A spatial debris feature in-embedding representation method through physical guided learning

Abstract

The application discloses a space debris feature in-embedding representation method through physical guidance learning, and comprises the following steps: S1, acquiring a time sequence image sequence of space debris; S2, extracting space-time features of the time sequence image sequence through a feature extraction network to form an initial feature vector; S3, introducing a physical constraint optimization layer, and calculating a physical constraint loss of the initial feature vector based on the laws of orbital dynamics and rigid body kinematics; S4, transmitting the gradient of the physical constraint loss to the feature extraction network through back propagation to optimize the weight parameters, so that the network learns to generate a feature vector embedded with physical consistency; and S5, outputting a general multi-dimensional feature representation embedded with physical consistency for downstream tasks. The application uses physical laws as gradient signals to guide feature learning in advance, guarantees the physical credibility and discriminability of the features, realizes the decoupling of the features and the tasks, and provides high-quality general bottom layer feature support for space debris identification, cataloging and orbit prediction.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of space target monitoring and deep learning, and particularly relates to a space debris feature embedded representation method through physical guided learning. BACKGROUND

[0002] The increasing frequency of space activities has led to a sharp increase in the number of space debris, posing a serious threat to on-orbit spacecraft safety. Against this background, target perception technology based on deep learning has become an important development direction for space debris monitoring. However, there are several key problems to be solved in the existing technical route:

[0003] Most current methods rely on data-driven models, such as detection networks that reconstruct anomalies based on autoencoders. Such methods learn completely from the statistical laws of image data, and the extracted features lack explicit physical meaning support. In extreme space environments such as dark backgrounds, weak textures, and strong noise, the features lack discriminability and have weak generalization ability. More importantly, trajectory prediction tasks based on such features often violate basic orbital mechanics laws, resulting in uncontrolled cumulative errors and potentially leading to false collision warnings.

[0004] To address the above shortcomings, the industry has begun to explore the path of combining physical models with deep learning. However, existing solutions mostly apply physical constraints to post-optimization at the task output level. For example:

[0005] Patent CN120524831A proposes modeling static scenes and dynamic trajectories using dynamic neural radiation fields and introducing rigid body motion equations as constraints. However, this method focuses on rendering and prediction optimization of the overall scene, and its feature extraction module is still data-driven, with physical laws not embedded in the feature learning process.

[0006] Patent CN119989894A uses a physical information neural network to fit kinematic equations and combines data and physical driving losses through a loss function to achieve trajectory mapping and error correction. However, its physical constraints only act on the output layer parameter inversion, and cannot guide the generation mechanism of feature representation in reverse.

[0007] Patent CN119919648A uses a hybrid expert model and image quality indicators to improve the adaptive robustness of the detection algorithm, but does not address the fundamental issue of whether the features themselves conform to physical laws.

[0008] The common limitation of these methods is that the physical model only plays the role of a "post-checker" or "output optimizer", and does not change the inherent learning mechanism of the feature extraction network. The feature representation is still in a "black box" state, lacking physical credibility and explainability.

[0009] In addition, existing solutions are usually tightly coupled with a single task such as "detection", "prediction", etc., and the network structure and loss function are designed around the output of a specific task. This makes it difficult for the features learned internally to be directly and effectively transferred to diversified upper-layer applications such as fragment identification, precise cataloging, attribute classification, and high-precision orbit determination, limiting the versatility and system efficiency of the technology.

[0010] In summary, the prior art has not yet achieved a feature extraction network that learns and generates a feature representation that conforms to physical laws. Whether data-driven or based on output optimization of physical constraints, physical laws have not been deeply embedded in the front-end process of feature learning as "guides". The present invention is proposed to break through this paradigm bottleneck. SUMMARY

[0011] To solve the existing problems, the present application provides a space debris feature embedded representation method learned by physical guidance, a computer system and a storage medium method, and the specific scheme is as follows:

[0012] A space debris feature embedded representation method learned by physical guidance, comprising the following steps:

[0013] S1, obtaining a time sequence image sequence of space debris;

[0014] S2, extracting the space-time features of the time sequence image sequence through a feature extraction network to form an initial feature vector;

[0015] S3, introducing a physical constraint optimization layer, calculating the physical constraint loss of the initial feature vector based on the laws of orbit dynamics and rigid body kinematics;

[0016] S4, transmitting the gradient of the physical constraint loss to the feature extraction network through back propagation to optimize its weight parameters, so that the network learns to generate a feature vector with embedded physical consistency;

[0017] S5, outputting the universal multi-dimensional feature representation with embedded physical consistency for downstream tasks.

[0018] Preferably, the feature extraction network in step S2 is a dual-flow feature extraction network, and step S2 specifically comprises the following steps:

[0019] S21, extracting the static geometric structure features of the fragments in the time sequence image sequence through an edge-enhanced geometric branch; and extracting the dynamic motion trajectory features of the fragments in the time sequence image sequence through an optical flow-LSTM motion branch;

[0020] S22, adaptively weighting and fusing the static geometric structure features and dynamic motion trajectory features through a space-time attention fusion module to generate the initial multi-dimensional feature vector.

[0021] Preferably, the edge-enhanced geometric branch in step S21 comprises an edge-enhanced convolution module, which adaptively fuses the standard convolution feature map F_cnn and the gradient feature map F_sobel extracted based on the Sobel operator through learnable weight parameter a, and the output is:

[0022] F_out = F_cnn + a · F_sobel

[0023] wherein the weight parameter a is optimized through gradient descent in the network training process.

[0024] Preferably, the physical constraint optimization layer in step S3 realizes physical guidance by minimizing a total loss function, which comprises a weighted sum of a task loss function, an orbit continuity loss function and a rigid consistency loss function; the orbit continuity loss function in step S3 is calculated based on the geocentric inertial coordinate system; the angular velocity in the rigid consistency loss function is defined in the debris body coordinate system and is converted to the geocentric inertial coordinate system through the attitude matrix, and then the kinematic consistency is calculated with the attitude angle in the coordinate system.

[0025] Preferably, the orbit continuity loss function L_orbit constrains the consistency of the predicted acceleration and the theoretical gravitational acceleration, so that the characteristic predicted motion trajectory conforms to the laws of celestial mechanics; the loss function is calculated in the geocentric inertial coordinate system, and the calculation formula is:

[0026] L_orbit = ‖ a_pred - a_theoretical ‖2

[0027] wherein a_pred is the acceleration calculated from the predicted velocity vector v_pred, and a_theoretical is the theoretical acceleration calculated from the predicted position vector r_pred according to the law of universal gravitation.

[0028] Preferably, the rigid consistency loss function L_rigid jointly constrains the angular velocity consistency and the angular acceleration consistency to ensure that the debris attitude motion conforms to the rigid kinematics; the loss function is calculated by:

[0029] L_rigid = L_angular_velocity + β · L_angular_acceleration

[0030] Wherein, L_angular_velocity is the norm of the difference between the predicted angular velocity ω_pred and the angular velocity obtained by differentiating the attitude angle θ_pred, L_angular_acceleration is the norm of the difference between the predicted angular acceleration and the angular acceleration obtained by second-order differentiating the predicted attitude angle, the term loss is an enhanced constraint on the angular velocity consistency loss L_angular_velocity, aiming to further regulate the smoothness and rationality of the attitude motion trajectory predicted by the network through higher-order kinematic continuity, and β is a weighting coefficient.

[0031] Preferably, the physical constraint loss calculation in step S4 is realized by a differential calculation module, which converts the physical law into a gradient signal, directly optimizes the weights of the feature extraction network through back propagation, and realizes the front-end guidance of the physical law to the feature learning process.

[0032] Preferably, the general multi-dimensional feature representation in step S5 is decoupled from the specific downstream task model, and can be used as a standardized input interface to seamlessly adapt to different task-specific networks, including but not limited to:

[0033] A fragment identification network for distinguishing spatial fragments from background stars;

[0034] A precise cataloging network for establishing a fragment feature database;

[0035] An attribute classification network for identifying fragment type, size, and material properties;

[0036] An orbit determination network for predicting fragment motion trajectories.

[0037] The application also discloses a computer readable storage medium and a computer system for feature-embedded representation of space debris monitoring.

[0038] The application has the following advantages:

[0039] The application embeds the physical law in the form of a gradient signal into network training, which brings the following fundamental improvements:

[0040] (1) Breakthrough of feature learning paradigm. In existing methods, physical laws are usually used as a posteriori verification or output optimization tools. The present application makes it a guiding signal in the training process, directly constraining the intrinsic parameters of the feature extraction network. This "physically guided embedded" mechanism ensures the physical credibility of the features from the source of feature generation, solving the core problem of the lack of physical meaning of pure data-driven model features.

[0041] (2) The obtained feature representation has inherent physical consistency and strong generalization ability. Since the features are learned under the strong constraints of orbital dynamics and rigid body kinematics, they inherently imply physical laws. This makes the features show much better stability and discriminability than data-driven models when facing extreme spatial environments such as strong noise and dark background, or unknown types of debris, significantly improving the practical value in complex scenarios.

[0042] (3) Effective decoupling of feature learning and task application is realized, providing system-level flexibility. The present application outputs a general, physically meaningful embedded representation, rather than a special output for a single task such as "detection" or "prediction". Therefore, the same set of high-quality feature representations can directly and efficiently support multiple downstream tasks such as identification, cataloging, and orbit determination, breaking the tightly coupled paradigm of "one task one model" in traditional solutions, greatly enhancing the overall design flexibility and scalability of the space debris monitoring system. BRIEF DESCRIPTION OF DRAWINGS

[0043] In order to more clearly illustrate the technical solutions of the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or prior art description. Obviously, the drawings in the following description are some embodiments of the present application, and for those skilled in the art, other drawings can also be obtained without creative labor on the basis of these drawings.

[0044] Figure 1 The method flowchart of the present application;

[0045] Figure 2 The detailed structure diagram of the double-flow feature extraction network of the present application;

[0046] Figure 3 The working principle diagram of the physical constraint optimization layer of the present application;

[0047] Figure 4 The training strategy diagram of the present application. DETAILED DESCRIPTION

[0048] In order to make the purposes, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are some embodiments but not all of the present application. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative work belong to the protection scope of the present application.

[0049] The present application aims to overcome the defects of the lack of physical laws and the tight coupling of features and tasks in the existing space debris feature extraction method, and provides a space debris feature embedding representation method through physical guided learning.

[0050] The present application aims to preposition the first principles such as orbital dynamics and rigid body kinematics from the post-checking link to the feature learning process. Through the differentiable physical constraint loss and its gradient back propagation, the intrinsic parameters of the feature extraction network are directly guided and constrained, so that the feature vectors output by the network have physical consistency in the generation source.

[0051] The universal multi-dimensional feature representation generated thereby will fundamentally improve its discriminability and generalization ability in extreme scenarios, and can serve as a unified bottom feature interface to directly support various downstream tasks such as space debris identification, cataloging, attribute classification and orbit determination.

[0052] To achieve the above-mentioned purposes, the technical solution core adopted by the present application is to construct a physically guided learning framework, taking physical laws as the guiding signal in the training process, and directly constraining the intrinsic parameters of the feature extraction network through the differentiable physical constraint loss and the back propagation mechanism, so that it learns to generate physically credible feature representation.

[0053] The present application is realized by the following steps, and the overall process is as shown in Figure 1

[0054] (1) Spatio-temporal feature extraction

[0055] Obtain the time sequence image sequence of the space debris, input it into the feature extraction network, and extract the spatio-temporal features of its static appearance and dynamic motion. Preferably, a double-flow network structure is adopted to extract static geometric structure features through an edge-enhanced geometric branch and to extract dynamic motion trajectory features through an optical flow-LSTM motion branch. The extracted features are adaptively weighted and fused through a spatio-temporal attention fusion module to form an initial feature vector.

[0056] (2) Physically guided embedding learning

[0057] The above initial feature vector is input into the physical constraint optimization layer. The layer is a differentiable calculation module without trainable parameters, and its functions include:​

[0058] Physical loss calculation: Based on orbital dynamics (such as the law of universal gravitation) and rigid body kinematics (such as angular velocity and angular acceleration consistency), a differentiable physical loss function is constructed.

[0059] Gradient guidance: Combine the calculated physical loss with the task loss into the total loss function, and pass its gradient directly to the weight parameters of the front-end feature extraction network through backpropagation, to drive the network to adjust its internal representation.

[0060] (3) Output of physically embedded representation

[0061] After the above training process guided by physical laws, the feature extraction network is optimized and has the ability to directly output a general multi-dimensional feature representation embedded with physical consistency. This feature representation is decoupled from the downstream task and can serve as a general and reliable input to seamlessly serve multiple tasks such as space debris identification, cataloging, attribute classification, and orbit determination.

[0062] To ensure the correctness of the physical law guidance, all physical quantity calculations are based on explicit coordinate system definitions: orbital dynamics constraints are calculated in the geocentric inertial coordinate system; rigid body kinematics constraints are defined in the debris body coordinate system, where the angular velocity ω_pred is expressed in the body coordinate system and converted to the geocentric inertial coordinate system through the attitude matrix for kinematics consistency calculation. The conversion from image observation data to the above coordinate system can be achieved with the help of camera calibration, platform attitude, etc. prior knowledge.

[0063] The embodiments of the present application are as follows:

[0064] I. Data preparation

[0065] The implementation effect of the present application depends on high-quality training data. To realize the "physical guidance learning" paradigm, the training data must be able to provide correct gradient guidance for the physical constraint loss function, which usually requires accurate physical law reference values. However, it is difficult to obtain real in-orbit images of space debris, and it is difficult to obtain accurate physical quantity labels at the pixel level. To solve this core contradiction, the present application designs a two-stage mixed data strategy from simulation to reality, gradually. This strategy aims to combine the respective advantages of simulation data and real data: use the reliable physical reference values of simulation data to lay a solid foundation for physical guidance learning; and use the complex characteristics of real data to ensure the generalization ability of the model in the real environment. The specific implementation is as follows:

[0066] First stage: pre-training based on high-fidelity physical simulation

[0067] The goal of this stage is to build an "initial teaching environment" with highly accurate physical laws for the network, laying a solid foundation for physical guidance.

[0068] Orbit and motion simulation: A numerical orbit dynamics model based on an accurate perturbation force model is adopted and coupled with an attitude dynamics model to generate the six-degree-of-freedom motion trajectories of space debris under various initial conditions, thereby obtaining physical quantities such as position, velocity, attitude, and angular velocity at each simulation time, which are used as reference states for calculating the physical constraint loss in training.

[0069] Realistic graphics rendering: A professional computer graphics engine (e.g., Unreal Engine or Blender) is used to render time-series image sequences that accurately correspond to the physical reference values, combined with accurate space lighting models, Earth backgrounds, and pre-set debris three-dimensional models. In this process, camera imaging defects such as image noise, motion blur, and brightness mutations are actively introduced to enhance the simulation data's ability to model real observation environments.

[0070] Dataset construction: The generated image sequences and physical reference values are integrated to form a large-scale simulation dataset D_sim. This dataset ensures that the physical constraint loss function can be calculated based on accurate reference values at the beginning of training, providing clear and reliable physical law guidance signals for the network.

[0071] Second stage: Fine-tuning and adaptation based on a small amount of real data

[0072] The goal of this stage is to guide the network to smoothly transition from an ideal simulation environment to a complex real-world application scenario, improving its generalization ability and robustness in actual tasks.

[0073] Real data collection and weak label generation: Real in-orbit observation image sequences D_real are collected. For this part of data, we generate approximate physical labels through various technical means to support weakly supervised calculation of the physical loss:

[0074] Trajectory interpolation and fitting: Based on sparse radar or telescope tracking data, high-precision orbit mechanics models are used for interpolation and fitting to calculate the position and velocity approximations of each frame of the image sequence that meet the accuracy requirements of orbit mechanics analysis.

[0075] Attitude estimation: The light curve characteristics of debris or its known geometric model are used to estimate the attitude change process in the sequence through visual techniques such as inverse rendering.

[0076] Key visual annotation: Pixel-level segmentation or keypoint annotation is performed on the images to provide real-world visual basis for feature learning of the geometric branch.

[0077] Mixed training strategy: After the network is preliminarily trained using D_sim, a mixed dataset of D_real and D_sim is used for fine-tuning. In this stage, the physical loss term is calculated on D_real using the approximate physical labels generated by the aforementioned method. Although its absolute accuracy is not as good as that of the simulation data, it is sufficient to constrain the network's feature output in the real scene to not deviate from the basic framework of the physical law, while prompting the network to adaptively learn the visual features and noise patterns in the real world.

[0078] Through the above-mentioned cooperative data strategy, the core advantage of the reliable physical benchmark reference value of the simulation data is fully utilized to provide a crucial benchmark training environment for the "physics-guided learning" paradigm. By introducing real data and its weak labels, the "simulation-to-reality gap" is effectively broken. This ensures that the model trained by the present solution not only has theoretical innovation, but also has solid engineering realizability and outstanding practical value.

[0079] II. Network construction

[0080] The present application builds the physics-guided learning network based on the PyTorch deep learning framework. The entire network adopts an end-to-end design, and its core is composed of a feature extraction backbone network and a physical constraint optimization layer. The design tenet of the network is to establish a dynamic learning system that can respond to the gradient of the physical law and adjust its internal feature representation accordingly. The specific structure of the network is as shown in Figure 2 .

[0081] (1) Feature extraction network: double-flow backbone with high guideability

[0082] This module is responsible for extracting rich spatio-temporal features from the input image, and its design emphasizes strong feature expression ability and smooth gradient flow to ensure that the guiding signal of the physical constraint can be effectively back-propagated and optimize the network parameters.

[0083] 1) Geometric feature branch

[0084] This branch aims to extract the static appearance features of spatial fragments, such as edges, contours, and structural symmetry. Its core processing flow is as follows:

[0085] Input: single-frame image I_t.

[0086] Edge enhancement convolution module: first, use a shared Sobel operator to calculate the gradient maps G_x, G_y in the x and y directions, and combine them to get the gradient amplitude map Meanwhile, the original image is sent into a standard convolutional layer to obtain the initial feature map F_cnn. Then, the two feature maps are adaptively fused by a learnable weight parameter a, and the output feature map is F_out = F_cnn + a · F_sobel. This design enables the network to adaptively adjust the contribution of contour information and texture information in geometric features according to the physical guidance.

[0087] Deep feature extraction: The fused feature map is sent to five improved inverted residual blocks in series for deep encoding. In each block, the original ReLU6 activation function is replaced by LeakyReLU with a negative slope of 0.1. This improvement aims to alleviate the problem of neuron "death" that may occur in low signal-to-noise ratio environments, significantly enhancing the smoothness of gradient flow, and is one of the key designs to ensure effective feedback of physical guidance signals.

[0088] 2) Motion feature branch

[0089] This branch is used to extract the dynamic motion trajectory features of spatial fragments.

[0090] Input: Three consecutive images (I_{t-1}, I_t, I_{t+1}).

[0091] Optical flow estimation: PWC-Net network is selected to calculate the dense optical flow fields OF_{t→t-1} and OF_{t→t+1} between adjacent frames to balance the calculation accuracy and efficiency.

[0092] Temporal modeling: The optical flow field sequence is stacked along the time dimension and input into a two-layer bidirectional LSTM network with 128 hidden units. This structure can simultaneously utilize past and future context information to accurately capture the temporal dependence of fragment motion. The output at the last time step is taken as the motion feature F_motion. The long-term temporal dependence learned by LSTM is the object of subsequent physical constraint guidance and correction, such as trajectory continuity loss.

[0093] 3) Spatio-temporal attention fusion module

[0094] This module aims to adaptively weight and fuse geometric and motion features to form a unified initial feature vector. We use a variant of the Convolutional Block Attention Module (CBAM) to achieve this:

[0095] Channel attention: The geometric feature F_geo and the motion feature F_motion are concatenated in the channel dimension, and a multi-layer perceptron (MLP) is used to generate channel attention weights to calibrate the importance of different feature channels.

[0096] Spatial attention: The weighted features are then passed through a spatial attention submodule to generate a spatial weight map, which is used to focus on key areas in the image (such as the fragment body).

[0097] Fused output: The final fused initial multi-dimensional feature vector is F_fused = M_s( M_c(F_concat)⊙ F_concat ) ⊙ F_concat, where ⊙ represents element-wise multiplication. The dimension of F_fused is 256. The learnable attention mechanism of this module enables the physical guidance to drive the network to learn to concentrate computational resources on the spatio-temporal information and feature channels that are most relevant to physical laws.

[0098] (2) Physical constraint optimization layer: Gradient generator of physical guidance

[0099] This layer is the core implementation of the "physical guidance learning" paradigm. It itself does not contain trainable parameters, but is a differentiable computational module based on automatic differentiation, whose function is to convert physical laws into gradient signals to guide the optimization of the feature extraction network.

[0100] Input: The initial feature vector F_fused output by the feature extraction network.

[0101] Process:

[0102] 1) Physical quantity decoding: Decode the predicted physical quantities from F_fused through a lightweight two-layer fully connected network (regression head), outputting the predicted position vector r_pred, velocity vector v_pred, attitude angle θ_pred, and predicted angular velocity vector ω_pred expressed in the body coordinate system.

[0103] 2) Physical loss calculation: Calculate the physical constraint loss based on the decoded physical quantities, which is the core of generating guiding gradients.

[0104] Orbit continuity loss L_orbit: This loss function forces the network to predict a motion trajectory that conforms to Newton's law of universal gravitation, and its calculation is based on the predicted position and velocity in the geocentric inertial coordinate system:

[0105] L_orbit = ‖ (Δv_pred / Δt) - (G * M * r_pred / ||r_pred|| 3 ) ‖2

[0106] Where G is the gravitational constant and M is the central celestial body mass. This loss constrains the predicted acceleration to be consistent with the theoretical gravitational acceleration.

[0107] Rigid consistency loss L_rigid: This loss function forces the network to predict a fragment attitude motion that conforms to the rigid kinematics law, and an enhanced design is adopted to introduce higher-order constraints:

[0108] L_rigid = L_angular_velocity + β * L_angular_acceleration

[0109] Where L_angular_velocity is used to constrain the consistency of angular velocity and attitude angular rate; L_angular_acceleration is used to constrain the consistency of angular acceleration. Its specific implementation involves converting body coordinate system angular velocity to the inertial system, see the "Physical loss implementation" section for details. β is the weighting coefficient.

[0110] 3) Joint optimization and back guidance: combine physical loss and task loss to form the total loss function L_total = L_task + * L_orbit + * L_rigid. After calling back propagation, the gradient generated by the above physical loss calculation process will pass through the regression head and be back propagated to all parameters of the feature extraction backbone network. The optimizer updates the parameters according to these gradients, forcing the feature extraction network to learn to produce features that can be decoded to meet the physical laws of physical quantities. It is these first-principle-based differentiable formulas that ensure the correctness of the gradient signal and form the mathematical basis of physical guidance.

[0111] (3) Collaborative design of network and data

[0112] The construction of this network is highly coordinated with the aforementioned "simulation-real" mixed data strategy:

[0113] In the simulation data pre-training phase, the network is under the environment of highly accurate physical benchmark reference values, and receives strict physical guidance, preliminarily establishing the correct association between features and physical laws.

[0114] In the real data fine-tuning phase, the inherent flexibility of the network structure (such as the learnable weight parameter α, attention mechanism) enables it to adapt to the real data distribution using physical priors, while not deviating from the basic framework of physical laws.

[0115] Through the above construction process, we get a complete, end-to-end trainable physically guided learning network. Its innovation lies in the integration of network structure and training mechanism into an intelligent system that can be dynamically guided by physical laws, achieving embedded physical learning of feature representation.

[0116] Three, physical loss implementation

[0117] The implementation of the physical constraint optimization layer is the core innovation of the present application, which converts physical priors into calculable gradient signals. This layer does not rely on a neural network with parameters, but through a self-defined differentiable computation module, maps the feature vector to the physical constraint loss, and back-propagates the gradient to the front-end network, thereby guiding the direction of feature learning. The working principle is as shown in Figure 3

[0118] (1) Decoding from feature vector to physical quantity

[0119] As a bridge between physical laws and feature representation, a lightweight regression head is responsible for decoding the physical quantity that can be used to calculate the physical loss from the fused feature vector F_fused.

[0120] Regression head structure: a two-layer fully connected network is adopted. The first layer (256-dimensional input, 256-dimensional output) uses a ReLU activation function; the second layer (256-dimensional input, 12-dimensional output) directly regresses the target physical quantity.

[0121] Output physical quantity: the 12-dimensional vector (corresponding to 3 positions, 3 velocities, 3 attitude angles, 3 angular velocities) [r_pred, v_pred, θ_pred, ω_pred] decoded and output:

[0122] r_pred: predicted position vector of the debris in the geocentric inertial coordinate system.

[0123] v_pred: predicted velocity vector of the debris in the geocentric inertial coordinate system.

[0124] θ_pred: predicted attitude angle (Z-Y-X Euler angle) of the debris from the body coordinate system to the geocentric inertial coordinate system.

[0125] ω_pred: predicted angular velocity vector of the debris expressed in the body coordinate system.

[0126] Design considerations: although the network input is a camera image, through end-to-end training and strong guidance of the physical loss, the network will learn to solve the feature representation with absolute physical meaning in the inertial space from the image sequence. The physical reference value in the geocentric inertial coordinate system in the training data provides a clear learning goal for the network.

[0127] (2) Calculation of the physical constraint loss function

[0128] The physical loss function converts the first principle into a mathematical constraint for network optimization.

[0129] 1) Implementation of the orbit continuity loss L_orbit

[0130] ​This loss function forces the network to predict the motion trajectory that complies with Newton's law of universal gravitation and Kepler's law of planetary motion.

[0131] Theoretical acceleration calculation: According to the predicted position r_pred, the theoretical acceleration that the debris should suffer is calculated by the law of universal gravitation:

[0132] a_theoretical = (G * M * r_pred) / (‖r_pred‖ 3 )

[0133] where the gravitational constant G = 6.67430 × 10 -11 m³ / (kg·s²), the mass of the Earth M = 5.972 × 10 24 kg.

[0134] Predicted acceleration calculation: The time derivative of the network-predicted velocity v_pred is calculated using automatic differentiation to obtain the predicted acceleration:

[0135] a_pred = ∂(v_pred) / ∂t

[0136] Loss calculation: The Euclidean distance between the predicted acceleration and the theoretical acceleration is calculated:

[0137] L_orbit = ‖ a_pred - a_theoretical ‖2

[0138] The minimization of this loss directly guides the network to learn the motion characteristics that comply with celestial mechanics.

[0139] 2) Implementation of rigid consistency loss L_rigid

[0140] This loss function constrains the network-predicted debris attitude motion to comply with the laws of rigid body kinematics. To ensure that all physical quantities are operated in a consistent coordinate system, the predicted angular velocity ω_pred in the body coordinate system needs to be converted to the geocentric inertial coordinate system through the rotation matrix R(θ_pred) determined by the predicted attitude angle θ_pred.

[0141] Angular velocity consistency constraint: The attitude angle rate is calculated using automatic differentiation to obtain the angular velocity estimate in the geocentric inertial coordinate system ω_from_θ = ∂(θ_pred) / ∂t. The predicted body coordinate system angular velocity is converted to the inertial system: ω_pred_inertial = R(θ_pred) · ω_pred. Then the difference between the two is calculated:

[0142] L_angular_velocity = ‖ ω_pred_inertial - ω_from_θ ‖2

[0143] Angular acceleration consistency constraint (enhanced): Derive the angular velocity ω_pred_inertial after conversion in the inertial system, and get α_pred_inertial = ∂(ω_pred_inertial) / ∂t, and the second-order derivative of the attitude angle θ_pred is α_from_θ = ∂²(θ_pred) / ∂t², and constrain them to be consistent:

[0144] L_angular_acceleration = ‖ α_pred_inertial - α_from_θ ‖2

[0145] Total rigid loss: Combine the above two losses by weighting, form a high-order constraint on rigid kinematics:

[0146] L_rigid = L_angular_velocity + β * L_angular_acceleration

[0147] Where β is the weighting coefficient (set to 0.5 in this embodiment). Introducing the second-order derivative constraint can more strictly guide the network to learn features that conform to the rigid rotation law.

[0148] (3) Loss fusion and physical guidance mechanism

[0149] This is the key step to convert physical knowledge into the driving force of network learning.

[0150] Total loss function: Physical loss and task loss together constitute the optimization goal:

[0151] L_total = L_task + * L_orbit + * L_rigid

[0152] In this embodiment, L_task adopts feature reconstruction loss to ensure basic representation ability. The hyperparameter is set to =0.5, = 0.3.

[0153] Backpropagation and guiding effect: After calling L_total.backward(), the gradient generated by the physical loss is backpropagated to all parameters of the feature extraction backbone network through the regression head. The optimizer updates the network weights according to these gradients containing physical laws. This process forces the feature extraction network to adjust its internal parameters so that the final output of the feature vector F_fused itself is physically consistent, rather than modifying the features later.

[0154] Through the above implementation, the first principle of physics is deeply integrated into the training loop of the deep learning model in the form of differentiable gradients, realizing the front-end guidance of physical laws to the feature learning process.

[0155] Four, training strategy

[0156] To realize the stable and efficient embedding of physical laws into feature representation, we designed a progressive multi-stage training strategy. This strategy introduces physical guidance signals in a controllable and phased manner, ensuring that the network can smoothly learn physical consistency constraints after mastering basic visual features, effectively avoiding training divergence caused by unstable physical gradients in the early stage. The complete process of the training strategy is shown in Figure 4

[0157] (1) Progressive multi-stage physical guidance training

[0158] The training process includes three main stages, the core of which is the progressive adjustment of the physical loss weight ( , ) and the implementation of the "simulation-real" mixed data strategy.

[0159] 1) First stage: basic feature learning (warm-up stage)

[0160] Training goal: initialize network parameters to enable the network to extract effective spatio-temporal features from image sequences, providing a stable optimization starting point for subsequent physical guidance.

[0161] Guiding strategy: No physical constraints are introduced in this stage, and the total loss function is simplified to L_total = L_task (feature reconstruction loss is used in this embodiment), so that the network focuses on learning the initial multi-dimensional feature representation of spatial fragments.

[0162] Training settings: Use simulation dataset, use a higher initial learning rate (1x10 -3 ), AdamW optimizer, and train about 40% of the total number of iterations. Training continues until the task loss converges and stabilizes.

[0163] 2) Second stage: physical law guidance introduction (core learning stage)

[0164] ​Training goal: On the basis of the initial multi-dimensional features obtained, gradually introduce physical loss as a guide signal, and start to embed track dynamics and rigid body kinematics rules into feature learning.

[0165] Guiding strategy: Start the physical constraint optimization layer, and introduce the physical loss with a small weight:

[0166] The initial hyperparameter setting is

[0167] = 0.1, = 0.05.

[0168] Use linear planning sampling to gradually increase and to the target value

[0169] ( = 0.5, = 0.3). This strategy allows the network to smoothly adapt to the guiding effect of physical gradients and avoid dramatic shocks in feature representation.

[0170] Training settings: Use a small learning rate (5×10 -5 ), continue to train mainly with simulation data, and use its accurate physical benchmark reference value to ensure the correctness of the guide direction. This stage of training accounts for about 40% of the total number of rounds.

[0171] 3) Mixed data joint fine-tuning (convergence and adaptation stage)

[0172] Training goal: Fine-tune network parameters, strengthen physical embedding effects, and adapt the model to real data distribution to improve generalization ability.

[0173] Guiding strategy: Keep and at the target value, and the physical law continues to provide a stable guide signal. Introduce a mixed set of simulation and real data for training, and use approximate physical labels to calculate the physical loss on real data, allowing the network to adapt to real observation characteristics while maintaining physical consistency.

[0174] Training settings: Use a smaller learning rate (1×10 -5 ), fine-tune all network parameters, and train the remaining 20% of the iteration rounds. Training terminates when the validation set loss no longer decreases or reaches the preset number of rounds.

[0175] (2) Optimizer and hyperparameter configuration

[0176] AdamW optimizer is selected, and its decoupled weight decay strategy helps to improve the generalization performance of the model.

[0177] The weight decay coefficient is set to 1x10 -4 , to control the model complexity and prevent overfitting.

[0178] The learning rate scheduling adopts a cosine annealing strategy, which is smoothly decayed from the initial value to the lower limit (such as 1x10 -6 ), which helps the model to jump out of the local optimum and converge to a better solution.

[0179] (3) Model verification and effect evaluation

[0180] Monitoring indicators:

[0181] Total loss L_total: Monitor the overall optimization process.

[0182] Physical loss terms L_orbit and L_rigid: Core evaluation indicators, and stable decline directly proves the effectiveness of physical guidance and the degree of embedding of physical laws.

[0183] Feature similarity: Calculate the average cosine similarity of the same type of fragment features on the validation set as an indirect measure of feature discriminability. Under physical guidance, the same type of features should show a more obvious clustering trend.

[0184] Model saving: Early stopping strategy. If the total loss of the validation set does not decrease for 15 consecutive epochs, training is terminated, and the model weight with the best validation performance is rolled back to ensure the generalization ability of the model.

[0185] This training strategy introduces physical guidance in a phased and controllable manner, ensuring that physical laws can be effectively encoded into feature representations, ensuring the stability of training and ultimately enabling the model to output physically consistent features.

[0186] The present application also discloses a computer readable storage medium and a computer system for feature-embedded representation for space debris monitoring. The computer program is stored on the readable storage medium, and after the computer program is run, the method as described in any of the above is executed. The computer system for feature-embedded representation for space debris monitoring includes a processor and a storage medium, and the computer program is stored on the storage medium. The processor reads and runs the computer program from the storage medium to execute the method as described in any of the above.

[0187] The steps of a method or algorithm described in connection with the embodiments disclosed herein can be embodied directly in hardware, in a software module executed by a processor, or in a combination of the two. A software module can reside in RAM memory, flash memory, ROM memory, EPROM memory, EEPROM memory, registers, hard disk, a removable disk, a CD-ROM, or any other form of storage medium known in the art. An exemplary storage medium is coupled to the processor such that the processor can read information from, and write information to, the storage medium. In the alternative, the storage medium can be integral to the processor. The processor and the storage medium can reside in an ASIC. The ASIC can reside in a user terminal. In the alternative, the processor and the storage medium can reside as discrete components in a user terminal.

[0188] The previous description of the disclosure is provided to enable any person skilled in the art to make or use the disclosure. Various modifications to the disclosure will be readily apparent to those skilled in the art, and the generic principles defined herein can be applied to other variations without departing from the spirit or scope of the disclosure. Thus, the disclosure is not intended to be limited to the examples described herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

[0189] Although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art will understand that the technical solutions recorded in the foregoing embodiments can be modified, or some of the technical features can be replaced by equivalent ones, without departing from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A method for spatial debris feature embedding representation by physical guidance learning, characterized in that, The method comprises the following steps: S1, acquiring a time sequence image sequence of space debris; S2, extracting space-time features of the time sequence image sequence through a feature extraction network to form an initial feature vector; S3, introducing a physical constraint optimization layer, calculating a physical constraint loss of the initial feature vector based on laws of orbit dynamics and rigid body kinematics; S4, transmitting a gradient of the physical constraint loss to the feature extraction network through back propagation to optimize weight parameters thereof, so that the network learns to generate a feature vector with embedded physical consistency; S5, outputting a general multi-dimensional feature representation with embedded physical consistency for a downstream task; the general multi-dimensional feature representation is decoupled from a specific downstream task model and can be used as a standardized input interface to seamlessly adapt to different task-specific networks, including but not limited to: a debris identification network for distinguishing space debris from background stars; a precise cataloging network for establishing a debris feature database; an attribute classification network for identifying debris types, sizes and material properties; an orbit determination network for predicting a debris motion trajectory.

2. The method of claim 1, wherein: The feature extraction network in step S2 is a double-flow feature extraction network, and step S2 specifically comprises the following steps: S21, extracting static geometric structure features of debris in the time sequence image sequence through an edge-enhanced geometric branch; and extracting dynamic motion trajectory features of debris in the time sequence image sequence through an optical flow-LSTM motion branch; S22, adaptively weighting and fusing the static geometric structure features and the dynamic motion trajectory features through a space-time attention fusion module to generate an initial multi-dimensional feature vector.

3. The method of claim 2, wherein: The edge-enhanced geometric branch in step S21 comprises an edge-enhanced convolution module, which adaptively fuses a standard convolution feature map F_cnn and a gradient feature map F_sobel based on a Sobel operator through learnable weight parameters α, and the output is: F_out = F_cnn + α · F_sobel wherein the weight parameter α is optimized through gradient descent during network training.

4. The method according to any one of claims 1 to 3, characterized in that: The physical constraint optimization layer in step S3 realizes physical guidance by minimizing a total loss function, and the total loss function comprises a weighted sum of a task loss function, an orbit continuity loss function and a rigid body consistency loss function; the orbit continuity loss function in step S3 is calculated based on a geocentric inertial coordinate system; the angular velocity in the rigid body consistency loss function is defined in a debris body coordinate system and is converted to a geocentric inertial coordinate system through an attitude matrix, and then kinematic consistency calculation is performed with an attitude angle in the coordinate system.

5. The method of claim 4, wherein: The orbit continuity loss function L_orbit constrains the consistency of predicted acceleration and theoretical gravitational acceleration, so that the motion trajectory predicted by the feature conforms to the laws of celestial mechanics; the loss function is calculated in a geocentric inertial coordinate system, and the calculation formula is: L_orbit = ‖ a_pred - a_theoretical ‖2 Wherein, a_pred is the acceleration calculated by the predicted velocity vector v_pred, a_theoretical is the theoretical acceleration calculated by the predicted position vector r_pred according to the law of universal gravitation.

6. The method of claim 4, wherein: The rigid consistency loss function L_rigid guarantees that the attitude motion of the debris conforms to the rigid kinematics by jointly constraining the angular velocity consistency and the angular acceleration consistency; the loss function is calculated by the following formula: L_rigid = L_angular_velocity + β · L_angular_acceleration Wherein, L_angular_velocity is the norm of the difference between the predicted angular velocity ω_pred and the angular velocity obtained by differentiating the attitude angle θ_pred, L_angular_acceleration is the norm of the difference between the predicted angular acceleration and the angular acceleration obtained by differentiating the predicted attitude angle twice, and β is a weighting coefficient.

7. The method of claim 4, wherein: The physical constraint loss calculation in step S4 is realized by a differential calculation module, which converts the physical law into a gradient signal, directly optimizes the weights of the feature extraction network through back propagation, and realizes the front-end guidance of the physical law to the feature learning process.

8. A computer-readable storage medium, characterized in that: The computer program is stored on the medium, and after the computer program is run, the method in any one of claims 1 to 7 is executed.

9. A computer system for in-features embedded characterization of space debris monitoring, characterized in that: The computer program is stored on the medium, and after the computer program is run, the method in any one of claims 1 to 7 is executed.

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