Radar target detection method based on deep manifold network and NP criterion

Abstract

The application relates to a radar target detection method based on a deep manifold network and an NP criterion. The method comprises the following steps: acquiring radar echo data, obtaining a time-frequency spectrum array through time-frequency transformation, constructing a time-frequency feature SPD matrix through symmetric positive definite processing and normalization processing. The SPD matrix is input into a preset SPDNet network, and features are extracted through a bilinear mapping layer, an eigenvalue correction layer, an eigenvalue logarithm layer and a full connection layer in sequence, and a sample classification score is output. Based on the differentiable loss function layer of the NP criterion, a detection probability and a false alarm rate are calculated according to the classification score, and a loss value is output. In combination with the loss value, the SPDNet network parameters are updated through gradient back propagation to complete training. The radar echo data to be detected is input into the trained network, and target and clutter are distinguished and detected according to the output classification score. The method has high radar target detection precision.

Description

Technical Field

[0001] This application relates to the field of radar target detection technology, and in particular to a radar target detection method based on deep manifold networks and NP criteria. Background Technology

[0002] Radar, as a key piece of equipment for all-weather, all-day target detection and surveillance, plays a vital role in early warning detection, search and surveillance, and battlefield reconnaissance. However, the actual clutter background is complex and variable, and clutter generally exhibits a composite of non-Gaussian, non-stationary, and non-uniform characteristics, making accurate statistical modeling of clutter difficult. Traditional clutter amplitude statistical modeling and energy accumulation detection methods have certain limitations and cannot meet the needs of practical applications.

[0003] Target detection essentially involves effectively distinguishing between targets and clutter based on the differences in radar echoes. Therefore, researchers have begun to explore extracting these differences from the echoes to improve radar target detection performance. By extracting one or more differential features between targets and clutter, including fractal features, time-frequency domain features, and polarization domain features, the two can be distinguished in a feature space, leading to a detection decision. Manual feature extraction is time-consuming. With the development of artificial intelligence, deep learning possesses the ability to automatically extract high-dimensional nonlinear features and powerful data analysis capabilities. Convolutional neural networks (CNNs) can extract these differential features and utilize prior data for training and optimization, achieving target-clutter distinction and superior detection performance. However, the space formed by the differential features extracted by the network is typically nonlinear and non-Euclidean. Representing and describing them in a linear Euclidean space will result in information loss, thus affecting detection performance.

[0004] As an emerging discipline that has developed in recent years, information geometry provides a new theoretical system for studying statistical and signal processing problems. Among them, matrix information geometry is a method that uses differential geometry on matrix manifolds to study the intrinsic information of data models. It has been widely used in image processing, signal detection and other fields. The MIG detection method transforms the radar target detection problem into a nonlinear geometric problem on a matrix manifold. It internalizes the difference between the target and clutter as a matrix manifold with a certain curvature. It uses the nonlinear geometric distance of the matrix manifold to quantify the difference between the characteristics of the target and clutter in order to distinguish between the two and complete the detection decision. At present, target detection methods based on MIG have been studied in many ways. Different geometric measures constitute different MIG detectors. The MIG detector initially used the Riemannian distance (RD) as a measure of the difference between the covariance matrix of the target and clutter on the manifold and applied it to the detection of aircraft wake targets

[17] . Subsequently, to avoid the high computational complexity of Riemann distance, geometric metrics for manifolds, such as information divergence (KL divergence, KLD) and logarithmic determinant divergence (JBLD), as well as spectral norms, were extended and applied to matrix information geometric detectors. However, in complex backgrounds, targets are easily obscured by strong clutter, and MIG detection methods cannot accurately measure the difference between the target and the clutter, thus limiting their detection performance. Summary of the Invention

[0005] Therefore, it is necessary to provide a radar target detection method based on deep manifold networks and NP criteria that can improve the accuracy of radar target detection, addressing the aforementioned technical problems.

[0006] A radar target detection method based on deep manifold networks and NP criteria, the method comprising:

[0007] Acquire radar echo data, perform time-frequency transformation on the radar echo data to obtain a time-frequency spectrum array; perform symmetric positive definiteness and normalization processing on the time-frequency spectrum array to construct a time-frequency feature SPD matrix; The time-frequency feature SPD matrix is ​​input into the preset SPDNet network, and features are extracted and processed sequentially through the bilinear mapping layer, the eigenvalue correction layer, the eigenvalue logarithm layer and the fully connected layer, and the classification score of the sample is output. The detection probability and false alarm rate are calculated based on the classification score in the differentiable loss function layer constructed based on the NP criterion, and the loss value is output. The SPDNet network is trained by updating its parameters through gradient backpropagation based on the loss value, resulting in a trained SPDNet network. The radar echo data to be detected is input into the trained SPDNet network, and the radar target and clutter are distinguished and detected based on the output classification score.

[0008] The radar target detection method based on deep manifold networks and the NP criterion described above first transforms the one-dimensional echo into a two-dimensional time-frequency spectrum array through STFT time-frequency transformation. This accurately captures the difference between the target's specific Doppler frequency spectrum and the zero-frequency concentration distribution of clutter, thus initially separating their characteristics. Subsequently, the time-frequency feature SPD matrix constructed through symmetric positive definiteness and trace normalization inherently incorporates key differences between the target and clutter, such as energy and instantaneous frequency correlation, into the matrix structure. This satisfies the manifold input requirements of SPDNet while fully preserving second-order statistical features, completely avoiding the information loss caused by traditional linear dimensionality reduction and laying a high-quality data foundation for subsequent feature learning. Finally, using SPDNet as the core, efficient feature learning is achieved through hierarchical collaboration. The bilinear mapping layer performs a high-dimensional to low-dimensional manifold mapping under the Stiefel manifold constraint, removing redundant information while preserving the geometric structure and avoiding damage to target features. The eigenvalue correction layer enhances the positive definiteness of the matrix through threshold correction and introduces nonlinearity to further amplify feature differences. The eigenvalue logarithm layer achieves a smooth transition from non-Euclidean manifold to Euclidean space, adapting to subsequent operations without losing intrinsic information. The three layers work together to enable SPDNet to accurately capture core differences such as instantaneous frequency correlation and energy, making it more sensitive to weak target features in complex clutter backgrounds, and its feature discrimination is significantly better than traditional CNNs such as ResNet18 and DarkNet19. Finally, the differentiable loss function designed based on the NP criterion maximizes the detection probability while strictly constraining the false alarm rate within a preset range, meeting the core requirements of radar detection without manual parameter tuning. A dedicated gradient formula derived for SPDNet's specific operations ensures effective loss value propagation. The Riemann gradient descent of the bilinear mapping layer and the stochastic gradient descent of the fully connected layer work together to achieve efficient parameter optimization, avoiding the drawbacks of traditional methods such as excessive manual intervention and poor adaptability. This allows the network to continuously iterate towards more accurate target-clutter differentiation. This application significantly improves detection performance and reliability in complex scenarios. The pre-processed, standardized data is input into the trained network, enabling rapid target and clutter discrimination. It effectively solves the problems of difficult clutter modeling, high feature loss, and uncontrollable false alarm rate in traditional methods. Especially in low signal-to-clutter ratio scenarios, it maintains a high detection probability, achieving a dual improvement in detection accuracy and reliability, and possesses strong engineering practical value. Attached Figure Description

[0009] Figure 1 This is a flowchart illustrating a radar target detection method based on deep manifold networks and NP criteria in one embodiment. Figure 2 This is a schematic diagram of the network structure of SPDNet in one embodiment; Figure 3 This is a schematic diagram of a PFA-controllable SPDNet network structure in one embodiment. Detailed Implementation

[0010] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0011] In one embodiment, such as Figure 1 As shown, a radar target detection method based on deep manifold networks and NP criteria is provided, including the following steps: Step 102: Acquire radar echo data, perform time-frequency transformation on the radar echo data to obtain a time-frequency spectrum array; perform symmetric positive definiteness and normalization processing on the time-frequency spectrum array to construct a time-frequency feature SPD matrix.

[0012] Radar echo data consists of reflected signals received during radar target detection, containing both target signals and clutter signals. Clutter typically exhibits a composite of non-Gaussian, non-stationary, and non-uniform characteristics. Time-frequency transformation converts one-dimensional radar echo data into a two-dimensional time-frequency distributed time-spectrum matrix to simultaneously reflect the signal's characteristics in both the time and frequency domains. In this embodiment, the STFT (Short Time Fourier Transform) method is used to implement the time-frequency transformation. Symmetric positive definiteness processing ensures that the matrix satisfies the symmetric positive definiteness property, providing a suitable input for subsequent SPDNet network processing. Normalization processing eliminates the influence of data dimensions, improving the stability of network training.

[0013] Step 104: Input the time-frequency feature SPD matrix into the preset SPDNet network, and perform feature extraction and processing sequentially through the bilinear mapping layer, eigenvalue correction layer, eigenvalue logarithmic layer and fully connected layer to output the classification score of the sample.

[0014] The network structure of SPDNet is as follows: Figure 2 As shown, the system includes a bilinear mapping layer (BiMap layer), an eigenvalue correction layer (ReEig layer), an eigenvalue logarithmic layer (LogEig layer), and a fully connected layer (FC layer). After the time-frequency feature SPD matrix is ​​input, each layer progressively extracts the differential features between the target and clutter, such as instantaneous frequency correlation, energy, and Doppler frequency. Finally, the fully connected layer outputs the classification score indicating whether the sample is a target or clutter. The classification score is the basis for subsequent calculations of detection probability, false alarm rate, and loss value, directly affecting the accuracy of the detection results.

[0015] Step 106: Calculate the detection probability and false alarm rate based on the classification score in the differentiable loss function layer constructed based on the NP criterion, and output the loss value.

[0016] The NP criterion is the fundamental theory of radar target detection, its core being to maximize the detection probability (PD) under a preset false alarm rate (PFA) constraint. The differentiable loss function layer transforms the NP criterion into a differentiable form, adapting it for end-to-end training of neural networks, replacing the traditional cross-entropy loss function, and achieving explicit constraints on PFA. The detection probability (PD) is the probability that a target sample is correctly detected as a target, the false alarm rate (PFA) is the probability that a clutter sample is misclassified as a target, and the loss value reflects the deviation between the current network output and the goal of "maximizing PD under controllable PFA," serving as the basis for updating network parameters. The PFA-controllable SPDNet network structure is as follows: Figure 3 As shown, the original SoftmaxLoss layer is replaced with an NPLouss layer.

[0017] Step 108: Based on the loss value, update the parameters of the SPDNet network through gradient backpropagation to complete the network training and obtain the trained SPDNet network.

[0018] Gradient backpropagation calculates the gradient of each layer's parameters with respect to the loss using a chain rule, based on the loss value, and then adjusts the parameters to reduce the loss. Because some layers in the SPDNet network involve special operations such as matrix eigenvalue decomposition, dedicated gradient calculation methods are required. After parameter updates, the network can better learn the differences between the target and clutter, achieving efficient detection under PFA constraints.

[0019] Step 110: Input the radar echo data to be detected into the trained SPDNet network, and realize the distinction and detection of radar targets and clutter based on the output classification score.

[0020] The radar echo data to be detected needs to undergo time-frequency transformation, symmetric positive definiteness, and normalization processing according to the method in step 102. After constructing the time-frequency feature SPD matrix, it is input into the trained network. The network outputs a classification score based on the learned feature patterns, and determines whether the sample is a target or clutter by judging the score, thus completing the detection decision.

[0021] The radar target detection method based on deep manifold networks and the NP criterion described above first transforms the one-dimensional echo into a two-dimensional time-frequency spectrum array through STFT time-frequency transformation. This accurately captures the difference between the target's specific Doppler frequency spectrum and the zero-frequency concentration distribution of clutter, thus initially separating their characteristics. Subsequently, the time-frequency feature SPD matrix constructed through symmetric positive definiteness and trace normalization inherently incorporates key differences between the target and clutter, such as energy and instantaneous frequency correlation, into the matrix structure. This satisfies the manifold input requirements of SPDNet while fully preserving second-order statistical features, completely avoiding the information loss caused by traditional linear dimensionality reduction and laying a high-quality data foundation for subsequent feature learning. Finally, using SPDNet as the core, efficient feature learning is achieved through hierarchical collaboration. The bilinear mapping layer performs a high-dimensional to low-dimensional manifold mapping under the Stiefel manifold constraint, removing redundant information while preserving the geometric structure and avoiding damage to target features. The eigenvalue correction layer enhances the positive definiteness of the matrix through threshold correction and introduces nonlinearity to further amplify feature differences. The eigenvalue logarithm layer achieves a smooth transition from non-Euclidean manifold to Euclidean space, adapting to subsequent operations without losing intrinsic information. The three layers work together to enable SPDNet to accurately capture core differences such as instantaneous frequency correlation and energy, making it more sensitive to weak target features in complex clutter backgrounds, and its feature discrimination is significantly better than traditional CNNs such as ResNet18 and DarkNet19. Finally, the differentiable loss function designed based on the NP criterion maximizes the detection probability while strictly constraining the false alarm rate within a preset range, meeting the core requirements of radar detection without manual parameter tuning. A dedicated gradient formula derived for SPDNet's specific operations ensures effective loss value propagation. The Riemann gradient descent of the bilinear mapping layer and the stochastic gradient descent of the fully connected layer work together to achieve efficient parameter optimization, avoiding the drawbacks of traditional methods such as excessive manual intervention and poor adaptability. This allows the network to continuously iterate towards more accurate target-clutter differentiation. This application significantly improves detection performance and reliability in complex scenarios. The pre-processed, standardized data is input into the trained network, enabling rapid target and clutter discrimination. It effectively solves the problems of difficult clutter modeling, high feature loss, and uncontrollable false alarm rate in traditional methods. Especially in low signal-to-clutter ratio scenarios, it maintains a high detection probability, achieving a dual improvement in detection accuracy and reliability, and possesses strong engineering practical value.

[0022] In one embodiment, the time-frequency feature SPD matrix is ​​constructed by performing symmetric positive definiteness and normalization on the time-frequency spectrum matrix, including: Multiply the time-frequency spectrum matrix by its transpose to obtain a symmetric matrix; perform eigenvalue decomposition on the symmetric matrix and ensure the positive definiteness of the matrix through thresholding to obtain the initial SPD matrix; perform trace normalization on the initial SPD matrix to obtain the final time-frequency feature SPD matrix.

[0023] In one embodiment, eigenvalue decomposition is performed on the symmetric matrix, and the positive definiteness of the matrix is ​​ensured by thresholding to obtain an initial SPD matrix, including: Eigenvalue decomposition is performed on the symmetric matrix, and the positive definiteness of the matrix is ​​ensured by thresholding, resulting in the initial SPD matrix.

[0024] in, For the threshold, It is the identity matrix. The eigenvector matrix, It is a diagonal matrix of eigenvalues.

[0025] In one embodiment, the radar echo data undergoes time-frequency transformation to obtain a time-spectrum array, including: Perform time-frequency transformation on the radar echo data to obtain the time-spectrum array.

[0026] in, It is a window function. It is a discrete time series. It is the distance cell number. It is the pulse sequence number.

[0027] Specifically, when radar employs coherent processing, the pulse-compressed echo signal Defined as

[0028] in, , and These are the number of pulses and the number of distance units, respectively.

[0029] Time-frequency features are extracted from radar echo data using STFT time-frequency analysis, and a time-frequency feature matrix is ​​constructed based on these features as input to SPDNet. STFT treats the signal within a window as a stationary signal over a short period by selecting a specific window function. The Fourier transform of the signal within the window is calculated by moving the window function at fixed intervals to obtain the spectrum at different times. Finally, these spectra are integrated, stitched together, and stacked to obtain the time-frequency spectrum matrix of the entire signal. For a given discrete-time series... Its STFT is defined as:

[0030] in, It is a window function.

[0031] The time-spectrum array obtained by performing STFT on radar echo data Symmetric positive definiteness (taking absolute value) is used to construct the time-frequency feature SPD matrix. First, the... Rather than transpose Multiply, the result is It must satisfy symmetry. Then, for Perform eigenvalue decomposition and use a threshold. ensure The positive definiteness of the SPD matrix is ​​obtained. To ensure stable training of SPDNet subsequently, Perform trace normalization and pass a threshold. To improve numerical stability, the normalized SPD matrix is ​​obtained. Based on the above ideas, the specific implementation of constructing the time-frequency feature SPD matrix can be expressed as follows:

[0032] in, The threshold is set as follows in this application: .

[0033] In one embodiment, the processing expression for the bilinear mapping layer is as follows:

[0034] in, It is a bilinear mapping. It is the input matrix. The transformation matrix is... and Representing different matrix dimensions, k Indicates the network layer number. T This indicates the transpose operation. This represents the current output matrix.

[0035] In one embodiment, the processing expression of the eigenvalue correction layer is as follows:

[0036] in, It is a nonlinear transformation. It is the input matrix. Indicates the correction threshold. k Indicates the network layer number. T This indicates the transpose operation. It is a diagonal matrix ,for: , It is the identity matrix. For the input matrix The eigenvalue diagonal matrix obtained after eigenvalue decomposition For the input matrix The eigenvector matrix obtained after eigenvalue decomposition has column vectors as follows: The unit orthogonal eigenvectors, T This indicates the transpose operation.

[0037] In one embodiment, the processing expression for the eigenvalue logarithmic layer is as follows:

[0038] in, Let be the transformation function of the logarithmic eigenvalue layer of the k-th layer. For the input matrix The eigenvalue diagonal matrix obtained after eigenvalue decomposition For the input matrix The eigenvector matrix obtained after eigenvalue decomposition has column vectors as follows: The unit orthogonal eigenvectors, T This indicates the transpose operation.

[0039] Specifically, the SPDNet network structure is as follows: Figure 2 As shown, it includes a bilinear mapping (BiMap) layer, an eigenvalue rectification (ReEig) layer, an eigenvalue logarithmic (LogEig) layer, and other layers. Each layer will be described in detail below.

[0040] The main function of the BiMap layer is to generate more compact and discriminative SPD moments through bilinear mapping. A matrix, in its specific implementation, can be represented as:

[0041] in, It is a bilinear mapping. It is the SPD matrix input to the BiMap layer. ( ) is the transformation matrix.

[0042] SPDNet's dimensionality reduction is primarily achieved through the BiMap layer. The BiMap layer takes as input all SPD matrices. The SPD manifold is constructed through a bilinear mapping. back, Vie Dimensional reduction Vie All This constructs a new SPD manifold. Following classic manifold learning theory, this layer maps the high-dimensional SPD manifold to a low-dimensional SPD manifold while preserving the inherent geometric structure of the data and learning its essential features, thereby improving classification performance. It is important to note that, in order to ensure… Symmetric positive definiteness, transformation matrix It needs to be a full-rank matrix, and all full-rank matrices constitute the weight space. Due to the weight space The distance function has no upper bound, so direct optimization is not feasible. To solve this problem, we will... Constrained in a tight Stiefel manifold Above, that is It is a semi-orthogonal matrix that satisfies Thus, optimization on a compact Stiefel manifold yields the transformation matrix. The optimal solution.

[0043] The ReEig layer is similar to the Rectified Linear Unit (ReLU) layer in CNNs. It ensures the positive definiteness of the dimensionality-reduced SPD matrix through nonlinear transformation. Specifically, it can be represented as:

[0044] in, It is a nonlinear transformation, for Perform eigenvalue decomposition to obtain For the eigenvalue matrix Make corrections. It is a threshold correction. It is a diagonal matrix Its definition can be expressed as:

[0045] The above formula will pass the threshold. eigenvalues ​​adjusted to This ensures that the eigenvalues ​​of the SPD matrix after the eigenvalue correction layer are all greater than or equal to 1. This enhances numerical stability and prevents the matrix from approaching non-positive definiteness, while also introducing nonlinearity.

[0046] The SPD matrix output by the ReEig layer resides on a non-Euclidean manifold. The LogEig layer performs Riemannian computation on the SPD matrix using a Log-Euclidian nonlinear metric, giving the SPD manifold a Lie group structure, allowing the manifold to be computed by performing matrix logarithm operations on the SPD matrix. This is reduced to a flat Euclidean space to fit subsequent classification layers. The specific implementation can be represented as follows:

[0047] in, It is a matrix logarithm operation ,right Perform eigenvalue decomposition to obtain .

[0048] After the LogEig layer, the subsequent classification layers are classic Euclidean network layers, including the FC layer and the SoftmaxLoss layer. The FC layer outputs the values ​​from the LogEig layer. Flattened into a column vector (dimension 1) ), assuming there are a total If there are one output matrix, then the flattened matrix... The vectors are combined to form a matrix. (dimension is) Then, performing a full connection operation can be represented as:

[0049] in, It is a weight matrix with dimension 1. .

[0050] Radar target detection is a binary classification problem, therefore After obtaining the output matrix (dimension is) After that, for The column vector Perform the following calculations:

[0051] in, It is the first The true label for each sample is 1, which represents that the sample is the target, and 0, which represents that the sample is clutter. Indicates the output of the FC layer. The score by which each sample is judged to be the true class. Indicates the output of the FC layer. The score by which a sample is judged as clutter. Indicates the output of the FC layer. The score by which each sample is judged as the target It is the first The probability that a sample is classified as the true class.

[0052] Using cross-entropy loss as the loss function , can be represented as:

[0053] in, It is the first The probability that a sample is classified as the true class. This represents the number of samples in a single training batch.

[0054] Ultimately, each sample is classified as the category with the highest probability value output by the softmax function.

[0055] For SPDNet, different BiMap layer transformation matrices The size corresponds to different network layers, determining the speed of dimensionality reduction. The aforementioned SPDNet receives SPD matrices as input, and all input SPD matrices form an SPD matrix manifold. Through manifold learning, the dimensionality of the SPD matrices is continuously reduced, mapping the original high-dimensional SPD matrix manifold to a low-dimensional one. During dimensionality reduction, by retaining the main components representing the target signal and removing redundant components representing clutter signals, the signal-to-clutter ratio is improved, enhancing the difference between the target and clutter, thus improving detection performance. Compared to traditional dimensionality reduction methods, SPDNet, through the design of the ReEig layer, avoids the loss of useful information while removing redundant information. However, the cross-entropy loss function used in SPDNet does not explicitly constrain the false alarm rate (PFA), resulting in a lack of PFA control in radar target detection based on SPDNet. This application also designs a differentiable loss function based on the NP criterion to replace the cross-entropy loss function, achieving effective constraint on the false alarm rate in SPDNet.

[0056] In one embodiment, the differentiable NP loss function in the differentiable loss function layer constructed based on the NP criterion is:

[0057] in, It is the result of the softmax function calculating the output score of the fully connected layer, that is, the output of the softmax function on the samples. The probability of being identified as a target. These are the true labels of the samples; 1 represents that the sample is the target, and 0 represents that the sample is clutter. The number of samples in a single training batch. It's a hyperparameter. These are the preset PFA constraint values.

[0058] Specifically, the radar target detection problem can be defined as a binary hypothesis test, which can be expressed as:

[0059] in, Indicates the echo signal. Indicates the target signal. Indicates noise.

[0060] The NP criterion is defined as specifying an allowable value for the PFA, such that the PD reaches a certain value while keeping the PFA constant. To the maximum. Based on the NP criterion, the differentiable NP loss function can be expressed as:

[0061] in, It's a hyperparameter. These are the preset PFA constraint values.

[0062] Replacing the traditional cross-entropy loss function with a differentiable NP loss function, the parameter updates during network training aim to minimize the differentiable NP loss function. This optimization process is essentially equivalent to constraining the PFA to a preset value. Under the premise of neighborhood, the goal is to gradually approach the theoretical optimal value of 1 using the NP criterion. It needs to be embedded into the backpropagation process of SPDNet to achieve end-to-end training, so It must be differentiable. The differentiability of PD and PFA is determined by their expressions. The mathematical expressions of PD and PFA will be derived and analyzed below.

[0063] The decision result of the above binary hypothesis test depends on the hard decision function. :

[0064] in, The output of the softmax function will be the sample Probability of being identified as a target , It is a sample The final verdict, A value of 1 indicates an assumption. Established, Sample It is the goal. A value of 0 indicates an assumption. Established, Sample It's noise.

[0065] Based on the hard decision function, the expressions for PD and PFA can be obtained as follows:

[0066] in, These are the true labels of the samples; 1 represents that the sample is the target, and 0 represents that the sample is clutter. The number of samples in a single training batch. The output of the softmax function is the sample Probability of being identified as a target .

[0067] because Since they are discontinuous, the expressions for PD and PFA are non-differentiable and cannot be embedded into the gradient backpropagation of the network using the chain rule. Considering that the optimization objective of the NP loss function is equivalent to... Assuming tending towards 1, in Assuming It tends to 0, so use Alternative Furthermore, when the proportion of a certain type of sample in the training batch is extremely low, the loss function exhibits significant fluctuations, leading to an unstable training process that is detrimental to network training and optimization. By fully utilizing all training samples, the final expressions for PD and PFA can be represented as: (1) because The output score of the softmax function on the fully connected (FC) layer is calculated. The PD and PFA in formula (1) are differentiable with respect to the network parameters. Substituting the differentiable PD and PFA into the formula... The final NP loss function expression is shown in the following formula:

[0068] By replacing the cross-entropy loss function with a differentiable NP loss function and the SoftmaxLoss layer with an NPLLoss layer, controllable PFA can be obtained. Layered SPDNet network structure as follows Figure 3 As shown, during the training phase, this network maximizes PD under the constraint of PFA through gradient backpropagation and parameter updates.

[0069] In one embodiment, during gradient backpropagation, the gradient calculation expression for the eigenvalue decomposition operation is:

[0070]

[0071] in, It's the learning rate. This is the current weight. This is the updated weight. It is the output. It is the first l The partial derivative of the loss function corresponding to the layer with respect to the current weight matrix W. It is the first l+1 The loss function corresponding to the layer affects the output. The partial derivatives, It is the first l The partial derivative of the forward propagation transformation function of the layer with respect to the current weight matrix W. It is the first l The input matrix of the layer.

[0072] In one embodiment, the parameter update method of the bilinear mapping layer is as follows:

[0073] in, For learning rate, For the retraction operation, It is the first The weights at the next iteration For the first The weights at the next iteration , For the Riemann gradient, Let be the normal component of the Euclidean gradient.

[0074] Specifically, SPDNet's backpropagation is based on layer-by-layer composite function relationships. ,in Indicates from the first Layer input To the final loss The mapping, Indicates function composition. It is the first The forward function of the layer, .exist Figure 3 In the SPDNet network structure shown, each layer uses different gradient calculation methods based on its mathematical structure, and parameter updates are performed in the BiMap layer and the FC layer. The following is based on... Figure 3 The network structure shown provides a detailed analysis of gradient propagation and parameter updates for each layer.

[0075] During forward propagation, the fully connected (FC) layer outputs a score for each sample that is judged as clutter. And the score that was judged as the target The number of samples in a single training batch is The scores of all samples constitute a dimension. matrix . Matrix Input the NPLose layer, calculate the power digit (PD) and power factor (PFA), and output the loss for a single training batch. During backpropagation, according to the chain rule, for the NPLlow layer, we have: , right and The gradient can be expressed as: (2) in, It is the first Sample The score for being judged as clutter. It is the first Sample The goal is to obtain point, , , , , ,

[0076] The gradient matrix output by the NPLoss layer can be represented as: (3) when When it is the target sample, This means that the score for classifying the target sample as clutter will decrease along the gradient descent direction; This indicates that the score for classifying the target sample as a target will increase along the gradient descent direction. When When it is a clutter sample, This means that the score for classifying a clutter sample as clutter will increase along the gradient descent direction; This indicates that the score for the clutter sample that is judged as a target will decrease along the gradient descent direction.

[0077] For an FC layer, the forward function is: According to the chain rule, the weight gradient and input gradient of this layer can be expressed as: (4) The fully connected (FC) layer uses the standard stochastic gradient descent algorithm for parameter updates, which can be represented as follows: (5) in, It's the learning rate. This is the current weight. This is the updated weight.

[0078] Both the LogEig and ReEig layers involve eigenvalue decomposition (EIG) in their forward functions. The traditional chain rule no longer applies. The general backpropagation formula for EIG operations is derived below.

[0079] For the Layer, defining differential mapping ,in Define the adjoint operator. ,satisfy , operator dot product of matrices Assume the first If the layer performs an EIG operation, then the matrix chain rule is as follows: (6) To calculate this gradient, the first... The forward propagation of a layer can be decomposed into Treating EIG operations as a separate virtual layer According to formula (6) and the inner product operation, we can obtain: (7) The variational formula is , and They can be represented as follows: (8) (9) in, Represents element-wise product. Represents symmetry, This means retaining the diagonal elements and setting the off-diagonal elements to zero. From eigenvalues The calculation yielded: (10) Substituting equations (8) and (9) into equation (7), and utilizing the properties of matrix inner products, we obtain the gradient backpropagation formula for the EIG operation as follows: (11) for Figure 3 The LogEig layer of SPDNet shown is shown. Its variational formula is Based on this formula and the properties of matrix inner products, we can obtain... For intermediate variables and The gradient is: (12) (13) for Figure 3 The first ReEig layer of SPDNet shown is shown. Its variational formula is .in, yes The derivative of can be expressed as (14) Based on this variational formula and the properties of matrix inner products, we can obtain... For intermediate variables and The gradient is: (15) (16) Substituting the gradient into formula (11), we can obtain the input gradient of the first LogEig layer as follows: and the input gradient of the first ReEig layer .

[0080] The weight matrix of the BiMap layer is constrained by the Stiefel manifold. Directly updating it using the Euclidean gradient would violate its orthogonality constraint. Therefore, it is necessary to use the Riemann optimization method to calculate the Riemann gradient in the tangent space of the Stiefel manifold and perform Riemann stochastic gradient descent to complete the parameter update.

[0081] for Figure 3 The first BiMap layer of SPDNet is shown. Its Euclidean gradient It can be represented as (17) in, It is the first The weights at the next iteration (on the Stifel manifold).

[0082] The normal component of the Euclidean gradient is ,Will Normal components in Subtracting the component that generates the component tangent to the Stiefel manifold yields the Riemann gradient. This direction is about The fastest descent direction on the Stiefel manifold It can be represented as: (18) Parameter updates are performed on the Stiefel manifold using the Riemann gradient descent algorithm: (19) in, For learning rate, For the retraction operation, It is the first The weights at the next iteration (on the Stifel manifold).

[0083] This application designs a network method for radar target detection on a manifold and designs a differentiable loss function based on the NP criterion to control the phase shift factor (PFA). Using SPDNet as the core detection network, a time-frequency feature SPD matrix is ​​constructed from the radar echo data after STFT time-frequency analysis and serves as the input to SPDNet. SPDNet distinguishes between the target and clutter by learning the differences in instantaneous frequency correlation, energy, and Doppler frequency. By using a differentiable loss function instead of the cross-entropy loss function, SPDNet can achieve end-to-end training under controllable PFA without manual intervention.

[0084] It should be understood that, although Figure 1 The steps in the flowchart are shown sequentially as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated in this application, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Furthermore, Figure 1 At least some of the steps in the process may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least some of the sub-steps or stages of other steps.

[0085] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0086] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of this application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these modifications and improvements all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended claims.

Claims

1. A radar target detection method based on deep manifold networks and NP criteria, characterized in that, The method includes: Acquire radar echo data, perform time-frequency transformation on the radar echo data to obtain a time-frequency spectrum array; perform symmetric positive definiteness and normalization processing on the time-frequency spectrum array to construct a time-frequency feature SPD matrix; The time-frequency feature SPD matrix is ​​input into a preset SPDNet network, and features are extracted and processed sequentially through a bilinear mapping layer, an eigenvalue correction layer, an eigenvalue logarithm layer, and a fully connected layer, and the classification score of the sample is output. The detection probability and false alarm rate are calculated based on the classification score in the differentiable loss function layer constructed based on the NP criterion, and the loss value is output. Based on the loss value, the parameters of the SPDNet network are updated through gradient backpropagation to complete the network training and obtain the trained SPDNet network. The radar echo data to be detected is input into the trained SPDNet network, and the radar target and clutter are distinguished and detected based on the output classification score.

2. The method according to claim 1, characterized in that, The time-frequency feature SPD matrix is ​​constructed by performing symmetric positive definiteness and normalization on the time-frequency spectrum matrix, including: Multiply the time-frequency spectrum matrix by its transpose to obtain a symmetric matrix; perform eigenvalue decomposition on the symmetric matrix and ensure the positive definiteness of the matrix through thresholding to obtain an initial SPD matrix; perform trace normalization on the initial SPD matrix to obtain the final time-frequency feature SPD matrix.

3. The method according to claim 1, characterized in that, The processing expression for the bilinear mapping layer is as follows: in, It is a bilinear mapping. It is the input matrix. The transformation matrix is... and Representing different matrix dimensions, k Indicates the network layer number. T This indicates the transpose operation. This represents the current output matrix.

4. The method according to claim 1, characterized in that, The processing expression for the eigenvalue correction layer is as follows: in, It is a nonlinear transformation. It is the input matrix. Indicates the correction threshold. k Indicates the network layer number. T This indicates the transpose operation. It is a diagonal matrix ,for: , It is the identity matrix. For the input matrix The eigenvalue diagonal matrix obtained after eigenvalue decomposition For the input matrix The eigenvector matrix obtained after eigenvalue decomposition has column vectors as follows: The unit orthogonal eigenvectors, T This indicates the transpose operation.

5. The method according to claim 1, characterized in that, The processing expression for the eigenvalue logarithmic layer is as follows: in, Let be the transformation function of the logarithmic eigenvalue layer of the k-th layer. For the input matrix The eigenvalue diagonal matrix obtained after eigenvalue decomposition For the input matrix The eigenvector matrix obtained after eigenvalue decomposition has column vectors as follows: The unit orthogonal eigenvectors, T This indicates the transpose operation.

6. The method according to claim 1, characterized in that, The differentiable NP loss function in the differentiable loss function layer constructed based on the NP criterion is: in, It is the result of the softmax function calculating the output score of the fully connected layer, that is, the output of the softmax function on the samples. The probability of being identified as a target. These are the true labels of the samples; 1 represents that the sample is the target, and 0 represents that the sample is clutter. The number of samples in a single training batch. It's a hyperparameter. These are the preset PFA constraint values.

7. The method according to claim 1, characterized in that, During the gradient backpropagation process, the gradient calculation expression for the eigenvalue decomposition operation is as follows: in, It's the learning rate. This is the current weight. This is the updated weight. It is the output. It is the first l The partial derivative of the loss function corresponding to the layer with respect to the current weight matrix W. It is the first l+1 The loss function corresponding to the layer affects the output. The partial derivatives, It is the first l The partial derivative of the forward propagation transformation function of the layer with respect to the current weight matrix W. It is the first l The input matrix of the layer.

8. The method according to claim 1, characterized in that, The parameter update method of the bilinear mapping layer is as follows: in, For learning rate, For the retraction operation, It is the first The weights at the next iteration For the first The weights at the next iteration , For the Riemann gradient, Let be the normal component of the Euclidean gradient.

9. The method according to claim 1, characterized in that, The radar echo data is subjected to time-frequency transformation to obtain a time-spectrum array, including: The radar echo data is subjected to time-frequency transformation to obtain the time-spectrum array. in, It is a window function. It is a discrete time series. It is the distance cell number. It is the pulse sequence number.

10. The method according to claim 2, characterized in that, The symmetric matrix is ​​subjected to eigenvalue decomposition, and the positive definiteness of the matrix is ​​ensured by thresholding to obtain the initial SPD matrix, including: The symmetric matrix is ​​subjected to eigenvalue decomposition, and the positive definiteness of the matrix is ​​ensured by thresholding, resulting in the initial SPD matrix. in, For the threshold, It is the identity matrix. The eigenvector matrix, It is a diagonal matrix of eigenvalues.

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