A clutter suppression method based on sample expansion

Abstract

The application belongs to the technical field of radar signal processing. The application provides a clutter suppression method based on sample expansion. In the case that the number of effective training samples that are uniform and meet the independent and identically distributed condition is seriously insufficient, the cubic spline interpolation method is used to complete preliminary expansion of the samples, and the samples formed by interpolation are corrected by referring to the CCM, so as to eliminate the mismatch of the clutter space-time structure and the false components introduced by the interpolation operation, correct the two-dimensional distribution characteristics of the clutter space-time, make the clutter space-time correctly reflect the statistical characteristics, obtain the expanded samples that meet the independent and identically distributed requirement with the clutter of the unit to be detected, and thus increase the number of effective training samples. Then, the existing effective training samples are combined to complete accurate estimation of the second covariance matrix, and then the optimal adaptive filtering weight is solved, so as to avoid sharp decline of the clutter suppression performance under the condition of small samples and improve the performance of the early warning radar in detecting the moving target.

Description

Technical Field

[0001] This disclosure relates to the field of radar signal processing technology, and in particular to a clutter suppression method based on sample augmentation. Background Technology

[0002] In radar signal processing, effective clutter suppression is a crucial prerequisite for ensuring that the radar system can detect moving targets. The performance of clutter suppression determines the radar system's ability to detect moving targets in a cluttered environment. Space-Time Adaptive Processing (STAP) technology achieves effective clutter suppression by jointly processing the spatial and Doppler domains. When using the STAP method for clutter suppression, the performance mainly depends on the accuracy of the clutter covariance matrix (CCM) estimation. According to the Reed-Mallett-Brennan (RMB) criterion, when using the STAP method for clutter suppression, the output signal-to-clutter plus noise ratio (SCNR) loss due to clutter noise covariance matrix estimation should not exceed 3dB. Furthermore, the number of training samples that satisfy independent and identically distributed (IID) relationships with the cell under test (CUT) should be no less than twice the system's degrees of freedom.

[0003] However, in real clutter environments, early warning radars face complex external conditions. The clutter echo distribution characteristics vary due to numerous factors, including high-speed platform movement, Earth's rotation, non-frontal side-looking array configurations, terrain reflection characteristics, strong scattering points, and clutter fluctuations. This results in severely non-uniform clutter distribution across range cells, exhibiting significant non-stationary and non-uniform characteristics. The statistical characteristics of clutter differ greatly across range cells, leading to a severe shortage of effective uniform training samples that meet IID requirements. This insufficiency directly results in a significant deviation between the estimated CCM and the actual CCM, drastically reducing the suppression capability of the STAP method based on clutter statistical characteristics, and even causing target signal self-cancellation. This severely restricts the radar system's detection capability and moving target detection performance.

[0004] Therefore, it is necessary to improve one or more of the problems existing in the above-mentioned related technical solutions.

[0005] It should be noted that this section is intended to provide background or context for the technical solutions of this disclosure as set forth in the claims. The description herein does not constitute an admission that it is prior art simply because it is included in this section. Summary of the Invention

[0006] The purpose of this disclosure is to provide a clutter suppression method based on sample augmentation, thereby overcoming at least to some extent one or more problems caused by the limitations and defects of related technologies.

[0007] According to embodiments of this disclosure, a clutter suppression method based on sample augmentation is provided, comprising: Step S1: Obtain data blocks and perform column vectorization on the data matrix of each distance cell to form an initial spatiotemporal two-dimensional data matrix; Step S2: Determine the number of new samples and the number of expanded samples between adjacent samples, and use the cubic spline interpolation method to expand the initial spatiotemporal two-dimensional data matrix to generate the new spatiotemporal two-dimensional data matrix; Step S3: Estimate the first covariance matrix based on the initial space-time two-dimensional data matrix, determine the noise power range, and add the corresponding noise to the newly added space-time two-dimensional data matrix to generate the newly added space-time two-dimensional data matrix after adding noise. Step S4: Construct a sample compensation matrix and use the sample compensation matrix to compensate the newly added spatiotemporal two-dimensional data matrix after adding noise, so as to generate the compensated newly added spatiotemporal two-dimensional data matrix. Step S5: Estimate the second covariance matrix based on the compensated new spatiotemporal two-dimensional data matrix and the initial spatiotemporal two-dimensional data matrix; Step S6: Solve for the optimal adaptive filter weights based on the second covariance matrix, and use the optimal adaptive filter weights to suppress clutter in the data block to generate clutter-suppressed data.

[0008] Furthermore, step S1 specifically includes: Obtain data blocks; where rows of data blocks represent spatial domain sampling, columns of data blocks represent temporal domain sampling, and the third dimension of data blocks represents distance cells; Arrange each column of the data matrix of each distance cell in the data block into a vector in sequence to obtain the spatiotemporal two-dimensional data of each distance cell; An initial spatiotemporal two-dimensional data matrix is ​​formed based on the spatiotemporal two-dimensional data of all distance cells; where, The initial spacetime two-dimensional data matrix is:

[0009] In the formula, The number of array elements. For the number of pulses, This represents the number of distance units.

[0010] Furthermore, step S2 specifically includes: In the initial space-time two-dimensional data matrix Each column of the data is used as a sample data point to determine the number of new samples. The number of augmented samples between adjacent samples The sample data of the existing distance cells are sorted to obtain the sorted initial spatiotemporal two-dimensional data matrix. Assign equally spaced interpolation node coordinates to the sample data of the existing distance cells, and determine the coordinates of the points to be interpolated within the interval of adjacent nodes; The space-time two-dimensional data corresponding to the sample data of the existing distance cell is decomposed into real part vector and imaginary part vector; Construct a system of tridiagonal linear equations for cubic spline interpolation for each element of the real and imaginary vectors; Set up a closed tridiagonal linear equation system with first-order derivative clamping boundary conditions, and use the chasing method to solve for the second-order bending moment at each node; Based on the obtained second-order bending moment, determine the cubic spline interpolation function on each interpolation interval, and calculate the real part interpolation result and the imaginary part interpolation result of the point to be interpolated; The real and imaginary interpolation results of the points to be interpolated are merged to generate a new two-dimensional spatiotemporal data matrix; where, The sorted initial space-time two-dimensional data matrix is ​​as follows:

[0011] The newly added spatiotemporal two-dimensional data matrix is ​​as follows:

[0012]

[0013] In the formula, For newly added sample data, This is sample data for existing distance cells.

[0014] Furthermore, step S3 specifically includes: Estimate the first covariance matrix based on the initial space-time two-dimensional data matrix; Singular value decomposition is performed on the first covariance matrix to obtain eigenvalues; Based on the eigenvalues, the clutter rank is determined using the improved MDL criterion to obtain the noise eigenvalues; Determine the noise power range based on noise characteristic values; Noise is generated based on the noise power range and added to the newly added spatiotemporal two-dimensional data matrix to generate the new spatiotemporal two-dimensional data matrix after noise addition; where, The newly added spatiotemporal two-dimensional data matrix after adding noise is:

[0015]

[0016] In the formula, The newly added sample data after adding noise. It is noise.

[0017] Furthermore, step S4 specifically includes: Construct CUT clutter echo data, and using the first covariance matrix as the standard, construct a sample compensation matrix and formulate an optimization problem; Solve the optimization problem to obtain the transformation matrix; The newly added spatiotemporal two-dimensional data matrix after noise is added is compensated using a transformation matrix to generate a compensated newly added spatiotemporal two-dimensional data matrix.

[0018] Furthermore, the optimization problem is as follows:

[0019] In the formula, Let be the transformation matrix. For the sample compensation matrix, Let be the first covariance matrix. It is the identity matrix. Indicates conjugate transpose; The elements in the newly added spatiotemporal two-dimensional data matrix after compensation are as follows:

[0020] In the formula, This is the sample data after noise has been added.

[0021] Furthermore, step S5 specifically includes: Based on the compensated newly added spatiotemporal two-dimensional data matrix and the initial spatiotemporal two-dimensional data matrix, the second covariance matrix is ​​estimated using the maximum likelihood method; where... The second covariance matrix is:

[0022] In the formula, The first element in the initial spacetime two-dimensional data matrix Data for each distance unit.

[0023] Furthermore, in step S6, the data after clutter suppression is as follows:

[0024]

[0025] In the formula, The spacetime two-dimensional steering vector of the target. These are the optimal adaptive filtering weights.

[0026] The technical solutions provided by the embodiments of this disclosure may include the following beneficial effects: In the embodiments of this disclosure, the above method addresses two main issues. First, when the number of uniform and identically distributed (i.i.d.) effective training samples is severely insufficient, cubic spline interpolation is used to initially expand the samples. Then, the interpolated samples are corrected using a reference CCM to eliminate clutter spatiotemporal structure mismatch and spurious components introduced by the interpolation operation, correcting the two-dimensional spatiotemporal distribution characteristics of the clutter to accurately reflect its statistical characteristics. This results in expanded samples that meet the i.i.d. requirement of independent distribution with the clutter of the target unit, thereby increasing the number of effective training samples. Furthermore, the existing effective training samples are combined to accurately estimate the second covariance matrix, and then the optimal adaptive filter weights are calculated. This avoids a sharp decline in clutter suppression performance under small sample conditions and improves the performance of the early warning radar in detecting moving targets. Second, this method effectively solves the problem of severely insufficient training samples and inaccurate estimation of the covariance matrix of the target range unit, which leads to a sharp decline in clutter suppression performance. This method can improve the performance of the early warning radar in detecting moving targets. Attached Figure Description

[0027] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this disclosure and, together with the description, serve to explain the principles of this disclosure. It is obvious that the drawings described below are merely some embodiments of this disclosure, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort.

[0028] Figure 1 The diagram illustrates the steps of a clutter suppression method based on sample augmentation in an exemplary embodiment of this disclosure. Figure 2 This illustrates a data block acquired within a CPI in an exemplary embodiment of this disclosure; Figure 3 The comparison of IF factors for the present method, the full-sample method, and the small-sample method in exemplary embodiments of this disclosure is shown. Detailed Implementation

[0029] Exemplary embodiments will now be described more fully with reference to the accompanying drawings. However, these exemplary embodiments can be implemented in many forms and should not be construed as limited to the examples set forth herein; rather, they are provided so that this disclosure will be more comprehensive and complete, and will fully convey the concept of the exemplary embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

[0030] Furthermore, the accompanying drawings are merely illustrative diagrams of embodiments of this disclosure and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and therefore repeated descriptions of them will be omitted. Some block diagrams shown in the drawings are functional entities and do not necessarily correspond to physically or logically independent entities.

[0031] This example implementation provides a clutter suppression method based on sample augmentation. (See reference...) Figure 1 As shown, the method may include: Step S1: Obtain data blocks and perform column vectorization on the data matrix of each distance cell to form an initial spatiotemporal two-dimensional data matrix; Step S2: Determine the number of new samples and the number of expanded samples between adjacent samples, and use the cubic spline interpolation method to expand the initial spatiotemporal two-dimensional data matrix to generate the new spatiotemporal two-dimensional data matrix; Step S3: Estimate the first covariance matrix based on the initial space-time two-dimensional data matrix, determine the noise power range, and add the corresponding noise to the newly added space-time two-dimensional data matrix to generate the newly added space-time two-dimensional data matrix after adding noise. Step S4: Construct a sample compensation matrix and use the sample compensation matrix to compensate the newly added spatiotemporal two-dimensional data matrix after adding noise, so as to generate the compensated newly added spatiotemporal two-dimensional data matrix. Step S5: Estimate the second covariance matrix based on the compensated new spatiotemporal two-dimensional data matrix and the initial spatiotemporal two-dimensional data matrix; Step S6: Solve for the optimal adaptive filter weights based on the second covariance matrix, and use the optimal adaptive filter weights to suppress clutter in the data block to generate clutter-suppressed data.

[0032] The above method addresses two main issues. First, when the number of uniform and identically distributed (i.i.d.) effective training samples is severely insufficient, cubic spline interpolation is used to initially expand the sample size. Then, the interpolated samples are corrected using a reference CCM to eliminate clutter spatiotemporal structure mismatch and spurious components introduced by the interpolation operation, correcting the two-dimensional spatiotemporal distribution characteristics of the clutter to accurately reflect its statistical properties. This results in expanded samples that meet the i.i.d. requirement of being identically distributed with the clutter of the target unit, thereby increasing the number of effective training samples. Furthermore, by combining these existing effective training samples, the second covariance matrix is ​​accurately estimated, and the optimal adaptive filter weights are solved. This avoids a sharp decline in clutter suppression performance due to small sample sizes and improves the performance of early warning radar in detecting moving targets. Second, this method effectively solves the problem of severely insufficient training samples and inaccurate estimation of the covariance matrix of the target range unit, which leads to a sharp decline in clutter suppression performance. This method can improve the performance of early warning radar in detecting moving targets.

[0033] Below, we will refer to Figures 1 to 3 The steps of the method described above in this example embodiment will be explained in more detail.

[0034] In step S1, data blocks are acquired, and the data matrices of each distance cell are column-vectorized to form an initial spatiotemporal two-dimensional data matrix.

[0035] Specifically, the data blocks obtained from the early warning radar are rearranged, and each range cell data matrix is ​​processed into a column vector. Each column of each range cell data matrix is ​​arranged into a vector in sequence to obtain the sampled two-dimensional spatiotemporal data.

[0036] The echo data blocks (i.e., data blocks) collected by the early warning radar are as follows: Figure 2 As shown. The rows of a data block represent spatial domain sampling, the columns represent temporal domain sampling, and the third dimension represents the sampling distance unit. For data blocks with... A linear array of elements, emitting within one CPI. The corresponding pulse, the first The data for each distance cell is:

[0037] With the first Data matrix of distance units For example, the vectorization process is as follows:

[0038] in, This indicates transpose.

[0039] After vectorizing the data of all distance cells, The matrix formed by the spatiotemporal two-dimensional data of each distance cell (i.e., the initial spatiotemporal two-dimensional data matrix) is as follows: .

[0040] In step S2, the number of new samples and the number of expanded samples between adjacent samples are determined, and the initial spatiotemporal two-dimensional data matrix is ​​expanded using the cubic spline interpolation method to generate a new spatiotemporal two-dimensional data matrix.

[0041] Specifically, step S21: The initial spatiotemporal two-dimensional data matrix... Each column in the dataset is considered as a sample data point. The required number of samples to be added is given, and the number of additional samples needed between every two adjacent distance units is calculated. The existing data is then used to... The samples from each distance unit are sorted, and the number of samples needed to be expanded is... The number of samples that need to be added between existing adjacent distance units is The total number of samples after expansion is For the existing After sorting the samples of each distance unit and adding new samples, the result is:

[0042]

[0043] in, For the new samples that need to be added, This is an existing sample.

[0044] Step S22: Sample augmentation process based on cubic spline interpolation.

[0045] If there are already adjacent samples, it is necessary to add more The number of samples added during the expansion was [number] samples. .

[0046] Step S221, define the spatial coordinates of the interpolation node and the point to be interpolated: 1. For Assign equally spaced interpolation node coordinates to the known distance cell samples: Let the first... Known samples The corresponding node coordinates are , Corresponding data matrix The The column ensures that the node coordinates of two adjacent known samples are spaced apart. Reserve for each interval There are 1, 2, 3, 4, 5, 6, 7, 8, 9, 1

[0047] 2. Determine the interpolation coordinates within each adjacent node interval: For each interpolation interval formed by adjacent known samples... , contains For each pair of adjacent distance units, the coordinates of the expanded sample to be interpolated within the interval are: ,common There are 10 interpolation points.

[0048] 3. Define the function values ​​corresponding to the nodes: Let the interpolation nodes... The corresponding function value is .

[0049] in, This is the spatiotemporal two-dimensional vectorized data corresponding to the distance cell.

[0050] Step S222, real and imaginary solutions of the complex vector: Since the data collected by the radar system is complex, the function value corresponding to each known node... Extract the real and imaginary parts of the complex vector respectively. The decomposition is as follows:

[0051] in, For complex vectors Real part vector, For complex vectors Imaginary part vector, The imaginary unit is used, and the same cubic spline interpolation operation is then performed on both the real and imaginary vectors.

[0052] Step S223, set interpolation boundary conditions: To solve the system of equations for closed cubic spline interpolation, first-order derivative clamped boundary conditions are used as interpolation boundary constraints, specifically defined as follows: First endpoint boundary constraint: starting node of the interpolation interval The first derivative at point is approximated by the first difference of the first two known samples, i.e. Calculate the first derivative values ​​for the real and imaginary parts respectively. The function value corresponding to the initial known node, i.e. The value, The function value corresponding to the second known node, i.e. The value of .

[0053] Tail endpoint boundary constraints: Termination node of interpolation interval The first derivative at that point is approximated by the first difference of the last two known samples, i.e. Calculate the first derivative values ​​for the real and imaginary parts respectively. The function value corresponding to the last known node, i.e. The value, The function value corresponding to the second-to-last known node, i.e. The value of .

[0054] Step S224: Construct a system of tridiagonal linear equations corresponding to cubic spline interpolation element by element: Each element of a spacetime complex vector forms an independent one-dimensional real-valued sequence along the distance dimension. Therefore, for the real part vector and the imaginary part vector, the first element... Each element is used to independently construct a system of interpolation equations, as follows: For the real part vector and the imaginary part vector, the first... Each element, representing a node. The corresponding element values ​​are:

[0055]

[0056] Fixed step size of adjacent nodes All intervals have the same step size. Define the variable to be calculated: node. Interpolation function The second derivative , also known as bending moment, is the unknown quantity to be solved in the tridiagonal system of equations. Combining the constraint of continuity of the first and second derivatives of the interpolation function, for all internal nodes... Construct the three bending moment equations:

[0057] in, For nodes Interpolation function The second derivative, For nodes Interpolation function The second derivative, For nodes Interpolation function The second derivative; The coefficients under a fixed step size are:

[0058] Right-hand item:

[0059] Based on the established first-order derivative clamping boundary conditions, supplement the equations for the first and last nodes to form a closed system of equations: First node equation:

[0060] Tail node equation:

[0061] in, For nodes Interpolation function The second derivative, For nodes Interpolation function The second derivative, For nodes Interpolation function The second derivative, For nodes Interpolation function The second derivative; Combining the internal node equations and the boundary equations, we obtain A complete tridiagonal linear system of equations of order 1:

[0062] Step S225, solve the tridiagonal linear equation system: The constructed tridiagonal linear equation system is solved using the Thomas algorithm to obtain the second-order bending moments at all nodes. The specific solution process is as follows: Standardization of the system of equations: The tridiagonal system of equations can be uniformly expressed as:

[0063] Among them, the first line : , , , ; Inner node row : , , , ;Tail line : , , , .

[0064] Forward elimination (tracing the process): Calculate the elimination coefficients and equivalent right-hand side terms sequentially to complete the upper diagonalization of the tridiagonal matrix: initialization: , ,right Calculate sequentially:

[0065] tail row hour ,therefore

[0066] Reverse substitution (rushing the process): Starting from the tail node, solve for the bending moment values ​​of all nodes in sequence: initialization: ,right Calculate in sequence

[0067] After completing the solution, the second-order bending moments of all nodes are obtained. Each interpolation interval can then be determined. The cubic spline interpolation function on the x-axis.

[0068] Step S226, Calculation of the sample to be interpolated and expanded: Traverse all adjacent node intervals and the interpolation points within those intervals to complete the calculation of all expanded samples. The specific process is as follows: Determining the interval cubic spline interpolation function: For each interpolation interval Combined with the bending moment obtained from the solution , The expression for the cubic spline interpolation function within this interval is:

[0069] in, With a fixed node step size, this expression holds true for every element of both the real and imaginary parts.

[0070] Calculation of interpolation point elements: For interval Each x-coordinate to be interpolated within By substituting the interpolation functions corresponding to each element of the real and imaginary parts in sequence, the interpolation results of all elements of the real part vector can be calculated. The interpolation result of all elements of the imaginary part vector .

[0071] Complex vector augmented sample synthesis: By merging the real and imaginary interpolation results at the corresponding positions, we obtain the augmented complex vector sample corresponding to that horizontal coordinate:

[0072] Iterate through all interpolation points in all intervals to complete the process. Calculation of one expanded sample.

[0073] Step S227, Sorting and outputting the sample sequences: Arrange the original known samples and the interpolated expanded samples in ascending order according to their spatial coordinates to obtain the new samples formed after interpolation (i.e., the newly added spatiotemporal two-dimensional data matrix):

[0074]

[0075] The new samples obtained through interpolation can be regarded as a fit to the deterministic trend of clutter data.

[0076] In step S3, the first covariance matrix is ​​estimated based on the initial space-time two-dimensional data matrix, and the noise power range is determined. Corresponding noise is added to the newly added space-time two-dimensional data matrix to generate the newly added space-time two-dimensional data matrix after adding noise.

[0077] Specifically, add noise: Use existing The first covariance matrix estimated for each distance cell is:

[0078] For matrix Singular value decomposition is used to obtain eigenvalues. .

[0079] The clutter rank is calculated using the improved MDL (Minimum Description Length) criterion. The cost function of the improved MDL criterion is as follows:

[0080] Will Substituting into the cost function, the value that minimizes the cost function is... That is, the number of eigenvalues ​​corresponding to clutter is less than the number of eigenvalues ​​corresponding to the minimum value. The characteristic value corresponding to the noise can be used to determine the power range corresponding to the noise.

[0081] The sample data obtained by adding noise to the new samples obtained through interpolation is as follows:

[0082] Furthermore, the newly added sample data meets the requirement of being independent and identically distributed.

[0083] The complete data sample after adding noise (i.e., the newly added spatiotemporal two-dimensional data matrix after adding noise) is as follows:

[0084]

[0085] In step S4, a sample compensation matrix is ​​constructed, and the sample compensation matrix is ​​used to compensate the newly added spatiotemporal two-dimensional data matrix after the addition of noise, so as to generate the compensated newly added spatiotemporal two-dimensional data matrix.

[0086] Specifically, the construction of the sample compensation matrix: To make the estimated CCM closer to the true CCM, compensation is performed on the interpolated and augmented samples, and on the samples with added noise. Multiplying a unitary matrix Transform it.

[0087] According to the clutter model, the first The azimuth dimension of each distance unit is divided into Number of clutter elements in the azimuth dimension Should meet ,in Represents the Doppler aliasing coefficient. The number of pulses within a Coherent Processing Interval (CPI). The number of array elements This indicates the operating speed of SBEWR. This indicates the pulse repetition frequency.

[0088] No. The distance unit of the first The space-time two-dimensional data of the echo of each clutter cell is as follows:

[0089] in, Indicates the first The distance unit of the first The echo amplitude of each clutter cell , These are the corresponding spatial and temporal steering vectors, respectively.

[0090] Let the first The distance unit of the first Each clutter cell corresponds to a slant distance According to the radar equations, the slant range is... The clutter echo amplitude at that location is:

[0091] in, This represents the peak power transmitted by the radar system. and These represent the radar transmit and receive gains, respectively. For system losses, This is the backscattering cross section (RCS) of the clutter block.

[0092] No. The distance unit of the first The spatial and temporal steering vector of each clutter cell is:

[0093]

[0094] in, Represents spatial angular frequency. Represents the normalized Doppler frequency. This indicates transpose.

[0095]

[0096]

[0097] in, and These represent the yaw angle and yaw magnitude caused by the Earth, respectively. The element spacing is typically half a wavelength. For the first The distance unit of the first Azimuth angle of each clutter cell For the first The distance unit of the first The elevation angle of each clutter unit.

[0098]

[0099]

[0100]

[0101] in, Represents the speed at the Earth's equator. Here, is the latitude of the sub-satellite point. It is the angle between the equatorial orbit and the operating orbit of the early warning radar.

[0102] Let the first The distance unit of the first Azimuth angle of each clutter cell The pitch angle is set according to the angle division. for:

[0103] in, H Indicates the height of SBEWR. This represents the Earth's radius.

[0104] No. The clutter echo data for each range cell is as follows:

[0105] The first after superimposed distance blur The clutter echo data for each range cell is as follows:

[0106] in, Indicates the first The number of fuzzy distance units corresponding to each distance unit. Represents reference distance unit The The clutter unit corresponding to the first The echo amplitude of a clutter cell at an ambiguous distance. , These are their corresponding spatial and temporal steering vectors, respectively.

[0107] The slant distance difference between two adjacent fuzzy locations in the distance dimension is:

[0108] in, It is the speed of light. Due to the The clutter echo data for each range cell is generated by The echo data of each clutter cell are superimposed, and the covariance matrix of the constructed CUT is used as the standard to construct... Solving for the unitary matrix of the matrix formed by the echo data of each clutter cell .

[0109] CUT's covariance matrix The expression is:

[0110] in, Represents reference distance cell The The clutter unit corresponding to the first The echo amplitude of a clutter cell at an ambiguous distance. , These are their corresponding spatial and temporal steering vectors, respectively.

[0111] The sample corresponding to the one after adding noise is constructed distance units The matrix formed by the echo data of each clutter cell is as follows:

[0112] in, .

[0113] The optimization problem to be constructed is:

[0114] The solution to the above optimization problem is:

[0115] unitary matrix in the above formula and For matrix The matrix obtained by performing Singular Value Decomposition (SVD):

[0116] Use the transformation matrix obtained in the above steps. For the sample with added noise After compensation and correction, the compensated and corrected samples (i.e., the newly added spatiotemporal two-dimensional data matrix after compensation) are as follows:

[0117] In step S5, the second covariance matrix is ​​estimated based on the compensated new spatiotemporal two-dimensional data matrix and the initial spatiotemporal two-dimensional data matrix.

[0118] Specifically, the estimation of the final covariance matrix (i.e., the second covariance matrix): For the compensated and corrected sample, plus the original sample, the final covariance matrix estimate using maximum likelihood estimation is:

[0119] In step S6, the optimal adaptive filter weights are solved based on the second covariance matrix, and the data blocks are suppressed using the optimal adaptive filter weights to generate clutter-suppressed data.

[0120] Specifically, the expression for the optimal weights (i.e., the optimal adaptive filter weights) and the results after clutter suppression are shown below:

[0121] in, This represents the spacetime two-dimensional steering vector of the target.

[0122] The output signal after optimal weight suppression is:

[0123] This application proposes a clutter suppression method based on sample expansion, which can effectively solve the problem of severe shortage of training samples and inaccurate estimation of the covariance matrix of the range cell to be detected, which leads to a sharp decline in clutter suppression performance. The above method can improve the clutter suppression performance of the early warning radar for moving targets.

[0124] In one specific embodiment, the effectiveness of this application is further verified by simulation experimental data.

[0125] (I) Simulation Experiment 1. Simulation parameters To verify the effectiveness of the method in this application, the simulation parameters are given below.

[0126] Table 1 Simulation Parameters

[0127] 2. Simulation results: Training samples generated from simulation experiments that satisfy more than twice the number of system degrees of freedom are called full samples, while training samples that do not satisfy more than twice the number of system degrees of freedom are called small samples. The proposed method is called interpolation-based transformation.

[0128] Simulation experiment settings: The number of training samples for small samples is set to half the system's degrees of freedom, and the number of training samples for full samples is set to twice or more the system's degrees of freedom. The clutter suppression performance results obtained by the proposed method, full-sample, and small-sample estimations of the second covariance matrix are compared below. Figure 3 As shown.

[0129] Based on the above experimental results, it can be seen that the clutter covariance matrix (i.e. the second covariance matrix) estimated from the full sample has the best clutter suppression effect. The proposed method uses the minimum error criterion in the sample compensation and correction process, which has a certain error with the real sample. Therefore, the clutter suppression effect of the estimated clutter covariance matrix cannot completely achieve the suppression effect of the full sample. However, compared with the suppression effect of the small sample, it is improved by about 78dB, and compared with the small sample, there is a clear and accurate clutter suppression notch.

[0130] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of embodiments of this disclosure, "a plurality of" means two or more, unless otherwise explicitly specified.

[0131] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this disclosure. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. In addition, those skilled in the art can combine and integrate the different embodiments or examples described in this specification.

[0132] Other embodiments of this disclosure will readily occur to those skilled in the art upon consideration of the specification and practice of the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of this disclosure that follow the general principles of this disclosure and include common knowledge or customary techniques in the art not disclosed herein. The specification and examples are to be considered exemplary only, and the true scope and spirit of this disclosure are indicated by the appended claims.

Claims

1. A clutter suppression method based on sample augmentation, characterized in that, include: Step S1: Obtain data blocks and perform column vectorization on the data matrix of each distance cell to form an initial spatiotemporal two-dimensional data matrix; Step S2: Determine the number of new samples and the number of expanded samples between adjacent samples, and use the cubic spline interpolation method to expand the initial spatiotemporal two-dimensional data matrix to generate the new spatiotemporal two-dimensional data matrix; Step S3: Estimate the first covariance matrix based on the initial space-time two-dimensional data matrix, determine the noise power range, and add the corresponding noise to the newly added space-time two-dimensional data matrix to generate the newly added space-time two-dimensional data matrix after adding noise. Step S4: Construct a sample compensation matrix and use the sample compensation matrix to compensate the newly added spatiotemporal two-dimensional data matrix after adding noise, so as to generate the compensated newly added spatiotemporal two-dimensional data matrix. Step S5: Estimate the second covariance matrix based on the compensated new spatiotemporal two-dimensional data matrix and the initial spatiotemporal two-dimensional data matrix; Step S6: Solve for the optimal adaptive filter weights based on the second covariance matrix, and use the optimal adaptive filter weights to suppress clutter in the data block to generate clutter-suppressed data.

2. The clutter suppression method based on sample augmentation according to claim 1, characterized in that, Step S1 specifically includes: Obtain data blocks; where rows of data blocks represent spatial domain sampling, columns of data blocks represent temporal domain sampling, and the third dimension of data blocks represents distance cells; Arrange each column of the data matrix of each distance cell in the data block into a vector in sequence to obtain the spatiotemporal two-dimensional data of each distance cell; An initial spatiotemporal two-dimensional data matrix is ​​formed based on the spatiotemporal two-dimensional data of all distance cells; where, The initial spacetime two-dimensional data matrix is: In the formula, The number of array elements. For the number of pulses, This represents the number of distance units.

3. The clutter suppression method based on sample augmentation according to claim 2, characterized in that, Step S2 specifically includes: In the initial space-time two-dimensional data matrix Each column of the data is used as a sample data point to determine the number of new samples. The number of augmented samples between adjacent samples The sample data of the existing distance cells are sorted to obtain the sorted initial spatiotemporal two-dimensional data matrix. Assign equally spaced interpolation node coordinates to the sample data of the existing distance cells, and determine the coordinates of the points to be interpolated within the interval of adjacent nodes; The space-time two-dimensional data corresponding to the sample data of the existing distance cell is decomposed into real part vector and imaginary part vector; Construct a system of tridiagonal linear equations for cubic spline interpolation for each element of the real and imaginary vectors; Set up a closed tridiagonal linear equation system with first-order derivative clamping boundary conditions, and use the chasing method to solve for the second-order bending moment at each node; Based on the obtained second-order bending moment, determine the cubic spline interpolation function on each interpolation interval, and calculate the real part interpolation result and the imaginary part interpolation result of the point to be interpolated; The real and imaginary interpolation results of the points to be interpolated are merged to generate a new two-dimensional spatiotemporal data matrix; where, The sorted initial space-time two-dimensional data matrix is ​​as follows: The newly added spatiotemporal two-dimensional data matrix is ​​as follows: In the formula, For newly added sample data, This is sample data for existing distance cells.

4. The clutter suppression method based on sample augmentation according to claim 3, characterized in that, Step S3 specifically includes: Estimate the first covariance matrix based on the initial space-time two-dimensional data matrix; Singular value decomposition is performed on the first covariance matrix to obtain eigenvalues; Based on the eigenvalues, the clutter rank is determined using the improved MDL criterion to obtain the noise eigenvalues; Determine the noise power range based on noise characteristic values; Noise is generated based on the noise power range and added to the newly added spatiotemporal two-dimensional data matrix to generate the new spatiotemporal two-dimensional data matrix after noise addition; where, The newly added spatiotemporal two-dimensional data matrix after adding noise is: In the formula, The newly added sample data after adding noise. It is noise.

5. The clutter suppression method based on sample augmentation according to claim 4, characterized in that, Step S4 specifically includes: Construct CUT clutter echo data, and using the first covariance matrix as the standard, construct a sample compensation matrix and formulate an optimization problem; Solve the optimization problem to obtain the transformation matrix; The newly added spatiotemporal two-dimensional data matrix after noise is added is compensated using a transformation matrix to generate a compensated newly added spatiotemporal two-dimensional data matrix.

6. The clutter suppression method based on sample augmentation according to claim 5, characterized in that, The optimization problem to be constructed is: In the formula, The transformation matrix is... For the sample compensation matrix, Let be the first covariance matrix. It is the identity matrix. Indicates conjugate transpose; The elements in the newly added spatiotemporal two-dimensional data matrix after compensation are as follows: In the formula, This is the sample data after noise has been added.

7. The clutter suppression method based on sample augmentation according to claim 6, characterized in that, Step S5 specifically includes: Based on the compensated newly added spatiotemporal two-dimensional data matrix and the initial spatiotemporal two-dimensional data matrix, the second covariance matrix is ​​estimated using the maximum likelihood method; where... The second covariance matrix is: In the formula, The first element in the initial spacetime two-dimensional data matrix Data for each distance unit.

8. The clutter suppression method based on sample augmentation according to claim 7, characterized in that, In step S6, the data after clutter suppression is as follows: In the formula, The spacetime two-dimensional steering vector of the target. These are the optimal adaptive filtering weights.

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