beam conversion matrix based on an iterative adaptive approach (IAA) in a complex environment, and a method for angle measurement and super-resolution after white processing. BACKGROUND

[0002] With the continuous development of modern unmanned aerial vehicles and stealth aircraft technology, the monitoring environment faced by radars is becoming increasingly complex. Dense targets generally refer to targets that are small in volume, large in number, and close in distance, Doppler, and angle. It is difficult to distinguish them according to the traditional resolution indicators of radars. The mutual interference between dense targets seriously affects the performance of radar detection, tracking, and identification, which puts higher requirements on the resolution capability of radar systems and the real-time performance of information processing. The conventional iterative adaptive algorithm IAA is an adaptive iterative super-resolution algorithm. This algorithm uses the spectral estimation result of the last iteration to construct a signal covariance matrix, and uses its inverse matrix as a weighting matrix in the weighted least squares method. However, the ordinary beam conversion matrix constructed by the IAA algorithm based on the beam space is a non-white process relative to noise when data is converted to the beam space, which will cause the noise to change from white noise to colored noise, resulting in a decrease in angle measurement accuracy.

[0003] Zheng Jiamin provides a radar angle measurement method in a complex environment based on the MUSIC algorithm in his published paper "Radar Angle Measurement Technology in Complex Environment" (Master's Thesis, Xi'an University of Electronic Science and Technology, 2022). This method estimates the target angle by decomposing the received echo covariance matrix and using the orthogonality of the signal subspace and the noise subspace. This method has two shortcomings. First, this method still processes data and measures angles in the array element domain, and also has the characteristics of general array models. As the number of array elements increases, the processing complexity will increase linearly when the number of array elements is large. Second, this method uses the MUSIC algorithm, which often requires information about the number of targets. However, in actual radar scenarios, the number of targets is unknown.

[0004] Jiang's published thesis "DOA estimation based on beam space super-resolution" (Master's thesis of Yangzhou University in 2022) provides a super-resolution method based on gridless compressed sensing, called atomic norm minimization (ANM). This method combines beam space processing with super-resolution methods such as atomic norm minimization by converting array data to beam domain using a beam conversion matrix; by utilizing the Tocplitz structure of the covariance matrix, DOA estimation is performed. However, this method has the following shortcomings: first, this method belongs to the compressed sensing algorithm, which uniformly shrinks all large coefficients, resulting in biased estimated signal amplitudes, limiting its estimation accuracy at low signal-to-noise ratios. Second, since the data conversion to the beam space is a non-whitening process, it will cause white noise to become colored noise, and the angle measurement accuracy of this method will be greatly reduced. SUMMARY

[0005] The purpose of the present application is to overcome the shortcomings of the prior art, and to provide a beam space whitening angle measurement method based on IAA in a complex environment, which solves the problem that the prior art affects the accuracy of target angle estimation when resolving dense targets in an interference environment. The dimension reduction process does not have whitening processing, which can cause the angle measurement accuracy to decrease. The angle measurement accuracy decreases at low signal-to-noise ratios, and the number of known signal sources is required, which has a large amount of computation.

[0006] To achieve the above purpose, the technical idea of the present application is: since the present application designs a beam conversion matrix with notches based on the covariance matrix of noise and interference, deep nulls are formed near the interference, which can effectively suppress the interference. This solves the problem that the prior art does not consider the presence of interference, which affects the angle measurement result and reduces the angle measurement accuracy. The present application converts the array data to beam space data by using a beam conversion matrix, and whitens the conversion matrix, so that the data conversion process to the beam space becomes a whitening process. The present application uses the whitening processing of the beam space noise to ensure that the noise after data conversion is still white noise. This solves the problem that the colored noise in the beam space of the prior art interferes with the angle measurement result and reduces the angle measurement accuracy. The present application uses IAA super-resolution angle measurement when measuring angles. The core of IAA is to iteratively solve the weighted least squares problem, completely avoiding the step of eigenvalue decomposition of the covariance matrix, and does not need to know the number of signal subspaces and noise subspaces, i.e. does not need to know the number of signal sources. Moreover, the iterative form of the weighted least squares makes it asymptotically unbiased, and the estimation efficiency is very high, with higher angle measurement accuracy at low signal-to-noise ratios.

[0007] To achieve the above purpose, the specific implementation steps of the present application include the following:

[0008] Step 1, constructing the echo signal of the radar echo array element;

[0009] Step 2, convert the echo signal to the beam domain by using the constructed notched beam conversion matrix to obtain the echo signal in the beam domain;

[0010] Step 3, whiten the echo signal in the beam domain by using the constructed whitening matrix;

[0011] Step 4, perform IAA super-resolution processing on the echo signal in the beam domain by using the scanning manifold matrix in the beam domain, search for the peak value in the iterated power spectrum, and measure the target angle.

[0012] Further, the echo signal is as follows:

[0013] ;

[0014] wherein, represents the radar array element echo signal containing targets, N represents the total number of radar antenna array elements, represents that each element in z belongs to a complex number field of dimensional complex matrix, the value of is a positive integer, the value of is a positive integer, represents the steering vector matrix corresponding to the angle of the kth target, , represents the total number of targets in the radar array element echo signal, , , represents the steering vector of the th target, , represents the exponential operation with the natural constant e as the base, and j represents the imaginary unit symbol, represents the circular constant, represents the angle corresponding to the th target, represents the array element spacing, represents the wavelength, and s represents the complex amplitude of the signal source, , , represents the complex amplitude of the signal source of the th target, represents the transposition operation, and n represents the Gaussian white noise vector, .

[0015] Further, the notched beam conversion matrix is:

[0016] ;

[0017] wherein, This represents the beam conversion matrix with a notch. B represents the beam conversion matrix. , The angle pointed to by the b-th beam is denoted as The corresponding steering vector, where R represents the interference suppression matrix. The covariance matrix representing the noise. , This represents the power of the noise in a single array element. Indicates that the order is equal to The identity matrix, The covariance matrix representing the disturbance. , This represents the power of interference in a single array element. This represents the steering vector corresponding to the direction of the interference. This indicates the conjugate transpose operation. This represents the matrix inversion operation.

[0018] Furthermore, the echo signal in the beam domain is as follows:

[0019] ;

[0020] in, This represents the echo signal in the beam domain. , This represents the echo signal in the beam domain when interference is present. This represents the echo signal in the beam domain when there is no interference.

[0021] Furthermore, the whitening matrix is:

[0022] ;

[0023] in, Represents the whitening matrix. ; Indicates matrix first Then, perform the inverse operation on the power of the power. This represents the whitening matrix when interference is present. This represents the whitening matrix when there is no interference.

[0024] Furthermore, the whitening process for the echo signal in the beam domain is accomplished by the following formula:

[0025] ;

[0026] in, This represents the echo signal in the whitened beam domain. , This represents the echo signal in the whitened beam domain when interference is present. denotes the beam domain echo signal after whitening when there is no interference.

[0027] Further, the scanning manifold matrix of the beam domain is:

[0028] ;

[0029] wherein, denotes the scanning manifold matrix of the beam domain, , denotes the total length of the angle scanning range, , denotes the beam domain steering vector corresponding to the angle . denotes the beam conversion matrix after whitening, , denotes the scanning manifold matrix of the array element domain, , denotes the array element domain steering vector corresponding to the angle .

[0030] Further, the step of performing IAA super-resolution processing on the echo signal of the beam domain is as follows:

[0031] First, estimate the initialized power spectrum : wherein, denotes the amplitude at the th angle grid point, , denotes the absolute value operation;

[0032] Second, estimate the covariance matrix of the signal in the current iteration process : wherein, denotes the operation of forming a diagonal matrix with the vector in the brackets as the main diagonal element, denotes the spatial power spectrum of the last iteration process, , denotes the maximum number of iterations, which is in the first iteration;

[0033] Third, calculate the IAA power spectrum in the current iteration process wherein, denotes the spatial power spectrum in the current iteration process, denotes the amplitude at the th angle grid point in the current iteration process, ;

[0034] The fourth step is to determine whether the difference between the IAA power spectra obtained from two adjacent iterations meets the termination condition. If so, proceed to the fifth step; otherwise, proceed to the second step.

[0035] Fifth step: Search for the peak values ​​of the power spectrum obtained in all iterations to find... The corresponding to each goal A peak value is used as the angle for measuring dense targets.

[0036] The termination condition being met refers to the situation where one of the following conditions is met:

[0037] Condition 1: The difference between the IAA power spectra obtained from two consecutive iterations is less than a threshold. threshold The possible values ​​of: ;

[0038] Condition 2: Reaching the maximum number of iterations .

[0039] Compared with the prior art, the present invention has the following advantages:

[0040] First, the present invention designs a beam conversion matrix with notches based on the covariance matrix of noise and interference, which can perform super-resolution in clutter and interference environments. This avoids the problem of false peaks or main lobe expansion caused by the lack of whitening in the prior art. As a result, the super-resolution effect of the present invention remains basically unchanged compared with the case without dimensionality reduction, which has good robustness, and the amount of computation is reduced while the resolution speed is improved.

[0041] Secondly, since the present invention performs whitening processing when constructing the beam conversion matrix, the process of converting data to beam space becomes a whitening process. It utilizes the whitening processing of beam space noise to overcome the shortcomings of the prior art, which is that the angle measurement accuracy is reduced due to the interference of colored noise in beam space on the angle measurement results. This makes the present invention, based on IAA super-resolution, able to distinguish dense targets without knowing the number of targets, and can also maintain almost the same angle measurement accuracy as the array element space IAA algorithm.

[0042] Third, because this invention uses a beamspace IAA algorithm for angle measurement, it overcomes the shortcomings of subspace algorithms, which require knowledge of the number of signal sources when distinguishing dense targets, and the limited estimation accuracy of compressed sensing algorithms under low signal-to-noise ratio. Compared with traditional element-domain IAA, this invention utilizes a beam transformation matrix to convert array data into beam-domain data, thereby reducing computational load and saving computation time. Attached Figure Description

[0043] Figure 1 This is a flowchart of the present invention;

[0044] Figure 2is the scanning curve diagram of the conventional DBF scanning method in the simulation experiment of the application, in which the angle difference of two targets is within a beam width;

[0045] Figure 3 is the dense target angle measurement scanning curve diagram of the beam space whitening IAA based on the simulation experiment of the application;

[0046] Figure 4 is the dense target angle measurement scanning curve diagram of the beam space non-whitening IAA based on the simulation experiment of the application;

[0047] Figure 5 is the angle measurement root mean square error diagram of the array element domain IAA, the beam space whitening IAA and the beam space non-whitening IAA under different signal-to-noise ratios in the simulation experiment of the application in the case of no interference;

[0048] Figure 6 is the dense target processing result diagram of the beam space non-whitening IAA without suppressing interference in the simulation experiment of the application in the case of interference;

[0049] Figure 7 is the dense target processing result diagram of the beam space whitening IAA with suppressing interference in the simulation experiment of the application in the case of interference;

[0050] Figure 8 is the beam pointing diagram of the notched beam conversion matrix in the simulation experiment of the application. DETAILED DESCRIPTION

[0051] The application will be further described below in combination with the drawings and examples.

[0052] Reference Figure 1 The implementation steps of the embodiment of the application will be further described.

[0053] Step 1, constructing radar echo array element data.

[0054] Taking an equidistant linear array as an example, the vector representation of the echo signal received by the radar is , , is the total number of array elements, represents the transpose operation of a matrix or a vector.

[0055] The model of the radar receiving echo signal can be represented as:

[0056] ;

[0057] wherein, , represents is a dimensional complex matrix, wherein each element belongs to the complex number field , express The complex amplitude of a signal source, , This is a Gaussian white noise vector. Assume that there exists... One goal, The angles of each objective are as follows: , , , for Angle-guided vector matrix for each target.

[0058] No. The guidance vector of each target It can be represented as:

[0059] ;

[0060] in, This indicates an exponential operation with base e, where j is the symbol for the imaginary unit. Pi Indicates the first The angle corresponding to each target Indicates wavelength. Indicates the spacing between array elements.

[0061] Step 2: Construct a notched beam conversion matrix and use this conversion matrix to convert the echo signal to the beam domain.

[0062] Step 2.1: Construct the beam conversion matrix with notch.

[0063] Step 2.1.1: Construct a beam conversion matrix using the method for converting conventional array data to beam domain data. Let the dimension of this beam conversion matrix be... , can be represented as:

[0064] ;

[0065] Among them, the beam conversion matrix After preprocessing, the approximate angles of the target and interference can be determined, allowing for the selection of a suitable beam direction. The beam direction is... , Indicates the angle as The corresponding guide vector.

[0066] Step 2.1.2 involves performing a notch-applied operation on the beam conversion matrix described above. Assume the power of the noise in a single element is... The power of single-element interference is The noise is known to be Gaussian white noise, and its covariance matrix is:

[0067] ;

[0068] wherein the covariance matrix of noise , denotes a unit matrix of order

[0069] The covariance matrix of interference is:

[0070] ;

[0071] wherein the covariance matrix of interference , denotes a steering vector of the interference in the corresponding direction, denotes a conjugate transpose operation.

[0072] Step 2.1.2, the interference suppression matrix is obtained according to the following formula:

[0073]

[0074] wherein, denotes a matrix inversion operation.

[0075] Step 2.1.3, the notched beamforming matrix is obtained according to the following formula:

[0076] ;

[0077] wherein the notched beamforming matrix .

[0078] Step 2.2, if the echo signal contains interference, the conjugate transpose of the notched beamforming matrix is directly multiplied with the array element data to obtain the beam domain data:

[0079] ;

[0080] If the echo signal does not contain interference, the conjugate transpose of the conventional beamforming matrix is directly multiplied with the array element data to obtain the beam domain data:

[0081] .

[0082] Step 3, construct a whitening matrix and perform whitening processing on the beam space data.

[0083] Step 3.1, construct a whitening matrix.

[0084] If the above beam conversion matrix is directly used to convert the element data to the beam domain, the Gaussian white noise becomes non-white noise with correlation. Therefore, the constructed beam conversion matrix needs to be whitened to ensure that the noise remains white noise. Generally, whitening is done by processing the beam conversion matrix:

[0085] ;

[0086] ;

[0087] The interference signal is filtered out when converting the element domain data to the beam domain data using the notch conversion matrix, represents the processed beam domain data:

[0088] ;

[0089] If there is no interference:

[0090] ;

[0091] According to step 2.2, directly convert the element data to the beam domain data without whitening operation, can be (with interference) and (no interference) as the whitening matrix:

[0092] ;

[0093] ;

[0094] Step 3.2, according to step 3.1 and the formula of step 2.2, the whitened data when there is interference can be obtained:

[0095] ;

[0096] The whitened data when there is no interference:

[0097] .

[0098] The scanning manifold matrix in the element domain is converted to the scanning manifold matrix in the beam domain using the conventional beam conversion matrix, , represents the total length of the angle scanning range.

[0099] ;

[0100] wherein the scanning manifold matrix in the beam domain: , is the scanning manifold matrix in the element domain, , .

[0101] Step 4, IAA super-resolution processing is performed on the data in the beam domain by using the scanning manifold matrix of the beam domain, a peak value is searched in the power spectrum after iteration, and the target angle is measured.

[0102] The essence of IAA is to estimate the amplitude of the signal source by weighted least squares method , so that is minimum. The steps of IAA are as follows:

[0103] Step 1, initialize the amplitude of the signal source: , calculate the signal power corresponding to each scanning frequency on the initial scanning grid .

[0104] Step 2, iteration process, set the maximum number of iterations as , :

[0105] (1) calculate the covariance matrix of the first iteration , where represents a diagonal matrix containing elements of the main diagonal vector.

[0106] (2) update the amplitude of the signal source in the first iteration .

[0107] (3) calculate the signal power corresponding to each scanning frequency on the scanning grid in the first iteration .

[0108] The scanning matrix in step 3.2 cannot be , because the division in the formula leads to the formation of a peak value at the interference, and the target that should be filtered out becomes a stronger signal.

[0109] The process is repeated until there is no significant difference between the power spectra of two adjacent iterations, i.e. , is a set threshold, or the maximum number of iterations is reached, and the iteration is exited.

[0110] If the first iteration reaches convergence, output .

[0111] Step 3, search for the peak value of , find the angles corresponding to the larger peak values as the angles of the target.

[0112] The effect of the present application will be further described in combination with a simulation experiment.​

[0113] 1. Simulation experiment conditions.

[0114] The hardware platform of the simulation experiment of the application is: the processor is Intel i5-10200 CPU, the main frequency is 2.4 GHz, and the memory is 16 GB.

[0115] The software platform of the simulation experiment of the application is: Windows 11 operating system and MATLAB R2023b.

[0116] The simulation experiment of the application is to generate radar echo signals according to the echo signal model of the radar antenna array in step 1 of the embodiment of the application.

[0117] The number of array elements in the simulation experiment of the application is , the signal frequency is MHz, the wavelength is m, and the array element spacing is m.

[0118] 2. Simulation content and result analysis.

[0119] The simulation experiment of the application is to perform angle estimation on radar echo signals by using the application and one prior art (IAA algorithm based on array element space), respectively, and to analyze the influence of various factors on angle measurement performance, as shown in Figures 2 to 8 .

[0120] The prior art IAA algorithm based on array element space refers to:

[0121] The IAA algorithm proposed by T. Yardibi et al. in the published paper "Source Localization and Sensing: A Nonparametric Iterative Adaptive Approach Based on Weighted Least Squares" (in IEEE Transactions on Aerospace and Electronic Systems, vol. 46, no. 1, pp. 425-443, Jan. 2010, doi: 10.1109 / TAES.2010.5417172.).

[0122] The influence of various factors on angle measurement performance after simulation of the application will be further described below in combination with the simulation results. Figures 2 to 8

[0123] Figure 2 ​is the scanning curve diagram of the beam domain digital beam forming (DBF) scanning method in the simulation experiment of the application, wherein the target angle is 2° and 5° respectively, and the scanning curve diagram of the conventional DBF scanning method in a beam width; Figure 2 The abscissa is the angle, the variation range is -40° to 40°, and the step is 0.05°. The ordinate is the normalized amplitude.

[0124] From Figure 2 It can be seen that when the two target angles are close to each other, the beam domain digital beam forming (DBF) scanning method cannot effectively separate the targets. Obviously, the super resolution algorithm of the application can effectively separate the targets.

[0125] Figure 3 is the scanning curve diagram of the beam space whitening IAA dense target angle measurement in the simulation experiment of the application, wherein when the target angle is 2° and 5°, the beam pointing of the beam conversion matrix is increased from -3° to 6° by 1.5° in sequence.

[0126] Figure 4 is the scanning curve diagram of the beam space non-whitening IAA dense target angle measurement in the simulation experiment of the application, wherein when the target angle is 2° and 5°, the beam pointing of the beam conversion matrix is increased from -3° to 6° by 1.5° in sequence.

[0127] Figure 3 and Figure 4 The abscissa is the angle, the variation range is -20° to 20°, and the step is 0.05°. The ordinate is the normalized amplitude.

[0128] From Figure 3 and Figure 4 It can be seen that the beam domain IAA algorithm can effectively distinguish the dense targets. The sidelobe of the scanning curve of the non-whitening IAA algorithm is higher, which indicates that a false peak may occur. Therefore, it can be seen that the sidelobe of the scanning curve of the whitening IAA algorithm is obviously lower than that of the non-whitening IAA algorithm.

[0129] Figure 5 is the angle measurement root mean square error diagram of the array element domain IAA, the beam space whitening IAA and the beam space non-whitening IAA under different signal-to-noise ratios in the simulation experiment of the application in the case of no interference;

[0130] Figure 5The x-axis represents the signal-to-noise ratio (SNR), ranging from -5dB to 15dB with a step size of 2dB, and the y-axis represents the root mean square error of angle measurement. For each SNR, 100 Monte Carlo experiments were performed with a target angle of 2°. The beam pointing of the beam conversion matrix increased sequentially from -3° to 6° by 1.5°. Three curves were plotted for the root mean square error of angle measurement using the element-domain IAA algorithm, the beam-domain whitened IAA algorithm, and the beam-domain unwhitened IAA algorithm. Figure 5 The curves marked with an asterisk represent the root mean square error variation curves of the angle measurement based on the IAA algorithm without beam space whitening. Figure 5 The curve marked with an asterisk represents the root mean square error variation curve of the angle measurement based on the IAA algorithm without beam space whitening. Figure 5 The curve marked with a dashed cross represents the change curve of the root mean square error of angle measurement based on the IAA algorithm with beam spatial whitening. Figure 5 The curve marked with a circle and a straight line represents the change curve of the root mean square error of the angle measurement in the array element domain IAA algorithm.

[0131] from Figure 5 It can be seen that under low signal-to-noise ratio (SNR) conditions, the root mean square (RMS) error of the IAA algorithm in both the whitened and unwhitened beam domains is larger than that in the element domain. As the SNR gradually increases, the difference between the RMS errors in the beam domain and the element domain gradually decreases. Under low SNR conditions, the RMS error of the whitened beam domain IAA algorithm is smaller than that of the unwhitened beam domain IAA algorithm. With increasing SNR, the difference between the RMS error of the whitened beam domain IAA algorithm and the RMS error of the element domain IAA algorithm gradually decreases, and when the SNR is greater than 5 dB, they are essentially the same. Whitening can improve the SNR. Therefore, whitening is necessary, especially under low SNR conditions. The reason is that the element domain IAA algorithm needs to repeatedly construct and update the covariance matrix in each iteration. , Its computational workload is approximately , No. Each scanning frequency needs to be solved The computational complexity of inverting the covariance matrix is ​​approximately Two matrix-vector multiplications are approximately equal to Therefore, the computational cost of each iteration is .

[0132] A dense target angle measurement method based on IAA beam spatial whitening: Its computational workload is approximately . No. Each scanning frequency needs to be solved The computational complexity of inverting the covariance matrix is ​​approximately Two matrix-vector multiplications are approximately equal to Therefore, the computational cost of each iteration is... From the simulation experiments of this invention, the number of array elements... number of beams The computational load of the whitened beam domain IAA is reduced, resulting in a slight decrease in performance.

[0133] Figure 6 This is a diagram showing the processing results of dense IAA targets in the beam space without whitening under interference conditions in the simulation experiment of this invention; Figure 7 This is a diagram showing the results of beam spatial whitening IAA dense target processing in the simulation experiment of this invention under the condition of interference suppression.

[0134] Figure 6 and Figure 7 The horizontal axis represents angles, ranging from 0° to 20° with a step size of 0.05°, while the vertical axis represents the normalized amplitude. The target angles are 2° and 5°, the interference target angle is -2°, and the beam pointing of the beam conversion matrix increases sequentially from 1° to 7°, with the beams pointing from 1° to 1.5°.

[0135] from Figure 6 It can be seen that, due to interference, the scanning curve of the IAA algorithm, which has no beam whitening and no interference suppression, has a peak near the target. However, due to the strong interference, the sidelobe peak is higher than the target, and the true angle of the target cannot be effectively measured.

[0136] from Figure 7 As can be seen, the scanning curve of the IAA algorithm with beam domain whitening and interference suppression forms two maximum peaks near the target, proving that the present invention can effectively measure the target angle.

[0137] Figure 8 The beam pointing diagram of the notched beam conversion matrix constructed according to the present invention is drawn based on the simulation experiment of the present invention.

[0138] Figure 8 The horizontal axis represents the angle, ranging from -20° to 20° with a step size of 0.05°, and the vertical axis represents the normalized amplitude.

[0139] from Figure 8 As can be seen, the beam pointing pattern of the beam conversion matrix with notch in this invention forms a deep null near the interference, which can effectively suppress the impact of interference on the target.

[0140] The simulation experiment shows that the dense target angle measurement method based on IAA beam space whitening in complex environment converts array element data to beam domain data, is simple and easy to implement, reduces dimension while ensuring that the noise is still Gaussian white noise, constructs an interference suppression matrix by using the noise and interference power covariance matrix, multiplies the conventional beam conversion matrix, makes the amplitude response of the beam pointing near the interference angle have a deep notch, and is used for suppressing interference. The method has good robustness in the unknown number of signal sources and complex environment, and reduces the operation amount without affecting the resolution effect.

[0141] The above is a detailed description of the present application in combination with specific preferred embodiments, which aims to better illustrate the principles and applications of the present application, but this does not mean that the actual application of the present application is limited to the above. For those skilled in the art, some simple deductions, adjustments or replacements can be made based on this without deviating from the basic concept of the present application, and these modifications and improvements should be considered within the reasonable protection scope of the present application.

Claims

1. A method for determining the angle of dense targets based on beam spatial whitening in complex environments, characterized in that, The specific steps of this method are as follows: Step 1: Construct the echo signal of the radar echo array element; Step 2: Use the constructed notched beam conversion matrix to convert the echo signal to the beam domain to obtain the echo signal in the beam domain. Step 3: Use the constructed whitening matrix to whiten the echo signal in the beam domain; Step 4: Using the scanning manifold matrix of the beam domain, perform IAA super-resolution processing on the echo signal in the beam domain, search for the peak value in the iterated power spectrum, and measure the target angle.

2. The method for measuring the angle of dense targets according to claim 1, characterized in that, The echo signal mentioned in step 1 is as follows: ； in, Indicates inclusion The radar array element echo signal of the target. N represents the total number of radar antenna array elements. This indicates that each element in z belongs to the complex field. of A complex matrix of dimension 1 The value can be a positive integer. The value of is a positive integer. This represents the steering vector matrix corresponding to the angle of the k-th target. , This indicates the total number of targets in the radar array element echo signal. , , Indicates the first The guidance vector of each target. , This indicates an exponential operation with base e, and j represents the imaginary unit. Represents pi (π). Indicates the first The angle corresponding to each target Indicates the spacing between array elements. s represents the wavelength, and s represents the complex amplitude of the signal source. , , Indicates the first The complex amplitude of the signal source for each target This represents the transpose operation, where n represents the Gaussian white noise vector. .

3. The method for measuring the angle of dense targets according to claim 2, characterized in that, The notch beam conversion matrix mentioned in step 2 is: ； in, This represents the beam conversion matrix with a notch. B represents the beam conversion matrix. , The angle pointed to by the b-th beam is denoted as The corresponding steering vector, where R represents the interference suppression matrix. The covariance matrix representing the noise. , This represents the power of the noise in a single array element. Indicates that the order is equal to The identity matrix, The covariance matrix representing the disturbance. , This represents the power of interference in a single array element. This represents the steering vector corresponding to the direction of the interference. This indicates the conjugate transpose operation. This represents the matrix inversion operation.

4. The method for measuring the angle of dense targets according to claim 3, characterized in that, The echo signal in the beam domain mentioned in step 2 is as follows: ； in, This represents the echo signal in the beam domain. , This indicates the echo signal in the beam domain when interference is present. This represents the echo signal in the beam domain when there is no interference.

5. The method for measuring the angle of dense targets according to claim 4, characterized in that, The whitening matrix mentioned in step 3 is: ； in, Represents the whitening matrix. ; Indicates matrix first Then, perform the inverse operation on the power of the power. This represents the whitening matrix when interference is present. This represents the whitening matrix when there is no interference.

6. The method for measuring the angle of dense targets according to claim 5, characterized in that, The whitening process of the echo signal in the beam domain described in step 3 is accomplished by the following formula: ； in, This represents the echo signal in the whitened beam domain. , This represents the echo signal in the whitened beam domain when interference is present. This represents the echo signal in the whitened beam domain when there is no interference.

7. The method for measuring the angle of dense targets according to claim 6, characterized in that, The scanning manifold matrix of the beam domain mentioned in step 4 is: ； in, The scanning manifold matrix represents the beam domain. , Indicates the total length of the angular scan range. , The angle is represented as The corresponding beam domain steering vector, This represents the whitened beam conversion matrix. , The matrix representing the scanned manifold of the element field. , The angle is represented as The corresponding guide vector.

8. The method for measuring the angle of dense targets according to claim 7, characterized in that, The steps for performing IAA super-resolution processing on the echo signal in the beam domain as described in step 4 are as follows: The first step is to estimate the initial power spectrum. : ,in, Indicates the first The amplitude at each angle grid point , This indicates the absolute value operation; The second step is to estimate the covariance matrix of the signal during the current iteration. : ,in, This indicates the operation of constructing a diagonal matrix using the vector within the brackets as its main diagonal element. This represents the spatial power spectrum of the previous iteration. , This represents the maximum number of iterations; the first iteration is... ; The third step is to calculate the IAA power spectrum during the current iteration. ,in, This represents the spatial power spectrum during the current iteration. Indicates the current iteration process. The amplitude at each angle grid point ; The fourth step is to determine whether the difference between the IAA power spectra obtained from two adjacent iterations meets the termination condition. If so, proceed to the fifth step; otherwise, proceed to the second step. Fifth step: Search for the peak values ​​of the power spectrum obtained in all iterations to find... The corresponding goal A peak value is used as the angle for measuring dense targets.

9. The method for measuring the angle of dense targets according to claim 8, characterized in that, The termination condition being met refers to the situation where one of the following conditions is met: Condition 1: The difference between the IAA power spectra obtained from two consecutive iterations is less than a threshold. threshold The possible values ​​of: ; Condition 2: Reaching the maximum number of iterations .

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