Space micro-motion target identification method based on networking radar multi-domain feature fusion

Abstract

The invention provides a novel spatial micro-motion target identification method based on a radar network system, and the method comprises the following steps: building a target micro-motion model and a signal model, and constructing a data set of an RCS sequence, a time Doppler image and an HRRP sequence for the spatial micro-motion target identification of a networking radar system; constructing an adaptive feature fusion sub-network; xCA and LA-Att modules with linear complexity are introduced, fine-grained features are effectively extracted, self-adaptive weighted fusion of multi-domain features is realized by adopting a CAFM module, and information useful for recognition is effectively enhanced; and designing a time-space modeling sub-network based on BiGRU and double-graph fusion. According to the method, multi-band and multi-view target features can be obtained, and more accurate information is provided for identification of a spatial micro-motion target; according to the method, the feature information of each radar in the heterogeneous radar network is fully utilized, the recognition precision of 96% or above can still be obtained under the condition that the signal-to-noise ratio is 0dB, and the effectiveness and robustness of the method are obvious.

Description

Technical Field

[0001] The present invention relates to signal and information processing technology, and in particular to a new method for spatial micro-motion target recognition based on multi-domain feature fusion of networked radar. Background Art

[0002] As humanity continues to explore and utilize outer space, a large amount of space debris and ballistic targets pose a significant threat to space and homeland security. These space targets often exhibit micro-motions such as precession, nutation, wobble, and tumble, producing time-varying modulations in radar echoes. Extracting effective features from these unique time-varying modulations for radar target recognition has attracted widespread attention.

[0003] Currently, the features used for spatial micro-motion target recognition primarily include radar cross-section (RCS) sequences, time Doppler images, and high-resolution range profile (HRRP) sequences. The RCS sequence reflects the overall scattering intensity of a target and can be obtained from both narrowband and wideband radars. Time Doppler images, obtained through time-frequency analysis, contain information such as the material's structure, size, distribution of scattering centers, and micro-motion characteristics. The HRRP sequence, obtained from wideband radars, represents the projection of scattering centers along the radar's line of sight. It can reflect the target's fine structure and micro-motion characteristics. Furthermore, a cadence-velocity diagram (CVD), obtained by performing a time-domain Fourier transform on the time Doppler image, can also be used for spatial micro-motion target recognition. Spatial micro-motion target recognition based on range Doppler images and ballistic trajectories has also been studied.

[0004] In recent years, thanks to the advancement of high-data-rate communication technologies and signal processing capabilities, networked radar systems have been widely studied for the recognition of micro-motion targets in space. Specifically, from the dual perspectives of radar configuration and feature domain, existing approaches for identifying micro-motion targets in space can be divided into three categories: single-domain feature extraction methods based on monostatic radar, multi-domain feature fusion methods based on monostatic radar, and single-domain feature extraction methods based on networked radar systems.

[0005] In the single-domain feature extraction method based on monostatic radar, features are mainly extracted from RCS sequence, time Doppler image, HRRP sequence, range Doppler image, CVD and ballistic trajectory for the recognition of spatial micro-motion targets.

[0006] Research on single-domain feature extraction based on monostatic radar has made great progress. However, in real-world scenarios, some radars can simultaneously acquire narrowband and broadband features. Multi-domain feature fusion can further improve target recognition accuracy. Therefore, some scholars have conducted research on multi-domain feature fusion recognition methods based on monostatic radar. These mainly include adaptive fusion recognition methods for RCS sequences, time Doppler images, and HRRP sequences; fusion recognition methods for time Doppler images and HRRP sequences; fusion recognition methods for extracting five-dimensional feature vectors from RCS sequences and time Doppler images; fusion recognition methods for time Doppler images and CVD; decision-level fusion recognition methods for RCS sequences, time Doppler images, and HRRP sequences; range instantaneous Doppler (RID) images; pixel-level fusion recognition methods for time Doppler images, HRRP sequences, and RID images; and time-range-velocity-power four-dimensional point cloud fusion recognition methods.

[0007] Networked radar systems can obtain multi-band and multi-view information of targets. They can effectively overcome the occlusion effect and improve the recognition performance of spatial micro-movement targets. In the single-domain feature extraction method based on networked radar systems, Meng Han et al. from Beijing University of Posts and Telecommunications proposed a spatio-temporal-frequency graph attention convolutional network (STFGACN) based on heterogeneous networked radar systems in "Spatio-Temporal-Frequency Graph Attention Convolutional Network for Aircraft Recognition Based on Heterogeneous Radar Network" (IEEE Transactions on Aerospace and Electronic Systems, 2022, 58(6): 5548-5559). On this basis, the team proposed a semantic feature-enhanced graph attention network for aircraft recognition in "Semantic Feature-Enhanced Graph Attention Network for Radar Target Recognition in Heterogeneous Radar Network" (IEEE Sensors Journal, 2023, 23 (7): 6369-6377). The above two methods are both used for aircraft target recognition. Currently, there are few studies on spatial micro-motion target recognition based on networked radar systems. Yuan-Peng Zhang et al. proposed a spatial target recognition method for networked radar systems based on BiGRU-Transformer and Dual Graph Fusion Network in "Space Target Recognition Based on Radar Network Systems with BiGRU-Transformer and Dual Graph Fusion Network" (IEEE Transactions on Radar Systems, 2024, 2: 950-965). This is the only study that uses networked radar systems for spatial micro-motion target recognition.

[0008] In reality, in networked radar systems, some radars can simultaneously obtain narrowband features (such as RCS sequences and time-Doppler images) and wideband features (such as HRRP sequences), while others can only obtain narrowband features. Even at low pulse repetition frequencies (PRFs), some radars can only obtain RCS sequences. Multi-domain feature-level fusion recognition methods for networked radar systems have yet to be studied.

[0009] If multiple features such as RCS sequence, time Doppler image and HRRP sequence can be comprehensively utilized, it is expected to further improve the effectiveness and robustness of spatial micro-motion target recognition based on networked radar systems. Summary of the Invention

[0010] In view of the problems existing in the prior art, the present invention provides a spatial micro-motion target recognition method based on multi-domain feature fusion of networked radar. The method is based on a radar network system.

[0011] The system consists of N radars. The networked radar system is considered as an undirected fully connected graph with N nodes. represents the set of nodes, ν i represents the i-th radar node; ε={e i,j} i,j＝1,2, ... N represents the set of edges between nodes, e i,j Represents node ν i and ν j The edge between them; A∈R N×N represents the adjacency matrix, R represents the set of real numbers; A={A i,j |i,j=1,2,...N};A i,j Represents node ν i and ν j The weight of the edge between the two nodes represents the connection strength between the two nodes;

[0012] Assume that in a networked radar system there are N1 low-PRF narrowband radars, radar A, which can only obtain RCS sequences; N2 high-PRF narrowband radars, radar B, which can obtain two features: RCS sequences and time Doppler images; and N-N1-N2 wideband radars, radar C, which can simultaneously obtain three features: RCS sequences, time Doppler images, and HRRP sequences. The feature set of the networked radar system is η = {N × RCS, (N-N1) × TF, N2 × HRRP}. A complex nonlinear function f(·) is trained on the graph to map the image signal X to the target category label Y∈{l1,l2,…,l C}, where C represents the number of target categories, li (i=1,2,...C) represents the i-th category; the recognition process of spatial micro-motion targets is expressed as

[0013] l c =f(X)(1)

[0014] The method is as follows:

[0015] Step 1: Create a 3D CAD model of the target and use electromagnetic calculation software to generate 360-degree multi-carrier static electromagnetic scattering data;

[0016] A 3D CAD model of the target was created. Then, the electromagnetic calculation software FEKO was used to generate 360-degree multi-carrier static electromagnetic scattering data for the three 3D geometric models. The ideal dynamic radar echo corresponding to the attitude angle was retrieved from the static electromagnetic scattering data. The noise was assumed to be Gaussian white noise. The dynamic radar echo generation process is described below.

[0017] The micro-motion forms of the target to be identified include precession, nutation, swing and roll; the micro-motion matrix R at time t is rot (t) is expressed as

[0018]

[0019] Among them, R C (t), R S (t), R W (t) and R T (t) represents the cone rotation matrix, spin matrix, swing matrix and roll matrix of the target respectively;

[0020] The position vector r(t) of the target symmetry axis is expressed as

[0021] r(t)=R rot (t)·R init (0,0,1) T (3)

[0022] Among them, R init Represents the initial Euler matrix, (0,0,1) T Represents the position of the target's rotational symmetry axis in the target's local coordinate system;

[0023] Target attitude angle β a (t) is expressed as

[0024]

[0025] Among them, n LOS Indicates the radar line of sight direction;

[0026] After obtaining the attitude angle, the value corresponding to the attitude angle is queried in the static electromagnetic scattering data to obtain the ideal dynamic radar echo data. Gaussian white noise is added to the echo data to simulate the actual radar echo data.

[0027] The precessing cone, precessing cone, nutating cone, nutating cone, oscillating cone, oscillating cone, tumbling cone, tumbling cone, and tumbling cylinder are named T1, T2, T3, T4, T5, T6, T7, T8, and T9, respectively. Multiple radars are used to simultaneously observe the target, and the observation data obtained include RCS sequences. To reduce the size of the dataset, time Doppler images and HRRP sequences are sampled to obtain time Doppler images and HRRP sequences. The dataset is divided into training, test, and validation sets according to the initial attitude angle. The model is trained.

[0028] Step 2: Construct an adaptive feature fusion subnetwork; introduce XCA and LA-Att modules with linear complexity to effectively extract fine-grained features; use CAFM module to achieve adaptive weighted fusion of multi-domain features, effectively enhancing information useful for recognition;

[0029] 1) Multi-domain feature extraction module MDFEM

[0030] A one-dimensional CNN is used to extract temporal features of RCS sequences, time Doppler images, and HRRP sequences. An MLP layer is used to unify the feature vectors into the same dimension. The one-dimensional CNN and MLP layers together form a multi-domain feature extraction module (MDFEM).

[0031] 2) XCA module

[0032] In order to extract deeper feature information, the linear attention module XCA module is introduced; the input feature map X is combined with the weight matrix W of the query, key and value Q 、W K and W V Multiply and linearly project it onto the query, key, and value; query Q = XW Q , key K = XW K Sum V = XW V ; XCA function is expressed as

[0033]

[0034] In the formula represents the L2 normalization of K; represents the L2 normalization of Q, and T represents the matrix transpose; the L2 normalization operation can enhance the stability of model training; the learnable temperature parameter τ is introduced; the Softmax(·) expression is

[0035] 3) LA-Att module

[0036] To further enhance the richness of feature information, the LA-Att module is introduced; in the linear angular attention module, the angular kernel is defined as the similarity measurement function Sim(Q i ,K j );

[0037]

[0038] Among them, Q i and K j Represent the i-th element of Q and the j-th element of K respectively, and m is a positive integer;

[0039] The LA-Att module is approximately

[0040]

[0041] Among them, M depthwise represents a deep convolutional neural network with fewer parameters, M SA represents a sparse attention mechanism;

[0042] The nonlinear term in the LA-Att mechanism can be used with a deep convolutional neural network M with fewer parameters. depthwise and sparse attention mechanism M SA Instead; therefore, the complexity of the LA-Att module can be regarded as linear; the sparse attention mechanism M SA It can be expressed as

[0043]

[0044] Among them, ε represents the sparse threshold, which is set to 0.02;

[0045] 4) Adaptive feature fusion module

[0046] Adaptive feature fusion module CAFM is introduced, which includes CAM and SAM; by merging the feature map F obtained by LA-Att LA Perform average pooling and maximum pooling to obtain two different channel descriptions: F LA First channel description and F LA The second channel description AvgPool represents the average pooling operation, MaxPool represents the maximum pooling operation; the feature map F obtained by XCA XCA Performing the same operation will produce two different channel descriptions: F XCA First channel description and F XCA The second channel description For the feature map F LA Channel description and For example, it is input into the weight-sharing multi-layer perceptron MLP, and then the obtained features are added and input into the ReLU activation function to obtain F LA The channel weight coefficient matrix M LA-CACM , and F XCA The channel weight coefficient matrix is ​​M XCA-CACM The calculation process is

[0047]

[0048] Where W1 and W0 represent the first and second learnable matrix parameters respectively;

[0049] Multiply the above two weight coefficient matrices to obtain the cross matrix M cross Through the Softmax activation function, and then with the feature map F LA and F XCA Multiply them separately to get the channel attention feature map CA LA and CA XCA The calculation process is expressed as

[0050] CA LA =Softmax(M cross )F LA (11)

[0051] CA XCA =Softmax(M cross )F XCA (12)

[0052] Channel attention feature map CA in SAFM LA and CA XCA Perform average pooling and maximum pooling operations respectively, CA LA The average pooling features and maximum pooling features are and CA XCA The average pooling features and maximum pooling features are and The two pooling features, average pooling feature and maximum pooling feature, are concatenated in the channel dimension and input into a shared convolutional layer to obtain the spatial weight coefficient M LA-SAFM and M XCA-SAFM The calculation process is expressed as

[0053]

[0054] in, Represents the feature splicing operation; the spatial weight coefficient M LA-SAFM and M XCA-SAFM After passing through the Softmax activation function and the feature map F LA and F XCA Multiply them separately to get the spatial attention feature map SA LA and SA XCA The calculation process is expressed as

[0055] SA LA =Softmax(M LA-SAM )F LA (15)

[0056] SA XCA =Softmax(M XCA-SAM )F XCA (16)

[0057] Add the residual connection to the fusion module; the final output F of the adaptive feature fusion module CAFM for

[0058] F CAFM =(SA LA +F LA )+(SA XCA +F XCA )(17)

[0059] The above content is for broadband radar. When there are only two features, RCS sequence and time Doppler image, the feature extraction and fusion process is the same as the above process. When there is only one feature, RCS sequence, only the feature extraction module is retained.

[0060] Step 3: Design a spatiotemporal modeling subnetwork based on BiGRU and dual-image fusion, and design a prediction output module;

[0061] A spatiotemporal feature extraction subnetwork combining BiGRU and DGFN, consisting of a temporal feature extraction module and a spatial feature extraction module; the temporal feature extraction module consists of M-layer BiGRU stacked; the spatial feature extraction module consists of P-layer DGFN stacked;

[0062] The geographical proximity between radars is used to calculate the predefined adjacency matrix A Re ; A Re The elements of

[0063]

[0064] Among them, d i,j Represents node ν i and node ν j The distance between i and fj Represents node ν respectively i and node ν j The radar operating frequency; constant λ∈[0,1), λ can be grid searched to obtain the corresponding λ with the best recognition performance;

[0065] In order to capture deeper spatial dependencies in the target echo, we stack P layers of GCN. Assume that the output of the p-1th layer is Then the output of layer p is Expressed as

[0066]

[0067] Among them, LeakyReLU(·) represents the leaky rectified linear unit activation function, Represents the weight coefficient, which is a learnable network parameter; represents the normalized adjacency matrix after adding self-loops; I N represents the N×N identity matrix; Represents the normalized adjacency matrix The measurement matrix of

[0068] Adopting the adaptive graph method, we learn the potential spatial features end-to-end in a data-driven way. Specifically, we randomly initialize two self-learning node embeddings E1 and E2, and the adaptive adjacency matrix Expressed as

[0069]

[0070] Output of adaptive graph convolution Expressed as

[0071]

[0072] in, represents the adaptive adjacency matrix after k updates in the p-th layer of GCN, Represents the weight coefficient matrix, which is learnable during network training;

[0073] The prediction output layer is composed of a multi-layer perceptron, and finally a feature vector O∈R is obtained. C , R represents the real number combination, C represents the dimension, and O outputs a probability distribution P(k) after passing through the Softmax function;

[0074] The recognition result corresponds to the category with the maximum likelihood function, that is, the category to which the target belongs; the cross entropy loss function is used as the cost function during model training; the accuracy P is usedacc And F1-score are used as quantitative evaluation indicators of target recognition effect.

[0075] In step 1 of a specific embodiment of the present invention, the data set is divided into a training set, a test set, and a validation set in a ratio of 7:2:1 according to the initial posture angle, and the model is trained using data with a signal-to-noise ratio of 5 dB.

[0076] In step three of another specific embodiment of the present invention, a grid search is performed in λ = [0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9] to obtain the overall recognition accuracy corresponding to the above 10 parameters. The parameter that achieves the best recognition effect is determined to be the corresponding λ.

[0077] The beneficial effects of the present invention are as follows: the existing space micro-motion target recognition methods based on single-base radars are limited by the observation angle of view, and the existing space micro-motion target recognition methods based on networked radar systems are all based on RCS sequences, and the feature dimensions are not rich enough. They fail to fully utilize the multi-feature fusion advantages of heterogeneous radar network systems, and the recognition performance of the above methods needs to be further improved. The space micro-motion target recognition method based on multi-feature level fusion of networked radar systems proposed in the present invention can obtain multi-band and multi-perspective target features, providing more accurate information for the identification of space micro-motion targets. The present invention makes full use of the feature information of each radar in the heterogeneous radar network. When the signal-to-noise ratio is 0dB, the method of the present invention can still obtain an identification accuracy of more than 96%. A large number of experiments have proved the effectiveness and robustness of the method of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0078] Figure 1(a) is a schematic diagram of a spatial micro-motion target observation scenario based on a heterogeneous radar network system, and Figure 1(b) is a graphical representation of spatiotemporal modeling based on a heterogeneous radar network system;

[0079] Figure 2(a) is a diagram of the overall network architecture of the method of the present invention, Figure 2(b) is a diagram of the structure of the feature extraction and adaptive fusion sub-network, and Figure 2(c) is a diagram of the GRU structure;

[0080] Figure 3(a) is a diagram of a cone-cylinder model in a three-dimensional geometric model of a space target, Figure 3(b) is a diagram of a cone model in a three-dimensional geometric model of a space target, and Figure 3(c) is a diagram of a cylinder model in a three-dimensional geometric model of a space target;

[0081] Figure 4 Flowchart for radar echo generation;

[0082] Figure 5These are some images of the dataset. T1, T2, T3, T4, T5, T6, T7, T8, and T9 in the figure represent the precessing cone, precessing cone, nutating cone, nutating cone, oscillating cone, oscillating cone, tumbling cone, tumbling cone, and tumbling cylinder, respectively.

[0083] Figure 6(a) is the confusion matrix when the RCS sequence is used for recognition, Figure 6(b) is the confusion matrix when the time Doppler image is used for recognition, Figure 6(c) is the confusion matrix when the HRRP sequence is used for recognition, Figure 6(d) is the confusion matrix when the RCS sequence and the time Doppler image are used for recognition, Figure 6(e) is the confusion matrix when the RCS sequence and the HRRP sequence are used for recognition, Figure 6(f) is the confusion matrix when the time Doppler image and the HRRP sequence are used for recognition, and Figure 6(g) is the confusion matrix when the RCS sequence, the time Doppler image and the HRRP sequence are used for recognition, which is the method proposed in the present invention;

[0084] Figure 7(a) is the confusion matrix when CAFM+BiGRU+DGFN is used for recognition, Figure 7(b) is the confusion matrix when Multi-Domain Feature Extraction Module (MDFEM)+BiGRU+DGFN is used for recognition, Figure 7(c) is the confusion matrix when MDFEM+CAFM+DGFN is used for recognition, Figure 7(d) is the confusion matrix when MDFEM+CAFM+BiGRU is used for recognition, Figure 7(e) is the confusion matrix when MDFEM+CAFM+BiGRU+Adaptive Graph is used for recognition, Figure 7(f) is the confusion matrix when MDFEM+CAFM+BiGRU+Predefined Graph is used for recognition, and Figure 7(g) is the confusion matrix when MDFEM+CAFM+BiGRU+DGFN is used for recognition, which is the method proposed in the present invention;

[0085] Figure 8(a) shows the recognition accuracy of the baseline method, and Figure 8(b) shows the F1-score of the baseline method;

[0086] Figure 9 is the recognition accuracy under different λ. DETAILED DESCRIPTION

[0087] The present invention will be further described below with reference to the accompanying drawings and examples of the present invention.

[0088] The present invention intends to extract and fuse features from the RCS sequence, time Doppler image and HRRP sequence collected by the networked radar system to realize spatial micro-motion target recognition.

[0089] As shown in Figure 1, the radar network system consists of N radars. The networked radar system can be regarded as an undirected fully connected graph with N nodes. represents the set of nodes, ν i Represents the i-th radar node. ε={e i,j} i,j＝1,2,...N represents the set of edges between nodes, e i,j Represents node ν i and ν j The edges between them. N×N A={A i,j |i,j=1,2,...N}. A i,j Represents node ν i and ν j The weight of the edge between two nodes can represent the strength of the connection between them.

[0090] Since the functions of the radars in the networked radar system are different, the features obtained are also different. Assume that there are N1 low-PRF narrowband radars (radar A) in the networked radar system, and this radar can only obtain the RCS sequence. There are N2 high-PRF narrowband radars (radar B), which can obtain two features: RCS sequence and time Doppler image. There are also N-N1-N2 broadband radars (radar C), which can simultaneously obtain three features of RCS sequence, time Doppler image and HRRP sequence. Therefore, the feature set of the networked radar system is η = {N×RCS, (N-N1)×TF, N2×HRRP}. The goal of the present invention is to A complex nonlinear function f(·) is trained on the graph to map the image signal X to the target category label Y∈{l1,l2,…,l C}, where C represents the number of target categories, l i (i=1,2,...C) represents the i-th category. The recognition process of spatial micro-motion targets can be expressed as

[0091] l c =f(X)(1)

[0092] The overall network architecture proposed in this invention is shown in Figure 2(a). First, the features collected by the networked radar system are input into the multi-domain feature extraction and adaptive fusion subnetwork to extract fine-grained features. The extracted features are then input into the BiGRU layer to extract temporal features. The BiGRU layer is well known to those skilled in the art. Subsequently, the DGFN module, which combines an adaptive graph with a predefined graph, is used to extract spatial dependencies between nodes. Finally, the extracted spatiotemporal feature vectors are input into the prediction layer, which uses an MLP (MLP layer is well known to those skilled in the art) to achieve classification and recognition of nine target categories, resulting in robust recognition results.

[0093] The multi-domain feature extraction and adaptive fusion subnetwork is shown in Figure 2(b). This subnetwork is described in detail using RCS sequence, temporal Doppler image, and HRRP sequence as examples. First, a one-dimensional CNN (well-known to those skilled in the art) and an MLP layer are used to unify the three features (RCS sequence, temporal Doppler image, and HRRP sequence) to the same dimension. Second, the three features are concatenated into a single feature vector, which is fed into the XCA module and the LA-Att module, respectively. The XCA module and the LA-Att module are processed in parallel, enabling efficient and parallel extraction of fine-grained features. Finally, the extracted features are fed into the CAFM for adaptive feature fusion. The CAFM primarily consists of two components, the CAM and the SAM, connected in series, focusing on important information that is beneficial for target recognition. The fused features are then fed into the spatiotemporal feature extraction subnetwork (comprising a BiGRU module and a DGFN module). Temporal features are extracted using a stack of BiGRU layers (well-known to those skilled in the art). The BiGRU layer consists of a bidirectional GRU structure, as shown in Figure 2(c). Spatial features are extracted using a stacked DGFN based on a predefined graph and an adaptive graph (as described in the subsequent step 3). The predefined graph can directly reflect the topological structure between radar nodes. Based on the predefined graph, the data-driven approach of the adaptive graph is used to extract potential spatial information end-to-end (as described before and after the subsequent formula (20)). Finally, the captured spatiotemporal feature vector is input into the prediction layer to obtain the final recognition result. The specific description is as follows:

[0094] Step 1: Create a 3D CAD model of the target (three geometric models: cone, cone-cylinder, and cylinder, used to simulate typical targets in space) and use electromagnetic calculation software to generate 360-degree multi-carrier static electromagnetic scattering data.

[0095] Figure 3 shows three-dimensional geometric models of three types of space targets, among which Figure 3(a) is a diagram of a cone-cylinder model in the three-dimensional geometric model of the space target, Figure 3(b) is a diagram of a cone model in the three-dimensional geometric model of the space target, and Figure 3(c) is a diagram of a cylinder model in the three-dimensional geometric model of the space target. To establish a three-dimensional CAD model of the target, three smooth and symmetrical three-dimensional models are established in the FEKO software, namely, a cone, a cone-cylinder and a cylinder. This is well known to those skilled in the art. Afterwards, the electromagnetic calculation software FEKO is used to generate 360-degree multi-carrier static electromagnetic scattering data of the above three three-dimensional geometric models. The ideal dynamic radar echo corresponding to the attitude angle can be queried in the static electromagnetic scattering data. Assume that the noise is Gaussian white noise. The process of generating dynamic radar echo is as follows: Figure 4 As shown, the details are as follows.

[0096] The micro-motion forms of the target to be identified by the present invention include precession, nutation, swing and tumble. The micro-motion matrix R at time t rot (t) can be expressed as

[0097]

[0098] Among them, R C (t), R S (t), R W (t) and R T (t) represents the cone rotation matrix, spin matrix, swing matrix and roll matrix of the target respectively.

[0099] The position vector r(t) of the target symmetry axis can be expressed as

[0100] r(t)=R rot (t)·R init (0,0,1) T (3)

[0101] Among them, R init Represents the initial Euler matrix, (0,0,1) T Represents the position of the target's rotational symmetry axis in the target's local coordinate system.

[0102] Target attitude angle β a (t) can be expressed as

[0103]

[0104] Among them, n LOS Indicates the radar line of sight direction.

[0105] After obtaining the attitude angle, the value corresponding to the attitude angle can be queried in the static electromagnetic scattering data, thereby obtaining the ideal dynamic radar echo data. Adding Gaussian white noise to the echo data can simulate the actual radar echo data.

[0106] In this paper, the precessing cone, precessing cone, nutating cone, nutating cone, oscillating cone, oscillating cone, tumbling cone, tumbling cone, and tumbling cylinder are named T1, T2, T3, T4, T5, T6, T7, T8, and T9, respectively. Each target is assumed to have 10 initial attitude angles. The radar parameter settings are shown in Table 1, and the micro-motion parameter settings are shown in Table 2. A precessing target has 100 continuous frequencies. A nutating target has 20 continuous frequencies and 5 oscillation frequencies. An oscillating target has 25 oscillation frequencies and 4 oscillation angles. A tumbling target has 100 tumbling frequencies. A total of nine radars were used: four P-band radars with a carrier frequency of 430 MHz, polarization mode HH, and a pulse repetition frequency (PRF) of 100 Hz; three C-band radars with a carrier frequency of 5.85 GHz, polarization mode VV, and a pulse repetition frequency (PRF) of 2000 Hz; and two X-band radars with a carrier frequency of 10 GHz, polarization mode HH, and a pulse repetition frequency (PRF) of 2000 Hz. These radars simultaneously observed targets within a 2-second period. Therefore, the observation data for each target consisted of 4000 RCS sequences with a dimension of 1 × 200 and 5000 RCS sequences with a dimension of 1 × 4000. Furthermore, to reduce the size of the dataset, the time Doppler images and HRRP sequences were sub-sampled. The dataset also includes 5000 sub-sampled time Doppler images with a dimension of 200 × 100 and 2000 HRRP sequences with a dimension of 256 × 200. Figure 5 Shows some samples of the dataset Figure 5 In the RCS sequence diagram, the horizontal axis represents time units, and the vertical axis represents normalized amplitude. In the time Doppler image, the horizontal axis represents time units, and the vertical axis represents frequency units. In the HRRP sequence diagram, the horizontal axis represents time units, and the vertical axis represents distance units. Based on the initial attitude angle, the dataset is divided into training, test, and validation sets, for example, in a ratio of 7:2:1. The model is trained using data with a signal-to-noise ratio of 5 dB.

[0107] Table 1 Radar parameter settings

[0108]

[0109] Table 2 Micro-motion parameter settings

[0110]

[0111] Step 2: Construct an adaptive feature fusion subnetwork. Introduce the linearly complex XCA and LA-Att modules (described later) to effectively extract fine-grained features. Adopt the CAFM module to achieve adaptive weighted fusion of multi-domain features, effectively enhancing information useful for recognition.

[0112] 1) Multi-Domain Feature Extraction Module (MDFEM)

[0113] RCS sequences are natural time series. Time Doppler images and HRRP sequences can also be viewed as multi-channel, one-dimensional time series data. Therefore, a one-dimensional CNN can be used to extract the spatial features of these time series. The MLP layer can be used to unify the feature vectors to the same dimension. Together, the one-dimensional CNN and the MLP layer form the multi-domain feature extraction module (MDFEM).

[0114] 2) XCA module

[0115] To extract deeper feature information, the linear attention module XCA module is introduced. The XCA module uses the self-attention mechanism between features to replace the explicit full pairing interaction between tokens in the traditional self-attention mechanism. Specifically, the interaction is achieved by obtaining the attention weight based on the cross-covariance matrix between the query and the key. This method can effectively capture important features and improve model performance. By combining the input feature map X with the weight matrix W of the query, key and value Q 、W K and W V Multiply and linearly project it onto the query, key, and value. Query Q = XW Q , key K = XW K Sum V = XW V The XCA function can be expressed as

[0116]

[0117] In the formula represents the L2 normalization of K. represents the L2 normalization of Q, and T represents the matrix transpose. The L2 normalization operation can enhance the stability of model training. At the same time, in order to obtain a more uniform weight distribution and enhance the feature representation ability, a learnable temperature parameter τ is introduced. Softmax(·) is the activation function used for multi-classification problems, and its expression is

[0118] 3) LA-Att module

[0119] To further enhance the richness of feature information, another linear attention module, namely LA-Att module, is introduced to complement XCA. The LA-Att mechanism calculates spectral similarity through angular kernel, replacing the existing Softmax-based attention mechanism. In the linear angular attention module, the angular kernel is defined as the similarity measure function Sim(Q i ,K j ).

[0120]

[0121] Among them, Q i and K jThey represent the i-th element of Q and the j-th element of K respectively, and m is a positive integer.

[0122] The LA-Att module can be approximated as

[0123]

[0124] Among them, M depthwise represents a deep convolutional neural network with fewer parameters, M SA represents the sparse attention mechanism.

[0125] The nonlinear term in the LA-Att mechanism can be represented by a deep convolutional neural network M with fewer parameters. depthwise and sparse attention mechanism M SA Instead. Therefore, the complexity of the LA-Att module can be regarded as linear. Sparse attention mechanism M SA It can be expressed as

[0126]

[0127] Here, ε represents the sparse threshold, which is set to 0.02.

[0128] 4) Adaptive feature fusion module

[0129] The present invention introduces an adaptive feature fusion module (CAFM) to promote the deep fusion of RCS sequence, time Doppler image and HRRP sequence. CAFM can enhance the important information useful for target recognition. CAFM mainly consists of CAM and SAM. CAM focuses on "what" is meaningful in the feature map, while SAFM focuses on "where" the meaningful information is located. By merging the feature map F obtained by LA-Att LA Perform average pooling and maximum pooling to obtain two different channel descriptions: F LA First channel description and F LA The second channel description AvgPool represents the average pooling operation, and MaxPool represents the maximum pooling operation. XCA Performing the same operation will produce two different channel descriptions: F XCA First channel description and F XCA The second channel description With feature map F LA Channel description and As an example, input it into the weight-sharing multi-layer perceptron MLP, then add the obtained features and input them into the ReLU activation function to get F LA The channel weight coefficient matrix MLA-CACM , and F XCA The channel weight coefficient matrix is ​​M XCA-CACM The calculation process is

[0130]

[0131] Where W1 and W0 represent the first and second learnable matrix parameters respectively.

[0132] Multiply the above two weight coefficient matrices to obtain the cross matrix Then M cross Through the Softmax activation function, and then with the feature map F LA and F XCA Multiply them separately to get the channel attention feature map CA LA and CA XCA The calculation process can be expressed as

[0133] CA LA =Softmax(M cross )F LA (11)

[0134] CA XCA =Softmax(M cross )F XCA (12)

[0135] Channel attention feature map CA in SAFM LA and CA XCA Perform average pooling and maximum pooling operations respectively, CA LA The average pooling features and maximum pooling features are and CA XCA The average pooling features and maximum pooling features are and The two pooling features, average pooling feature and maximum pooling feature, are concatenated in the channel dimension and input into a shared convolutional layer to obtain the spatial weight coefficient M LA-SAFM and M XCA-SAFM The calculation process can be expressed as

[0136]

[0137] in, Represents the feature splicing operation. The spatial weight coefficient M LA-SAFM and M XCA-SAFM After passing through the Softmax activation function and the feature map F LA and F XCA Multiply them separately to get the spatial attention feature map SA LA and SAXCA The calculation process can be expressed as

[0138] SA LA =Softmax(M LA-SAM )F LA (15)

[0139] SA XCA =Softmax(M XCA-SAM )F XCA (16)

[0140] Finally, the residual connection is added to the fusion module. The final output F of the adaptive feature fusion module is CAFM It can be expressed as

[0141] F CAFM =(SA LA +F LA )+(SA XCA +F XCA )(17)

[0142] The above discussion uses broadband radar as an example to illustrate the feature extraction and adaptive fusion process for three features: RCS sequence, time Doppler profile, and HRRP sequence. When only RCS sequence and time Doppler profile are used, the feature extraction and fusion process is the same as above. When only RCS sequence is used, only the feature extraction module is retained.

[0143] Step 3: Design a spatiotemporal modeling subnetwork based on BiGRU and dual-image fusion, and design a prediction output module.

[0144] A spatiotemporal feature extraction subnetwork combining the BiGRU (well-known to those skilled in the art) and the DGFN is proposed. The BiGRU effectively extracts temporal features of targets. The DGFN effectively models the explicit topology and implicit dependencies between radar nodes by co-optimizing a predefined graph and an adaptive graph. A prediction output module consisting of a multilayer perceptron is designed. The high-dimensional spatiotemporal feature vectors extracted by the DGFN are input into the prediction output module to obtain the final category prediction result.

[0145] The spatiotemporal feature extraction subnetwork consists of a temporal feature extraction module and a spatial feature extraction module. The temporal feature extraction module consists of M layers of stacked BiGRUs. The spatial feature extraction module consists of P layers of stacked DGFNs. In the stacked DGFN, a combination of predefined and adaptive graphs is used to extract spatial dependencies between nodes. The predefined graph, constructed based on the Euclidean distance between radars, directly reflects the topological structure between nodes and enables the initial extraction of relatively accurate spatial features. Simultaneously, an adaptive graph is constructed based on the predefined graph to extract deeper spatial features end-to-end. GRU is a gating mechanism in recurrent neural networks. It is used to mitigate the vanishing or exploding gradient phenomenon that occurs during backpropagation in RNNs. In a GRU, the update gate modulates previous information, and the reset gate controls how much previous information is forgotten. The GRU layer structure is shown in Figure 2(c).

[0146] The geographical proximity between radars is used to calculate a predefined adjacency matrix A of a predefined graph Re . A Re The elements of can be represented as

[0147]

[0148] Among them, d i,j Represents node ν i and node ν j The distance between i and f j Represents node ν respectively i and node ν j The radar operating frequency. A constant λ∈[0,1) can be used to perform a grid search on λ, finding the λ with the best recognition performance. For example, the search method is to divide the range from 0 to 1 into P equal parts, such as 0, 0.1, 0.2, ..., 0.9, 1. The parameter that yields the best recognition performance is determined as the corresponding λ.

[0149] In order to capture deeper spatial dependencies in the target echo, the present invention stacks P layers of GCN. Assume that the output of the p-1th layer is Then the output of layer p is It can be expressed as

[0150]

[0151] Where LeakyReLU(·) represents the leaky rectified linear unit (rectified linear unit with leakage) activation function (Andrew L. Maas, Awni Y. Hannun, and Andrew Y. Ng, "Rectifier Nonlinearities Improve Neural Network Acoustic Models"), Represents the weight coefficient, which is a learnable network parameter. represents the normalized adjacency matrix after adding self-loops. I N Represents the N×N identity matrix. Represents the normalized adjacency matrix The measurement matrix of

[0152] The factors that influence RCS sequences are complex, including the relative positioning of radar deployments, the size, structure, and micro-motion type of the target, and the radar's carrier frequency and polarization mode. Predefined graphs based on Euclidean distance are insufficient to fully characterize the interactions between RCS sequences. Therefore, the use of adaptive graphs can significantly improve spatial feature extraction.

[0153] First, we randomly initialize two self-learnable node embeddings E1 and E2, and the adaptive adjacency matrix It can be expressed as

[0154]

[0155] Output of adaptive graph convolution It can be expressed as

[0156]

[0157] in, represents the adaptive adjacency matrix after k updates in the p-th layer of GCN, Represents the weight coefficient matrix, which is learnable during network training.

[0158] The combination of predefined graph and adaptive graph can effectively extract the spatial dependencies of objects.

[0159] The prediction output layer is composed of a multi-layer perceptron, and finally a feature vector O∈R is obtained. C , R represents the real number combination, C represents the dimension, and O outputs a probability distribution P(k) after passing the Softmax function. Finally, the recognition result corresponds to the category with the maximum likelihood function, that is, the category to which the target belongs. The cross entropy loss function is used as the cost function during model training. The accuracy P is used. accAnd F1-score are used as quantitative evaluation indicators of target recognition effect.

[0160] Example: Simulation experiment of spatial micro-motion target recognition based on multi-domain feature-level fusion of networked radar system

[0161] Simulation experiments: The effectiveness and robustness of the proposed spatial micro-motion target recognition method based on multi-domain feature-level fusion in a networked radar system were analyzed. All experiments were conducted on a computer equipped with an Intel Xeon Platinum 8362 CPU @ 2.80 GHz and an NVIDIA RTX 3090 GPU. The operating system was Ubuntu 22.04. The PyTorch version was 2.1.0, the Python version was 3.10, and the CUDA version was 12.1. The network architecture was based on the PyTorch framework. The experimental parameter settings are shown in Table 3. The Adaptive Moment Estimation with Weighted Decay (AdamW) optimizer was used. A dynamic learning rate adjustment strategy was adopted. The learning rate was decreased every 5 iterations with a decay factor of 0.5. During training, if the loss did not improve after 10 consecutive iterations, training was terminated early.

[0162] Table 3 Experimental parameter settings

[0163]

[0164] Experiment 1 (comparative experiment): To show the superiority of the network proposed in this invention, it is compared with seven baseline methods.

[0165] (1) RCSNet: Convolutional Neural Network for Classifying Space Target of the Same Shape by Using RCS Time Series. RCSNet is a one-dimensional convolutional neural network architecture specifically designed for processing RCS sequences of spatially slightly moving targets.

[0166] (2) SW-S-GRU 《Radar Target Shape Recognition Using A Gated Recurrent Unit Based on RCS Time Series' Statistical Features by Sliding Window Segmentation》. Sliding Window-Statistical-GRU (SW-S-GRU) uses a sliding window to segment the RCS sequence and then inputs its statistical features into the GRU for radar target shape recognition.

[0167] (3) STPCNet《Space Precession Target Classification Based on Radar High-Resolution Range Profiles》In this model, CNN is used to identify HRRP of spatial micro-motion targets.

[0168] (4) STMRNet “Deep CNN for micromotion recognition of space targets” In this model, a convolutional neural network consisting of 3 convolutional layers and 2 fully connected layers was designed to classify and identify three types of micromotion: spin, precession, and nutation. The feasibility of identifying different micromotion forms based on time-frequency images was verified.

[0169] (5) MMFCNet《Multi-mode Fusion and Classification Method for Space Targets Based on Convolutional Neural Network》In this model, a multi-mode fusion method is proposed to classify and identify three types of targets: cones, small cones, and cylinders. First, time-frequency images and HRRP sequences of the three types of targets are generated in the S-band and X-band, respectively. Second, in order to make full use of frequency domain information, spatial information, structural characteristics, and micro-motion characteristics, the time-frequency images and HRRP sequences of different frequency bands and the same frequency band are fused based on the spatial domain fusion method. This multi-mode data fusion method enhances the effectiveness of data feature extraction.

[0170] (6) STFGACN 《Spatio-temporal-frequency graph attention convolutional network for aircraft recognition based on heterogeneous radar network》. STFGACN is a spatio-temporal-frequency graph attention convolutional network based on heterogeneous radar network. It is used to extract features from RCS sequences and achieve reliable recognition of aircraft targets.

[0171] (7) BiGT-DGF《Space Target Recognition Based on Radar Network Systemswith BiGRU-Transformerand Dual Graph Fusion Network》. BiGT-DGF is a method for spatial micro-motion target recognition in radar network systems based on BiGRU-Transformer and dual graph fusion network.

[0172] RCSNet, SW-S-GRU, STPCNet, and STMRNet belong to single-domain feature extraction and recognition methods based on monostatic radar (the first category). MMFCNet belongs to multi-domain feature fusion and recognition methods based on monostatic radar (the second category). STFGACN and BiGT-DGF belong to single-domain feature extraction and recognition methods based on networked radar systems (the third category). To compare the recognition performance of baseline models under different signal-to-noise ratios, test sets with signal-to-noise ratios of -5dB, 0dB, 10dB, and 15dB were generated, each with 100 samples. The recognition accuracy of different methods under different signal-to-noise ratios is shown in Figure 8. It can be seen that the recognition accuracy of each method improves with increasing signal-to-noise ratio. Compared with the best-performing STPCNet in the first category, this method achieves an average improvement of 17.24%. Compared with MMFCNet in the second category, this method achieves an average improvement of 6.88%. Compared with STFGACN and BiGT-DGF in the third category, this method achieves average improvements of 25.12% and 18.92%, respectively. Therefore, the proposed method achieves optimal recognition accuracy under all signal-to-noise ratios, demonstrating its effectiveness and robustness. It can be seen that the recognition accuracy and F1-score of the proposed method are significantly higher than those of the baseline model. Experimental results also demonstrate the superiority of this method.

[0173] Experiment 2 (ablation experiment): The contribution of each module in the network proposed in this invention to the recognition results is verified through the ablation experiment.

[0174] 1) Impact of feature combination patterns on recognition performance

[0175] In order to demonstrate the superiority of the multi-domain feature-level fusion method proposed in this invention, all six combination modes of the three features are traversed, and the method proposed in this invention is compared with these six combination modes. The six feature combination modes are: (1) RCS sequence (2) time Doppler image (3) HRRP sequence (4) RCS sequence and time Doppler image (5) RCS sequence and HRRP sequence (6) time Doppler image and HRRP sequence. The recognition accuracy of different feature combination modes is shown in Table 4. It can be seen that compared with the above six feature combination modes, the recognition accuracy of the three-feature fusion method proposed in this invention is improved by 11.22%, 4.67%, 15.11%, 2.45%, 8.11% and 0.89% respectively. This method has good recognition performance. The results show that the fusion of RCS sequence, time Doppler image and HRRP sequence can provide richer information for target recognition. Compared with the feature combination mode of time Doppler image and HRRP sequence, this method only improves by 0.89%. It can be seen that the contribution of the RCS sequence to the overall recognition accuracy is not obvious. It seems that the RCS sequence can be ignored. However, the reason why the RCS sequence is still considered in the method of the present invention is that the RCS sequence has a significant contribution to the recognition accuracy of specific categories. The confusion matrix under different feature combinations is shown in Figure 6. The horizontal axis in Figure 6 represents the predicted category and the vertical axis represents the true category. Comparing Figure 6(f) and Figure 6(g), it can be seen that the RCS sequence improves the recognition accuracy of T5 and T9 by 4% and 3% respectively. Therefore, the RCS sequence plays a positive role in the recognition of specific categories. It can also be seen that the values ​​on the diagonal of the confusion matrix of the method of the present invention are almost all higher than those of other methods, which shows the superiority of the method of the present invention.

[0176] Table 4 Comparison of recognition accuracy of different modules

[0177]

[0178]

[0179] 2) Impact of different modules on recognition performance

[0180] In order to illustrate the contribution of each module in the network to the recognition accuracy, ablation experiments were performed on each module. The six ablation models compared with the proposed method include: (1) CAFM+BiGRU+DGFN. (2) MDFEM+BiGRU+DGFN. (3) MDFEM+CAFM+DGFN. (4) MDFEM+CAFM+BiGRU. (5) MDFEM+CAFM+BiGRU+adaptive graph. (6) MDFEM+CAFM+BiGRU+predefined graph. The recognition accuracy of the six ablation models and the proposed method are shown in Table 5. It can be seen that when the multi-domain feature extraction module is removed from the network structure, the recognition accuracy decreases by 21.11%. After removing the adaptive feature fusion module, the recognition accuracy decreases by 4.33%. After removing the BiGRU module, the recognition accuracy decreases by 10.56%. When there is no DGFN to extract spatial features, the recognition accuracy decreases by 36.78%. The recognition accuracy of retaining only the predefined graph is 95.89%, which is 4.00% lower than the recognition accuracy of the proposed module. The results show that the introduction of the predefined graph can improve the recognition accuracy by 5.11%. The recognition accuracy of the method retaining only the adaptive graph is 94.78%, which is 5.11% lower than the recognition accuracy of the proposed module. The results show that the introduction of the adaptive graph can improve the recognition accuracy by 4.00%. The above experimental results prove that each module in the proposed network structure has an indispensable positive contribution to the recognition performance. Figure 7 is the confusion matrix of the six ablation models, where the horizontal axis represents the predicted category and the vertical axis represents the true category. The values ​​on the diagonal of the confusion matrix proposed by the present invention are almost all higher than those of the four ablation models, indicating that each module plays an important role in target recognition.

[0181] Table 5 Comparison of recognition accuracy of different modules

[0182]

[0183] Experiment 3 (Hyperparameter Selection Experiment): Impact of Parameter Selection on Recognition Performance

[0184] In order to explore the effect of parameter selection on recognition performance, a grid search is performed in λ = [0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9] to obtain the overall recognition accuracy corresponding to the above 10 parameters. The overall recognition accuracy changes under the 10 parameters are shown in the following figure. Figure 9 The experimental results show that the optimal recognition accuracy can be achieved when λ = 0.3.

[0185] The purpose of the present invention is to fully exploit the fusion features of RCS sequences, time Doppler images, and HRRP sequences. For the first time, the present invention proposes a multi-domain feature-level fusion method based on a networked radar system. This method breaks through the bottleneck of limited feature dimension of single-base radar by jointly utilizing the complementary information of multi-base radar RCS sequences, time-frequency images, and HRRP sequences, and can significantly improve the recognition performance of complex spatial micro-motion targets. First, a flexible feature extraction subnetwork is designed based on the heterogeneous feature acquisition capabilities of the networked radar system. The cross-covariance attention (XCA) and linear angular attention (LA-Att) modules with linear complexity are introduced to effectively extract fine-grained features. The cross-attention fusion module (CAFM) is used to achieve adaptive weighted fusion of multi-domain features, effectively enhancing the information useful for recognition. Secondly, a spatiotemporal feature extraction subnetwork is proposed that combines a bidirectional gated recurrent unit (BiGRU) and a dual graph fusion network (DGFN). The DGFN fuses an adaptive graph with a predefined graph. By co-optimizing the predefined and adaptive graphs, the DGFN effectively models the explicit topology and implicit dependencies between radar nodes. Finally, the spatiotemporal feature vector is input into the prediction layer to obtain robust recognition results.

Claims

1. A spatial micro-motion target recognition method based on multi-domain feature fusion of networked radar, the method is based on a radar network system, The system consists of N radars. The networked radar system is considered as an undirected fully connected graph with N nodes. represents the set of nodes, ν i represents the i-th radar node; ε={e i,j } i,j＝1,2, ... N represents the set of edges between nodes, e i,j Represents node ν i and ν j The edge between them; A∈R N×N represents the adjacency matrix, R represents the set of real numbers; A={A i,j |i,j=1,2,...N};A i,j Represents node ν i and ν j The weight of the edge between the two nodes represents the connection strength between the two nodes; Assume that a networked radar system consists of N1 low-PRF narrowband radars (Radar A), which can only obtain RCS sequences; N2 high-PRF narrowband radars (Radar B), which can obtain two features: RCS sequences and time Doppler images; and N-N1-N2 wideband radars (Radar C), which can simultaneously obtain three features: RCS sequences, time Doppler images, and HRRP sequences. The characteristic set of the networked radar system is η = {N × RCS, (N-N1) × TF, N2 × HRRP}; A complex nonlinear function f(·) is trained on the graph to map the image signal X to the target category label Y∈{l1,l2,…,l C }, where C represents the number of target categories, l i (i=1,2,...C) represents the i-th category; the recognition process of spatial micro-motion targets is expressed as l c =f(X)(1) It is characterized by: The method is as follows: Step 1: Create a 3D CAD model of the target and use electromagnetic calculation software to generate 360-degree multi-carrier static electromagnetic scattering data; A 3D CAD model of the target was created. Then, the electromagnetic calculation software FEKO was used to generate 360-degree multi-carrier static electromagnetic scattering data for the three 3D geometric models. The ideal dynamic radar echo corresponding to the attitude angle was retrieved from the static electromagnetic scattering data. The noise was assumed to be Gaussian white noise. The dynamic radar echo generation process is described below. The micro-motion forms of the target to be identified include precession, nutation, swing and roll; the micro-motion matrix R at time t is rot (t) is expressed as Among them, R C (t), R S (t), R W (t) and R T (t) represents the cone rotation matrix, spin matrix, swing matrix and roll matrix of the target respectively; The position vector r(t) of the target symmetry axis is expressed as r(t)=R rot (t)·R init ·(0,0,1) T (3) Among them, R init Represents the initial Euler matrix, (0,0,1) T Represents the position of the target's rotational symmetry axis in the target's local coordinate system; Target attitude angle β a (t) is expressed as Among them, n LOS Indicates the radar line of sight direction; After obtaining the attitude angle, the value corresponding to the attitude angle is queried in the static electromagnetic scattering data to obtain the ideal dynamic radar echo data. Gaussian white noise is added to the echo data to simulate the actual radar echo data. The precessing cone, precessing cone, nutating cone, nutating cone, oscillating cone, oscillating cone, tumbling cone, tumbling cone, and tumbling cylinder are named T1, T2, T3, T4, T5, T6, T7, T8, and T9, respectively. Multiple radars are used to simultaneously observe the target, and the observation data obtained include RCS sequences. To reduce the size of the dataset, time Doppler images and HRRP sequences are sampled to obtain time Doppler images and HRRP sequences. The dataset is divided into training, test, and validation sets according to the initial attitude angle. The model is trained. Step 2: Construct an adaptive feature fusion subnetwork; introduce XCA and LA-Att modules with linear complexity to effectively extract fine-grained features; use CAFM module to achieve adaptive weighted fusion of multi-domain features, effectively enhancing information useful for recognition; 1) Multi-domain feature extraction module MDFEM A one-dimensional CNN is used to extract temporal features of RCS sequences, time Doppler images, and HRRP sequences. An MLP layer is used to unify the feature vectors into the same dimension. The one-dimensional CNN and MLP layers together form a multi-domain feature extraction module (MDFEM). 2) XCA module In order to extract deeper feature information, the linear attention module XCA module is introduced; the input feature map X is combined with the weight matrix W of the query, key and value Q 、W K and W V Multiply and linearly project it onto the query, key, and value; query Q = XW Q , key K = XW K Sum V = XW V ; XCA function is expressed as In the formula represents the L2 normalization of K; represents the L2 normalization of Q, and T represents the matrix transpose; the L2 normalization operation can enhance the stability of model training; the learnable temperature parameter τ is introduced; the Softmax(·) expression is 3) LA-Att module To further enhance the richness of feature information, the LA-Att module is introduced; in the linear angular attention module, the angular kernel is defined as the similarity measurement function Sim(Q i ,K j ); Among them, Q i and K j Represent the i-th element of Q and the j-th element of K respectively, and m is a positive integer; The LA-Att module is approximately Among them, M depthwise represents a deep convolutional neural network with fewer parameters, M SA represents a sparse attention mechanism; The nonlinear term in the LA-Att mechanism can be used with a deep convolutional neural network M with fewer parameters. depthwise and sparse attention mechanism M SA Instead; therefore, the complexity of the LA-Att module can be regarded as linear; the sparse attention mechanism M SA It can be expressed as Among them, ε represents the sparse threshold, which is set to 0.02; 4) Adaptive feature fusion module Adaptive feature fusion module CAFM is introduced, which includes CAM and SAM; by merging the feature map F obtained by LA-Att LA Perform average pooling and maximum pooling to obtain two different channel descriptions: F LA The first channel description and F LA The second channel description AvgPool represents the average pooling operation, MaxPool represents the maximum pooling operation; the feature map F obtained by XCA XCA Performing the same operation will produce two different channel descriptions: F XCA First channel description and F XCA The second channel description For the feature map F LA Channel description and For example, it is input into the weight-sharing multi-layer perceptron MLP, and then the obtained features are added and input into the ReLU activation function to obtain F LA The channel weight coefficient matrix M LA-CACM , and F XCA The channel weight coefficient matrix is ​​M XCA-CACM The calculation process is Where W1 and W0 represent the first and second learnable matrix parameters respectively; Multiply the above two weight coefficient matrices to obtain the cross matrix M cross Through the Softmax activation function, and then with the feature map F LA and F XCA Multiply them separately to get the channel attention feature map CA LA and CA XCA The calculation process is expressed as CA LA =Softmax(M cross )F LA (11) CA XCA =Softmax(M cross )F XCA (12) Channel attention feature map CA in SAFM LA and CA XCA Perform average pooling and maximum pooling operations respectively, CA LA The average pooling features and maximum pooling features are and CA XCA The average pooling features and maximum pooling features are and The two pooling features, average pooling feature and maximum pooling feature, are concatenated in the channel dimension and input into a shared convolutional layer to obtain the spatial weight coefficient M LA-SAFM and M XCA-SAFM The calculation process is expressed as in, Represents the feature splicing operation; the spatial weight coefficient M LA-SAFM and M XCA-SAFM After passing through the Softmax activation function and the feature map F LA and F XCA Multiply them separately to get the spatial attention feature map SA LA and SA XCA The calculation process is expressed as YOUR LA =Softmax(M LA-SAM )F LA (15) YOUR XCA =Softmax(M XCA-SAM )F XCA (16) Add the residual connection to the fusion module; the final output F of the adaptive feature fusion module CAFM for F CAFM =(IN LA +F LA )+(IN XCA +F XCA ) (17) The above content is for broadband radar. When there are only two features, RCS sequence and time Doppler image, the feature extraction and fusion process is the same as the above process. When there is only one feature, RCS sequence, only the feature extraction module is retained. Step 3: Design a spatiotemporal modeling subnetwork based on BiGRU and dual-image fusion, and design a prediction output module; A spatiotemporal feature extraction subnetwork combining BiGRU and DGFN, consisting of a temporal feature extraction module and a spatial feature extraction module; the temporal feature extraction module consists of M-layer BiGRU stacked; the spatial feature extraction module consists of P-layer DGFN stacked; The geographical proximity between radars is used to calculate the predefined adjacency matrix A Re ; A Re The elements of Among them, d i,j Represents node ν i and node ν j The distance between i and f j Represents node ν respectively i and node ν j The radar operating frequency; constant λ∈[0,1), λ can be grid searched to obtain the corresponding λ with the best recognition performance; In order to capture deeper spatial dependencies in the target echo, we stack P layers of GCN. Assume that the output of the p-1th layer is Then the output of layer p is Expressed as Among them, LeakyReLU(·) represents the leaky rectified linear unit activation function, Represents the weight coefficient, which is a learnable network parameter; represents the normalized adjacency matrix after adding self-loops; I N represents the N×N identity matrix; Represents the normalized adjacency matrix The measurement matrix of Adopting the adaptive graph method, we learn the potential spatial features end-to-end in a data-driven way. Specifically, we randomly initialize two self-learning node embeddings E1 and E2, and the adaptive adjacency matrix Expressed as Output of adaptive graph convolution Expressed as in, represents the adaptive adjacency matrix after k updates in the p-th layer of GCN, Represents the weight coefficient matrix, which is learnable during network training; The prediction output layer is composed of a multi-layer perceptron, and finally a feature vector O∈R is obtained. C , R represents the real number combination, C represents the dimension, and O outputs a probability distribution P(k) after passing through the Softmax function; The recognition result corresponds to the category with the maximum likelihood function, that is, the category to which the target belongs; the cross entropy loss function is used as the cost function during model training; the accuracy P is used acc And F1-score are used as quantitative evaluation indicators of target recognition effect.

2. The spatial micro-motion target recognition method based on multi-domain feature fusion of networked radar according to claim 1 is characterized in that: In step 1, the dataset is divided into training set, test set, and validation set in a ratio of 7:2:1 according to the initial posture angle, and the model is trained using data with a signal-to-noise ratio of 5dB.

3. The spatial micro-motion target recognition method based on multi-domain feature fusion of networked radar according to claim 1 is characterized in that: In step 3, a grid search is performed in λ = [0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9] to obtain the overall recognition accuracy corresponding to the above 10 parameters. The parameter that gives the best recognition effect is determined as the corresponding λ.

Images