Method for determining sea clutter sparsity of small array shipborne ground wave radar and application

Abstract

The application discloses a method for determining the sparsity of sea clutter of a small-array shipborne ground wave radar and application thereof, and comprises the following steps: constructing a signal model of the small-array shipborne ground wave radar; extracting a sea clutter region of the small-array shipborne ground wave radar; judging the sailing state of the shipborne platform by using inertial navigation data; extracting a sea clutter ridge of the small-array shipborne ground wave radar; constructing a sea clutter characteristic spectrum; calculating the rank of a sea clutter covariance matrix of the small-array shipborne ground wave radar; determining the rank of the sea clutter covariance matrix based on the Brennan rule for the case of no yaw phenomenon, and the rank of the sea clutter is doubled for the case of yaw phenomenon; and determining the sparsity of the small-array shipborne ground wave radar. The method is applied to sea clutter suppression of the shipborne ground wave radar. The present application overcomes the defect that the sparsity of the existing ground wave radar is uncertain, which leads to limited performance of a sparse recovery algorithm, comprehensively analyzes the influence of factors such as the ship speed, yaw angle and backlobe balance on the sparsity of the sea clutter, and realizes effective determination of the sparsity of the sea clutter of the small-array shipborne ground wave radar.

Description

Technical Field

[0001] This invention relates to a method for determining the sparsity of sea clutter in a shipborne ground wave radar, specifically to a method and application for determining the sparsity of sea clutter in a small array shipborne ground wave radar, belonging to the field of shipborne radar technology. Background Technology

[0002] Ground wave radar, also known as high-frequency surface wave radar, operates in the high-frequency (3-30MHz) band. Utilizing the diffraction propagation characteristics of vertically polarized high-frequency electromagnetic waves along the coastal surface, it can detect targets beyond line-of-sight. Compared to other marine monitoring equipment, ground wave radar has advantages such as long observation range, large coverage area, and continuous all-weather operation, playing a crucial role in monitoring my country's exclusive economic zone, safeguarding national interests, and protecting the marine environment. Ground wave radar is classified into shore-based ground wave radar and shipborne ground wave radar based on the platform on which the radar system is deployed. Compared to shore-based ground wave radar, shipborne ground wave radar is more flexible and mobile, expanding its detection range. Furthermore, small-array shipborne ground wave radar, employing a small array of less than 100 meters, overcomes the problem of scarce land and marine resources, further expanding the applicability of shipborne ground wave radar.

[0003] While small-array shipborne ground-wave radars offer significant advantages, they face two challenges in sea clutter suppression compared to shore-based ground-wave radars: First, the size of the shipborne platform limits the number of receiving antennas that can be deployed, resulting in a smaller radar array aperture and poorer spatial resolution. Second, the movement of the shipborne platform broadens the spectrum of first-order sea clutter (hereinafter referred to as sea clutter), and the greater the platform's speed, the larger the broadening range. Many slow-moving vessels fall within the sea clutter spectrum, leading to a low signal-to-clutter-to-noise ratio and severely impacting the sea clutter suppression performance of small-array shipborne ground-wave radars. Therefore, sea clutter suppression is more difficult for small-array shipborne ground-wave radars, hindering accurate target detection in subsequent operations.

[0004] Sea clutter suppression methods for shore-based ground wave radar rely on signal differences in the time, frequency, or spatial domains. However, when a target is submerged in broadened sea clutter, making the target's frequency, range, and amplitude identical to the sea clutter, it becomes undetectable. To address the sea clutter suppression problem of small-array shipborne ground wave radar, some research has been conducted both domestically and internationally, with two representative approaches: spatial filtering and space-time joint methods. Considering the space-time coupling of sea clutter, suppression results obtained from a single spatial domain are not ideal. Therefore, using Space-time Adaptive Processing (STAP) technology to suppress sea clutter can yield better results. However, the performance of STAP depends on the accuracy of the clutter covariance matrix (CCM) estimated using sample data. In practice, the CCM of target cells is difficult to obtain directly and needs to be estimated using training samples that satisfy the Independent and Identically Distributed (IID) condition. However, the small aperture of the small-array shipborne platform array causes the range cells of nearby target cells to not meet the IID condition, resulting in insufficient uniform sample size. Therefore, improving the sea clutter suppression performance of small-array shipborne ground wave radar under small sample conditions is a key factor restricting the development of STAP technology. Sparse Recovery STAP (SR-STAP) can improve the performance of STAP technology under small sample conditions and has become a research hotspot. Sparsity is the foundation and prerequisite of SR-STAP theory and method. Research on sea clutter sparsity analysis and sparsity determination is crucial for the application of SR-STAP method and has important theoretical significance and practical application value. However, existing literature does not provide specific solution steps for clutter sparsity, especially lacking a method for determining sea clutter sparsity under the small-array shipborne ground wave radar system. Summary of the Invention

[0005] The purpose of this invention is to provide a method and application for determining the sparsity of a small-array shipborne ground wave radar based on sea clutter sparsity, which solves the problem of limited performance of sparsity recovery algorithms caused by sparsity uncertainty, and provides a theoretical basis and parameter basis for subsequent sea clutter suppression algorithms.

[0006] This method extracts the sea clutter region based on the signal model of a small-array shipborne ground-wave radar. Considering that shipborne platforms are significantly affected by wind and waves in the actual marine environment, resulting in yaw phenomena, inertial navigation data is used to determine the navigation status of the shipborne platform. Drawing on the sparsity analysis under the airborne radar system, the sea clutter ridge of the small-array shipborne ground-wave radar is extracted, and the rank of the sea clutter covariance matrix is ​​calculated. The influence of different ship speeds, yaw angles, and back lobe balances on the sea clutter sparsity is analyzed, enabling real-time estimation of the sparsity of the small-array shipborne ground-wave radar.

[0007] A method for determining sea clutter sparsity using a small-array shipborne ground-wave radar is characterized by the following steps:

[0008] Step 1: Construct a small array shipborne ground wave radar signal model.

[0009] Step 2: Extract the sea clutter region from the small array shipborne ground wave radar:

[0010] For the location A single clutter unit, making The unit vector pointing from the shipboard platform to the clutter cell is defined as follows: if the velocity vector is aligned with the array axis, there is no yaw phenomenon. The Doppler frequency of this clutter unit is defined as

[0011] ,

[0012] in, For the speed of movement of the shipborne platform, The speed of movement of the shipborne platform, It is the unit vector of the X-axis in the Cartesian coordinate system. For radar wavelength, It is the first-order Bragg scattering frequency.

[0013] Step 3: Use inertial navigation data to determine the navigation status of the shipborne platform:

[0014] Let the yaw angle be ,when At that time, it was believed that there was no yaw phenomenon; otherwise, when This would be considered a case of veergence.

[0015] Step 4: Extract sea clutter ridges from the small-array shipborne ground wave radar:

[0016] clutter spatial frequency is

[0017] ,

[0018] in, D Let be the position vector between elements of a uniform linear array. d The distance between adjacent antennas;

[0019] For the case of no yaw, the Doppler frequency can be obtained from the above formula. With spatial frequency The following relationship exists:

[0020] ,

[0021] in, For the coherent accumulation period, let The slope of the clutter line represents the number of half-element spacings the platform traverses during one PRI cycle. It can be seen that the normalized Doppler is linear in spatial frequency.

[0022] The above equation defines the trajectory in the angle-Doppler domain of clutter in the case of no yaw, which is called the "clutter ridge";

[0023] The spatial frequency of clutter remains unchanged during yaw, while the normalized Doppler frequency of clutter becomes

[0024] ,

[0025] It is a major axis of The axis and minor axis are The ellipse along the axis first The axis is translated, and then rotated around the origin.

[0026] Step 5: Construct the sea clutter characteristic spectrum and calculate the rank of the sea clutter covariance matrix of the small-array shipborne ground wave radar:

[0027] For covariance matrix Perform eigenvalue decomposition

[0028] ,

[0029] in It is an eigenvalue The diagonal matrix is ​​decomposed into eigenvectors and eigenvalues. The eigenvalues ​​are arranged in descending order to obtain the eigenspectrum. The eigenspectrum consists of eigenvalues ​​of interference and noise, where the effective rank is the number of eigenvalues ​​greater than the noise power.

[0030] For the case without yaw, the rank of the sea clutter covariance matrix is ​​derived based on Brennan's rule. The clutter rank is then expressed as:

[0031] ,

[0032] in, In the case of yaw, the Doppler frequency is no longer linearly related to the spatial frequency, and Brennan's law no longer applies. Severe yaw reduces the Doppler domain available for target detection, leading to a doubling of the number of potential clutter units. More degrees of freedom are needed to effectively suppress clutter. In this case, the number of potential clutter resolution units increases, and the clutter rank approximately doubles, as shown in the following equation:

[0033] .in, N Indicates shipborne ground wave radar N The number of channels, or array elements, is also known as the number of channels. M This indicates that the data received within the coherent accumulation period is... M A pulse signal.

[0034] Step 6: Determine the sparsity of the small array shipborne ground wave radar:

[0035] The sparsity of sea clutter in a small array shipborne ground wave radar is approximately equal to the rank of the covariance matrix. For the case of no yaw, the sparsity is... ;

[0036] In the case of yaw, the corresponding sparsity also increases with the increase of rank, and the sparsity...

[0037] .

[0038] Step 1: Constructing a small-array shipborne ground wave radar signal model, as detailed below:

[0039] Shipborne platform with constant velocity vector Motion, the true azimuth angle as an angle variable Indicates, points to A unit vector of direction The formula is given

[0040] ,

[0041] in , These are the unit vectors of the X and Y axes in a Cartesian coordinate system. Let the receiving array direction of the uniform linear array be determined by the position vectors between array elements. The specified number of array elements is The distance between adjacent antennas is When the antenna is placed horizontally, ;

[0042] Shipborne ground wave radar Each channel in the coherent accumulation period Internally received A pulse signal, after sampling and distance processing, yields a... Three-dimensional data matrix blocks, Indicates distance, , No. distance units The data matrix is

[0043] ,

[0044] At a certain point in time The array data at the location is , Represents transposition;

[0045] Will Stacked according to the slow time dimension column vectors This is a spacetime snapshot. Represented as

[0046] ,

[0047] The received target signal is represented as the target amplitude. and target spacetime guidance vector The product form, and Representing sea clutter and noise, respectively, the target space-time steering vector. Represented as

[0048] ,

[0049] ,

[0050] ,

[0051] In the formula, It is the target time-oriented vector. It is the target space guidance vector. Indicates the target Doppler frequency. This indicates the angle between the target and the main axis of the shipborne radar. This represents the Kronecker product.

[0052] The method for determining sea clutter sparsity in small-array shipborne ground wave radar is applied to sea clutter suppression in shipborne ground wave radar.

[0053] The application of the method for determining the sparsity of sea clutter in a small array shipborne ground wave radar is characterized by performing a sparse recovery space algorithm on the sea clutter of the shipborne ground wave radar.

[0054] The method for determining the sparsity of sea clutter in a small-array shipborne ground-wave radar is characterized by the inclusion of an orthogonal matching pursuit (OMP) algorithm in the sparse recovery space algorithm. This algorithm requires setting a termination condition: when the rank of the clutter in the radar system can be estimated relatively accurately, i.e., the sparsity is known, then... The appropriate number of iterations for the algorithm.

[0055] Through extensive derivation and analysis, it was discovered that the sparsity of small-array shipborne ground wave radar is affected by factors such as ship speed, yaw, and back lobe balance. Based on the influence of these factors, this invention proposes a sparsity determination method for sea clutter in small-array shipborne ground wave radar, solving the problem of limited performance of sparsity recovery algorithms caused by sparsity uncertainty. In particular, this method systematically elucidates the sparsity of sea clutter in small-array shipborne ground wave radar.

[0056] Therefore, for the above reasons, the innovation of this invention compared with the prior art is reflected in the following aspects:

[0057] 1. By constructing a small array shipborne ground wave radar sea clutter signal model, the sea clutter region and sea clutter ridge were extracted, and the influence of the shipborne platform speed on the sea clutter ridge was given, which is not done in conventional sea clutter characteristic analysis.

[0058] 2. By using inertial navigation data to determine different navigation states of the shipborne platform, the sparsity analysis and sparsity estimation of sea clutter are implemented in two typical cases to achieve sparsity estimation that is more in line with the actual situation.

[0059] 3. Based on Brennan's rule for airborne radar ground clutter, the rank of the sea clutter covariance matrix of a small-array shipborne ground wave radar was theoretically derived. Traditional clutter rank requires empirical judgment by constructing sea clutter characteristic spectra, which is complex and inaccurate.

[0060] 4. In the theoretical derivation of the rank of the sea clutter covariance matrix of a small-array shipborne ground wave radar, an analysis of the influence of the back lobe balance on the clutter rank was added. Conventional sea clutter characteristic analysis only considers the radar's forward direction, i.e., its azimuth. Clutter.

[0061] 5. In the theoretical derivation of the rank of the sea clutter covariance matrix of the small-array shipborne ground wave radar, an analysis of the influence of yaw on the clutter rank was added. By analyzing the influence of factors such as shipborne platform speed, yaw angle, and back lobe balance on the sea clutter characteristic spectrum, a more accurate estimate of sparsity can be obtained, which is closer to the actual marine environment. This estimate has been verified by the analysis of measured data from the small-array shipborne ground wave radar. Furthermore, the estimated sparsity can provide effective parameter basis for subsequent sea clutter suppression algorithms.

[0062] This invention overcomes the limitation of existing sparsity recovery algorithms caused by the uncertainty of sparsity in ground wave radar. By constructing a small array shipborne ground wave radar signal model, it comprehensively analyzes the influence of factors such as ship speed, yaw angle, and back lobe balance on sea clutter sparsity, and realizes the effective determination of sea clutter sparsity of small array shipborne ground wave radar, namely twice the theoretical value of Brennan's rule, providing a theoretical basis and parameter basis for subsequent sea clutter suppression algorithms. Attached Figure Description

[0063] Figure 1 This is a schematic diagram of the basic process of the present invention.

[0064] Figure 2 This is a schematic diagram of a small array of shipborne ground wave radar detection under the geometry of a shipborne platform.

[0065] Figure 3 A schematic diagram of a small-array shipborne ground wave radar for simplifying the coordinate system.

[0066] Figure 4 This is a schematic diagram of a small array shipborne ground wave radar for yaw detection.

[0067] Figure 5 For sea clutter ridges of small-array shipborne ground wave radar at different ship speeds,

[0068] Among them, (a) the boat speed is 0 m / s, (b) the boat speed is 2.5 m / s, (c) the boat speed is 5 m / s, and (d) the boat speed is 7.5 m / s.

[0069] Figure 6 For sea clutter ridges of small-array shipborne ground wave radars at different yaw angles,

[0070] Among them, (a) the yaw angle is 0 degrees, (b) the yaw angle is 5 degrees, (c) the yaw angle is 45 degrees, and (d) the yaw angle is 90 degrees.

[0071] Figure 7 The sea clutter ridge for a small array shipborne ground wave radar during yaw.

[0072] Figure 8 This is the array element pattern of a small-array shipborne ground wave radar.

[0073] Figure 9 The characteristic spectrum of sea clutter at different ship speeds.

[0074] Figure 10 for At that time, the characteristic spectrum of sea clutter under different back lobe balances.

[0075] Figure 11 The characteristic spectrum of sea clutter at different yaw angles.

[0076] Figure 12for At that time, the characteristic spectrum of sea clutter under different back lobe balances.

[0077] Figure 13 The sea clutter characteristic spectrum is from the measured data. Detailed Implementation

[0078] This invention presents a technical solution for determining the sparsity of sea clutter in a small-array shipborne ground-wave radar based on sparsity. A flowchart illustrating the sparsity determination process is shown below. Figure 1 This includes the following steps:

[0079] Step 1: Construct a small array shipborne ground wave radar signal model:

[0080] Each ship target can be considered a point target in a single direction. Sea clutter consists of numerous independent clutter sources, evenly distributed around the radar at the azimuth angle. The shipborne platform moves at a constant velocity vector...

[0081] Motion. Angular variable. This refers to the actual azimuth angle, pointing towards A unit vector of direction Given by equation (1):

[0082] (1)

[0083] in , These are the unit vectors of the X and Y axes in a Cartesian coordinate system. Let the receiving array direction of the uniform linear array be determined by the position vectors between array elements. The specified number of array elements is The distance between adjacent antennas is When the antenna is placed horizontally, .

[0084] Shipborne ground wave radar Each channel in the coherent accumulation period Internally received A pulse signal, which is obtained after sampling and distance processing, yields a... Three-dimensional data matrix blocks, Indicates distance. (The first...) distance units The data matrix is

[0085] (2)

[0086] At a certain point in time The array data at the location is , This represents transposition.

[0087] Will Stacked according to the slow time dimension column vectors This is a spacetime snapshot. It can be represented as

[0088] (3)

[0089] The received target signal can be represented as the amplitude of the target. and its spacetime steering vector The product form, and These represent sea clutter and noise, respectively. Target spacetime steering vector. Represented as

[0090] , (4)

[0091] , (5)

[0092] , (6)

[0093] In the formula, It is the target time-oriented vector. It is the target space guidance vector. Indicates the target Doppler frequency. This indicates the angle between the target and the main axis of the shipborne radar. This represents the Kronecker product.

[0094] Step 2: Extract the sea clutter region from the small array shipborne ground wave radar:

[0095] In small-array shipborne ground wave radar, due to the movement of the radar platform, the Doppler frequency center of sea clutter is no longer fixed and will change with the speed of the platform and the azimuth of the antenna, which will cause the clutter spectrum to broaden.

[0096] For small-array shipborne ground-wave radars, the movement of the shipborne platform causes a shift in the positive and negative first-order Bragg peaks, considering the azimuth... A single clutter unit, making Let be the unit vector pointing from the platform to this clutter cell. Assume the velocity vector is aligned with the array axis, i.e., there is no yaw. The Doppler frequency of this clutter element is defined as...

[0097] (7)

[0098] in, For the speed of movement of the shipborne platform, The speed of movement of the shipborne platform, The first-order Bragg scattering frequency is given by equation (7). Equation (7) shows the spatiotemporal coupling relationship of sea clutter in a small-array shipborne ground wave radar, i.e., the azimuth sine of the sea clutter scatterer. With sea clutter Doppler frequency They are linearly coupled.

[0099] Sea waves in different directions have different first-order Bragg frequencies. Radar, due to its certain beamwidth, introduces different offsets to clutter in different directions, resulting in spectral broadening. As can be seen from equation (7), under ideal conditions, the platform motion will cause sea clutter to broaden from a single frequency value to cover the Doppler domain. The range.

[0100] Step 3: Use inertial navigation data to determine the navigation status of the shipborne platform:

[0101] In real marine environments, shipborne platforms are often affected by wind and waves, resulting in yaw. This affects the sparsity of small array shipborne ground wave radar. Inertial navigation data is used to determine the different navigation states of the shipborne platform.

[0102] Let the yaw angle be ,when At that time, it was believed that there was no yaw phenomenon; otherwise, when This would be considered a case of veergence.

[0103] Step 4: Extract sea clutter ridges from the small-array shipborne ground wave radar:

[0104] clutter spatial frequency is

[0105] (8)

[0106] For the case of no yaw, the normalized Doppler frequency can be obtained from formulas (7) and (8). With spatial frequency The following relationship exists:

[0107] (9)

[0108] make The slope of the clutter line represents the number of half-element spacings the platform traverses during one PRI cycle. It can be seen that the normalized Doppler is linear in spatial frequency.

[0109] Equation (9) defines the clutter ridge in the angle-Doppler domain under no-yaw conditions. Generally, the clutter ridge can span a part of the Doppler domain or the entire Doppler domain, depending on the platform speed, operating wavelength, and radar PRF.

[0110] The spatial frequency of clutter remains unchanged during yaw, while the normalized Doppler frequency of clutter becomes

[0111] (10)

[0112] Yaw angle is When, by transforming equation (10), then Further processing of the above equations yields...

[0113] (11)

[0114] Furthermore, transforming equation (11) into elliptic form, it is expressed as:

[0115] (12)

[0116] In the above formula, non-zero The existence of the term indicates that a major axis is The axis and minor axis are The ellipse along the axis first The axis is translated, and then rotated around the origin. According to EW Swokowski's published literature, the rotation angle of this type of oblique ellipse is... satisfy

[0117] (13)

[0118] The rotation angle is from The axis rotates counterclockwise. Let... and These are the lengths of the major and minor axes, respectively. Using the coordinate transformation formula again, we can obtain the information about the major and minor axes of the ellipse:

[0119] (14)

[0120] in

[0121] (15)

[0122] Therefore, the clutter ridges in the yaw case are respectively along... After the axis is translated vertically, it then passes through... The standard equation of two oblique ellipses rotated at an angle is:

[0123] (16)

[0124] When yaw angle When it becomes non-zero, the back lobe portion of the clutter ridge becomes more pronounced; For example, in some cases there are essentially two clutter ridges, such as at the target angle. At this time, there are clutters at two Doppler frequencies, one from the front lobe and one from the back lobe. Therefore, in the subsequent analysis, we must consider not only the front lobe clutter but also the back lobe clutter.

[0125] Step 5: Construct the sea clutter characteristic spectrum and calculate the rank of the sea clutter covariance matrix of the small-array shipborne ground wave radar:

[0126] For covariance matrix Perform eigenvalue decomposition

[0127] (17)

[0128] in It is an eigenvalue The diagonal matrix can be decomposed into eigenvectors and eigenvalues. Arranging the eigenvalues ​​in descending order yields the eigenspectrum, which consists of eigenvalues ​​of interference and noise. The effective rank (the number of eigenvalues ​​greater than the noise power) determines the minimum degrees of freedom and minimum sample number required by the filter. Therefore, it is necessary to calculate the rank of the sea clutter covariance matrix of the small array shipborne ground wave radar.

[0129] However, in reality, this rank is unknown. It is necessary to analyze the sparsity of first-order sea clutter in shipborne ground-wave radar based on Brennan's rule to derive the theoretical rank of the sea clutter covariance matrix, assuming the platform velocity vector... With antenna array axis vector When perfectly aligned, i.e., without yaw, the clutter rank is expressed as:

[0130] (18)

[0131] in, However, in the actual marine environment, shipborne platforms are often affected by wind and waves, and their direction of motion may be slightly deviated from the array axis, resulting in yaw, which leads to a significant increase in clutter rank, exceeding the clutter rank predicted by formula (18).

[0132] All the preceding analyses that lead to the clutter covariance matrix remain valid under yaw conditions, except that the normalized Doppler frequency of a single clutter resolution cell changes from (9) to (10), causing the normalized Doppler to no longer have a linear relationship with the spatial frequency. Brennan's rule, however, relies on a linear relationship between Doppler and spatial frequency. That is no longer applicable.

[0133] Severe backlobe clutter and yaw reduce the Doppler domain available for target detection. In other words, yaw doubles the number of potential clutter units, requiring more degrees of freedom to effectively suppress clutter. At this point, the number of potential clutter resolution units increases, and the clutter rank increases by about twice, as shown in Equation (19):

[0134] (19).

[0135] Step 6: Determine the sparsity of the small array shipborne ground wave radar:

[0136] The sparsity of sea clutter in a small array shipborne ground wave radar is approximately equal to the rank of the covariance matrix. For the case of no yaw, the sparsity is... .

[0137] In the case of yaw, the corresponding sparsity also increases with the increase of rank, and the sparsity... .

[0138] In subsequent sea clutter suppression, sparse recovery space-time adaptive processing is required. Sparse recovery algorithms, such as the Orthogonal Matching Pursuit (OMP) algorithm, need to set an iteration termination condition. When the rank of the clutter in the radar system can be estimated relatively accurately, i.e., the sparsity is known, the iteration termination condition can be set to the number of iterations being equal to or slightly greater than the sparsity. Therefore, it can be considered that... It is the appropriate number of iterations for the algorithm.

[0139] Example

[0140] Step 1: Figure 2 , 3 This is a schematic diagram of a small-array shipborne ground wave radar detection system. Figure 2 Let 3 represent the geometry of the shipborne platform, and 3 represent a simplified coordinate system. Unit vectors in the simplified coordinate system can be used to model the signal of a small-array shipborne ground-wave radar. For shipborne ground-wave radar... Each channel in the coherent accumulation period Internally received A pulse signal, which is obtained after sampling and distance processing, yields a... Three-dimensional data matrix blocks, Indicates distance. (The first...) distance units Data Matrix Stacked according to the slow time dimension column vectors This is a spacetime snapshot. It can be represented as the superposition of the target signal, sea clutter signal, and noise signal.

[0141] Step 2: Based on the constructed small-array shipborne ground wave radar signal model, extract the sea clutter region of the small-array shipborne ground wave radar. For the small-array shipborne ground wave radar, the Doppler frequency of the clutter element without yaw phenomenon... Platform movement causes frequency broadening of sea clutter, and the sea clutter region is... .

[0142] Step 3: Figure 4 This is a schematic diagram of a small-array shipborne ground-wave radar detection under yaw conditions. The navigation status of the shipborne platform is determined using inertial navigation data, with the yaw angle set as... ,when At that time, it was believed that there was no yaw phenomenon; otherwise, when This would be considered a case of veergence.

[0143] Step 4: Based on Step 3, and combining the measured peak values ​​with the theoretical spatial-Doppler frequencies, extract the sea clutter ridges for both the no-yaw and yaw scenarios. The result can be obtained from Equation 9 in Step 4. Figure 5 The results shown Figure 5 Four examples of sea clutter ridges for a small-array shipborne ground-wave radar at different ship speeds are shown, with platform speeds of 0 m / s, 2.5 m / s, 5 m / s, and 7.5 m / s. It can be seen that, with... With the increase in doppler density, the main lobe clutter occupies a larger portion of the Doppler domain. In this case, side lobe clutter at multiple angles may have the same Doppler density as the target, making suppression more difficult. From Equation 10 in step 4, we can obtain... Figure 6 The results shown Figure 6 For sea clutter ridges at different yaw angles, the portion of the ellipse corresponding to the front half of the antenna space is drawn with a solid blue line, and the portion corresponding to the back lobe clutter is drawn with a solid yellow line. The aligned case is considered a degenerate ellipse, where the front and back lobes are located at their tops. It can be seen that when the yaw angle... When it becomes non-zero, the posterior lobe becomes more prominent. Figure 7 When yaw Partial illustration of sea clutter ridges shows that at the target angle At this time, clutter exists at two Doppler frequencies, one from the front lobe and one from the back lobe, essentially meaning there are two clutter ridges. Therefore, severe back lobe clutter and yaw reduce the Doppler domain available for target detection; that is, yaw doubles the number of potentially interfering clutter elements. Figure 8 This is the array element radiation pattern, which is cosine in azimuth. Black represents the front lobe region, and the back lobe region is labeled with the back lobe level. They are -10 dB, -25 dB, -45 dB, -50 dB, and -85 dB, respectively.

[0144] Step 5: Based on Step 3, calculate the rank of the sea clutter covariance matrix for both the no-yaw and yaw cases. This can be obtained from formulas 17, 18, and 19 in Step 5. Figure 9-13 The results shown, in which, Figure 9The characteristic spectrum of sea clutter at different ship speeds is represented by the dashed line obtained from Brennan's rule. It can be seen that the characteristic spectrum exhibits a gradually decreasing trend, and Brennan's rule accurately predicts the inflection points in the characteristic spectrum. It should also be noted that the rank increases with increasing platform speed. Figure 10 for The characteristic spectrum of sea clutter at different back lobe levels was obtained with the shipboard platform traveling at a speed of 3 m / s. It can be seen that the tail of the characteristic spectrum shows a level decrease that is essentially linearly related to the back lobe level. This part of the characteristic spectrum is entirely caused by the back lobe portion of the clutter ridge. The effect of different back lobe levels is negligible under no-yaw conditions, and the numerical level of the clutter is approximately equal to the level predicted by Brennan's rule. Figure 11 The characteristic spectra of sea clutter at different yaw angles are given, with the shipborne platform speed at 3 m / s. For all non-zero... Due to the presence of back lobe clutter ridges, the number of non-zero eigenvalues ​​is approximately twice that expected. Figure 12 for The sea clutter characteristic spectrum at different back lobe levels, with a yaw angle of 50° and a platform speed of 3 m / s, shows a level decrease at the tail of the characteristic spectrum that is essentially linearly related to the back lobe level. This part of the characteristic spectrum is entirely caused by the back lobe portion of the clutter ridge. When the back lobe level is very low, the clutter rank is approximately equal to the rank predicted by Brennan's rule. If the back lobe level is high, the clutter rank will increase by about double. Furthermore, it can be seen that when the back lobe balance is less than -50 dB, the sea clutter characteristic spectrum tends to be uniform, at which point the influence of the back lobe region is negligible. Figure 13 The image shows the sea clutter characteristic spectrum based on measured data, with a yaw angle of 3° and a platform speed of 4.4 m / s. It can be seen that the inflection point in the characteristic spectrum is located at twice the prediction level of Brennan's rule.

[0145] Step 6: Based on steps 4 and 5, the rank of the sea clutter covariance matrix of the small array shipborne ground wave radar is obtained. For the case of no yaw, the sparsity is... For the case of yaw, the corresponding sparsity also increases with the increase of rank, making... The sparsity of the small-array shipborne ground-wave radar was finally determined.

Claims

1. A method for determining sea clutter sparsity using a small-array shipborne ground-wave radar, characterized by: Includes the following steps: Step 1: Construct a small array shipborne ground wave radar signal model; Step 2: Extract the sea clutter region from the small array shipborne ground wave radar: For the location A single clutter unit, making The unit vector pointing from the shipboard platform to the clutter cell is defined as follows: if the velocity vector is aligned with the array axis, there is no yaw phenomenon. The Doppler frequency of this clutter unit is defined as ， in, For the speed of movement of the shipborne platform, The speed of movement of the shipborne platform, It is the unit vector of the X-axis in the Cartesian coordinate system. For radar wavelength, The first-order Bragg scattering frequency; Step 3: Use inertial navigation data to determine the navigation status of the shipborne platform: Let the yaw angle be ,when At that time, it was believed that there was no yaw phenomenon; otherwise, when This would be considered a case of veergence; Step 4: Extract sea clutter ridges from the small-array shipborne ground wave radar: clutter spatial frequency is ， in, D Let be the position vector between elements of a uniform linear array. d The distance between adjacent antennas; For the case of no yaw, the Doppler frequency can be obtained from the above formula. With spatial frequency The following relationship exists: ， in, For the coherent accumulation period, let The slope of the clutter line represents the number of half-element spacings the platform traverses during one PRI cycle. It can be seen that the normalized Doppler is linear in spatial frequency. The above equation defines the trajectory in the angle-Doppler domain where clutter exists without yaw, and is called the "clutter ridge". The spatial frequency of clutter remains unchanged during yaw, while the normalized Doppler frequency of clutter becomes ， It is a major axis of The axis and minor axis are The ellipse along the axis first Translate along the axis, then rotate around the origin; Step 5: Construct the sea clutter characteristic spectrum and calculate the rank of the sea clutter covariance matrix of the small-array shipborne ground wave radar: For covariance matrix Perform eigenvalue decomposition ， in It is an eigenvalue The diagonal matrix is ​​decomposed into eigenvectors and eigenvalues. The eigenvalues ​​are arranged in descending order to obtain the eigenspectrum. The eigenspectrum consists of eigenvalues ​​of interference and noise, where the effective rank is the number of eigenvalues ​​greater than the noise power. For the case without yaw, the rank of the sea clutter covariance matrix is ​​derived based on Brennan's rule. The clutter rank is then expressed as: ， in, In the case of yaw, the Doppler frequency is no longer linearly related to the spatial frequency, and Brennan's law no longer applies. Severe yaw reduces the Doppler domain available for target detection, leading to a doubling of the number of potential clutter units. More degrees of freedom are needed to effectively suppress clutter. In this case, the number of potential clutter resolution units increases, and the clutter rank approximately doubles, as shown in the following equation: ， N Indicates shipborne ground wave radar N The number of channels, or array elements, is also known as the number of channels. M This indicates that the data received within the coherent accumulation period is... M A pulse signal; Step 6: Determine the sparsity of the small array shipborne ground wave radar: The sparsity of sea clutter in a small array shipborne ground wave radar is approximately equal to the rank of the covariance matrix. For the case of no yaw, the sparsity is... ; In the case of yaw, the corresponding sparsity also increases with the increase of rank, and the sparsity... 。 2. The method for determining sea clutter sparsity of a small-array shipborne ground wave radar as described in claim 1, characterized in that step 1: constructing a small-array shipborne ground wave radar signal model, specifically as follows: Shipborne platform with constant velocity vector Motion, the true azimuth angle as an angle variable Indicates, points to A unit vector of direction Given by the following formula ， in , These are the unit vectors of the X and Y axes in a Cartesian coordinate system. Let the receiving array direction of the uniform linear array be determined by the position vectors between array elements. The specified number of array elements is The distance between adjacent antennas is When the antenna is placed horizontally, ; Shipborne ground wave radar Each channel in the coherent accumulation period Internally received A pulse signal, after sampling and distance processing, yields a... Three-dimensional data matrix blocks, Indicates distance, , No. distance units The data matrix is ， in, At a certain point in time The array data at the location is , Represents transpose; Will Stacked according to the slow time dimension column vectors This is a spacetime snapshot. Represented as ， The received target signal is represented as the target amplitude. and target spacetime guidance vector The product form, and Representing sea clutter and noise, respectively, the target space-time steering vector. Represented as ， ， ， In the formula, It is the target time-oriented vector. It is the target space guidance vector. Indicates the target Doppler frequency. This indicates the angle between the target and the main axis of the shipborne radar. This represents the Kronecker product.

3. The application of the method described in claim 1 or 2 in the suppression of sea clutter in shipborne ground wave radar.

4. The application as described in claim 3, characterized in that: A sparse recovery space algorithm is used to process sea clutter from shipborne ground wave radar.

5. The application as described in claim 4, characterized in that: The sparse recovery space algorithm includes Orthogonal Matching Pursuit (OMP). This algorithm requires setting a condition for the iteration to terminate. When the rank of clutter in the radar system can be estimated relatively accurately, i.e., the sparsity is known, then... The appropriate number of iterations for the algorithm.

Images