A method for estimating micro-motion parameters of a spatial cone target under echo defect condition

Abstract

The application provides a spatial precession cone target micro-motion parameter estimation method based on deep learning under echo defect conditions; the method comprises the following steps: generating a time-frequency image dataset containing different defect degrees; pre-processing the time-frequency graph, including defect simulation, curve repair and peak feature enhancement; constructing a double-branch anti-defect parameter estimation network (DAPE-Net), which has a shared feature extraction backbone, a space-time attention mechanism, a double-branch feature decoupling structure and an independent regression head, realizes end-to-end estimation of precession period and precession angle from the defective time-frequency graph, and verifies the robustness and high precision of the model under various defect proportions through training and testing; experimental results show that under certain defect conditions, the model can accurately estimate the micro-motion period and precession angle of the target, and is significantly better than mainstream deep learning models, and is suitable for real-time estimation of radar target micro-motion parameters in complex electromagnetic environments.

Description

Technical Field

[0001] This invention relates to radar signal and information processing technology, specifically to a method for estimating the micro-motion parameters of a spatially precessing cone target based on deep learning under conditions of echo loss. Background Technology

[0002] During radar target motion, in addition to the translation of the center of mass, there are usually micromotions (or micro-dynamics) such as rotation and vibration (e.g., the spin of a ballistic missile in the air, the swinging of a person's arms and legs while walking). These micromotions modulate the radar echo signal and generate sidebands near the target's Doppler frequency, a phenomenon known as the micro-Doppler effect (mD effect). Micro-Doppler features are considered unique characteristics of micro-moving targets and can provide important information for target identification and radar imaging. For narrowband radar, the echo signal of a target with multiple micro-moving components can generally be considered as a multi-component mD signal, exhibiting aliasing in the time-frequency plane. Furthermore, in real-world scenarios, interrupted radar illumination or target obstruction leads to defects in the micro-Doppler curve, further increasing the difficulty of micro-movement feature extraction. This year, our research group has proposed several methods for micro-motion feature extraction. Dr. Wang Huan proposed an incomplete mD signal decomposition method to address the problem of overlapping time-frequency domain echoes and missing sampling data in narrowband radar micro-motion targets under complex observation environments. This method decomposes m-dimensional signal components based on the reconstructed time-frequency domain. Yuan Hang et al. estimated three-dimensional micro-motion parameters under narrowband single-base radar conditions, but this method relies on complete signals and ignores the effects of obstruction. The Dynamic Mode Decomposition (DMD) algorithm proposed by Dai Xiaonan et al. can still accurately extract micro-motion frequencies under low signal-to-noise ratio conditions, but its performance drops sharply when the micro-motion curve is incomplete.

[0003] In recent years, deep learning has been widely applied in many fields such as speech, image, and text recognition, and has also provided new ideas for radar signal processing. In the classification and recognition of space ballistic targets, Dr. Chen Jian from the National University of Defense Technology designed a one-dimensional convolutional neural network-gated recurrent unit (CNN-GRU), which can accurately classify multiple types of missiles under complex conditions. Professor Feng Cunqian's team from the Air Force Engineering University proposed using a Bayesian optimization algorithm to automatically obtain network hyperparameters to improve the network's classification performance, and on this basis, classified three micro-motion forms: spin, precession, and nutation. Bai Xueru's team from Xi'an University of Electronic Science and Technology used AlexNet and ResNet-18 networks to classify the CVD maps of six different shaped precession ballistic targets. In terms of micro-motion feature extraction, Professor Ding Dazhi's team from Nanjing University of Science and Technology used convolutional neural networks to estimate the geometric parameters of multiple types of warheads; Professor Bai Xueru's team constructed a denoising convolutional neural network to estimate the precession period and precession angle of the warhead target, thereby obtaining the inertia ratio for distinguishing between true and false targets. The above research provides a preliminary exploration of radar micro-motion target parameter estimation based on deep learning, but most of it focuses on processing complete signals. For the problem of missing time-frequency curves caused by incomplete signals, deep learning technology can extract high-dimensional features from images, and through data augmentation and the addition of spatiotemporal attention mechanisms, it can achieve strong robustness against defects. Therefore, deep learning technology is very suitable for extracting micro-motion features from missing time-frequency images. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention proposes a method for estimating the micro-motion parameters of a spatial cone target under echo-deficient conditions, specifically including the following steps:

[0005] Step 1: Dataset generation and preprocessing;

[0006] Under narrowband radar conditions, target echo signals are simulated and generated based on a scattering model of a precessing conical target. Gabor transform is used to perform time-frequency analysis on the echo signals, yielding time-frequency grayscale images. By changing the micro-motion period and precession angle, time-frequency image samples with different parameter combinations are generated, and the corresponding true period and precession angle labels are annotated.

[0007] (1) Data preprocessing:

[0008] The complete time-frequency image is enhanced by performing a defect simulation; a random rectangular masking technique is used to randomly generate occlusion regions in the time-frequency image with a certain probability. ,in Indicates the obscured area. Indicates the starting position of the occluded area on the timeline. Indicates the width of the obscured area. This indicates the starting position of the blocked area on the frequency axis. Indicates the height of the obscured area, "This represents a scenario where the signal is completely lost from the starting position to the ending position, constructing a missing sample; in order to unify input images of different sizes into a fixed size to facilitate neural network processing, the input image is cropped, and then the cropped time-frequency image is grayscaled; grayscaled converts the color or high-dimensional time-frequency image into a single-channel grayscale image to reduce computational complexity and retain key features;

[0009] (2) Extract and repair the micro-motion curve of the input grayscale image:

[0010] By performing row and column projections on the grayscale time-frequency plot, the integral curves in the time and frequency dimensions are obtained as follows:

[0011]

[0012]

[0013] in, For time-dimensional projection, For frequency dimension projection, The input is a grayscale time-frequency image. For time, For frequency, Represents the row index of an image pixel. The column index representing the image pixels. Indicates the image width. The height of the image is represented; a Gaussian kernel is used to suppress noise. Smooth the projection curve:

[0014]

[0015] In the formula, The integral curve in the time dimension. This is the time-dimensional projection curve after Gaussian kernel smoothing. The frequency-dimensional integral curve, This is the frequency-dimensional projection curve after Gaussian kernel smoothing. It is a one-dimensional Gaussian kernel function.

[0016] Represents one-dimensional convolution operation

[0017] To address the missing data issue, the "missing data" is modeled as data gaps in certain intervals of the curve; a binary mask is defined. Identify the valid data area. Indicates the position index on the curve:

[0018]

[0019] in, Indicates the curve at Location data size, This represents the largest data point on the curve. The threshold is an empirical threshold; for missing regions spline interpolation function is used Repair:

[0020]

[0021] In the formula, This indicates the curve after repair. This represents a spline interpolation function constructed based on valid data points, used to repair data in missing regions. It is the set of all valid data points. This represents the k-th position on the curve. This is the position index number;

[0022] The peak feature extraction and fusion process is as follows:

[0023] Step 1, on the repaired curve Above, a peak detection algorithm based on dual constraints of amplitude and distance is used to accurately locate the set of significant peak points. ,in Characterizing the peak position, Characterizes its amplitude intensity;

[0024] Step 2 involves quantizing and extracting four core attributes for each identified peak point: existence, normalized height, significance, and normalized width; based on these attributes, a 4-channel feature map is constructed that finely characterizes the above four core attributes. , To normalize the curve length, This represents a 4-row, L-column matrix;

[0025] Step 3, by modifying the original time-frequency diagram Compared with the upsampled peak feature map The stitching is performed along the channel dimension, here. The 4-channel peak feature map obtained in step 2 The feature map obtained after upsampling has the same spatial size as the original time-frequency map; via the fusion function Integrate the data to generate an enhanced network input. In the formula, This represents the original time-frequency diagram. This indicates a concatenation operation along the channel dimension;

[0026] Step 2: Design the network model;

[0027] The dual-branch defect-resistant parameter estimation network DAPE-Net includes the following modules:

[0028] (1) Input layer: The input layer receives the preprocessed image after time-frequency curve processing and peak feature enhancement. ;

[0029] (2) Shared feature extraction backbone: Input the preprocessed time-frequency map, extract shallow features through a large kernel convolutional layer, followed by a normalization layer, activation function and pooling layer to initially capture the contextual information of the time-frequency structure;

[0030] (3) Spatiotemporal attention module STA: Based on shared features, global average pooling is performed along the time dimension and frequency dimension respectively. The spatiotemporal dependency is learned through a lightweight one-dimensional convolutional bottleneck structure to generate time and frequency attention weights and perform dual modulation on the feature map.

[0031] (4) Dual-branch feature extractor: Design two parallel feature extraction branches with the same structure but completely independent parameters, which are used for dedicated feature learning of period and precession angle, respectively, to achieve deep decoupling of the task;

[0032] The specific structure of each branch is as follows: Four Enhanced ResBlocks are stacked for deep feature extraction, and GroupNorm is used within each Enhanced ResBlock; feature reuse is achieved through shortcut connections; two Channel Attention modules are connected in series after the four Enhanced ResBlocks. The first Channel Attention module performs global average pooling on each channel of the input features, learns the channel importance weights through two fully connected layers, and initially filters out the feature channels relevant to the target task, achieving initial suppression of noisy channels. The second Channel Attention module takes the output of the first module as input and performs secondary recalibration to achieve refined feature enhancement; each branch outputs a high-dimensional feature tensor, which has been fully optimized and decoupled for its respective task.

[0033] (5) Regression output head; The high-dimensional features extracted from each branch are then fed into an independent multilayer perceptron (MLP) regression head after global average pooling, and the estimated values ​​of the period and precession angle are output; The regression head adopts a fully connected layer structure, and layer normalization and Dropout are introduced between layers to prevent overfitting;

[0034] Step 3: Network training and optimization;

[0035] In terms of dataset partitioning, the generated dataset is divided into training set, validation set and test set according to the proportion; the training set is used for model parameter learning, the validation set is used for hyperparameter tuning, and the test set is used for final performance evaluation; by training the optimized network model, the estimation of two micro-motion parameters, the cone rotation period and precession angle, of the spatial cone target is realized.

[0036] In the first step of a specific embodiment of the present invention, the value range of the micro-motion period is 0.5~2s, with a step of 0.01s; the value range of the precession angle is 5°~20°, with a step of 0.1°. Take 0.1.

[0037] In the first step (1) of another specific embodiment of the present invention, an occlusion region is randomly generated in the time-frequency diagram with a probability of 50%.

[0038] In Step 3 of yet another specific embodiment of the present invention, the fusion function It is a 1x1 convolution.

[0039] In the second step (1) of another specific embodiment of the present invention, the input layer receives the preprocessed image after time-frequency curve processing and peak feature enhancement. The space dimensions are 256×256. (2) is a single-channel grayscale image; the kernel convolutional layer has a size of 7×7 and the activation function is SiLU; in (4), the group normalization GroupNorm contains 16 channels and each branch outputs a 512 high-dimensional feature tensor.

[0040] In the third step of another specific embodiment of the present invention, the training set is set to 70%, the validation set is set to 15%, and the test set is set to 15%.

[0041] Furthermore, in the third step of a specific embodiment of the present invention, the training configuration is as follows:

[0042] (1) Optimizer configuration: The AdamW optimizer is used to optimize the network parameters, and the initial learning rate is set to 1×10. -4 The weight decay parameter is set to 1×10. -5 ;

[0043] (2) Loss function design: The loss function uses the mean squared error loss function, which calculates the error between the estimated value and the true label for the period and the precession angle respectively. The total loss function is the sum of the two. By minimizing this joint loss function, the joint optimization and collaborative learning of the two parameters are achieved.

[0044] (3) Mixed precision training: The automatic mixed precision training AMP strategy is introduced. During the forward propagation and gradient calculation process, some operations are automatically accelerated using half-precision floating-point numbers FP16, while the weight update remains single precision FP32.

[0045] (4) Dynamic adjustment of learning rate: The ReduceLROnPlateau learning rate scheduler is used to achieve adaptive adjustment of the learning rate. The specific strategy is as follows: after each training round, the change of the validation set loss is monitored. If the validation set loss does not decrease for several consecutive rounds, the current learning rate is multiplied by a decay factor, so as to continue searching for the optimal solution with a smaller step size. The early stopping patience value is set to 5, that is, the learning rate adjustment is triggered when the validation set loss does not decrease for 5 consecutive rounds. The learning rate decay factor is set to 0.5, that is, the current learning rate is multiplied by 0.5 when the adjustment is triggered. The effectiveness of each module (such as attention mechanism, dual-branch structure, etc.) is verified by ablation experiments. On this basis, the hyperparameters such as network depth, convolution kernel size, and attention mechanism weights are optimized and adjusted to obtain the best performance.

[0046] (5) Iterative training: The total number of training rounds is set to 150 rounds; in each training round, the model performs the following operations in sequence: load batch data from the training set, input the image into the network for forward propagation, calculate the joint loss function, calculate the gradient through the backpropagation algorithm, and finally update the network parameters by the optimizer; during the training process, the model performance is evaluated on the validation set after each round, and the model weight with the lowest loss on the validation set is saved as the best model for subsequent testing.

[0047] The advantages of this invention are as follows:

[0048] 1. Dual-branch feature decoupling and robustness against echo loss. This invention employs a dual-branch network structure to decouple and extract features related to the micro-motion period and precession angle, avoiding feature interference between tasks. Combined with a spatiotemporal attention mechanism and data preprocessing strategies (such as curve restoration and peak enhancement), the robustness of parameter estimation under echo loss conditions is significantly improved, maintaining high accuracy even with up to 50% loss.

[0049] 2. Integrating physical priors and deep learning features. A physical prior fusion strategy based on peak feature extraction is introduced during the data preprocessing stage. This explicitly enhances the key modulation information in the time-frequency curves, improving the interpretability and discriminative power of the features, enabling the network to more accurately perceive the characteristic patterns of micro-motion periods and precession angles.

[0050] 3. End-to-end robust estimation of defect-resistant parameters. By enhancing the data-level defect simulation and curve restoration, combined with the network-level bi-branch feature extraction, end-to-end robust estimation of micro-motion parameters from the defect time-frequency plot is achieved without relying on the complete signal structure, significantly simplifying traditional multi-step processing methods.

[0051] 4. Excellent generalization and real-time processing capabilities: The model exhibits stable estimation performance under various loss ratios and has high computational efficiency, with a single inference time of approximately 0.6 seconds. It is suitable for deployment in embedded radar signal processing systems to meet the real-time processing requirements in complex electromagnetic environments.

[0052] 5. Outperforms traditional methods and mainstream deep learning models under both intact and defective conditions. The DAPE-Net proposed in this invention significantly outperforms mainstream deep learning models such as CNN-LSTM, ResNet-50, and ViT in terms of accuracy in estimating micro-motion period and precession angle, demonstrating stronger engineering applicability. Attached Figure Description

[0053] Figure 1 A schematic diagram of a wingless, precessing conical target in space is shown.

[0054] Figure 2 The results of time-frequency analysis of the echo from a wingless conical target are shown, in which... Figure 2 (a) shows the time-frequency image of the complete echo. Figure 2 (b) is the time-frequency image with 10% echo loss. Figure 2 (c) is the time-frequency image with 30% echo loss. Figure 2 (d) is the time-frequency image with 50% echo loss. Figure 2 (e) is a time-frequency image with 70% echo loss;

[0055] Figure 3 The topology diagram of the designed neural network is shown;

[0056] Figure 4 The specific architecture of the designed dual-branch feature extraction module is shown;

[0057] Figure 5 The graph shows the changes in training loss and validation loss during the training process.

[0058] Figure 6 The results of network training phase test set cycle estimation are shown, where Figure 6 (a) shows the estimated precession period of the tailless cone. Figure 6 (b) shows the estimated result of the precession angle of the tailless cone;

[0059] Figure 7 A scatter plot showing the estimation results for test sets with different degrees of echo loss is presented, where... Figure 7(a) shows the estimated precession period of the tailless cone under 10% defect. Figure 7 (b) shows the estimated precession angle of the tailless cone under 10% defect. Figure 7 (c) shows the estimated precession period of the tailless cone under 30% defect. Figure 7 (d) shows the estimated precession angle of the tailless cone under 30% damage. Figure 7 (e) shows the estimated precession period of the tailless cone under 50% defect. Figure 7 (f) shows the estimated precession angle of the tailless cone under 50% damage. Figure 7 (g) shows the estimated precession period of the tailless cone under 70% defect. Figure 7 (h) shows the estimated precession angle of the tailless cone under 70% damage.

[0060] Figure 8 This paper compares the estimation results of precession period and precession angle of different networks under different degrees of defect, where... Figure 8 (a) shows a comparison of the precession period estimation results. Figure 8 (b) shows a comparison of the precession angle estimation results. Detailed Implementation

[0061] The present invention will now be described in further detail with reference to the embodiments and accompanying drawings.

[0062] This invention proposes a method for estimating the micro-motion parameters of a spatially precessing cone target based on a dual-branch anti-missing parameter estimation network under echo loss conditions, comprising the following steps:

[0063] Step 1: Dataset generation and preprocessing;

[0064] In narrowband radar systems, based on a scattering model of a precessing conical target (including a stable scattering point at the apex and a sliding scattering point at the base), target echo signals are simulated and generated using simulation software (such as MATLAB). Gabor transform is used to perform time-frequency analysis on the echo signals, yielding time-frequency grayscale images. By changing the micro-motion period (e.g., range: 0.5~2s, step 0.01s) and precession angle (e.g., range: 5°~20°, step 0.1°), time-frequency image samples with different parameter combinations are generated, and the corresponding true period and precession angle labels are attached.

[0065] In terms of data preprocessing strategy, the complete time-frequency map is first enhanced by defect simulation; then, a random rectangular masking technique is used to randomly generate occlusion regions in the time-frequency map with, for example, a 50% probability. ),in Indicates the obscured area. Indicates the starting position of the occluded area on the timeline. Indicates the width of the obscured area. This indicates the starting position of the blocked area on the frequency axis. Indicates the height of the obscured area, "" represents the distance from the starting position to the ending position. Generating occluded regions simulates scenarios where signals are completely lost due to packet loss, electromagnetic shielding, or partial frequency band failure. Constructing incomplete samples that are difficult to learn from continuously challenges the model, forcing the feature extraction network to abandon its over-reliance on complete signal structures and instead learn robust inference and feature completion from residual, incomplete time-frequency cues, establishing a powerful generalization ability to infer the global from the local. To unify input images of different sizes into a fixed size for easier neural network processing, the input images are cropped, and then the cropped time-frequency images are converted to grayscale. Grayscale conversion transforms color or high-dimensional time-frequency images into single-channel grayscale images to reduce computational complexity and retain key features.

[0066] Subsequently, the input grayscale image is subjected to micro-motion curve extraction and repair. First, the grayscale time-frequency image is projected into rows and columns to obtain the integral curves of the time and frequency dimensions:

[0067]

[0068]

[0069] in, For time-dimensional projection (frequency curve). For frequency dimension projection (time curve). The input is a grayscale time-frequency image. For time, For frequency, Represents the row index (vertical direction) of image pixels. Column index (horizontal direction) representing the image pixels. Indicates the image width. This represents the image height. A Gaussian kernel is used to suppress noise. Smooth the projection curve:

[0070]

[0071] In the formula, The integral curve in the time dimension. This is the time-dimensional projection curve after Gaussian kernel smoothing. The frequency-dimensional integral curve, This is the frequency-dimensional projection curve after Gaussian kernel smoothing. It is a one-dimensional Gaussian kernel function.

[0072] Represents one-dimensional convolution operation

[0073] To address the missing data issue, the "missing data" is modeled as data gaps in certain intervals of the curve. A binary mask is defined. Identify the valid data area. Indicates the position index on the curve:

[0074]

[0075] in, Indicates the curve at Location data size, This represents the largest data point on the curve. This is an empirical threshold (in one specific embodiment of the invention, Take 0.1). For missing regions. spline interpolation function is used Repair:

[0076]

[0077] In the formula, This indicates the curve after repair. This represents a spline interpolation function constructed based on valid data points, used to repair data in missing regions. It is the set of all valid data points. This represents the k-th position on the curve. This is the position index number;

[0078] By using the repair method, the original envelope and periodic characteristics of the curve can be effectively preserved, providing high-quality input for subsequent feature extraction.

[0079] Finally, peak feature enhancement is performed. To strengthen the model's perception of peak features, this invention designs a peak feature extraction and fusion process:

[0080] Step 1, on the repaired curve Above, a peak detection algorithm based on dual constraints of amplitude and distance is used to accurately locate the set of significant peak points. ,in Characterizing the peak position, Characterizes its amplitude intensity;

[0081] Step 2 involves quantizing and extracting four core attributes for each identified peak point: presence, normalized height, significance, and normalized width. The specific calculation methods for these attributes are signal processing techniques well-known to those skilled in the art. Based on this, a 4-channel feature map that finely characterizes the aforementioned four core attributes is constructed. , To normalize the curve length, This represents a 4-row, L-column matrix;

[0082] Step 3, by modifying the original time-frequency diagram Compared with the upsampled peak feature map The stitching is performed along the channel dimension, here. The 4-channel peak feature map obtained in step 2 The feature map obtained after upsampling has the same spatial size as the original time-frequency map. It is then processed by an efficient fusion function. (e.g., 1x1 convolutions) are integrated to generate enhanced network input. In the formula, This represents the original time-frequency diagram. This indicates a concatenation operation along the channel dimension. Essentially, this fusion strategy deeply integrates physical features extracted from prior knowledge of signal processing with the original data features, thereby injecting explicit physical guidance into the subsequent deep neural network. This enables it to more keenly focus on and learn discriminative features most relevant to the physical meaning of the micro-motion parameters, effectively improving the interpretability and estimation accuracy of the feature representation.

[0083] Step 2: Design the network model;

[0084] This invention designs a dual-branch defect-resistant parameter estimation network (DAPE-Net), the structure of which is as follows: Figure 3 As shown, it mainly includes the following modules:

[0085] (1) Input layer: The input layer receives the preprocessed image after time-frequency curve processing and peak feature enhancement. Its spatial dimensions are 256×256. In one embodiment of the present invention, A single-channel grayscale image means that each pixel contains only one grayscale value, used to characterize the energy intensity at that time-frequency point. The single-channel design aims to reduce the dimensionality of the network input, decrease computational complexity, while preserving key time-frequency distribution features. In other embodiments of the invention, the input can also be a multi-channel time-frequency image (such as a color time-frequency image or a time-frequency image fused from multiple sources), but the number of input channels in the first convolutional layer of the network needs to be adjusted accordingly.

[0086] (2) Shared feature extraction backbone. The preprocessed time-frequency map is input and passed through a large kernel convolutional layer (e.g., 7×7) to extract shallow features, followed by a normalization layer, activation function (SiLU) and pooling layer to initially capture the contextual information of the time-frequency structure.

[0087] (3) Spatiotemporal Attention Module (STA). Based on shared features, global average pooling is performed along the time and frequency dimensions respectively. Spatiotemporal dependencies are learned through a lightweight one-dimensional convolutional bottleneck structure to generate time and frequency attention weights. The feature map is then doubly modulated to enhance the focusing ability on key time and frequency units. The design of this attention mechanism is a conventional technique that can be implemented by those skilled in the art based on convolutional neural networks and attention mechanisms.

[0088] (4) Dual-branch feature extractor. This is the core innovative module of this invention, such as... Figure 4 As shown, in order to solve the problem that the two estimation tasks of micro-motion period and precession angle have different feature focus and are easy to be coupled with each other, this invention designs two parallel feature extraction branches with the same structure but completely independent parameters, which are used for dedicated feature learning of period and precession angle respectively, thereby achieving deep decoupling of tasks.

[0089] like Figure 4 As shown, the specific structure of each branch is as follows: First, four enhanced residual blocks are stacked for deep feature extraction. Each enhanced residual block uses group normalization (GroupNorm) instead of traditional batch normalization to overcome the problem of unstable statistical estimation during small-batch training. Each group contains 16 channels to ensure training stability. Simultaneously, feature reuse is achieved through shortcut connections to ensure smooth gradient propagation. Based on this, to further improve the discriminative power of the features, this invention connects two channel attention modules after the four enhanced residual blocks. The first channel attention module performs global average pooling on each channel of the input features and learns channel importance weights through two fully connected layers, initially filtering out feature channels related to the target task (such as periodicity or precession angle), achieving initial suppression of noisy channels. The second channel attention module takes the output of the first module as input for secondary recalibration. Since redundant information in the features has been effectively suppressed after the first round of filtering, the second module can more accurately focus on the few most discriminative key channels, achieving refined feature enhancement. After processing by the four enhanced residual blocks and two channel attention modules, each branch outputs a 512-dimensional high-dimensional feature tensor, which has been fully optimized and decoupled for its respective task.

[0090] (5) Regression Output Head. The high-dimensional features extracted from each branch are global average pooled and then fed into independent multilayer perceptron (MLP) regression heads to output estimated values ​​of period and precession angle. The regression heads adopt a fully connected layer structure, with interlayer normalization and Dropout introduced to prevent overfitting.

[0091] Step 3: Network training and optimization;

[0092] In terms of dataset partitioning, the generated dataset is divided proportionally into a training set (e.g., 70%), a validation set (e.g., 15%), and a test set (e.g., 15%). The training set is used for model parameter learning, the validation set is used for hyperparameter tuning, and the test set is used for final performance evaluation. By training the optimized network model, the estimation of two micro-motion parameters—the cone rotation period and the precession angle—of the spatial cone target is achieved.

[0093] Regarding the training configuration, the specific implementation is as follows:

[0094] (1) Optimizer Configuration: This invention uses the AdamW optimizer to optimize the network parameters. Compared with the traditional Adam optimizer, AdamW achieves decoupled weight decay, which can more effectively regularize the model and suppress overfitting. In a specific embodiment of this invention, the initial learning rate is set to 1×10⁻⁶. -4 The weight decay parameter is set to 1×10. -5 The selection of these two hyperparameters effectively balances training speed and generalization ability while ensuring rapid model convergence.

[0095] (2) Loss function design: The loss function uses the mean squared error loss function, which calculates the error between the estimated value and the true label for the period and the precession angle respectively. The total loss function is the sum of the two. By minimizing this joint loss function, the joint optimization and collaborative learning of the two parameters are achieved.

[0096] (3) Mixed precision training: In order to improve training efficiency and reduce memory usage, this invention introduces the automatic mixed precision training (AMP) strategy (this technology is implemented and promoted by NVIDIA in its Apex library and PyTorch framework). In the forward propagation and gradient calculation process, some operations are automatically accelerated using half-precision floating-point numbers (FP16), while the weight update still maintains single precision (FP32) to ensure numerical stability.

[0097] (4) Dynamic Learning Rate Adjustment: To enable the model to converge to the optimal solution more precisely in the later stages of training, this invention employs the ReduceLROnPlateau learning rate scheduler to achieve adaptive adjustment of the learning rate. This scheduler is a standard learning rate adjustment strategy provided by the PyTorch framework. Specifically, after each training epoch, the change in the validation set loss is monitored. If the validation set loss no longer decreases after several consecutive epochs, the current learning rate is multiplied by a decay factor, thereby continuing to search for the optimal solution with a smaller step size. In a specific embodiment of this invention, the early stopping patience value is set to patience=5, meaning that learning rate adjustment is triggered when the validation set loss has not decreased for 5 consecutive epochs; the learning rate decay factor is set to factor=0.5, meaning that the current learning rate is multiplied by 0.5 when adjustment is triggered. Through the above dynamic adjustment strategy, the model can optimize parameters with a more precise step size in the later stages of training, effectively improving the convergence effect. In addition, the effectiveness of each module (such as curve repair, peak enhancement, spatiotemporal attention, and dual-branch structure) was verified through ablation experiments, and hyperparameters such as network depth, convolutional kernel size, and attention mechanism weights were optimized.

[0098] (5) Iterative Training: In one specific embodiment of the present invention, the total number of training rounds is set to 150. In each training round, the model performs the following operations in sequence: load batch data from the training set, input images into the network for forward propagation, calculate the joint loss function, calculate the gradient through the backpropagation algorithm, and finally update the network parameters by the optimizer. During the training process, the model performance is evaluated on the validation set after each round, and the model weights with the lowest loss on the validation set are saved as the best model for subsequent testing.

[0099] from Figure 5 As can be seen, both the training loss and validation loss decreased rapidly in the early stages of training. This is because the network initially initialized the parameter values ​​in the model randomly. After the network learned the features of the time-frequency images, it significantly adjusted the weights and biases. As training continued, the adjustment magnitude of the weights gradually decreased, and eventually both the training loss and validation loss remained at a low value, indicating that the model has good generalization ability. Finally, the training loss and validation loss for the precessing cone target stabilized at around 0.0088, indicating that the network training was complete.

[0100] Step 4: Conduct network testing

[0101] Five datasets were used for testing time-frequency maps with different degrees of loss (in another specific embodiment of the invention, the four different echo loss degrees were 0%, 10%, 30%, 50%, and 70%). Using relative root mean square error as the evaluation criterion, the designed network model was first used to estimate the period and precession angle of the five datasets under different loss degrees. Then, the model was compared with networks such as CNN-LSTM, ResNet-50, ViT, and GoogLeNet, generating a bar chart to reflect the superior parameter estimation accuracy and noise resistance of the model.

[0102] Example: Algorithm Feasibility Analysis and Simulation Verification

[0103] The simulation parameters for the narrowband radar and the space conical target used in the example are shown in Table 1. The precession model of the conical target is as follows: Figure 1 As shown, scattering point A at the cone apex belongs to the stable scattering center, while points B and C, the intersections of the plane formed by the radar line of sight and the target's axis of symmetry with the edge of the cone's base, belong to the sliding scattering center. Let the radar line of sight (LOS) direction be perpendicular to the cone's rotation axis. The included angle is The angle between the Z-axis and the Z-axis is ,Right now ,in Let A be the precession angle (the angle between the spin axis and the conical axis). Let point A be the center of the base circle. The height of the point is The base radius is center of mass The length from point C to point C is , The angle between the line connecting point A and point B and the target axis of symmetry is... From point A to the center of mass The height of the point is Target centroid to the center of the bottom surface The height of the point is That is, the total height of the cone The semi-cone angle of the cone is used Indicates the target centroid. The radial distance from the point to the radar is

[0104]

[0105] Under the condition of radar head-on illumination of a target, considering the obstruction effect, the time-frequency diagram of the echo of a spatially precessing conical target after Gabor transformation is as follows: Figure 2 As shown, where Figure 2 (a) is a time-frequency image of the complete echo of the precessing cone target. Figure 2(b)-(e) are time-frequency images obtained under different degrees of echo loss of the precessing cone target. It can be seen that the micro-motion curve of the cone apex scattering point exhibits a sinusoidal variation law, while the micro-motion curve of the cone bottom scattering point is not a standard sine, but it also has obvious periodic characteristics.

[0106] The proposed Dual-Branch Robust Parameter Estimation Network (DAPE-Net) is a deep neural network architecture designed for the structural characteristics of radar time-frequency maps. This model collaboratively extracts local and global micro-motion features from damaged time-frequency maps through convolutional operations and a time-frequency attention mechanism. It also utilizes a dual-branch structure to decouple and learn key information about the micro-motion period and precession angle, ultimately achieving high-precision parameter estimation through independent regression heads. During training, after initialization, the network parameters are gradually adjusted using a backpropagation algorithm combined with a gradient optimization strategy. In the early stages of training, the model quickly learns the basic features in the time-frequency map, and both training and validation losses decrease rapidly. As iterations deepen, parameter updates become more gradual, and the loss curve converges to a stable low value, indicating that the model exhibits good generalization ability and robustness on time-frequency map data with varying degrees of damage.

[0107] according to Figure 6 The results shown demonstrate that the network model performs well in estimating the period and precession angle for the complete time-frequency plot. The red dashed line in the figure represents the ideal estimation result, where the true value and the estimated value satisfy... The linear relationship between the two is called the standard line. The closer the actual estimation result is to the standard line, the more accurate the estimation result is. As can be seen, most data points are concentrated near the standard line, indicating that the model's predicted values ​​are very close to the true values, and the prediction accuracy is high. This shows that the model has a significant advantage in capturing local features and periodic information, and can accurately estimate the period and precession angle of the precessing cone target from the time-frequency plot.

[0108] Experimental verification

[0109] To verify the robustness of the method under echo loss conditions, random loss levels of 10%, 30%, 50%, and 70% were set in the target echo, generating four datasets under echo loss conditions for testing. The simulation parameters for the radar and the space cone target are shown in Table 1, and the precession diagram of the space cone target is shown in... Figure 1 As shown.

[0110] The relative root mean-square error (RRMSE) was used as the evaluation criterion. Table 2 shows the estimation results of the precession angle of the micro-motion period of the precession cone target. Experimental results show that, under severe echo loss conditions, although the time-frequency plot curve is incomplete, the model can still maintain good parameter estimation ability. The relative root mean-square error of its prediction results is still controlled within 10% even when the loss degree is as high as 70%, showing strong anti-loss performance. When the echo loss degree is ≤50%, the error is significantly reduced to below 2.5%, indicating that the model has excellent parameter estimation performance under good observation conditions.

[0111]

[0112] To verify that the dual-branch robust parameter estimation network (DAPE-Net) designed in this invention has certain performance advantages in the task of estimating period and precession angle using time-frequency maps, we conducted comparative experiments with mainstream deep networks such as CNN-LSTM, ResNet-50, ViT, and GoogLeNet under the same dataset and training conditions, using the relative root mean-square error (RRMSE) as the evaluation metric. Figure 8 The comparison results are shown. As the defect ratio increases, the estimation error of all models shows an upward trend, but the DAPE-Net model proposed in this invention exhibits superior estimation accuracy and stronger robustness across different defect ratios. Regarding precession period estimation, DAPE-Net's estimation error is significantly lower than that of comparative models such as CNN-LSTM, ResNet-50, ViT, and GoogLeNet within the defect range of 10% to 50%. Especially at a high defect ratio of 70%, DAPE-Net shows the smallest increase in error, indicating its stronger ability to learn temporal structural features. In contrast, the ViT model, due to its weaker ability to model local continuity, shows the most significant performance degradation at higher defect ratios. Regarding precession angle estimation, DAPE-Net also maintains the lowest estimation error across all defect ratios, and its error curve changes the most smoothly. This indicates that the dual-branch structure and spatiotemporal attention module employed by DAPE-Net effectively preserve frequency domain modulation information and enhance the perception of local features. Models like CNN-LSTM and ResNet-50 show a rapid increase in precession angle estimation error as the proportion of missing data increases, indicating a strong dependence on global structure and difficulty in extracting robust features from partially missing data. Overall, DAPE-Net not only demonstrates excellent performance under complete data conditions but also maintains high estimation accuracy under partially missing scenarios, showing good engineering applicability and promotional value.

[0113] This method addresses the problem of missing time-frequency curves by designing corresponding data preprocessing strategies and modifying the network structure based on residual networks. Preliminary research reveals that no existing technologies explicitly utilize deep learning to process missing time-frequency maps in spatial target parameter identification tasks. This invention addresses the challenge of feature extraction from missing radar time-frequency maps by constructing a collaborative optimization mechanism from data preprocessing to network architecture. This effectively overcomes the coexistence of gradient anomalies and overfitting in traditional methods, significantly improving the model's training stability and convergence speed under missing conditions. This design combines theoretical rigor with engineering practicality. By introducing modules such as batch normalization, random dropout, and multi-scale pooling, it further enhances the model's generalization ability and robustness, making it suitable for robust processing of radar time-frequency maps in complex electromagnetic environments.

Claims

1. A method for estimating the micro-motion parameters of a spatial cone target under echo-deficient conditions, characterized in that, Specifically, the following steps are included: Step 1: Dataset generation and preprocessing; Under narrowband radar conditions, target echo signals are simulated and generated based on a scattering model of a precessing conical target. Gabor transform is used to perform time-frequency analysis on the echo signals, yielding time-frequency grayscale images. By changing the micro-motion period and precession angle, time-frequency image samples with different parameter combinations are generated, and the corresponding true period and precession angle labels are annotated. (1) Data preprocessing: The complete time-frequency image is enhanced by performing a defect simulation; a random rectangular masking technique is used to randomly generate occlusion regions in the time-frequency image with a certain probability. ,in Indicates the obscured area. Indicates the starting position of the occluded area on the timeline. Indicates the width of the obscured area. This indicates the starting position of the blocked area on the frequency axis. Indicates the height of the occluded area, "This represents a scenario where the signal is completely lost from the starting position to the ending position, and a missing sample is constructed. In order to unify the input images of different sizes into a fixed size to facilitate neural network processing, the input images are cropped, and then the cropped time-frequency image is grayscaled. Grayscale conversion transforms color or high-dimensional time-frequency maps into single-channel grayscale images to reduce computational complexity and preserve key features; (2) Extract and repair the micro-motion curve of the input grayscale image: By performing row and column projections on the grayscale time-frequency plot, the integral curves in the time and frequency dimensions are obtained as follows: in, For time-dimensional projection, For frequency dimension projection, The input is a grayscale time-frequency image. For time, For frequency, Represents the row index of an image pixel. The column index representing the image pixels. Indicates the image width. The height of the image is represented; a Gaussian kernel is used to suppress noise. Smooth the projection curve: In the formula, The integral curve in the time dimension. This is the time-dimensional projection curve after Gaussian kernel smoothing. The frequency-dimensional integral curve, This is the frequency-dimensional projection curve after Gaussian kernel smoothing. It is a one-dimensional Gaussian kernel function. Represents one-dimensional convolution operation To address the missing data issue, the "missing data" is modeled as data gaps in certain intervals of the curve; a binary mask is defined. Identify the valid data area. Indicates the position index on the curve: in, Indicates the curve at Location data size, This represents the largest data point on the curve. The threshold is an empirical threshold; for missing regions spline interpolation function is used Repair: In the formula, This indicates the curve after repair. This represents a spline interpolation function constructed based on valid data points, used to repair data in missing regions. It is the set of all valid data points. This represents the k-th position on the curve. This is the position index number; The peak feature extraction and fusion process is as follows: Step 1, on the repaired curve Above, a peak detection algorithm based on dual constraints of amplitude and distance is used to accurately locate the set of significant peak points. ,in Characterizing the peak position, Characterizes its amplitude intensity; Step 2 involves quantizing and extracting four core attributes for each identified peak point: existence, normalized height, significance, and normalized width; based on these attributes, a 4-channel feature map is constructed that finely characterizes the above four core attributes. , To normalize the curve length, This represents a 4-row, L-column matrix; Step 3, by modifying the original time-frequency diagram Compared with the upsampled peak feature map The stitching is performed along the channel dimension, here. The 4-channel peak feature map obtained in step 2 The feature map obtained after upsampling has the same spatial size as the original time-frequency map; via the fusion function Integrate the data to generate an enhanced network input. In the formula, This represents the original time-frequency diagram. This indicates a concatenation operation along the channel dimension; Step 2: Design the network model; The dual-branch defect-resistant parameter estimation network DAPE-Net includes the following modules: (1) Input layer: The input layer receives the preprocessed image after time-frequency curve processing and peak feature enhancement. ; (2) Shared feature extraction backbone: Input the preprocessed time-frequency map, extract shallow features through a large kernel convolutional layer, followed by a normalization layer, activation function and pooling layer to initially capture the contextual information of the time-frequency structure; (3) Spatiotemporal attention module STA: Based on shared features, global average pooling is performed along the time dimension and frequency dimension respectively. The spatiotemporal dependency is learned through a lightweight one-dimensional convolutional bottleneck structure to generate time and frequency attention weights and perform dual modulation on the feature map. (4) Dual-branch feature extractor: Design two parallel feature extraction branches with the same structure but completely independent parameters, which are used for dedicated feature learning of period and precession angle, respectively, to achieve deep decoupling of the task; The specific structure of each branch is as follows: Four Enhanced ResBlocks are stacked for deep feature extraction, and GroupNorm is used within each Enhanced ResBlock; feature reuse is achieved through shortcut connections; two Channel Attention modules are connected in series after the four Enhanced ResBlocks. The first Channel Attention module performs global average pooling on each channel of the input features, learns the channel importance weights through two fully connected layers, and initially filters out the feature channels relevant to the target task, achieving initial suppression of noisy channels. The second Channel Attention module takes the output of the first module as input and performs secondary recalibration to achieve refined feature enhancement; each branch outputs a high-dimensional feature tensor, which has been fully optimized and decoupled for its respective task. (5) Regression output head; The high-dimensional features extracted from each branch are then fed into an independent multilayer perceptron (MLP) regression head after global average pooling, and the estimated values ​​of the period and precession angle are output; The regression head adopts a fully connected layer structure, and layer normalization and Dropout are introduced between layers to prevent overfitting; Step 3: Network training and optimization; In terms of dataset partitioning, the generated dataset is divided into training set, validation set and test set according to the proportion; the training set is used for model parameter learning, the validation set is used for hyperparameter tuning, and the test set is used for final performance evaluation; by training the optimized network model, the estimation of two micro-motion parameters, the cone rotation period and precession angle, of the spatial cone target is realized.

2. The method for estimating the micro-motion parameters of a spatial cone target under echo-deficient conditions as described in claim 1, characterized in that, In the first step, the value range of the micro-motion period is 0.5~2s, with a step of 0.01s; the value range of the precession angle is 5°~20°, with a step of 0.1°. Take 0.

1.

3. The method for estimating the micro-motion parameters of a spatial cone target under echo-deficient conditions as described in claim 1, characterized in that, In the first step (1), occlusion regions are randomly generated in the time-frequency graph with a 50% probability.

4. The method for estimating the micro-motion parameters of a spatial cone target under echo-deficient conditions as described in claim 1, characterized in that, In the first step, Step 3, the fusion function It is a 1x1 convolution.

5. The method for estimating the micro-motion parameters of a spatial cone target under echo defect conditions as described in claim 1, characterized in that, In the second step (1), the input layer receives the preprocessed image after time-frequency curve processing and peak feature enhancement. The space dimensions are 256×256. (2) is a single-channel grayscale image; the kernel convolutional layer has a size of 7×7 and the activation function is SiLU; in (4), the group normalization GroupNorm contains 16 channels and each branch outputs a 512 high-dimensional feature tensor.

6. The method for estimating the micro-motion parameters of a spatial cone target under echo-deficient conditions as described in claim 1, characterized in that, In the third step, the training set is set to 70%, the validation set to 15%, and the test set to 15%.

7. The method for estimating the micro-motion parameters of a spatial cone target under echo-deficient conditions as described in claim 1, characterized in that, In the third step, the specific training configuration is as follows: (1) Optimizer configuration: The AdamW optimizer is used to optimize the network parameters, and the initial learning rate is set to 1×10. -4 The weight decay parameter is set to 1×10. -5 ; (2) Loss function design: The loss function uses the mean squared error loss function, which calculates the error between the estimated value and the true label for the period and the precession angle respectively. The total loss function is the sum of the two. By minimizing this joint loss function, the joint optimization and collaborative learning of the two parameters are achieved. (3) Mixed precision training: The automatic mixed precision training AMP strategy is introduced. During the forward propagation and gradient calculation process, some operations are automatically accelerated using half-precision floating-point numbers FP16, while the weight update remains single precision FP32. (4) Dynamic adjustment of learning rate: The ReduceLROnPlateau learning rate scheduler is used to achieve adaptive adjustment of the learning rate. The specific strategy is as follows: after each training round, the change of the validation set loss is monitored. If the validation set loss does not decrease for several consecutive rounds, the current learning rate is multiplied by a decay factor, so as to continue searching for the optimal solution with a smaller step size. The early stopping patience value is set to 5, that is, the learning rate adjustment is triggered when the validation set loss does not decrease for 5 consecutive rounds. The learning rate decay factor was set to 0.5, meaning that the current learning rate was multiplied by 0.5 when adjustment was triggered. The effectiveness of each module (such as the attention mechanism and the dual-branch structure) was verified through ablation experiments. Based on this, the hyperparameters such as network depth, convolutional kernel size, and attention mechanism weights were optimized and adjusted to obtain the best performance. (5) Iterative training: The total number of training rounds is set to 150 rounds; in each training round, the model performs the following operations in sequence: load batch data from the training set, input the image into the network for forward propagation, calculate the joint loss function, calculate the gradient through the backpropagation algorithm, and finally update the network parameters by the optimizer; During training, the model performance is evaluated on the validation set after each round, and the model weights with the lowest loss on the validation set are saved as the best model for subsequent testing.

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