Air target classification method based on uncertainty interval estimation physical feature extraction

Abstract

This invention discloses an aerial target classification method based on uncertainty interval estimation for physical feature extraction. It addresses the problems of low tolerance for feature fluctuations and susceptibility to misclassification in existing technologies, achieving high-precision feature extraction and robust classification. The method includes: constructing a modular, three-dimensional parametric geometric model, describing the module size layout using parameter vectors; determining the imaging projection matrix based on radar tracking and satellite orbit information, acquiring two-dimensional radar images, and establishing a three-dimensional-to-two-dimensional geometric mapping; projecting the model onto a two-dimensional plane using the projection matrix, and obtaining estimated three-dimensional physical features by minimizing the matching error between the projected contour and the target edge contour; establishing an explicit observation equation to describe the mapping relationship between feature values ​​and observation points, thereby correcting feature value errors and quantifying the uncertainty interval; and integrating the corrected feature values ​​and uncertainty interval into a classifier to achieve robust classification of aerial targets.

Description

Technical Field

[0001] This invention relates to the field of radar signal processing and target classification technology, and in particular to an aerial target classification method based on uncertainty interval estimation physical feature extraction. Background Technology

[0002] Radar imaging technology can acquire high-resolution images of aerial targets under all-weather, all-time, and long-range conditions. These images contain rich geometric structures and electromagnetic scattering characteristics of the targets, providing key data support for the classification of typical aerial targets such as early warning aircraft, bombers, and tankers.

[0003] However, target radar imaging can essentially be understood as the vertical projection of the target's three-dimensional scattering points onto the two-dimensional radar imaging plane. Due to the influence of observation geometry, the radar imaging plane usually differs significantly from the principal plane of the fuselage, which is composed of the target's fuselage and wings. This difference leads to a significant deviation between the target's two-dimensional projected size in the image and its true three-dimensional size. Taking the wing as an example, its projected length may be significantly compressed at a specific observation angle. Furthermore, the projection process may disrupt the symmetry of the wing in the two-dimensional radar image, resulting in deviations in key geometric features directly extracted from the image, such as wingspan, fuselage length, and wing-to-body ratio, thus affecting classification performance.

[0004] Furthermore, traditional classification methods typically treat the physical features extracted from images as precise point estimates and construct classification decision boundaries accordingly. However, in actual radar observations, due to measurement noise interference and residual algorithm errors, the extracted physical features are not deterministic values ​​but rather fluctuating distributions within a certain range. Traditional methods ignore the inherent uncertainty of the features themselves, causing samples to easily cross the classification boundary when the features fluctuate slightly, resulting in classification errors and severely impacting the robustness of the classification algorithm.

[0005] Existing methods for classifying and recognizing aerial targets based on radar imaging can be broadly categorized into traditional methods based on manually designed features and end-to-end methods based on deep learning. In traditional methods, researchers typically extract physical features such as geometric structure, scattering center, and texture statistics from radar images, and then use classifiers such as template matching or support vector machines to achieve target recognition. Deep learning methods, on the other hand, utilize neural networks to automatically learn discriminative features and attempt to introduce scattering mechanisms to improve the interpretability of the model.

[0006] In the technical approach closest to this invention, which utilizes target priors to construct parametric models, representative work such as Chen Yujie et al.'s "A Method for Extracting Aircraft Target Features from SAR Images Based on a Variable Parametric Geometric Model" proposes a method that simplifies the aircraft into a geometric assembly composed of components such as the fuselage, wings, and tail by constructing a parametric model describing the aircraft's outline. This method constructs an objective function to measure the fit between the model projection and the image region for input measured image slices, and uses a genetic algorithm to search for the optimal solution in a multidimensional parameter space, thereby extracting geometric features such as fuselage length, wingspan, and sweep angle for subsequent classification tasks. Furthermore, Xin Meng et al., in their patent "A Method for Estimating the Attitude and Size Features of Aerial Targets Based on ISAR Image Sequences," further explored obtaining physical line features through corner detection and convex hull extraction, and constructing a projection matrix from the three-dimensional structure to the two-dimensional imaging plane, thereby achieving joint inversion estimation of the target's three-dimensional attitude and true physical size in the image sequence.

[0007] While existing methods have made progress in physical feature extraction, they still have the following limitations: First, most existing methods do not fully consider the three-dimensional geometric relationships of radar imaging, leading to a significant deviation between the estimated planar projection size and the actual physical size of the target. Second, existing research focuses primarily on extracting geometric features such as the fuselage and wings, lacking descriptions of key structural features such as the top-mounted disc antenna of the early warning aircraft, resulting in insufficient target representation capabilities. Furthermore, existing technologies generally treat feature extraction results as "point estimates" with definite spatial positions, and construct classification decision boundaries accordingly. However, due to measurement noise and algorithm residuals, features actually exhibit a probability distribution constrained by the error interval. Ignoring this inherent uncertainty leads to a low tolerance of the classification decision boundary for feature fluctuations, easily causing misjudgments and affecting the robustness of the classification algorithm. Summary of the Invention

[0008] This invention provides an aerial target classification method based on uncertainty interval estimation physical feature extraction, which solves the problem of low tolerance for feature fluctuations and easy misjudgment in the prior art, and achieves high-precision extraction and robust classification of the three-dimensional physical features of aerial targets.

[0009] This invention provides an aerial target classification method based on physical feature extraction using uncertainty interval estimation, the method comprising: A modular design is adopted to construct a three-dimensional parametric geometric model of the aerial target, and the structural dimensions and spatial layout of each module are described by parametric vectors. Based on radar tracking information and satellite orbital mechanics principles, an imaging projection matrix is ​​determined, and a two-dimensional radar image of the target is obtained according to the imaging projection matrix; wherein, the imaging projection matrix is ​​used to establish the geometric mapping relationship from the three-dimensional target to the two-dimensional imaging plane; The stereo parameterized geometric model is projected onto a two-dimensional plane using the imaging projection matrix. By minimizing the matching error between the projected contour of the stereo parameterized geometric model and the target edge contour in the two-dimensional radar image, the estimated value of the stereo physical features of the airborne target is obtained by inversion. An explicit observation equation is established to describe the mapping relationship between the estimated value of the three-dimensional physical features of the airborne target and the observation points in the edge contour of the target. Based on the explicit observation equation, the estimated value of the three-dimensional physical features of the airborne target is corrected for error, and the uncertainty range of the feature parameters is quantified. The estimated values ​​of the three-dimensional physical features of the aerial target and the uncertainty interval are incorporated into the classifier to achieve robust classification of aerial targets.

[0010] One or more technical solutions provided in this invention have at least the following technical effects or advantages: This invention first employs a modular design to construct a three-dimensional parametric geometric model of an aerial target, describing the structural dimensions and spatial layout of each module using parameter vectors. This three-dimensional model includes fuselage units represented by cylinders, wing units represented by quadrilateral facets, and a top antenna unit represented by a circular plane, comprehensively describing the target's three-dimensional structure. In particular, it incorporates key identification structures of aircraft such as early warning aircraft, laying a solid foundation for subsequent accurate feature extraction. The modular design allows the model to flexibly adapt to different aircraft types, effectively improving its generalization ability and applicability, and solving the problem of incomplete description of key target structures caused by the use of two-dimensional planar models in existing technologies. Next, based on radar tracking information and satellite orbital mechanics principles, an imaging projection matrix is ​​determined, and a two-dimensional radar image of the target is obtained according to the imaging projection matrix. The imaging projection matrix is ​​used to establish the geometric mapping relationship from the three-dimensional target to the two-dimensional imaging plane. By accurately constructing a projection matrix, the projected geometric relationship of a 3D target on a 2D plane during radar imaging can be precisely described. This corrects the projection size deviation caused by differences in observation perspective, providing an accurate geometric transformation basis for subsequent inversion of the true 3D physical size from the image. This overcomes the defect of traditional methods that ignore 3D imaging geometry, leading to size estimation distortion. Then, the stereo parameterized geometric model is projected onto a 2D plane using the imaging projection matrix. By minimizing the matching error between the projected contour of the stereo parameterized geometric model and the target edge contour in the 2D radar image, the estimated value of the airborne target's stereo physical features is obtained. This step uses an objective function based on bidirectional distance constraints, which can effectively adapt to the actual situation of sparse, missing, or unevenly dense target contour points in radar images, improving the robustness of contour matching. Iterative solutions using nonlinear optimization methods such as genetic algorithms obtain physical feature parameters that are highly close to the true 3D size of the target, significantly improving the accuracy of feature extraction and solving the problem of geometric size deviation caused by ignoring 3D projection relationships in existing technologies. Subsequently, an explicit observation equation is established to describe the mapping relationship between the estimated values ​​of the three-dimensional physical features of the aerial target and the observation points in the target edge contour. Based on the explicit observation equation, the estimated values ​​of the three-dimensional physical features of the aerial target are corrected for errors, and the uncertainty interval of the feature parameters is quantified. By constructing a differentiable explicit observation equation through a fixed attribution strategy, the non-differentiability problem caused by the nearest neighbor operation in the contour matching objective function is effectively solved, creating conditions for subsequent error propagation analysis. Based on the linearized observation equation, the weighted least squares method is used to solve for the parameter correction amount, and the error propagation law is used to map the fitting residual of the image layer into the covariance matrix of the feature parameters. This extends the traditional deterministic point estimation to an interval estimation that includes confidence information, quantifies the credibility of the feature extraction results, makes up for the defect of traditional methods ignoring the inherent uncertainty of features, and provides key support for subsequent robust classification.Finally, the estimated values ​​of the three-dimensional physical features of the aerial target and the uncertainty interval are integrated into the classifier to achieve robust classification of the aerial target. This step models each sample as a multivariate Gaussian distribution, using the corrected feature estimate as the mean and the covariance matrix as the uncertainty measure, and incorporates them into the expectation hinge loss function of the support vector machine classifier for optimization. This makes the classification decision boundary more tolerant to fluctuations in feature values, significantly improving the accuracy and robustness of target classification under complex observation conditions, and effectively solving the problem of misclassification caused by feature fluctuations in existing technologies. Through the organic combination of the above steps, this invention achieves high-precision extraction and robust classification of the three-dimensional physical features of aerial targets, which has important application value in the field of radar imaging target recognition. Attached Figure Description

[0011] Figure 1 A flowchart illustrating the steps of an aerial target classification method based on uncertainty interval estimation physical feature extraction provided in this embodiment of the invention; Figure 2 A schematic diagram of a stereoparametric model provided in an embodiment of the present invention; Figure 3 Simplified external diagrams of three typical aircraft types provided for embodiments of the present invention; Figure 4 This is a flowchart illustrating the construction of a projection matrix that combines the orbital motion characteristics and tracking information of a spaceborne radar, as provided in an embodiment of the present invention. Figure 5 CAD model diagrams of three types of targets provided in embodiments of the present invention; Figure 6 These are simulation images of the E3-A early warning aircraft from different observation angles provided in this embodiment of the invention. Figure 7 These are simulation images of the B-52 early warning aircraft from different observation angles provided in this embodiment of the invention. Figure 8 These are simulation images of the IL-78 refueling aircraft from different viewing angles provided in this embodiment of the invention. Figure 9 The matching result diagram between the parameterized model and the E3-A early warning aircraft provided in the embodiments of the present invention; Figure 10 The matching result diagram between the parameterized model and the B-52 bomber provided in the embodiments of the present invention; Figure 11 The matching result diagram between the parameterized model and the IL-78 refueling aircraft provided in the embodiments of the present invention; Figure 12 This is a schematic diagram of the target edge point contour extracted from an image according to an embodiment of the present invention; Figure 13This is a diagram showing the correspondence between observation points and model contours provided in an embodiment of the present invention. Figure 14 The confusion matrix diagram of each method when SNR=20dB is provided for the embodiments of the present invention. Detailed Implementation

[0012] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0013] This invention provides an aerial target classification method based on physical feature extraction using uncertainty interval estimation. (See also...) Figure 1 The method includes the following steps S101 to S105.

[0014] S101 adopts a modular design, constructs a three-dimensional parametric geometric model of the aerial target, and describes the structural dimensions and spatial layout of each module through parameter vectors; Specifically, in step S101, a modular design is adopted to construct a three-dimensional parametric geometric model of the air target, and the structural dimensions and spatial layout of each module are described by parameter vectors, including the following steps S1011 to S1012.

[0015] S1011, construct a three-dimensional parametric geometric model consisting of fuselage units represented by cylinders, wing units represented by quadrilateral surface elements, and top antenna units represented by circular planes. S1012 describes the structural substructure and spatial layout of the fuselage unit, wing unit, and top antenna unit using parameter vectors.

[0016] For example, based on the structural commonalities of various aerial targets—that is, all aircraft consist of a fuselage, left and right wings, and possibly a top antenna—a three-dimensional geometric parameterized model is constructed to achieve a mathematical representation of the aerial target. For instance... Figure 2 As shown, the model adopts a modular design principle and is mainly composed of the following three geometric units: First, a cylinder is used to represent the main body of the fuselage, and the proportion of different aircraft models is adapted by parameterizing the axial and radial directions; Second, a quadrilateral surface element structure is used to simulate the wings symmetrically distributed on both sides of the fuselage, and the wings can be transformed into typical airfoils such as rectangles and trapezoids by adjusting the parameters; At the same time, a circular planar component is introduced to represent the top radar antenna equipment to ensure that any key structures that may exist are effectively represented.

[0017] The parameter vector describing this parameterized geometric model is: (1.1) in, There are 10 components, which are the length of the fuselage. and the width of the fuselage wingtip chord length wing root width The contact point between the wing and the fuselage is located relative to the fuselage. The length of the swept wings The trailing edge sweep angle of the wing Considering the symmetrical distribution of the wings, the above parameters are shared between the left and right wings. Furthermore, to characterize the layout of the top antenna assembly, the position of the center of the circle relative to the fuselage is defined. Height of the fuselage circle diameter Based on the above definition, this invention can adaptively adjust... The numerical values ​​are used to simulate the structural changes of different aerial targets, for example, when the wing sweep angle... As the size decreases, the trailing edge of the wing extends rearward, causing the airfoil to gradually evolve from a straight wing to a typical swept wing. For example... Figure 3 The third image, when This allows for the formation of a delta wing structure, a typical feature of bombers. Similarly, adjusting the diameter of the top antenna... The presence or absence of an antenna can be controlled, such as... Figure 3 The antenna device in the second image is an important classification feature of early warning aircraft. Figure 3 Three scenarios of parametric geometric models are presented as simplified aircraft to simulate several typical aerial targets studied in this invention.

[0018] S102, based on radar tracking information and satellite orbital mechanics principles, determines the imaging projection matrix and obtains a two-dimensional radar image of the target based on the imaging projection matrix; wherein, the imaging projection matrix is ​​used to establish the geometric mapping relationship from the three-dimensional target to the two-dimensional imaging plane; Specifically, in step S102, the imaging projection matrix is ​​determined based on radar tracking information and satellite orbital mechanics principles, including the following steps S1021 to S1023.

[0019] S1021, based on the target position vector and target velocity vector in radar tracking information, constructs the target body coordinate system, and based on the principle of satellite orbit mechanics, uses the six orbital roots to calculate the satellite position vector and satellite velocity vector in the Earth-fixed coordinate system; S1022, Based on the satellite position vector and the target position vector, the line-of-sight vector of the satellite relative to the target is calculated, and the line-of-sight vector is projected onto the target body coordinate system to obtain the radar line-of-sight vector in the target body coordinate system; S1023, based on the change in radar line of sight during the imaging accumulation time, determine the range dimension unit vector and azimuth dimension unit vector of the imaging plane, and form the imaging projection matrix by the range dimension unit vector and the azimuth dimension unit vector.

[0020] For example, firstly, based on radar tracking information of the target, the target position vector is used... With the target velocity vector Construct a target body coordinate system. Specifically, with the target's center of mass as the origin, take the direction of the target's velocity vector as the Y-axis to represent the fuselage axis, take the direction perpendicular to the plane formed by the velocity vector and the geocentric vector as the X-axis to represent the wing span, and determine the Z-axis according to the right-hand rule to represent the vertical direction of the fuselage.

[0021] Secondly, such as Figure 4 Based on the principles of satellite orbital mechanics, the real-time position and velocity of the satellite in the Earth-fixed coordinate system are calculated using the six orbital elements. The line-of-sight vector of the satellite relative to the target is calculated, which is equal to the satellite position vector minus the target position vector. This line-of-sight vector is then projected and transformed into the previously constructed target body coordinate system using a coordinate transformation matrix, thus obtaining the radar line-of-sight vector in the target body coordinate system.

[0022] Suppose that during the imaging accumulation time, the azimuth and elevation angles of the radar line of sight at the intermediate time are respectively... and Then the radar line-of-sight vector at the intermediate time point is expressed as: (1.2) The distance dimension of the imaging plane is a unit vector. The radar line of sight is usually taken at the midpoint of the imaging accumulation time. Then, the radar line-of-sight vector in the target's coordinate system is represented as: (1.3) Unit vector of azimuth dimension Perpendicular to the distance dimension and radar line of sight change The plane formed is: (1.4) Radar line-of-sight change The direction can be determined by the initial radar line-of-sight vector corresponding to the imaging accumulation time. and termination radar line-of-sight vector Determined by the right-hand rule, i.e. The direction is: (1.5) Based on the above analysis, it can be concluded that by combining the satellite's orbital motion characteristics with radar tracking information of the target, the range dimension unit vector can be determined. and azimuth unit vector ,and Then by and The projection plane is formed, and the image projection matrix is: (1.6) in, , Represents the identity matrix.

[0023] S103: The stereo parameterized geometric model is projected onto a two-dimensional plane using the imaging projection matrix. By minimizing the matching error between the projected contour of the stereo parameterized geometric model and the target edge contour in the two-dimensional radar image, the estimated value of the stereo physical features of the air target is obtained by inversion. Specifically, in step S103, the stereo parameterized geometric model is projected onto a two-dimensional plane using an imaging projection matrix. By minimizing the matching error between the projected contour of the stereo parameterized geometric model and the target edge contour in the two-dimensional radar image, the estimated value of the stereo physical features of the airborne target is obtained through inversion, including the following steps S1031 to S1034.

[0024] S1031, using the imaging projection matrix, the key points of each component in the three-dimensional parametric geometric model are projected onto the two-dimensional imaging plane to generate the two-dimensional projection contours of each component. S1032, extracts target edge contours from two-dimensional radar images; S1033, Construct an objective function based on bidirectional distance constraints. This objective function measures the matching error between the two-dimensional projected contour and the target edge contour. Here, the objective function is expressed as: (1.7) in, This indicates the number of contour points extracted from a two-dimensional radar image; Indicates the number of geometric units in the projected profile; Represents the target edge contour; Represents the projected outline.

[0025] S1034 uses a nonlinear optimization algorithm to iteratively solve the objective function, minimizing it to obtain the parameter vector that best matches the two-dimensional radar image, which is then used as an estimate of the three-dimensional physical features of the airborne target.

[0026] For example, this step uses the projection matrix obtained in S102 to map the three-dimensional parametric model constructed in S101 onto the two-dimensional imaging plane, and solves for the real physical parameters by matching it with the actual radar image. Since the geometric key points in the parametric model are naturally defined in the target body coordinate system, their two-dimensional projection coordinates on the radar image... Directly through the projection matrix Coordinates of key points in the 3D model The matrix multiplication is used to calculate the result, that is: (1.8) Specifically, for the wing components, the coordinates of the eight vertices determined by the model parameters are projected onto a two-dimensional plane and connected sequentially to form a closed polygonal projection profile. For the top antenna device, to avoid the computational burden caused by dense sampling of the circumference, a fast projection method guided by key feature points is adopted. The center of the circle and the endpoints of the diameter along the projection-invariant direction are selected as feature points for projection, and then the rotation angle and major and minor axis parameters of the projected ellipse are calculated to reconstruct the elliptical projection profile of the top antenna device.

[0027] Based on this, target edge contours are extracted from two-dimensional radar images. Furthermore, an objective function based on bidirectional distance constraints is constructed to measure the projected profile of the stereo parametric geometric model. With respect to the actual target edge contour The matching error between the two. This function calculates the shortest Euclidean distance from the contour points extracted from the image to the geometric contour generated by the model projection, which includes multiple line segments and elliptical curves, and the shortest distance from the sampling point on the model projection contour to the target edge contour point. The degree of matching is measured by minimizing the sum of the distance errors in these two directions. Its mathematical expression is Equation (1.7).

[0028] Finally, a genetic algorithm is used to solve this nonlinear optimization problem. By performing selection, crossover, and mutation operations within a predefined parameter space, the optimal parameter vector that minimizes the objective function value is iteratively searched. The final converged parameter combination is the estimated value of the three-dimensional physical characteristics of the aerial target.

[0029] S104. Establish an explicit observation equation describing the mapping relationship between the estimated value of the three-dimensional physical features of the airborne target and the observation points in the target edge contour. Based on the explicit observation equation, correct the error of the estimated value of the three-dimensional physical features of the airborne target and quantify the uncertainty range of the feature parameters. Specifically, in step S104, an explicit observation equation is established to describe the mapping relationship between the estimated value of the three-dimensional physical features of the airborne target and the observation points in the target edge contour, including the following steps S1041 to S1042.

[0030] S1041, assign each observation point in the target edge contour to the geometric unit corresponding to the projected contour of the three-dimensional parametric geometric model; S1042, under the attribution relationship, the theoretical corresponding points of each observation point are expressed as explicit functions of the estimated value of the three-dimensional physical characteristics of the airborne target, and an explicit observation equation is constructed.

[0031] For example, to measure the consistency between the observed contour and the model projected contour, since the objective function includes nearest neighbor operations, the matching relationship may switch when the parameters undergo small perturbations, causing the objective function to exhibit non-smooth characteristics locally. Although this characteristic does not affect the point estimation solution, it directly hinders subsequent gradient-based error propagation analysis. To address this, this section proposes a "fixed attribution" strategy: first, determine the optimal corresponding geometric unit for each observation point at the current parameter approximation value, and write the corresponding point as the parameter point on that geometric unit. This constructs a differentiable explicit local observation equation near the point estimation result, laying the foundation for subsequent linearization and interval estimation.

[0032] Specifically, firstly, at the current approximate value of the parameter At each observation point Calculate the distance from the observation point to each geometric unit within the theoretical profile. The theoretical profile consists of several line segment units and elliptical units; therefore, distance calculations can be performed at the geometric unit level. By comparing the distances between units, the unit with the smallest distance is selected as the unit to which the observation point belongs, denoted as . The non-differentiability caused by the nearest neighbor operation is "frozen" in the current attribution relation. Linearization is only performed in the local neighborhood where the attribution relation remains unchanged, thus obtaining a piecewise differentiable explicit observation equation.

[0033] After the attribution unit is determined, the nearest point needs to be further transformed into a parameter point so that it can be written as an explicit function of the parameter to be estimated. Therefore, for any observation point... Each of these can provide its corresponding point on the theoretical outline. Furthermore, a preliminary explicit observation equation is constructed: (1.9) in, This represents the position parameter, which is taken when the belonging unit is a straight line segment. When the belonging unit is an elliptical arc, take , This indicates the observation error. It should be noted that... The attribution relationship calculated at the location With position parameters The parameters remain unchanged during the current linearization process, thus avoiding the non-differentiability problem caused by nearest neighbor switching. If iterative parameter updates are subsequently adopted, the attribution and location parameters can be updated synchronously with the iteration, but each linearization is still completed in the local model with a fixed attribution.

[0034] Representative closed-form expressions for two types of geometric units are given to illustrate the expression in formula (1.9). How can this be written as an explicit function, and how can its derivative be used to obtain the coefficient matrix? For functions belonging to a line segment... The theoretical corresponding point of the observation point is written as: (1.10) in, and These are the projected coordinates of the two endpoints of the line segment in the imaging plane.

[0035] For observation points belonging to elliptical arc elements, their theoretical corresponding points are written as: (1.11) in, Let be the coordinates of the center of the ellipse in the imaging plane. and These are the lengths of the semi-major and semi-minor axes of the ellipse, respectively. and Let be the unit vector along the principal axis of the ellipse. Let be the ellipse parameter angle. Formulas (1.10) and (1.11) provide a unified parameterized form for the line segment and the corresponding point on the ellipse unit.

[0036] It should be noted that the endpoints mentioned above are all determined by the relationship between the geometric model and the imaging projection, and therefore can be explicitly written as parameters. The function.

[0037] Since the observed contour points are located on the imaging plane, a single observation point Corresponding point to its theory Scalar explicit observation equations can be established on both coordinate axes, namely: (1.12) From formula (1.12), it can be seen that when the number of observation points is... At that time, it can form An explicit observation equation. Parameter vector. The dimension is ,here Then the degrees of freedom for the error uncertainty estimate are: .

[0038] Specifically, in step S104, error correction is performed on the estimated values ​​of the three-dimensional physical features of the airborne target based on the explicit observation equation, including: (1) Linearize the explicit observation equation at the estimated value of the three-dimensional physical characteristics of the air target to obtain the linearized explicit observation equation. (2) Based on the linearized explicit observation equation, the weighted least squares method is used to solve the parameter correction amount and obtain the corrected stereo physical characteristic parameter estimate.

[0039] Specifically, in step S104, the uncertainty range of the quantized feature parameters includes: Based on the error propagation law, the covariance matrix of the corrected three-dimensional physical characteristic parameter estimates is calculated using the coefficient matrix of the linearized explicit observation equation and the observation residuals, in order to quantify the uncertainty interval of each physical characteristic parameter.

[0040] Here, the covariance matrix of the corrected estimates of the three-dimensional physical characteristic parameters is calculated, including: (1.13) in, Represents the Jacobian coefficient matrix of the linearized explicit observation equation; This represents the observation weight matrix set according to the accuracy of the observation points; Let represent the covariance matrix.

[0041] For example, after the explicit observation equations are established, the current parameter approximations can be used. First-order linearization is performed at this point. For ease of unified representation, all observations are stacked according to their coordinates, denoted as... .right exist Performing a first-order Taylor expansion, we obtain: (1.14) in, For parameter correction, For the observation error vector, Let be the coefficient matrix, which is defined as: (1.15) Further, by moving the constant term to the left, we define the equivalent observation vector. This yields the standard linearized explicit observation equation: (1.16) in, This represents the error between the observation and the theory at the current approximation. This reflects the sensitivity of the observations to parameter changes and provides gradient information for subsequent error propagation. Therefore, the linearized model of Equation (1.16) can be directly embedded into the framework of weighted least squares adjustment and covariance propagation.

[0042] According to the weighted least squares criterion, the parameter correction... The estimated value can be expressed as: (1.17) in, The Jacobian coefficient matrix is... Let be the observation weight matrix. Based on this, the estimation accuracy of the parameter vector is determined by the cofactor matrix. Description, which is defined as: (1.18) This matrix characterizes the anisotropic nature of observation errors transmitted to the parameter space via the geometric projection model, with its diagonal elements corresponding to the cofactors of each model parameter.

[0043] Regarding the observation weight array The setting of the observation weight matrix essentially reflects the contribution weight of the observations to the parameter estimation. In the SAR image aerial target feature extraction task in this paper, the observation data comes from the extraction of target contour points. Considering that the acquisition process of the geometric coordinates of each contour point on the imaging plane is relatively independent, and in the absence of prior accuracy, it is usually assumed that each observation has the same observation accuracy. Therefore, this paper uses the observation weight matrix... Setting it as an identity matrix means that each contour observation point has an equal constraint on the model parameter error estimation.

[0044] Furthermore, in order to assess the overall confidence level of the feature extraction results, it is necessary to construct the posterior unit-weighted variance using the matching residuals. By substituting the estimated parameter corrections into the formula for calculating the sum of squared residuals... And expand, combining the law of cofactor propagation, the first The error variance of the estimated values ​​of each physical characteristic parameter can ultimately be derived in the following form: (1.19) in, The degrees of freedom of the observation equation, The corresponding diagonal line of the cofactor matrix The elements of each parameter. Formula (1.17) comprehensively reflects the sources of uncertainty in physical feature extraction: the numerator reflects the residual energy after the observations are projected into the parameter space, the magnitude of which is affected by imaging noise and the accuracy of the fitting algorithm; the denominator reflects the gain effect of redundant observations on the estimation accuracy; the coefficient matrix The structure includes the influence of observation geometry on error propagation.

[0045] Therefore, the standard deviations of each key physical characteristic are obtained. Then, interval estimates of the physical feature extraction results can be constructed in a targeted manner. At a given confidence level... Assuming the error approximately follows a normal distribution, then the th The interval representation of a physical parameter can be derived from its point estimate. Constructed by multiplying with the corresponding quantile: (1.20) in, This indicates that the standard normal distribution is at a confidence level of 100%. The quantiles below.

[0046] The interval representation method based on error propagation theory can adaptively reflect the combined impact of imaging noise and algorithm accuracy on feature extraction quality, effectively compensating for the inability of traditional point estimation to assess the confidence level of feature extraction results. Furthermore, by explicitly defining the error boundaries of the feature results, it can provide more sufficient decision-making basis for subsequent classification and identification processes.

[0047] This yields the variance matrix of the characteristic parameter estimation results, and the elements on the diagonal of this matrix quantify the uncertainty range of each physical characteristic parameter.

[0048] S105 integrates the estimated values ​​and uncertainty intervals of the three-dimensional physical features of aerial targets into the classifier to achieve robust classification of aerial targets.

[0049] Specifically, in step S105, the estimated value and uncertainty range of the three-dimensional physical feature estimate of the air target are incorporated into the classifier to achieve robust classification of the air target, including the following steps S1051 to S1052.

[0050] S1051, the corrected three-dimensional physical feature parameter estimates are used as the mean vector, and the covariance matrix corresponding to the uncertainty interval is used as the variance measure, and each sample is modeled as a multivariate Gaussian distribution. S1052 incorporates a multivariate Gaussian distribution into the expectation hinge loss function of a support vector machine classifier, thereby optimizing the classification hyperplane parameters to achieve robust classification of aerial targets.

[0051] For example, a support vector machine classifier capable of utilizing feature uncertainty interval information is employed. This classifier treats each sample as a probabilistic model following a multivariate Gaussian distribution, where the mean vector is taken from the modified feature estimates described above, and the covariance matrix is ​​taken from the feature uncertainty interval information calculated above. This is achieved by optimizing the expected hinge loss function that incorporates this probabilistic model: (1.21) in, Represents the classification hyperplane weight vector; Indicates the bias term; Indicates the first The category labels of each sample; Represents the eigenvector; Indicates the first The feature mean vector of each sample; Indicates the first The feature covariance matrix of each sample; This represents the regularization parameter.

[0052] By using the stochastic gradient descent algorithm to update the parameters of the classification hyperplane, the classification task of typical aerial targets can be completed by incorporating feature variance information.

[0053] The effects of this invention can be further illustrated by the following simulation experiments.

[0054] The simulation conditions for this invention are as follows: the central processing unit is a 13th Gen Intel(R) Core(TM) i7-13700 2.10 GHz CPU, the operating system is Windows 11, and the simulation is performed using MATLAB 2022b developed by Mathworks.

[0055] Example 1: Accuracy Verification and Comparative Analysis of Physical Feature Extraction Based on Stereo Parametric Model Projection. Data Description: The radar images used in this example were obtained by simulating target echoes using a target CAD model combined with physical optics methods and employing the RD imaging algorithm. This method allows for the acquisition of two-dimensional radar images of the target from a specific viewpoint. Figure 5 CAD models for three types of targets are given. Figure 6 , Figure 7 and Figure 8 Simulated radar images of three icon types under different observation viewpoints are presented. Radar images effectively reflect information such as the target's structure, attitude, and size. The simulated images from different viewpoints show that the observation viewpoint significantly affects the relationship between the imaging plane and the plane formed by the fuselage and wings (the fuselage principal plane). When the angular difference between these two planes is large, there will be a significant deviation between the target's size in the two-dimensional radar image and its true three-dimensional size.

[0056] Specific Example Setup: To verify the effectiveness of this invention, a planar parametric model was selected as the comparison method. This method only constructs a planar model, without considering 3D imaging geometry, and the model itself has certain limitations, failing to adapt to aircraft with specific structures such as early warning aircraft, resulting in a significant discrepancy between the learned model parameters and the target's true physical characteristics. This invention requires the combined extraction of true physical features from multiple radar images; therefore, in the experiment, we selected three radar images of the target from different viewpoints for analysis. To ensure fairness in the comparison, the comparison method also selected three images, and the average of the feature extraction results from these three images was taken as the final result of the comparison method. Under the condition that the plane formed by the fuselage and wings (the main fuselage plane) differs significantly from the imaging plane, the performance of this invention and the comparison method in feature extraction was compared. To quantify the difference between the imaging plane and the main fuselage plane, we measured it by calculating the angle between the normal vectors of the two planes. Specifically, we assumed that the normal vectors of the plane formed by the imaging plane and the plane formed by the fuselage and wings were respectively... and The difference can be calculated using the included angle between the two surfaces, as shown in the following formula: ; The above formula can quantitatively describe the difference between the imaging plane and the main fuselage plane. It should be noted that this experiment uses three radar images of the target for analysis. Although there are some differences between the imaging planes of each image, these differences are relatively small because a continuous sequence of radar images was selected. The average angle between the imaging plane and the main fuselage plane of the three images was calculated in the experiment as a measure of the difference between the two planes. In this experimental setup, when the two planes are identical, the angle between them is 0°; while when the difference between the two planes is large, the angle is set to approximately 45°.

[0057] Table 1. Results of physical feature extraction for E3-A early warning aircraft

[0058] Table 2 Results of physical feature extraction of B-52 bomber

[0059] Table 3. Results of physical feature extraction from IL-78 refueling aircraft

[0060] Experimental conclusions: Table 1-3 presents the physical feature extraction results and error magnitudes for the three types of aircraft. Figure 9 , Figure 10 and Figure 11The matching results between the parametric geometric model and the target are visually demonstrated. Experimental results show that this invention has significant advantages in extracting the physical features of aerial targets. Specifically, for fuselage length and width, both this invention and the comparative method can extract parameter values ​​from radar images that are relatively close to the dimensions in the image. However, because this invention considers three-dimensional imaging geometry, its retrieved parameter results are closer to the true three-dimensional physical dimensions of the target. The comparative method, limited by its two-dimensional model assumptions, ignores three-dimensional imaging geometric relationships, resulting in parameters that, while acceptable at the image level, deviate significantly from the actual three-dimensional scale of the target. In wing feature extraction, the two methods show significant differences. The three-dimensional model constructed by this invention introduces a priori wing symmetry, effectively reducing the impact of imaging geometric distortion on the accuracy of parameter extraction, thus obtaining wing parameters with high accuracy and clear physical meaning. The comparative method is based on two-dimensional radar image modeling, and its model itself does not have the ability to describe three-dimensional symmetrical structures; the inherent perspective effect of the radar imaging projection process severely disrupts the symmetry of the wing on the two-dimensional radar image plane, leading to significant errors in the wing parameters extracted by the comparative method, which are seriously inconsistent with the true physical characteristics of the target. Furthermore, in terms of key structural features, such as the identification of the top lightning antenna disk, this invention can robustly detect and extract parameters of the actual structure, while effectively avoiding misjudgment when the target does not have this structure, thus exhibiting high reliability and accuracy.

[0061] Example 2: Characteristic uncertainty interval estimation and quantitative analysis based on linearization of observation equations.

[0062] Experimental setup: Taking E-3A early warning aircraft radar images as an example, physical feature estimation results were obtained based on a pre-constructed parametric geometric model and a genetic algorithm. Figure 12 and Figure 13 The results of extracting target edge point contours and attribution determinations from the image are presented. Based on these results, the corresponding observation equation can be determined. Subsequently, error correction and uncertainty interval estimation are performed.

[0063] Table 4. Uncertainty Modeling of Real Physical Characteristic Parameters and Feature Extraction Results of E-3A Early Warning Aircraft

[0064] Conclusions and Analysis: Table 4 presents the actual physical characteristic parameters of the E-3A early warning aircraft, the estimated results of these parameters, and their uncertainty modeling. Based on obtaining parameter estimation results close to the true values, the magnitude of uncertainty for each parameter estimation result was also obtained. Specifically, the estimation errors and uncertainties for fuselage length and width are small, mainly due to the large number of observation points extracted along the fuselage's main axis, providing strong constraints, and the stability of the line segment fitting model. In contrast, the estimation error for the wing sweep angle is relatively large, primarily due to the sensitivity of the angle parameter to changes in image contour curvature and the error propagation effect introduced by the feature linearization approximation. The estimation errors and uncertainties for the disk size and height are relatively high, mainly because the occlusion of the disk antenna section leads to sparse extracted contour points, thus affecting the feature fitting accuracy.

[0065] Example 3: Comparative Experiment on Classification Robustness under Complex Observation Conditions Based on Feature Uncertainty Interval Estimation. Example Setup and Data Description: To verify the classification robustness of this invention under complex observation environments and noise interference, this example constructs radar image datasets containing different signal-to-noise ratio (SNR) gradients for comparative testing. The experimental data comes from three types of targets: E-3A early warning aircraft, B-52 bomber, and IL-78 tanker aircraft. By adding Gaussian white noise to the original echoes, three test datasets with SNRs of 20dB (low noise), 10dB (medium noise), and 0dB (high noise) were generated to simulate different radar observation environment qualities.

[0066] Comparison Method Setup: To comprehensively evaluate the performance of the technical solution of this invention, this experiment uniformly employs a support vector machine classifier utilizing feature uncertainty interval information for classification decisions. Four different levels of feature extraction schemes were set as inputs. For the first three methods, which cannot calculate the feature uncertainty interval, their input feature covariance matrix was set to an all-zero matrix, i.e., treated as error-free deterministic point estimates during the classification stage. Specific settings are as follows: Method 1 is a feature extraction method based on a planar parametric model. This method uses the comparative planar model from Example 1 for feature extraction. Although the feature dimension is increased compared to Method 1, the extracted feature values ​​deviate significantly from the true physical properties of the target because 3D projection distortion is not considered. During classification, this planar model feature vector containing projection distortion error, along with a zero covariance matrix, is input into the classifier.

[0067] Method two is a simple geometric feature classification method based on 3D projection inversion. This method considers the 3D geometric projection relationship of radar imaging during the feature extraction stage, and can obtain physical dimensions such as fuselage length and wingspan close to the true values ​​through inversion. However, because this method does not construct a full-element parametric geometric model, the feature dimension is too low, lacking descriptions of key discriminative structures such as wing sweep angle, airfoil details, and top antenna. During classification, the extracted simple geometric feature vectors, along with a zero covariance matrix, are input into the classifier.

[0068] Method 3 is a feature point estimation classification method based on a stereo parametric model. This method, used in the ablation experiment of this invention, extracts full-dimensional physical features using the stereo parametric model constructed in this invention. This method solves the projection deformation problem through 3D modeling, resulting in high physical accuracy of the obtained feature values. However, it does not perform uncertainty calculations based on the observation equations, ignoring the feature fluctuation range caused by noise. During classification, the precise feature vector extracted from the stereo model, along with a zero covariance matrix, is input into the classifier.

[0069] Method four is a robust classification method based on a stereo model and uncertainty interval estimation proposed in this invention. This method uses the stereo parameterized model of this invention to extract physical features, and further calculates the covariance matrix of the feature parameters based on the linearized observation equation and the error propagation law to quantify the uncertainty interval of the features. During classification, the stereo model feature vector and the calculated true covariance matrix are input into the classifier to achieve robust classification with tolerance to feature errors.

[0070] Experimental Results Analysis: The model was trained on a training set containing a mixture of three target classes and validated on test sets with different signal-to-noise ratios. The average classification accuracy of each method is shown in the table below: Table 5 Comparison of target classification performance under different signal-to-noise ratios

[0071] Experimental results comparing methods one through three demonstrate that the 3D parametric geometric model constructed in this paper not only effectively corrects the deviation between the planar projected dimensions and the actual physical dimensions using the 3D projection mechanism, but also covers key components such as the fuselage, wings, and top-mounted disc antenna. This effectively solves the problem of incomplete description of key target structures in existing technologies, achieving a comprehensive description of the physical properties of aerial targets. Further comparison between methods three and four shows that introducing feature uncertainty interval estimation on the basis of identical features significantly improves classification accuracy. Figure 14The performance improvement was intuitively verified in the confusion matrix, particularly the significant reduction in confusion between similar targets such as early warning aircraft and refueling aircraft. This performance improvement is mainly attributed to the algorithm's effective use of the key feature of the top disc antenna and error modeling: the stereo model explicitly extracts this structure as the core basis for distinguishing early warning aircraft, and for the numerical fluctuations of features caused by measurement noise or fitting residuals, the uncertainty estimation algorithm quantifies them into error distribution intervals through the covariance matrix, so that the classification decision boundary can effectively tolerate the uncertainty of features, thereby improving the robustness of the classification algorithm.

[0072] This invention effectively corrects the planar projection size deviation caused by differences in observation perspective by constructing a three-dimensional parametric geometric model and combining it with imaging projection relationships. This improves feature extraction accuracy while addressing the problem of incomplete description of key structural features of the target's three-dimensional physical characteristics in existing technologies. Furthermore, this invention achieves feature uncertainty interval estimation by constructing observation equations and utilizing the error propagation law, transforming measurement noise and fitting residuals into the covariance matrix of feature parameters. This overcomes the limitation of traditional methods that simplify features to deterministic point estimates. Finally, by incorporating this uncertainty information into the classifier optimization process, the tolerance of the decision boundary to feature fluctuations is effectively enhanced, significantly improving the robustness of aerial target classification under complex observation conditions.

[0073] The various embodiments described in this specification are presented in a progressive manner. Similar or identical parts between embodiments can be referred to interchangeably. Each embodiment focuses on its differences from other embodiments. All or part of this invention can be used in numerous general-purpose or special-purpose computer system environments or configurations. Examples include: personal computers, server computers, handheld or portable devices, tablet devices, mobile communication terminals, multiprocessor systems, microprocessor-based systems, programmable electronic devices, network PCs, minicomputers, mainframe computers, and distributed computing environments including any of the above systems or devices, etc.

[0074] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the present invention.

Claims

1. An aerial target classification method based on uncertain interval estimation physical feature extraction, characterized in that, include: A modular design is adopted to construct a three-dimensional parametric geometric model of the aerial target, and the structural dimensions and spatial layout of each module are described by parametric vectors. Based on radar tracking information and satellite orbital mechanics principles, an imaging projection matrix is ​​determined, and a two-dimensional radar image of the target is obtained according to the imaging projection matrix; wherein, the imaging projection matrix is ​​used to establish the geometric mapping relationship from the three-dimensional target to the two-dimensional imaging plane; The stereo parameterized geometric model is projected onto a two-dimensional plane using the imaging projection matrix. By minimizing the matching error between the projected contour of the stereo parameterized geometric model and the target edge contour in the two-dimensional radar image, the estimated value of the stereo physical features of the airborne target is obtained by inversion. An explicit observation equation is established to describe the mapping relationship between the estimated value of the three-dimensional physical features of the airborne target and the observation points in the edge contour of the target. Based on the explicit observation equation, the estimated value of the three-dimensional physical features of the airborne target is corrected for error, and the uncertainty range of the feature parameters is quantified. The estimated values ​​of the three-dimensional physical features of the aerial target and the uncertainty interval are incorporated into the classifier to achieve robust classification of aerial targets.

2. The aerial target classification method based on uncertainty interval estimation physical feature extraction according to claim 1, characterized in that, The modular design constructs a three-dimensional parametric geometric model of the aerial target, and describes the structural dimensions and spatial layout of each module using parameter vectors, including: Construct a three-dimensional parametric geometric model consisting of fuselage units represented by cylinders, wing units represented by quadrilateral surface elements, and top antenna units represented by circular planes. The structural and spatial layout of the fuselage unit, the wing unit, and the top antenna unit are described using the parameter vectors.

3. The aerial target classification method based on uncertainty interval estimation physical feature extraction according to claim 1, characterized in that, The determination of the imaging projection matrix based on radar tracking information and satellite orbital mechanics principles includes: The target body coordinate system is constructed based on the target position vector and target velocity vector in the radar tracking information, and the satellite position vector and satellite velocity vector in the Earth fixed coordinate system are calculated using the orbital six roots based on the principle of satellite orbital mechanics. Based on the satellite position vector and the target position vector, the line-of-sight vector of the satellite relative to the target is calculated, and the line-of-sight vector is projected onto the target body coordinate system to obtain the radar line-of-sight vector in the target body coordinate system; Based on the changes in radar line of sight during the imaging accumulation time, the range dimension unit vector and the azimuth dimension unit vector of the imaging plane are determined, and the imaging projection matrix is ​​formed by the range dimension unit vector and the azimuth dimension unit vector.

4. The aerial target classification method based on uncertainty interval estimation physical feature extraction according to claim 1, characterized in that, The process of projecting the stereo parameterized geometric model onto a two-dimensional plane using the imaging projection matrix, and obtaining an estimate of the stereo physical features of the airborne target by minimizing the matching error between the projected contour of the stereo parameterized geometric model and the target edge contour in the two-dimensional radar image, includes: Using the imaging projection matrix, the key points of each component in the stereo parametric geometric model are projected onto the two-dimensional imaging plane to generate the two-dimensional projection contours of each component. Extract the target edge contour from the two-dimensional radar image; A target function based on bidirectional distance constraints is constructed, which is used to measure the matching error between the two-dimensional projected contour and the target edge contour. The objective function is minimized by iteratively solving a nonlinear optimization algorithm, resulting in a parameter vector that best matches the two-dimensional radar image, which serves as an estimate of the three-dimensional physical features of the airborne target.

5. The aerial target classification method based on uncertainty interval estimation physical feature extraction according to claim 4, characterized in that, The objective function is expressed as: ； in, This indicates the number of contour points extracted from a two-dimensional radar image; Indicates the number of geometric units in the projected profile; Represents the target edge contour; Represents the projected outline.

6. The aerial target classification method based on uncertainty interval estimation physical feature extraction according to claim 1, characterized in that, The explicit observation equation that establishes the mapping relationship between the estimated three-dimensional physical features of the airborne target and the observation points in the target's edge contour includes: Each observation point in the target edge contour is assigned to the geometric unit corresponding to the projected contour of the stereo parameterized geometric model; Under the attribution relationship, the theoretical corresponding points of each observation point are expressed as explicit functions of the estimated value of the three-dimensional physical characteristics of the aerial target, and an explicit observation equation is constructed.

7. The aerial target classification method based on uncertainty interval estimation physical feature extraction according to claim 1, characterized in that, The error correction of the estimated three-dimensional physical features of the airborne target based on the explicit observation equation includes: The explicit observation equation is linearized and expanded at the estimated value of the three-dimensional physical characteristics of the airborne target to obtain the linearized explicit observation equation. Based on the linearized explicit observation equation, the weighted least squares method is used to solve for the parameter correction, and the corrected estimated values ​​of the stereoscopic physical characteristic parameters are obtained.

8. The aerial target classification method based on uncertainty interval estimation physical feature extraction according to claim 7, characterized in that, The uncertainty range of the quantized feature parameters includes: Based on the error propagation law, the covariance matrix of the corrected three-dimensional physical characteristic parameter estimates is calculated using the coefficient matrix and observation residuals of the linearized explicit observation equation, in order to quantify the uncertainty interval of each physical characteristic parameter.

9. The aerial target classification method based on uncertainty interval estimation physical feature extraction according to claim 8, characterized in that, The calculation of the covariance matrix of the corrected three-dimensional physical feature parameter estimates includes: ； in, Represents the Jacobian coefficient matrix of the linearized explicit observation equation; This represents the observation weight matrix set according to the accuracy of the observation points; Let represent the covariance matrix.

10. The aerial target classification method based on uncertainty interval estimation physical feature extraction according to claim 1, characterized in that, The step of incorporating the estimated value of the three-dimensional physical features of the aerial target and the uncertainty interval into the classifier to achieve robust classification of aerial targets includes: The corrected three-dimensional physical feature parameter estimates are used as the mean vector, and the covariance matrix corresponding to the uncertainty interval is used as the variance measure. Each sample is modeled as a multivariate Gaussian distribution. By incorporating the multivariate Gaussian distribution into the expected hinge loss function of the support vector machine classifier, robust classification of aerial targets is achieved by optimizing the classification hyperplane parameters.

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