Ballistic analysis method based on space-time rotation coding and dynamic mask reconstruction

Abstract

The invention discloses a ballistic analysis method based on space-time rotation coding and dynamic mask reconstruction. The ballistic analysis method comprises the following steps: acquiring ballistic trajectory data observed by a radar; performing normalization processing on the ballistic trajectory data by adopting a split-axis normalization method, and mapping each trajectory point into a space-time Token sequence in a high-dimensional feature space; constructing a feature extraction network comprising a multi-layer space-time rotation attention mechanism; 2, performing mask processing on the space-time Token sequence generated in the step 1 by adopting a double-layer mask strategy, extracting feature representation through a space-time rotation Transform encoder, mapping back to an original physical space through a physical perception reconstruction task head, and optimizing model parameters based on a physical perception composite loss function to complete self-supervised pre-training; respectively setting corresponding lightweight task heads and loss functions for downstream trajectory prediction, missile classification or drop point prediction tasks based on the weight of the pre-training model, and splicing each task head with a space-time rotation Transformer encoder; and finishing model fine tuning of a specific task by training a task head. The precision and adaptability of ballistic analysis in a complex battlefield environment are improved.

Description

TECHNICAL FIELD

[0001] The present application relates to a trajectory analysis and impact point prediction technology based on radar observation data, in particular to a trajectory analysis method based on space-time rotation coding and dynamic mask reconstruction. BACKGROUND

[0002] Trajectory analysis has strategic significance in modern military defense and aerospace engineering. Traditional methods mainly rely on analytical calculation of physical equations, which have significant limitations in complex real combat environments: when the target motion trajectory evolves nonlinearly, the environment is strongly disturbed, or the observation data is sparse, the classical model is difficult to guarantee the prediction accuracy.

[0003] Deep learning provides a new paradigm for trajectory modeling, which can automatically learn complex nonlinear laws in the trajectory. Applying deep learning methods to the field of trajectory prediction still needs to solve the following problems: First, the dependence on trajectory data, supervised learning models require a large amount of labeled data for training, while valuable trajectory samples are scarce in actual battlefield environments, and there are significant domain differences between simulation data and real radar monitoring data. Using a special model architecture (such as separating trajectory prediction network and projectile classification network) has the problem of insufficient task generalization, and different feature extraction methods need to be designed for specific tasks, and knowledge is difficult to transfer across tasks. Each time a new task is deployed, it needs to be retrained; when the commonly used general time series model (such as LSTM, Transformer) is directly transferred, it cannot embed the physical constraints of trajectory motion (such as the velocity-displacement differential relationship), and the prediction results often violate the laws of kinematics.

[0004] In recent years, large language models (LLMs) have achieved revolutionary breakthroughs through self-supervised pre-training frameworks. Models with Transformer as the core architecture (such as the autoregressive pre-training of the GPT series and the bidirectional mask modeling of BERT) learn general representations on hundreds of billions of text data, building multi-level semantic understanding capabilities. Its core advantage lies in its unified encoding capability, which can fuse the semantic and sequential relationships of discrete symbols through word embedding layers and position encoding; it can learn the context content (ICL) of the text and quickly adapt to new tasks with only a small number of examples; the pre-training-fine-tuning framework flexibly supports multi-task generalization, and the unified framework supports heterogeneous tasks such as text generation, classification, and question answering.

[0005] The generalization ability of LLMs comes from the hierarchical feature extraction mechanism and the course mask strategy in the pre-training pretext task. The model captures local grammar patterns (such as word order constraints) at the bottom layer, and models global logical structures (such as causal relationships) at the high layer, and then gradually transitions from masking single words to masking grammatical components through dynamic mask strategies, which is a process of simulating human progressive learning.

[0006] It is worth noting that there is a deep structural isomorphism between the ballistic trajectory data and natural language: the time-sequenced trajectory points can be analogous to the lexical units in language, the kinematic constraints between adjacent trajectory points (such as the differential relationship between displacement and velocity) are similar to the restrictions of grammar rules on word combination, and the complete ballistic trajectory constitutes a "motion sentence" with clear physical semantics. This isomorphism provides a theoretical basis for the successful experience of transferring LLM. However, directly applying existing frameworks faces core obstacles: the bag-of-words position encoding of language models cannot capture the continuous physical quantities of ballistic points (such as the rate of change of three-dimensional coordinates), the random masking strategy destroys the continuity of motion differentiation, and there are essential differences between the discrete prediction task of natural language and the continuous trajectory regression and discrete projectile classification that need to be handled simultaneously in the ballistic field. In addition, existing deep learning methods mostly model spatial coordinates and temporal evolution separately, lack a unified spatio-temporal joint encoding mechanism, and are difficult to simultaneously characterize coupled motion features at different time scales and spatial scales. SUMMARY

[0007] The present application aims to propose a ballistic analysis method based on spatio-temporal rotation encoding and dynamic mask reconstruction to break through the technical limitations of existing ballistic analysis models in multi-source data fusion, cross-task generalization, and physical law modeling.

[0008] The technical solution to achieve the purpose of the present application is: a ballistic analysis method based on spatio-temporal rotation encoding and dynamic mask reconstruction, the steps are as follows:

[0009] Step 1, data construction and Tokenization: obtain the ballistic trajectory data observed by radar, including spatial coordinates , velocity components and timestamps ; use the split-axis normalization method to normalize the ballistic trajectory data, and map each trajectory point to a spatio-temporal Token sequence in a high-dimensional feature space;

[0010] Step 2, build a spatio-temporal rotation Transformer encoder (STRFormer): build a feature extraction network containing multiple layers of spatio-temporal rotation attention mechanisms; this network uses spatio-temporal rotation position encoding (STR-RoPE) to inject time information as a modulation phase into the rotation transformation of spatial coordinates through a learnable projection matrix, to jointly model the relative spatial displacement and non-uniform time interval between trajectory points;

[0011] Step 3, self-supervised pre-training: a double-layer mask strategy is adopted to mask the spatio-temporal Token sequence generated in step 1, and after extracting feature representations via the spatio-temporal rotation Transformer encoder in step 2, the physical perception reconstruction task head is mapped back to the original physical space, and the model parameters are optimized based on the physical perception composite loss function, and the self-supervised pre-training is completed; the double-layer mask strategy includes global masking of consecutive time periods, and feature-level random masking of specific dimensions of spatial coordinates or velocity vectors in the feature dimension;

[0012] Step 4, task adaptation and fine-tuning: based on the pre-trained model weights obtained in step 3, for the downstream trajectory prediction, projectile classification or impact point prediction tasks, the corresponding lightweight task heads and loss functions are set, and the task heads and spatio-temporal rotation Transformer encoder are spliced; the pre-trained encoder parameters are frozen or slightly adjusted, and the model fine-tuning for specific tasks is completed through training the task head.

[0013] Further, in step 2, the specific calculation process of the spatio-temporal rotation position encoding is:

[0014] For each Token in the input sequence , the normalized spatial coordinates and time stamp are mapped using the learnable spatial projection matrix and time embedding matrix ;

[0015] The spatial and temporal features are fused by element-wise multiplication (Hadamard Product) to generate a spatio-temporal phase vector :

[0016]

[0017] The spatio-temporal phase vector is used to construct a rotation matrix , which is used to rotate the query vector and key vector in the attention mechanism, so that the dot product of the transformed and only depends on the relative spatio-temporal difference between Tokens;

[0018] .

[0019] Further, in step 2, the constructed spatio-temporal rotation Transformer encoder (STRFormer) specifically includes:

[0020] (1) Multimodal embedding layer: includes spatial coordinate embedding layer, velocity vector embedding layer and time embedding layer, which respectively project the normalized trajectory point spatial coordinates, velocity vector and timestamp onto the feature space of the same dimension to obtain independent three-modal embedding vectors;

[0021] (2) Modality Mixer: used to fuse heterogeneous physical information within the same time step; the spatial, velocity and temporal embeddings at the same time are concatenated and input into a lightweight Transformer encoder, which calculates the interaction weights between modes through a self-attention mechanism and outputs the fused hybrid modal feature sequence;

[0022] (3) STRFormer spatiotemporal encoder: It consists of multiple identical layers stacked together. In each layer, a multi-head self-attention module containing a spatiotemporal rotation position encoding (STR-RoPE) and a feedforward network are used to perform hierarchical feature extraction on the mixed modality feature sequence and output a trajectory table containing global spatiotemporal dependencies.

[0023] Furthermore, in step 3, the dual-layer masking strategy specifically includes:

[0024] (1) Global Trajectory Masking: In the time dimension, several consecutive time spans are randomly selected for masking, and their corresponding tokens are replaced with learnable mask tokens to force the model to reconstruct the missing trajectory segments using contextual information and learn long-range spatiotemporal dependencies.

[0025] (2) Feature-level random masking: At time steps where the model is not globally masked, specific feature dimensions of spatial coordinates or velocity vectors are randomly masked with independent probability to enhance the model’s robustness to the loss of local physical features.

[0026] Furthermore, in step 3, the physical perception reconstruction task head adopts a lightweight linear structure, specifically constructed by acquiring the hidden feature representation extracted by the spatiotemporal rotation Transformer encoder. A single-layer linear regression layer is used as the mapping layer to directly map the feature representation of each masked token to the corresponding spatial location prediction value. Compared with speed prediction value To achieve regression reconstruction from high-dimensional feature space to physical state space;

[0027] The loss function for the physical perception reconstruction task employs a multi-objective joint optimization strategy, including:

[0028] Location reconstruction loss : Calculate the mean square error of the predicted coordinates and the true coordinates, the formula is:

[0029] ;

[0030] Velocity vector loss : Calculate the mean square error between the predicted velocity and the true velocity of the masked position, the formula is:

[0031] ;

[0032] Kinematic consistency constraint loss : Introduce smoothness constraints to penalize the deviation between position change rate and velocity vector:

[0033] ;

[0034] The total loss function is: , where is the balance coefficient.

[0035] Further, in step 4, the task head structure configured for different downstream tasks includes:

[0036] (1) Trajectory prediction task: direct multi-step generation or recursive generation mode is adopted; linear regression head is used to directly map the future position and velocity sequence from the features output by the encoder;

[0037] (2) Shell classification task: an attention pooling layer is used to aggregate global spatio-temporal features, and a fully connected layer is used to output the class probability distribution of the shell;

[0038] (3) Launch and landing point prediction task: a double-branch regression structure is adopted, which aggregates the features of the initial segment and the final segment of the trajectory respectively, and directly regresses to predict the three-dimensional spatial coordinates of the launch point and the landing point.

[0039] Further, in step 3, the pre-training stage adopts a curriculum learning strategy, gradually increasing the dynamic mask proportion from 20% to 50% while keeping the spatio-temporal joint encoding structure unchanged, guiding the model to first learn local short-range spatio-temporal patterns, and then learn long-range dependencies; in step 4, the fine-tuning stage adopts a task adapter mechanism, while freezing most of the parameters of the spatio-temporal joint encoding and attention backbone network in the base model, only training the downstream task head and the corresponding adaptation layer to improve the cross-task transfer efficiency and maintain the consistency of the general spatio-temporal representation.

[0040] A trajectory analysis system based on space-time rotation coding and dynamic mask reconstruction, comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor implements the trajectory analysis method based on space-time rotation coding and dynamic mask reconstruction when executing the program.

[0041] An electronic device, comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor implements the trajectory analysis method based on space-time rotation coding and dynamic mask reconstruction when executing the program.

[0042] A non-transitory computer-readable storage medium having a computer program stored thereon, wherein the computer program is executed by a processor to implement the trajectory analysis method based on space-time rotation coding and dynamic mask reconstruction.

[0043] Compared with the prior art, the present application has the following advantages:

[0044] (1) Strong space-time coupling modeling capability: the STRFormer proposed by the present application creatively modulates the timestamp information into the space rotation coding using the STR-RoPE technology. Compared with the traditional method of simply splicing time and space features, this method can more essentially capture the dynamic coupling law of "position changing with time" in the trajectory, effectively solving the problems of non-uniform sampling and long-range dependence modeling.

[0045] (2) High physical consistency and robustness: by introducing kinematic consistency constraints and physical perception data enhancement (simulating radar spherical coordinate noise), the present application forces the model to learn trajectory representations that conform to physical laws, rather than simply fitting data distribution. This enables the model to generate prediction results that conform to the laws of dynamics when faced with noise interference or missing data.

[0046] (3) High generalization ability and training efficiency: using the "pre-training-fine-tuning" paradigm, the present application learns general ballistic physical features through a double-layer mask task using large-scale unlabeled data. In downstream tasks, only a small number of parameters need to be fine-tuned to adapt to multiple tasks such as trajectory prediction, classification and impact point estimation, greatly reducing the dependence on specific task labeled data and improving the deployment efficiency and universality of the model. BRIEF DESCRIPTION OF DRAWINGS

[0047] Figure 1 Figure 1 is a schematic diagram of the overall architecture of the general ballistic trajectory base model of the present application.

[0048] Figure 2 Figure 4 is a schematic diagram of the dynamic mask strategy of the present application.

[0049] Figure 3Trajectory prediction effect diagram based on radar observation data of the present application.

[0050] Figure 4 Curve diagram of trajectory prediction error changing with prediction step of the present application.

[0051] Figure 5 Confusion matrix diagram of projectile type recognition accuracy of the present application.

[0052] Figure 6 Distribution diagram of launch point / impact point prediction error of the present application. DETAILED DESCRIPTION

[0053] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings. Obviously, the described embodiments are only some of the embodiments of the present application, not all the embodiments.

[0054] As shown in the drawings, Figure 1 The present application proposes a trajectory analysis basic model based on spatio-temporal rotation encoding and dynamic mask reconstruction. The core of the model is to construct in two-stage paradigm, and use a shared backbone network composed of a modal mixed encoder and a spatio-temporal rotation transformer (STRFormer) core. The architecture is first optimized in the self-supervised pre-training stage, and then further adjusted through the lightweight fine-tuning stage, which uses a compact head structure customized for diversified downstream applications including trajectory prediction, projectile classification and event prediction. The specific implementation steps are as follows:

[0055] Step 1: Data construction and Tokenization

[0056] Step 1 mainly performs data construction and Tokenization, which converts radar observation data into high-dimensional feature tensors. This step specifically includes the following three sub-steps: Step 11: Obtain the discrete sequence of the trajectory of the radar observation, extract the three-dimensional space coordinates, velocity components and time stamp data. In view of the problem that the dimensions of each physical quantity are significantly different, a split-axis normalization strategy is adopted to calculate the mean and standard deviation of the space and velocity data in each axis, and perform Z-Score standardization transformation to map the original physical values to dimensionless feature inputs with consistent distribution.

[0057] Step 12: Construct parallel multi-modal embedding layers to map the normalized physical data to high-dimensional feature space. The standardized space vector, velocity vector and time scalar are input into three independent linear projection layers for dimension transformation, and processed by LeakyReLU activation function, which converts low-dimensional observation data into high-dimensional feature vectors with unified dimensions to independently represent the initial feature distribution of each modality.

[0058] Step 13: Fusion of heterogeneous features using modal mixer, generating spatio-temporal Token sequence. The spatial, velocity, and temporal embedding vectors at the same time step are concatenated in the feature dimension, integrated into a single feature representation, and organized in time sequence order to form an input tensor with shape , which is the standard input data for the subsequent spatio-temporal rotation Transformer encoder.

[0059] Step 2: Construction of spatio-temporal rotation encoder (STRFormer)

[0060] As shown in Figure 1 , step 2 is mainly responsible for constructing a feature extraction network STRFormer with multiple layers of stacking. The core innovation lies in the introduction of spatio-temporal rotation position encoding (STR-RoPE). STR-RoPE implicitly encodes the spatio-temporal dependencies between trajectory points by performing rotation transformation in the feature space.

[0061] This step specifically includes the following two sub-steps:

[0062] Step 21: Construction of spatio-temporal rotation position encoding module to explicitly model the relative spatio-temporal dependencies between trajectory points. For each Token in the input sequence, the normalized spatial coordinates and timestamps are linearly mapped using the learnable spatial projection matrix and temporal embedding matrix , respectively. By element-wise multiplication, the spatio-temporal phase vector is generated:

[0063]

[0064] where denotes element-wise multiplication. The phase vector contains both spatial position information and temporal information for the point.

[0065] Then, a rotation matrix is constructed based on the phase vector. In multi-head self-attention calculation, the feature dimensions of the query vector and key vector are divided into multiple two-dimensional subspaces. For the th subspace, a two-dimensional rotation matrix is constructed using the corresponding phase value :

[0066]

[0067] For the vector at time step (Indicating query or key), the rotation matrix acts on its corresponding 2D feature slice , encapsulating Method: To complete the spatio-temporal rotation transformation of attention.

[0068] Finally, by splicing the slices that have undergone independent rotation transformation on all subspaces, the complete rotation query vector and the rotation key vector are obtained. Based on these spatio-temporal rotation transformed representations, the attention score matrix will be calculated by standard inner product, that is

[0069]

[0070] So that the attention weight only depends on the relative spatial displacement and relative time interval between tokens.

[0071] Step 22: Establish a multi-layer stacked spatio-temporal rotation Transformer encoder to extract global spatio-temporal context features. Take the spatio-temporal Token sequence generated in step 1 as input, and pass it through multiple encoder layers one by one. Each layer internally contains a self-attention sublayer based on the rotation position encoding described in step 21 and a feedforward neural network sublayer, supplemented by layer normalization and residual connection structure to optimize gradient propagation. The input tensor undergoes hierarchical feature extraction and is finally converted into a hidden feature representation containing complete trajectory dynamics information, which will serve as input features for subsequent pre-training tasks or downstream tasks.

[0072] Step 3: Self-supervised pre-training and double-layer masking strategy

[0073] Step 3 mainly performs self-supervised pre-training, and constructs a physical perception auxiliary task training model through a double-layer masking mechanism and a trajectory reconstruction head. This step specifically includes the following three sub-steps:

[0074] Step 31: Perform a double-layer dynamic masking strategy to generate training samples. The program calls the dynamic masking generator to process the spatio-temporal Token sequence generated in step 1, as shown in the double-layer masking strategy: Figure 2

[0075] (1) Global trajectory masking: In the time dimension, randomly select several consecutive time spans (e.g. mask 15%-30% of the trajectory segment), and replace them with special [MASK] vectors. This forces the model to use the context's historical and future information (bidirectional encoding) or only historical information (unidirectional encoding) to infer the missing trajectory segment, learning long-range motion trends.

[0076] ​(2) Feature-level Masking: On the time steps that are not globally masked, we randomly mask certain feature dimensions of the spatial coordinates or velocity vectors with a certain probability (e.g., 30%). This enhances the model's robustness to local sensor failures or partial data loss.

[0077] Step 32: Feature extraction using the spatio-temporal rotation Transformer encoder. The masked sequence is input into the encoder constructed in step 2, and forward propagation calculation is performed. The encoder uses multiple layers of spatio-temporal rotation attention mechanisms to capture global spatio-temporal dependencies by combining unmasked context information, and outputs deep hidden feature representations corresponding to the masked positions, providing high-dimensional feature support for subsequent physical quantity reconstruction. Step 33: Constructing a physical perception reconstruction task head and performing joint optimization.

[0078] A parallel linear structure containing three independent branches of spatial reconstruction, velocity reconstruction, and time-aided prediction is established. Single-layer linear regression layers are used to map the hidden features output by step 32 back to the original physical state space, obtaining physical prediction values for the masked positions. A physical perception multi-objective joint optimization strategy is used to calculate the total loss function :

[0079] a) Position reconstruction loss : The masked mean square error is used to calculate the coordinate prediction error of the visible segment, and the formula is:

[0080] b) Velocity vector loss : The mean square error between the predicted velocity of the masked position and the true velocity is calculated, and the calculation formula is:

[0081] c) Kinematic consistency constraint : To ensure that the predicted trajectory conforms to the physical motion law, a smoothness constraint is introduced to penalize the deviation between the position change rate and the velocity vector:

[0082]

[0083] The total loss function is:

[0084] The total loss is minimized using the backpropagation algorithm to update the parameters of the encoder and the reconstruction head. In the pre-training phase, a curriculum learning strategy is used, starting from a lower masking ratio (e.g., 20%) and gradually increasing to a high ratio (e.g., 50%), guiding the model to learn the trajectory law from easy to difficult.

[0085] Step 4, multi-task adaptation and fine-tuning, in the present invention, the downstream tasks include trajectory prediction, trajectory classification and landing point prediction.

[0086] As Figure 1 As shown on the right, step 4 mainly performs multi-task adaptation and supervised fine-tuning, using pre-trained weights to build a ballistic analysis model for specific downstream tasks, which specifically includes the following two sub-steps:

[0087] Step 41: Build a lightweight task head and splice with the encoder to complete model architecture adaptation. First, load the pre-trained spatio-temporal rotary Transformer encoder weights from step 3 as the backbone network, and build the corresponding task head structure according to the specific tactical analysis requirements: a) Trajectory prediction task head: this task sets two modes, including:

[0088] Direct multi-step generation mode: reuse the trajectory reconstruction head in step 3, use a linear regression layer to output the complete trajectory sequence of the future steps at once, avoiding error accumulation, suitable for fixed-length prediction.

[0089] Regression generation mode: predict the next state in an autoregressive manner, and use the output as the input for the next step.

[0090] b) Shell classification task head: use attention pooling layer to aggregate the global features of the entire trajectory sequence, and output the probability distribution of the shell category (such as grenade, rocket, etc.) through the fully connected layer and Softmax activation function;

[0091] c) Launch point prediction task head: use a regression structure to aggregate the trajectory starting segment features to predict the launch point, and the backward branch aggregates the trajectory ending segment features to predict the landing point, and directly outputs the three-dimensional spatial coordinates.

[0092] Step 42: Perform supervised fine-tuning training to obtain the optimal task model. During fine-tuning, freeze the main parameters of the base model (STRFormer layers) or set a very low learning rate, set the specific loss function for the downstream task, and update the parameters of each task head and a small number of adaptation layers through backpropagation to maximize the preservation of the universal physical representation ability learned during pre-training. This efficient parameter fine-tuning mechanism not only preserves the universal physical knowledge learned during pre-training, but also significantly reduces the training cost for new tasks.

[0093] The specific training details are as follows: Adam optimizer is used for training, learning rate linear decay strategy is used, the first 10% of the total training steps are set as the warm-up phase, and the learning rate is gradually increased from 0 to the set 0.002 (pre-training) and 0.0002 (fine-tuning training), and then gradually decays to 0; The size of each training batch is 128, and the maximum training epoch number for pre-training is set to 30 and the maximum epoch number for fine-tuning training is set to 25.

[0094] The application further provides a trajectory analysis system based on space-time rotation coding and dynamic mask reconstruction, comprising a memory, a processor and a computer program stored in the memory and capable of running on the processor, and when the processor executes the program, the trajectory analysis method based on space-time rotation coding and dynamic mask reconstruction is realized.

[0095] An electronic device comprises a memory, a processor and a computer program stored in the memory and capable of running on the processor, and when the processor executes the program, the trajectory analysis method based on space-time rotation coding and dynamic mask reconstruction is realized.

[0096] A non-transitory computer readable storage medium has a computer program stored thereon, and when the computer program is executed by a processor, the trajectory analysis method based on space-time rotation coding and dynamic mask reconstruction is realized.

[0097] In summary, the application constructs a space-time rotation Transformer encoder (STRFormer), uses space-time rotation position encoding (STR-RoPE) to jointly model the space-time dependence of trajectory, and combines a double-layer dynamic mask pre-training mechanism to construct a general basic model supporting unified learning of multiple tasks such as trajectory prediction, projectile classification and launch point positioning, thereby significantly improving the accuracy and adaptability of trajectory analysis in complex battlefield environments.

[0098] Embodiments

[0099] In order to verify the effectiveness of the application scheme, the following experimental design is carried out.

[0100] As shown in Figure 3 , under different projectile types and different range scenarios, the model can reconstruct the complete trajectory only by relying on part of the observed trajectory, and the predicted curve is highly consistent with the real trajectory in terms of height change and lateral drift, indicating that the STRFormer backbone based on space-time joint rotation coding can effectively extract stable space-time motion patterns. As shown in Figure 4 , as the prediction step length gradually expands from short range to longer time domain, the final position error (FDE) smoothly increases with the step length but remains within an acceptable range of hundreds of meters, indicating that the application still has good stability and physical consistency in long-term trajectory extrapolation.

[0101] In the projectile classification task, the application uses a small number of observation points in the front section of the trajectory to complete multi-class projectile identification through a lightweight classification head. Experimental results show that compared with the baseline model (overall accuracy of about 86%) that is not pre-trained and is directly trained from random initialization, the overall classification accuracy of the application model loaded with self-supervised pre-training weights is improved to about 95%. As shown in Figure 5In the normalized confusion matrix shown, the recall rates of most classes are close to or reach 1.00 on the main diagonal, there is only limited confusion between a few types of ammunition with highly similar physical characteristics, and the overall performance shows good inter-class separability and early discriminability.

[0102] In the launch / impact point prediction task, the present application employs attention-weighted pooling and regression head to estimate the key event locations. Compared with the unpretrained baseline model, the relative errors of the launch point and impact point of the present application model are reduced from about 0.44 / 0.47 to about 0.25 / 0.32, with an error reduction of about 40%. As shown in the figure, in a plurality of representative launch clusters, the predicted point cloud is highly concentrated around the true location, and the system bias is generally controlled within the range of 1.5-10.7m, and the corresponding circular probable error CEP50 radius is about 25-31m, indicating that the present application has both small system bias and stable random dispersion in event-level spatial positioning, and can meet the requirements of engineering applications for launch / impact point prediction accuracy. Figure 6

[0103] The technical features of the above embodiments can be combined in any manner. To make the description concise, not all possible combinations of the technical features in the above embodiments are described, but as long as the combinations of the technical features do not exist contradictions, they should be considered as the scope of the present application.

[0104] The above embodiments only express several implementation manners of the present application, and the description is specific and detailed, but it should not be understood as a limitation on the scope of the present application. It should be pointed out that for ordinary skilled in the art, without departing from the concept of the present application, a number of modifications and improvements can be made, which all belong to the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the appended claims.​

Claims

1. A ballistic analysis method based on spatiotemporal rotation coding and dynamic mask reconstruction, characterized in that, The steps are as follows: Step 1, Data Construction and Tokenization: Acquire ballistic trajectory data observed by radar, including spatial coordinates. velocity components and timestamp The ballistic trajectory data is normalized using a split-axis normalization method, and each trajectory point is mapped to a spatiotemporal token sequence in a high-dimensional feature space. Step 2, Construct a Spatiotemporal Rotation Transformer Encoder (STRFormer): Construct a feature extraction network that includes a multi-layer spatiotemporal rotation attention mechanism; this network utilizes Spatiotemporal Rotation Position Encoding (STR-RoPE) to inject temporal information as a modulation phase into the rotation transformation of spatial coordinates through a learnable projection matrix, so as to jointly model the relative spatial displacement and non-uniform time intervals between trajectory points; Step 3, Self-supervised pre-training: A two-layer masking strategy is used to mask the spatiotemporal token sequence generated in Step 1. After the feature representation is extracted by the spatiotemporal rotation Transformer encoder in Step 2, it is mapped back to the original physical space through the physical perception reconstruction task head. The model parameters are then optimized based on the physical perception composite loss function to complete the self-supervised pre-training. The two-layer masking strategy includes a global mask for continuous time periods and a feature-level random mask for specific dimensions of spatial coordinates or velocity vectors in the feature dimension. Step 4, Task Adaptation and Fine-tuning: Based on the pre-trained model weights obtained in Step 3, set corresponding lightweight task heads and loss functions for downstream trajectory prediction, projectile classification, or impact point prediction tasks, and concatenate each task head with the spatiotemporal rotation Transformer encoder; keep the pre-trained encoder parameters frozen or make minor adjustments, and complete the model fine-tuning for specific tasks by training the task heads.

2. The ballistic analysis method based on spatiotemporal rotation coding and dynamic mask reconstruction according to claim 1, characterized in that, In step 2, the specific calculation process for the spatiotemporal rotation position encoding is as follows: For each Token in the input sequence Using a learnable spatial projection matrix and temporal embedding matrix Normalized spatial coordinates and timestamp Perform mapping; By fusing spatial and temporal features through element-wise multiplication (Hadamard Product), a spatiotemporal phase vector is generated. : ； Using the spacetime phase vector Construct rotation matrix For the query vector in the attention mechanism and key vector Perform a rotation transformation so that the transformed... and The dot product depends only on the relative spatiotemporal difference between tokens; 。 3. The ballistic analysis method based on spatiotemporal rotation coding and dynamic mask reconstruction according to claim 1, characterized in that, In step 2, the constructed spatiotemporal rotation Transformer encoder (STRFormer) specifically includes: (1) Multimodal embedding layer: includes spatial coordinate embedding layer, velocity vector embedding layer and time embedding layer, which respectively project the normalized trajectory point spatial coordinates, velocity vector and timestamp onto the feature space of the same dimension to obtain independent three-modal embedding vectors; (2) Modality Mixer: used to fuse heterogeneous physical information within the same time step; the spatial, velocity and time embeddings at the same moment are concatenated and input into a lightweight Transformer encoder, which calculates the interaction weights between modes through a self-attention mechanism and outputs the fused hybrid modal feature sequence; (3) STRFormer spatiotemporal encoder: It consists of multiple identical layers stacked together. In each layer, a multi-head self-attention module containing a spatiotemporal rotation position encoding (STR-RoPE) and a feedforward network are used to perform hierarchical feature extraction on the mixed modality feature sequence and output a trajectory table containing global spatiotemporal dependencies.

4. The ballistic analysis method based on spatiotemporal rotation coding and dynamic mask reconstruction according to claim 1, characterized in that, In step 3, the dual-layer masking strategy specifically includes: (1) Global Trajectory Masking: In the time dimension, several consecutive time spans are randomly selected for masking, and their corresponding tokens are replaced with learnable mask tokens to force the model to reconstruct the missing trajectory segments using contextual information and learn long-term spatiotemporal dependencies. (2) Feature-level random masking: At time steps where the model is not globally masked, specific feature dimensions of spatial coordinates or velocity vectors are randomly masked with independent probability to enhance the model’s robustness to the loss of local physical features.

5. The ballistic analysis method based on spatiotemporal rotation coding and dynamic mask reconstruction according to claim 1, characterized in that, In step 3, the physical perception reconstruction task head adopts a lightweight linear structure. The specific construction method is as follows: obtain the hidden feature representation extracted by the spatiotemporal rotation Transformer encoder. A single-layer linear regression layer is used as the mapping layer to directly map the feature representation of each masked token to the corresponding spatial location prediction value. Compared with speed prediction value To achieve regression reconstruction from high-dimensional feature space to physical state space; The loss function of the physical perception reconstruction task adopts a multi-objective joint optimization strategy, including: Location reconstruction loss The formula for calculating the mean square error between the predicted and actual coordinates is: ； Velocity vector loss Calculate the mean square error between the predicted velocity and the true velocity at the masked position. The formula is: ； Kinematic Consistency Constraint Loss Introduce a smoothness constraint to penalize the deviation between the rate of change of position and the velocity vector. ； The total loss function is: ,in This is the balance coefficient.

6. The ballistic analysis method based on spatiotemporal rotation coding and dynamic mask reconstruction according to claim 1, characterized in that, In step 4, the task header structure configured for different downstream tasks includes: (1) Trajectory prediction task: adopt direct multi-step generation or recursive generation mode; use linear regression head to directly map the future position and velocity sequence from the features output by the encoder; (2) Ammunition type classification task: Attention pooling is used to aggregate global spatiotemporal features, and the probability distribution of ammunition type is output through a fully connected layer; (3) Launch and landing point prediction task: A two-branch regression structure is adopted to aggregate the features of the initial and final segments of the trajectory, and directly regress to predict the three-dimensional spatial coordinates of the launch point and landing point.

7. The ballistic analysis method based on spatiotemporal rotation coding and dynamic mask reconstruction according to claim 1, characterized in that, In step 3, the pre-training stage adopts a course learning strategy. While keeping the spatiotemporal joint coding structure unchanged, the proportion of dynamic mask is gradually increased from 20% to 50%, guiding the model to first learn local short-range spatiotemporal patterns and then learn long-range dependencies. In step 4, the fine-tuning stage adopts a task adapter mechanism. While freezing most of the parameters of the spatiotemporal joint coding and attention backbone network in the base model, only the downstream task heads and their corresponding adaptation layers are trained to improve cross-task transfer efficiency and maintain the consistency of general spatiotemporal representation.

8. A ballistic analysis system based on spatiotemporal rotation coding and dynamic mask reconstruction, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the ballistic analysis method based on spatiotemporal rotation coding and dynamic mask reconstruction as described in any one of claims 1 to 7.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the ballistic analysis method based on spatiotemporal rotation coding and dynamic mask reconstruction as described in any one of claims 1 to 7.

10. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the ballistic analysis method based on spatiotemporal rotation coding and dynamic mask reconstruction as described in any one of claims 1 to 7.

Images