Deep learning-driven positioning formation and mode intelligent optimization method

Abstract

The invention discloses a deep learning-driven positioning formation and mode intelligent optimization method, and aims to solve the problem of dynamic optimization of formation and positioning mode in passive positioning of an air-based platform cluster. According to the method, a simulation data set containing various errors is generated through a simulation environment and an air-based platform passive positioning mathematical model, a theoretically optimal positioning formation and mode combination is obtained in combination with an error transfer model based on a geometric accuracy factor GDOP, and a pre-training data set is constructed. Then designing a deep convolutional network based on a feature pyramid structure, inputting navigation parameters, observed quantity and observation errors of the air-based platform, and predicting estimated values of optimal positioning mode confidence, air-based platform node confidence and geometric precision factors; and finally, improving the real-time performance and the edge deployment capability of the model by adopting a model compression strategy. The method has the advantages of quick response, adaptive optimization, high positioning precision and the like, and is particularly suitable for air-based platform cooperative positioning tasks under resource limited conditions.

Description

Technical Field

[0001] This invention belongs to the field of wireless positioning technology, specifically relating to a deep learning-driven method for intelligent optimization of positioning arrays and patterns. Background Technology

[0002] Airborne platform clusters, with their high mobility, rapid response and deployment capabilities, and ability to operate deep in hazardous areas, provide a revolutionary approach to building dynamic and resilient airborne passive positioning networks, effectively overcoming the inherent limitations of traditional ground stations. Based on technologies such as Time Difference of Arrival (TDOA) and Frequency Difference of Arrival (FDOA), passive signal reception and measurement significantly reduce the risk of exposure while achieving high positioning accuracy, offering a significant stealth advantage compared to active positioning that actively transmits signals. In their paper "A Positioning Node Selection Method for TDOA Passive Positioning," Hao Benjian et al. transformed the positioning array selection problem into a non-convex optimization problem of minimizing the trace of the position error covariance matrix. They then relaxed this non-convex optimization problem into a semi-positive definite programming problem, thus quickly and effectively solving for the optimal positioning array combination. However, this method relies on a precisely constructed observation error covariance model. In actual engineering, error distributions are often non-ideal, and the environment changes frequently, making this type of analytical method unstable and exhibiting poor generalization ability in unmodeled situations. Furthermore, this method focuses on the TDOA positioning mode and is difficult to cope with the joint optimization requirements in multi-mode fusion scenarios. Summary of the Invention

[0003] This invention proposes a deep learning-driven method for intelligent optimization of positioning array and pattern, aiming to solve the problems of limited deployment and poor survivability of traditional fixed stations, as well as the difficulty of existing airborne platform positioning schemes in intelligently optimizing arrays and effectively fusing multi-source and multi-type positioning information according to dynamic environments.

[0004] The technical solution for implementing this invention is: a deep learning-driven method for intelligent selection of positioning arrays and patterns, comprising the following steps:

[0005] Step 1: Assuming there are N airborne platforms performing passive localization of the target, generate a simulation dataset of the airborne platforms and the target based on the simulation environment and the mathematical model of passive localization of the airborne platforms.

[0006] The simulation dataset contains the following four types of data: navigation parameters of the airborne platform, observations, observation errors, and target positions;

[0007] The navigation parameters for the i-th airborne platform include the airborne platform position P. i and the velocity V of the air-based platformi , i = 1, 2, 3, ..., N;

[0008] Observations include the angle of arrival. Time difference of arrival and frequency difference

[0009] Observation errors include clock error D t Frequency difference error D f Pitch angle error D pit Azimuth error D azi and navigation error D x ;

[0010] The target position is represented by a three-dimensional position vector P in the Earth coordinate system. e Or latitude, longitude, and altitude P in the geographic coordinate system n This is represented by a coordinate transformation model, which is used to standardize the data.

[0011] Step 2: Construct a positioning mode library M = {M1, M2, M3, M4}, which includes the following four modes: single-station direction finding positioning mode M1, dual-station time-frequency difference positioning mode M2, three-station time-frequency difference positioning mode M3, and three-station time-frequency difference positioning mode M4. Since there are N airborne platforms performing passive positioning of the target, there are a total of Q possible array combination libraries Z, Z = {Z1, Z2, ..., Z...}. Q The formation combination library Z is constructed based on permutations and combinations of different numbers of airborne platforms, including single-station, dual-station, and triple-station configurations. Based on simulation datasets of airborne platforms and targets, the Geometric Dilution of Precision (GDOP) is used as the evaluation metric to calculate the formation-mode combination (Z). k M j Theoretical positioning error Where Tr(·) represents the trace operation of the matrix, Σ theo The covariance matrix represents the target location estimation error; iterates through all the theoretical positioning errors of the array-pattern combinations and selects the optimal array Z corresponding to the one with the smallest error. opt and optimal positioning mode M opt .

[0012] Step 3: Construct a pre-training dataset for the airborne platform and target. The pre-training dataset includes the navigation parameters, observations, and observation errors of the airborne platform obtained in Step 1, as well as the optimal formation Z obtained in Step 2. opt Optimal positioning mode M opt And GDOP.

[0013] Step 4: Construct a deep convolutional network based on feature pyramids. The deep convolutional network based on feature pyramids includes an input encoding layer, a multi-scale feature extraction module, a bidirectional cross-scale attention fusion module, and an adaptive output layer.

[0014] Step 5: Use the pre-trained dataset of the empty base platform and target constructed in Step 3 to train the feature pyramid-based deep convolutional network to obtain the trained feature pyramid-based deep convolutional model.

[0015] Step 6: Use model compression strategies to improve the real-time performance of deep convolutional models based on feature pyramids.

[0016] Compared with the prior art, the significant advantages of this invention are:

[0017] (1) Supports joint modeling and intelligent selection of multiple positioning modes:

[0018] This invention incorporates single-station direction finding positioning, dual-station time-frequency difference positioning, three-station time-frequency difference positioning, and three-station time-frequency difference positioning modes into a unified model architecture. Through a deep learning model, it achieves integrated intelligent optimization of positioning array and mode, significantly improving the system's adaptability and generalization ability.

[0019] (2) Combining theoretical error assessment with data-driven learning:

[0020] This invention uses GDOP as the core indicator, integrates error propagation model calculation and deep learning training, and effectively achieves synergistic optimization of "theoretical guidance + data learning", which has both physical interpretability and modeling flexibility.

[0021] (3) Possesses real-time inference capabilities and edge deployment adaptability:

[0022] By employing compression strategies involving model distillation, quantization, and pruning, network complexity and computational resource consumption are effectively reduced, enabling the model to achieve rapid response on low-power platforms and meeting the real-time decision-making requirements of space-based platforms.

[0023] (4) It has good structural scalability:

[0024] This invention employs flexible feature encoding and input organization methods, supporting the dynamic participation of varying numbers of space-based platform nodes in localization tasks. By constructing adjacency tensors or node feature maps in a structured manner, the model input can be adaptively expanded without modifying the backbone network structure, exhibiting good module versatility and task adaptability. Attached Figure Description

[0025] Figure 1 This is a schematic diagram of the training and inference process of the model of the present invention.

[0026] Figure 2This represents the accuracy of the model in this invention on the test set. Detailed Implementation

[0027] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0028] The technical solutions of the various embodiments of the present invention can be combined with each other, but only if they can be implemented by those skilled in the art. When the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such combination of technical solutions does not exist and is not within the scope of protection claimed by the present invention.

[0029] The following section will further introduce the specific implementation method, as well as the technical difficulties and inventive points of this invention, using this design example as an example.

[0030] Combination Figure 1 The deep learning-driven intelligent optimization method for positioning arrays and patterns described in this invention comprises the following steps:

[0031] Step 1: Assuming there are N airborne platforms performing passive localization of the target, generate a simulation dataset of the airborne platforms and the target based on the simulation environment and the mathematical model of passive localization of the airborne platforms.

[0032] The simulation dataset contains the following four types of data: navigation parameters of the airborne platform, observations, observation errors, and target positions.

[0033] The navigation parameters for the i-th airborne platform include the airborne platform position P. i and the velocity V of the air-based platform i , i = 1, 2, 3, ..., N.

[0034] Observations include the angle of arrival. Time difference of arrival and frequency difference

[0035] Observation errors include clock error D t Frequency difference error D f Pitch angle error D pit Azimuth error D azi and navigation error D x .

[0036] The target position is represented by a three-dimensional position vector P in the Earth coordinate system. e Or latitude, longitude, and altitude P in the geographic coordinate system nThis is represented by a coordinate transformation model, which is used to standardize the data.

[0037] Specifically, in the data generation stage, it is necessary to drive design and scenario-based perturbation simulation through multi-dimensional physical characteristics, and to systematically design around key factors such as airborne platform trajectory, sensor errors, and target behavior to construct a highly generalizable dataset covering the entire parameter space. First, the airborne platform trajectory should encompass various forms, including uniform straight-line motion, acceleration / deceleration, S-shaped maneuvers, and random maneuvers, combined with high and low speed variations, different altitude levels, and different baseline lengths to comprehensively simulate real mission scenarios. The speed range should cover the typical operating range of the airborne platform, superimposed with Gaussian perturbations, and coupled with the trajectory pattern design. Regarding sensor errors, the error variances of TDOA, FDOA, pitch angle, azimuth angle, and airborne platform navigation parameters should be set within a reasonable range based on the actual system performance, and random sampling should be performed within this range to simulate sensors of different precision. The target trajectory should cover motion states such as stationary, uniform speed, acceleration / deceleration, serpentine, and abrupt changes. Spatially, the focus should be on constructing the forward main lobe region, lateral side lobe region, and critical scenario at the edge of the maximum effective distance of the airborne platform formation detection envelope to simulate real air-to-ground interaction scenarios. Data sampling should employ a hierarchical strategy and Latin hypercube sampling to comprehensively cover the high-dimensional parameter space. Extreme combinations should be incorporated to create adversarial examples, enhancing model robustness. Complex electromagnetic environments and geographical obstacles should be simulated to increase scene complexity. For annotation, error-free navigation parameters generated through simulation should be used as the ground truth for high-precision positioning. The theoretical positioning accuracy under different parameter combinations should be derived using an error propagation model and the geometrical factor of precision (GDOP) as a supervisory signal. Distribution consistency checks should be performed during model training, and the data generation strategy should be dynamically adjusted based on the model's performance in different error regions. This will effectively improve the generalization ability of deep learning models in complex, dynamic, and interference-prone environments.

[0038] Step 2: Construct a positioning mode library M = {M1, M2, M3, M4}, which includes the following four modes: single-station direction finding positioning mode M1, dual-station time-frequency difference positioning mode M2, three-station time-frequency difference positioning mode M3, and three-station time-frequency difference positioning mode M4. Since there are N airborne platforms performing passive positioning of the target, there are a total of Q possible array combination libraries Z, Z = {Z1, Z2, ..., Z...}. Q The formation combination library Z is constructed based on permutations and combinations of different numbers of airborne platforms, including single-station, dual-station, and triple-station configurations. Based on simulation datasets of airborne platforms and targets, the geometrical precision factor (GDOP) is used as the evaluation metric to calculate the formation-mode combination (Z). k M j Theoretical positioning error Where Tr(·) represents the trace operation of the matrix, Σ theoThe covariance matrix represents the target location estimation error; iterates through all the theoretical positioning errors of the array-pattern combinations and selects the optimal array Z corresponding to the one with the smallest error. opt and optimal positioning mode M opt .

[0039] Each formation-pattern combination (Z) k M j The theoretical positioning error E) theo The structure is as follows:

[0040] For a given formation Z k and positioning mode M j Based on the assumed statistical characteristics of the error sources, the covariance matrix Σ of the target position estimation error can be derived. theo The localization process typically involves the nonlinear observation equation m = h(P) e ,P i )+n, where m is the observation vector, h(·) is the nonlinear observation function, and n is the observation noise. By applying the observation equation to the actual target location... and the actual location of the air-based platform P i0 Linearization of the vicinity yields: Δm≈H Pe ΔP e +H P ΔP i +n, where Δm is the observation vector error, ΔP e It is the target position error, ΔP i It is the navigation error of the air-based platform, the Jacobian matrix. Jacobian matrix

[0041] Assuming the covariance of the observation noise n is R, and the navigation error of the airborne platform is ΔP i The covariance is Σ nav,i Since the two are uncorrelated, the covariance of the equivalent observation noise is: The superscript T denotes the matrix transpose. According to weighted least squares estimation theory, the covariance matrix of the target position estimation error is approximately: To uniformly measure the error amplification effect of various array and positioning mode combinations in terms of geometry, this invention uses the geometric accuracy factor as an evaluation index, and its calculation formula is as follows: A smaller GDOP indicates that the combination has better geometric observability and error stability under the current observation conditions.

[0042] It is important to note that the selection of the nonlinear observation function varies depending on the positioning mode. Specifically, in the single-station orientation-finding positioning mode, the nonlinear observation function is related to the elevation angle error D. pit Azimuth error Dazi and navigation error D x Related to; in dual-station time-frequency difference positioning mode and clock error D t Frequency difference error D f and navigation error D x Related to; in the three-station time difference positioning mode and clock error D t and navigation error D x Related to; in the three-station time-frequency difference positioning mode, and clock error D t Frequency difference error D f and navigation error D x related.

[0043] Optimal Formation Z opt and optimal positioning mode M opt The selection is as follows:

[0044] For all feasible formation-pattern combinations (Z) in the predefined formation combination library Z and positioning pattern library M. k M j Given the target location, air-based platform configuration, and error statistics, calculate the theoretical positioning error E. theo (Z k M j The combination pair with the smallest theoretical error is selected through a traversal search as the theoretically optimal configuration for the current scenario, denoted as: The resulting combination can not only provide high-precision labels for deep learning model training, but also serve as an accuracy evaluation benchmark in task planning, supporting the robustness evaluation and dynamic adjustment of mode selection strategies.

[0045] Step 3: Construct a pre-training dataset for the airborne platform and target. The pre-training dataset includes the navigation parameters, observations, and observation errors of the airborne platform obtained in Step 1, as well as the optimal formation Z obtained in Step 2. opt Optimal positioning mode M opt And GDOP.

[0046] Step 4: Construct a deep convolutional network based on feature pyramids. The deep convolutional network based on feature pyramids includes an input encoding layer, a multi-scale feature extraction module, a bidirectional cross-scale attention fusion module, and an adaptive output layer.

[0047] The input encoding layer employs a standard convolutional layer. This layer performs preliminary processing on the structured input data. The input data includes navigation parameters, observations, and observation errors from multiple airborne platforms, which are then structured into a feature matrix. This layer uses standard two-dimensional convolutional operations to extract local receptive field features and increase the channel dimensionality of the input tensor, outputting an increased-dimensional spatial feature map for use by subsequent modules.

[0048] The multi-scale feature extraction module consists of alternating stacked Transformer Blocks and MobileNetV3's Bottleneck layer. The Transformer Blocks are responsible for capturing long-range dependencies and global attention features between nodes, while the lightweight Bottleneck layer has strong local modeling capabilities and computational efficiency. The alternating modules maintain expressive power while reducing computational complexity.

[0049] A bidirectional cross-scale attention fusion module combines a Feature Pyramid Network (FPN) and a Path Aggregation Network (PAN) structure. The FPN performs top-down information upsampling and lateral connections to enhance high-level semantic features, while the PAN provides bottom-up supplementary information to strengthen low-level details. Two attention mechanisms are introduced during the fusion process to improve feature discriminative power: first, a Spatial Pyramid Pooling (SPP) module, which expands the receptive field of high-level features through multi-scale pooling; and second, a Coordinate Attention (CA) mechanism, which explicitly models the spatial location information and channel dependencies of low-level features.

[0050] The adaptive output layer introduces GRU to model historical positioning patterns, predict positioning pattern confidence, optimal array combination confidence, and GDOP.

[0051] Step 5: Using the pre-trained dataset of the airborne platform and target constructed in Step 3, train the feature pyramid-based deep convolutional network to obtain the trained feature pyramid-based deep convolutional model, as follows:

[0052] S5.1. The navigation parameters, observations, and observation errors of the space-based platform from step 1 are structured into a feature matrix I as the network input, as follows:

[0053] The spatiotemporal relationships and signal characteristics of N airborne platform nodes are constructed into a feature matrix of dimension N×N×20, where each element (i,j) represents the interaction parameters between the i-th and j-th airborne platforms. This matrix is ​​formed by concatenating 12 types of adjacency matrices along the channel dimension, including:

[0054] 1) Position adjacency matrix [Δx] ij ,Δy ij ,Δz ij ]∈N×N×3, encoding three-dimensional relative coordinates, where Δx ij Δy ij Δz ijThese represent the positional differences between the i-th and j-th overhead base platforms along the x, y, and z axes, respectively.

[0055] 2) Velocity diagonal matrix [v ix ,v iy ,v iz ]∈N×N×3, off-diagonal elements are set to zero, where v ix ,v iy ,v iz denoted as the velocities of the i-th airborne platform along the x-axis, y-axis, and z-axis, respectively.

[0056] 3) TDOA / FDOA measurement matrix [T ij ,F ij ]∈N×N×2.

[0057] 4) Pitch and azimuth matrices

[0058] 5) Noise matrix of parameters corresponding to position, velocity, TDOA, FDOA, and AOA of the airborne platform [σ] pos ,σ vel ,σ TDOA ,σ TDOA ,σ angle [∈N×N×11]. After coordinate system normalization and parameter normalization, all sub-matrices are concatenated in the channel dimension to form an N×N×20 feature matrix I, realizing the joint representation of geometric topological relationships and signal features under a unified spatial reference.

[0059] S5.2. The feature matrix I is used as the network input. The input encoding layer performs local feature extraction on the feature matrix I to obtain the spatial feature map after dimensionality increase, as follows:

[0060] The input encoding layer adopts a standard two-dimensional convolutional structure to model the spatial relationships and channel interactions of local regions. Through convolution operations, the number of feature channels in feature matrix I in S5.1 is increased from 20 dimensions to 64 dimensions. The final output is a high-resolution spatial feature map with preliminarily extracted local semantic information for further processing by the subsequent backbone network.

[0061] S5.3. Use the multi-scale feature extraction module to extract features from the upgraded spatial feature map to obtain high-dimensional semantic features F. out It includes high-level semantic features and low-level detailed features, as follows:

[0062] The input encoding layer in S5.2 uses standard convolutions for initial local feature extraction. The core multi-scale feature extraction module (backbone network) employs a hybrid architecture that integrates global and local information, combining TransformerBlock and MobileNetV3's Bottleneck layer. TransformerBlock introduces a global self-attention mechanism to capture long-range dependencies between base platforms, while the Bottleneck structure is used to extract efficient local features. Through layer-by-layer pooling and convolution, this module outputs a set of multi-scale semantic feature maps C2, C3, C4, and C5, corresponding to different resolutions and receptive fields, collectively referred to as high-dimensional semantic features F. out .

[0063] S5.4, High-dimensional semantic features F out Entering the bidirectional cross-scale attention fusion module, the bidirectional feature path, namely the upsampling structure of FPN and the downsampling structure of PAN, effectively fuses high-level semantic features and low-level detail features through the bidirectional cross-scale attention fusion module. High-level semantic features extract multi-scale global context information through spatial pyramid pooling, and low-level detail features strengthen the coupling ability between spatial position and channel response through coordinate attention mechanism to obtain a high-dimensional feature map.

[0064] S5.5. The high-dimensional feature map enters the adaptive output layer, and a gated recurrent unit (GRU) is introduced to perform temporal modeling of historical localization patterns. Finally, the confidence p of the optimal localization pattern is regressed. i Confidence N of the optimal array combination of airborne platforms under each positioning mode i The estimated values ​​of the geometrical factor of precision (GDOP) are as follows:

[0065] In the output stage, a GRU module is introduced to process time-series information, combining the high-dimensional feature map of the current frame with features from historical frames to achieve state memory and dynamic modeling. The output after GRU is connected to three output heads: the first branch outputs the probability distribution vector p = [p1, p2, ..., p4] of the optimal localization pattern through a softmax layer. T , where p j Is it to select the j-th positioning mode M? j The confidence level, and ∑p j =1. The second branch outputs the confidence level N of the optimal array combination of the airborne platform under each mode through the sigmoid layer. i The third branch outputs an estimate of the geometric precision factor (GDOP) under the current configuration through a linear layer. This output structure combines classification, regression, and multi-label prediction to achieve a high-dimensional, structured joint output.

[0066] S5.6, The confidence level p of the optimal positioning mode obtained from S5.5 iConfidence N of the optimal array combination of airborne platforms under each positioning mode i The estimated value of GDOP is obtained, and the parameters of the feature pyramid-based deep convolutional network are jointly optimized using the total loss function to complete the model training, thereby obtaining the trained feature pyramid-based deep convolutional model, as detailed below:

[0067] Construct the total loss function L total =λ p L p +λ N L N +λ GDOP L GDOP It is the weighted sum of the losses of each branch, where λ p L is the weighting coefficient of the system classification loss branch. p It is the cross-entropy loss, λ N L is the weight coefficient of the node confidence loss branch. N It is a binary cross-entropy loss, λ GDOP L is the weighting coefficient of the GDOP error estimation loss branch. GDOP This is quantile loss. By optimizing the above objectives through end-to-end joint training, a trained deep convolutional model based on feature pyramids with high accuracy and strong generalization ability is finally obtained.

[0068] Step 6: Employ model compression strategies to improve the real-time performance of feature pyramid-based deep convolutional models, as detailed below:

[0069] To meet the limitations of computing platforms in terms of computing resources, storage, and power consumption, as well as the requirements for model inference speed, it is necessary to compress and accelerate the trained feature pyramid-based deep convolutional models. This invention employs three complementary compression strategies: model distillation, quantization, and pruning, which can be used in combination to achieve the optimal accuracy-efficiency tradeoff.

[0070] S6.1, Distillation and Compression: Define the deep convolutional model based on feature pyramids trained in step 5 as the teacher model, and use the optimal localization pattern confidence p output by the teacher model. i Confidence N of the optimal array combination of airborne platforms under each positioning mode i The estimated value of the geometric precision factor GDOP is used as a soft label to guide student model learning; knowledge transfer is achieved by minimizing the KL divergence between the student and teacher output distributions, resulting in a compressed model.

[0071] The loss function of distillation compression consists of two parts: Among them, L distill This represents the total distillation loss, with a loss weighting coefficient α∈[0,1], L CE(·) is the cross-entropy loss, σ(·) is the softmax function, and z s It is the logit vector output by the student model, z t This is the logit vector output by the teacher model, where T0 is the temperature coefficient, and L... KL (·) represents the KL divergence. This loss function ensures that the student model fits the true labels while mimicking the teacher model's decision distribution across all categories as closely as possible, thus achieving knowledge transfer.

[0072] S6.2 Quantization and Compression: Based on the student model obtained by distillation, its network parameters are quantized and compressed, and the student model weights W are... f Fixed-point weights W mapped to 8-bit fixed-point representation q :W f ≈Δ·W q +Z, where Δ is the scaling factor, Z is the zero point, and the floating-point weights W corresponding to each layer in the student model are used. f The statistical distribution is dynamically calculated, and then the alignment weights are quantized to obtain the quantization model;

[0073] Quantization strategies can be implemented in two ways: Post-Training Quantization (PTQ), which directly quantizes the model without changing the original model structure and weights, suitable for rapid deployment where high accuracy is not required; and Quantization-Aware Training (QAT), which introduces a quantization simulation module during the training phase to adapt the model to accuracy fluctuations caused by quantization, suitable for high-precision deployment scenarios. To ensure high accuracy of the model output, this invention adopts the QAT method.

[0074] S6.3, Pruning and Compression: Based on the quantized model, the importance of its weights is evaluated, and the absolute values ​​|w are removed. ij Connections smaller than the pruning threshold τ are used to remove redundant parameters, improve model sparsity and running efficiency. After pruning, the pruned model is fine-tuned to restore accuracy, and finally a compressed deep convolutional model based on feature pyramids is obtained.

[0075] In summary, the compression and acceleration strategy described in this invention can significantly reduce computing resource consumption while maintaining model output accuracy. It is suitable for deployment in scenarios such as edge computing platforms and low-power space-based platform devices, and has good practicality and scalability.

[0076] Example 1

[0077] This embodiment is based on the collaborative passive positioning task of six airborne platforms to target ground targets. It adopts the deep learning-driven intelligent optimization method for positioning array and pattern as described in this invention. The specific process is as follows:

[0078] Step 1: Use 6 airborne platforms to perform passive positioning of the target. Based on the simulation environment and the mathematical model of passive positioning of the airborne platforms, generate a simulation dataset of the airborne platforms and the target.

[0079] The simulation dataset contains the following four types of data: navigation parameters of the airborne platform, observations, observation errors, and target positions.

[0080] The navigation parameters for the i-th airborne platform include the airborne platform position P. i and the velocity V of the air-based platform i , i = 1, 2, 3, ..., 6.

[0081] Observations include the angle of arrival. Time difference of arrival and frequency difference

[0082] Observation errors include clock error D t Frequency difference error D f Pitch angle error D pit Azimuth error D azi and navigation error D x .

[0083] The target position is represented by a three-dimensional position vector P in the Earth coordinate system. e Or latitude, longitude, and altitude P in the geographic coordinate system n This is represented by a coordinate transformation model, which is used to standardize the data.

[0084] Step 2: Construct a positioning mode library M = {M1, M2, M3, M4}, containing the following four modes: single-station direction-finding positioning mode M1, dual-station time-difference positioning mode M2, three-station time-difference positioning mode M3, and three-station time-difference positioning mode M4. Based on these four positioning modes, enumerate all combinations of 1, 2, 3, and 3 aircraft from the 6 airborne platforms, resulting in a total of... The combinations form a formation combination library Z = {Z1, Z2, ..., Z...} 61 Based on the simulation dataset of the airborne platform and target, the Geometric Dilution of Precision (GDOP) is used as the evaluation index to calculate the Z-mode combination for each formation. k M j Theoretical positioning error Where Tr(·) represents the trace operation of the matrix, Σ theoThe covariance matrix represents the target location estimation error; iterates through all the theoretical positioning errors of the array-pattern combinations and selects the optimal array Z corresponding to the one with the smallest error. opt and optimal positioning mode M opt .

[0085] Step 3: Construct a pre-training dataset for the airborne platform and target. The pre-training dataset includes the navigation parameters, observations, and observation errors of the airborne platform obtained in Step 1, as well as the optimal formation Z obtained in Step 2. opt Optimal positioning mode M opt And GDOP.

[0086] Step 4: Construct a deep convolutional network based on feature pyramids. The deep convolutional network based on feature pyramids includes an input encoding layer, a multi-scale feature extraction module, a bidirectional cross-scale attention fusion module, and an adaptive output layer.

[0087] Step 5: Use the pre-trained dataset of the empty base platform and target constructed in Step 3 to train the feature pyramid-based deep convolutional network to obtain the trained feature pyramid-based deep convolutional model.

[0088] The navigation parameters, observations, and observation errors of the space-based platform from step 1 are structured into a feature matrix I and used as network input, as follows:

[0089] The spatiotemporal relationships and signal characteristics of the six airborne platform nodes are constructed into a 6×6×20 feature matrix, where each element (i,j) represents the interaction parameters between the i-th and j-th airborne platforms. This matrix is ​​formed by concatenating 12 types of adjacency matrices along the channel dimension, including: 1) positional adjacency matrix [Δx ij ,Δy ij ,Δz ij ]∈6×6×3, encoding three-dimensional relative coordinates, where Δx ij ,Δy ij ,Δz ij Represent the position differences of the i-th and j-th overhead base platforms along the x, y, and z axes, respectively; 2) Velocity diagonal matrix [v ix ,v iy ,v iz ]∈6×6×3, off-diagonal elements are set to zero, where v ix ,v iy ,v iz These represent the velocities of the i-th airborne platform along the x, y, and z axes, respectively; 3) TDOA / FDOA measurement matrix [T ij ,F ij ]∈6×6×2;4) Pitch and azimuth matrices 5) Noise matrix of parameters corresponding to position, velocity, TDOA, FDOA, and AOA of the airborne platform [σ] pos ,σ vel ,σ TDOA ,σ FDOA ,σ angle [∈6×6×11. After coordinate system normalization and parameter normalization, all sub-matrices are concatenated in the channel dimension to form a 6×6×20 feature matrix I, realizing the joint representation of geometric topological relationships and signal features under a unified spatial reference.]

[0090] Step 6: Use model compression strategies to improve the real-time performance of deep convolutional models based on feature pyramids.

[0091] The training of the feature pyramid-based deep convolutional model in this invention is performed in a high-performance computing environment. The computing nodes are equipped with two Intel Xeon E5-2698 v4 processors, each with 20 physical cores and 40 threads, a base frequency of 2.2GHz, and a maximum turbo frequency of 3.6GHz. This powerful multi-core parallel capability provides ample computational support for data preprocessing, loading, and model scheduling, effectively improving overall training efficiency. For acceleration, the system is configured with two NVIDIA GeForce RTX 3090 GPUs, using the Ampere architecture. Each GPU has 10496 CUDA cores and 24GB of GDDR6X memory, providing powerful floating-point arithmetic capabilities and high-speed memory bandwidth, efficiently supporting forward and backward propagation calculations in large-scale neural networks.

[0092] like Figure 2 The graph clearly demonstrates the model's excellent performance on the test set. The curve rises rapidly in the early stages of training, indicating that the model can quickly learn and generalize to new data. Subsequently, the accuracy value stabilizes at a high level of approximately 0.95 to 0.96 with minimal fluctuations, fully demonstrating the model's stable performance on the test set and its extremely high accuracy in predicting optimal formations and patterns. The graph does not show overfitting (where training set accuracy continuously increases while test set accuracy decreases) nor underfitting (where the model fails to capture key patterns in the data), indicating a good match between model complexity and data complexity, and strong generalization ability.

Claims

1. A deep learning-driven method for intelligent selection of positioning arrays and patterns, characterized in that, The steps are as follows: Step 1: Assuming there are N airborne platforms performing passive localization of the target, generate a simulation dataset of the airborne platforms and the target based on the simulation environment and the mathematical model of passive localization of the airborne platforms. The simulation dataset contains the following four types of data: navigation parameters of the airborne platform, observations, observation errors, and target positions; The navigation parameters for the i-th airborne platform include the airborne platform position P. i and the velocity V of the air-based platform i , i = 1, 2, 3, ..., N; Observations include the angle of arrival. Time difference of arrival and frequency difference Observation errors include clock error D t Frequency difference error D f Pitch angle error D pit Azimuth error D azi and navigation error D x ; The target position is represented by a three-dimensional position vector P in the Earth coordinate system. e Or latitude, longitude, and altitude P in the geographic coordinate system n This is represented, and data standardization is achieved through a coordinate transformation model; Step 2: Construct a positioning mode library M = {M1, M2, M3, M4}, which includes the following four modes: single-station direction finding positioning mode M1, dual-station time-frequency difference positioning mode M2, three-station time-frequency difference positioning mode M3, and three-station time-frequency difference positioning mode M4. Since there are N airborne platforms performing passive positioning of the target, there are a total of Q possible array combination libraries Z, Z = {Z1, Z2, ..., Z...}. Q The formation combination library Z is constructed based on permutations and combinations of different numbers of airborne platforms, including single-station, dual-station, and triple-station configurations. Based on simulation datasets of airborne platforms and targets, the Geometric Dilution of Precision (GDOP) is used as the evaluation metric to calculate the formation-mode combination (Z). k M j Theoretical positioning error Where Tr(·) represents the trace operation of the matrix, Σ theo The covariance matrix represents the target location estimation error; iterates through all the theoretical positioning errors of the array-pattern combinations and selects the optimal array Z corresponding to the one with the smallest error. opt and optimal positioning mode M opt ; Step 3: Construct a pre-training dataset for the airborne platform and target. The pre-training dataset includes the navigation parameters, observations, and observation errors of the airborne platform obtained in Step 1, as well as the optimal formation Z obtained in Step 2. opt Optimal positioning mode M opt and GDOP; Step 4: Construct a deep convolutional network based on feature pyramids. The deep convolutional network based on feature pyramids includes an input encoding layer, a multi-scale feature extraction module, a bidirectional cross-scale attention fusion module, and an adaptive output layer. Step 5: Use the pre-trained dataset of the empty base platform and target constructed in Step 3 to train the deep convolutional network based on the feature pyramid, and obtain the trained deep convolutional model based on the feature pyramid. Step 6: Use model compression strategies to improve the real-time performance of deep convolutional models based on feature pyramids.

2. The deep learning-driven intelligent optimization method for positioning arrays and patterns according to claim 1, characterized in that, In step 2, calculate each formation-pattern combination (Z). k M j Theoretical positioning error Where Tr(·) represents the trace operation of the matrix, Σ theo The covariance matrix representing the target location estimation error is as follows: The covariance matrix Σ of the target position estimation error theo Based on the linearization of the first-order Taylor expansion of the nonlinear observation function, the combined effects of observation noise and navigation error of the airborne platform are considered. The selection of the nonlinear observation function varies depending on the positioning mode. Specifically, in the single-station orientation-finding positioning mode, the nonlinear observation function is related to the elevation angle error D. pit Azimuth error D azi and navigation error D x Related to; in dual-station time-frequency difference positioning mode and clock error D t Frequency difference error D f and navigation error D x Related to; in the three-station time difference positioning mode and clock error D t and navigation error D x Related to; in the three-station time-frequency difference positioning mode, and clock error D t Frequency difference error D f and navigation error D x related.

3. The deep learning-driven intelligent optimization method for positioning arrays and patterns according to claim 2, characterized in that, In step 4, a deep convolutional network based on feature pyramids is constructed. This deep convolutional network based on feature pyramids includes an input encoding layer, a multi-scale feature extraction module, a bidirectional cross-scale attention fusion module, and an adaptive output layer, as detailed below: The input encoding layer uses a standard convolutional layer; The multi-scale feature extraction module consists of alternating stacked Transformer Blocks and MobileNetV3's Bottleneck layer; A bidirectional cross-scale attention fusion module combines a feature pyramid network (FPN) and a path aggregation network (PAN) structure. The adaptive output layer introduces GRU to model historical positioning patterns and predict the confidence of the optimal positioning pattern, the confidence of the optimal array combination, and GDOP.

4. The deep learning-driven intelligent optimization method for positioning arrays and patterns according to claim 3, characterized in that, In step 5, the feature pyramid-based deep convolutional network is trained using the pre-trained dataset of the space-based platform and the target, resulting in a trained feature pyramid-based deep convolutional model, as detailed below: S5.

1. Structure the navigation parameters, observations, and observation errors of the airborne platform from step 1 into a feature matrix I as the network input; S5.2 The feature matrix I is used as the network input. The input encoding layer performs local feature extraction on the feature matrix I to obtain the spatial feature map after dimensionality increase. S5.

3. Use the multi-scale feature extraction module to extract features from the upgraded spatial feature map to obtain high-dimensional semantic features F. out This includes high-level semantic features and low-level detailed features; S5.4, High-dimensional semantic features F out Entering the bidirectional cross-scale attention fusion module, the bidirectional feature path, namely the upsampling structure of FPN and the downsampling structure of PAN, effectively fuses high-level semantic features and low-level detail features through the bidirectional cross-scale attention fusion module. High-level semantic features extract multi-scale global context information through spatial pyramid pooling, and low-level detail features strengthen the coupling ability between spatial position and channel response through coordinate attention mechanism to obtain a high-dimensional feature map. S5.

5. The high-dimensional feature map is fed into the adaptive output layer, and a GRU is introduced to perform temporal modeling of historical localization patterns. Finally, the confidence p of the optimal localization pattern is regressed. i Confidence N of the optimal array combination of airborne platforms under each positioning mode i and the estimated value of GDOP; S5.6, The confidence level p of the optimal positioning mode obtained from S5.5 i Confidence N of the optimal array combination of airborne platforms under each positioning mode i The model training process involves obtaining the estimated value of GDOP and jointly optimizing the parameters of the feature pyramid-based deep convolutional network using the total loss function to complete the model training, thereby obtaining a trained feature pyramid-based deep convolutional model.

5. The deep learning-driven intelligent optimization method for positioning arrays and patterns according to claim 4, characterized in that, In step 6, a model compression strategy is adopted to improve the real-time performance of the feature pyramid-based deep convolutional model, as detailed below: S6.1, Distillation and Compression: Define the deep convolutional model based on feature pyramids trained in step 5 as the teacher model, and use the optimal localization pattern confidence p output by the teacher model. i Confidence N of the optimal array combination of airborne platforms under each positioning mode i The estimated value of GDOP is used as a soft label to guide student model learning; knowledge transfer is achieved by minimizing the KL divergence between the student and teacher output distributions, and finally a student model with a smaller structure but similar accuracy is obtained. S6.2 Quantization and Compression: Based on the student model obtained by distillation, its network parameters are quantized and compressed, and the student model weights W are... f Fixed-point weights W mapped to 8-bit fixed-point representation q : IN f ≈Δ·W q +Z, Where Δ is the scaling factor, Z is the zero point, and W is the floating-point weight W corresponding to each layer in the student model. f The statistical distribution is dynamically calculated, and then the alignment weights are quantized to obtain the quantization model; S6.3, Pruning and Compression: Based on the quantized model, the importance of its weights is evaluated, and the absolute values ​​|w are removed. ij Connections smaller than the pruning threshold τ are used to remove redundant parameters, improve model sparsity and running efficiency. After pruning, the pruned model is fine-tuned to restore accuracy, and finally a compressed deep convolutional model based on feature pyramids is obtained.

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