A lightweight remote sensing image geometric positioning method, system and device

Abstract

The application discloses a kind of lightweight remote sensing image geometric positioning method, system and equipment, the method includes the following steps: S1. Obtain remote sensing image and create coordinate dataset;S2. The parameters of remote sensing image geometric positioning model are initialized, and input weight matrix is generated using orthogonal random projection;S3. Remote sensing image geometric positioning model is trained according to coordinate dataset, hidden layer output is generated by nonlinear feature mapping, and output weight matrix is constructed according to regularized least squares method combined with multi-level solution strategy;S4. According to cross-validation division, the performance of the model is evaluated, and the model is retrained after optimizing the regularization parameter;S5. Based on the model parameters of training completion, test data is input into the trained remote sensing image geometric positioning model to perform regression calculation, and the calculated coordinate data are compared with the coordinates calculated by satellite sensor model, and the running time is recorded, to verify the efficiency and accuracy of the model. The application is applied to the technical field of photogrammetry.

Description

Technical Field

[0001] This invention is applied to the technical field of photogrammetry, and particularly relates to a lightweight method, system and device for geometric positioning of remote sensing images. Background Technology

[0002] Geometric positioning models for satellite imagery are a crucial step in remote sensing data processing, and their accuracy and efficiency directly impact the effectiveness of subsequent analysis and applications. Commonly used geometric positioning models, such as rational function models, calculate positioning coordinates through iterative solutions when performing back projection calculations. This leads to increased computation time when performing a large number of coordinate calculations. In resource-constrained embedded platforms or scenarios with high real-time requirements, this may not meet the expected timeliness for needs requiring real-time responses.

[0003] In recent years, deep learning models (such as multilayer perceptrons, convolutional neural networks, and Transformers) have been widely used in remote sensing. Some studies have attempted to use deep learning models to fit satellite sensor models to improve model performance. Although deep learning performs well in specific tasks, it typically relies on deep network structures and large-scale parameters. The training and inference processes consume significant computational resources, and redundant network layer designs and parameter scales lead to increased inference latency, making it difficult to meet real-time requirements. Furthermore, its strong dependence on hardware accelerators limits its applicability in edge computing environments. In addition, satellite image geometric localization involves accurately mapping satellite imagery to the Earth's three-dimensional geographic coordinate system. The mapping relationship between its input and output has clear mathematical constraints, resulting in relatively limited task complexity. Using complex network structures not only significantly increases training and inference time due to parameter redundancy but also makes efficient operation difficult in scenarios with high real-time requirements or limited resources, thus it is not the optimal solution. Furthermore, while overly simplified models can reduce computational overhead, they may lead to insufficient localization accuracy, failing to meet application requirements. Therefore, a balance needs to be struck between model complexity, computational efficiency, and accuracy to achieve efficient remote sensing image geometric localization. Summary of the Invention

[0004] To address the aforementioned problems, this invention proposes a lightweight remote sensing image geometric localization method, system, and device. This method abandons traditional iterative optimization and complex network structures, and instead utilizes orthogonal projection initialization and regularized analytical solutions based on extreme learning machines. This significantly reduces training and inference time while maintaining localization accuracy. Compared to the iterative problem of backprojection calculation using rational function models, its non-iterative nature avoids convergence delays. Furthermore, compared to commonly used deep learning methods, its parameter size and computational complexity are greatly reduced, avoiding the surge in computational complexity caused by multi-layer stacking, and making it more suitable for low-power hardware environments.

[0005] The technical solution adopted in this invention is as follows: This invention includes a lightweight remote sensing image geometric positioning method, system, and device, wherein the method includes the following steps: Step 1: Acquire remote sensing imagery and create a coordinate dataset; Step 2: Initialize the parameters of the remote sensing image geometric positioning model, generate the input weight matrix using orthogonal random projection, generate a random bias vector, and adaptively determine the hidden layer dimension based on the statistical characteristics of the input feature data; Step 3: Train a geometric localization model for remote sensing images based on the coordinate dataset, generate hidden layer output through nonlinear feature mapping, and construct the output weight matrix based on regularized least squares method combined with multi-level solution strategy; Step 4: Evaluate model performance based on cross-validation, optimize regularization parameters, retrain the model, and save all key parameters of the final model in a unified standardized file format. Step 5: Based on the trained model parameters, input the test data into the trained remote sensing image geometric positioning model to perform regression calculation. The model outputs the predicted coordinate data, which is compared with the coordinates calculated by the satellite sensor model. The running time of the lightweight remote sensing image geometric positioning model and the satellite sensor model on the test data is recorded to verify the efficiency and accuracy of the model.

[0006] Furthermore, in step 1, acquiring remote sensing images and creating a coordinate dataset involves using a satellite sensor model to calculate the three-dimensional spatial coordinates of virtual grid points, creating a dataset containing image pixel coordinates and object space coordinates, and then normalizing the remote sensing image coordinate data.

[0007] Furthermore, the specific steps for generating the input weight matrix and the random bias vector using orthogonal random projection in step 2 are as follows: Step 201: Generate a random matrix. For the given coordinate dataset, randomly generate a temporary matrix. Where R represents the set of real numbers, For the hidden layer dimension, Let be the dimension of the coordinates, and let its elements follow a standard normal distribution. Independent sampling in the middle; Step 202: Generate the orthogonalized input weight matrix using the QR decomposition method. ,right Performing QR matrix decomposition yields: , in It is an orthogonal matrix. column vectors satisfy , It is an upper triangular matrix. elements for , yes The List; Take orthogonal matrix transpose matrix The construction dimension is Input weight matrix: , Step 203: Generate a random bias vector, with elements following a standard normal distribution. Sampling.

[0008] Furthermore, the specific steps for adaptively determining the hidden layer dimension in step 2 are as follows: Step 204: Based on the standardized coordinate matrix The complexity of calculating the input coordinate data, and the variance of each coordinate dimension are: , In the above formula, Indicates the first The variance of the 3D coordinates; Representation matrix The Middle line, number Column elements; For the first The mean of the dimensional coordinates; Step 205: Use the total variance to characterize the feature space complexity. The expression for the total variance is: , Step 206: Calculate the hidden layer dimension based on the input feature variance : , In the above formula, For constant terms; This is the variance scaling factor; and These are the upper and lower limits of the number of neurons; This is a truncation function.

[0009] Furthermore, the specific steps for generating the hidden layer output in step 3 are as follows: Step 301: Network architecture design. The model structure is divided into three main parts: input layer, hidden layer, and output layer. The input layer is set to have a dimension of 3 to receive the normalized coordinate data. The output of the hidden layer performs a non-linear transformation on the input data through an activation function to generate a high-dimensional feature representation. The output layer is set to have a dimension of 2 and directly outputs the calculated coordinate values. Step 302: Calculate the hidden layer output matrix With the target value matrix The linear relationship between them is used to construct the output weight matrix. The solution form is as follows: , in, For regularization parameters; To optimize the operator; Denotes the Frobenius norm; The analytical solution for regularized least squares is: , in, To output the weight matrix; This is the output matrix of the hidden layer; for The transpose of the matrix; For regularization parameters; For unit array; Inverse operator for a matrix; This is the target value matrix.

[0010] Step 303: Calculate in batches and The dataset is divided into several batches, and calculations are performed on each batch. and Sum the results of all batches , , Total number of batches; Step 304: Calculate the result of adding a regularization term to the hidden layer output covariance matrix. When the matrix is ​​positive definite, a linear equation based on Cholesky decomposition is used to solve it; when the matrix is ​​non-positive definite but symmetrical, a linear equation based on LU decomposition is used to solve it; when the matrix is ​​ill-conditioned, the SVD pseudo-inverse is used as a degenerate strategy. , in, Let be a right singular vector matrix, satisfying ; It is a diagonal matrix, and its diagonal elements are: , It is a singular value. The set threshold is used to filter out outliers that are too small. Let be a left singular vector matrix, satisfying ; Step 305: Construct the output of the geometric positioning model of the remote sensing image, and use the model to predict the data: , in, For the first The first sample Dimensional prediction output value; For sample index; To define the dimensions of the output data; For hidden layer index; For the hidden layer dimension; This is for accumulating neurons in the hidden layer; For activation functions; Index the dimensions of the input data; The coordinate dimension; For the first The first sample 3D coordinate values; For the first Dimensional input coordinates and the first The weights of each neuron; For the first The bias vectors of each hidden layer neuron; For the first The hidden layer neuron and the first The output weights of the dimension.

[0011] Step 306: Evaluation metrics, calculate root mean square error (RMSE), mean absolute error (MAE), and coefficient of determination. The formula used to quantify the accuracy and reliability of the model output is: .

[0012] Furthermore, the specific steps of step 4 are as follows: Step 401: Data partitioning. Use the KFold method to randomly divide the data into K subsets; Step 402: Model retraining. Each time, select one subset as the validation set and the rest as the training set. Repeat the model training process and record the evaluation metrics each time. Step 403: Indicator statistics, statistics for each discount MAE The mean and standard deviation of training time and condition number are used to evaluate model stability. Step 404: Search for the optimal regularization parameter, searching for the optimal parameter in the logarithmic space. By traversing the preset Range, for each Cross-validation is performed to minimize the model's prediction error on the validation set, as shown in the formula: ; Step 405: Determine the optimal hyperparameters through the aforementioned optimization process. The model is then retrained. After training, key model parameters are saved, including hidden layer dimensions, regularization parameters, input weights, biases, and output weights. These parameters are then combined with other relevant model configurations and saved into a single model file for easy loading and application later.

[0013] Furthermore, the lightweight remote sensing image geometric positioning system includes: The data acquisition module is used to acquire remote sensing image data and its corresponding coordinate information; The data preprocessing module is used to perform preliminary processing on the acquired remote sensing image data and standardize the remote sensing image data; The data training module is used to execute the model training process, calculate the hidden layer output based on the preprocessed dataset, and optimize the weight output layer. The inference module is used to quickly predict the coordinates of new input data using pre-trained model weights. The results processing and output module is used to de-standardize and convert the inference results, and output them in a suitable format for use by users or other systems.

[0014] Furthermore, the lightweight remote sensing image geometric positioning device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the aforementioned lightweight remote sensing image geometric positioning method.

[0015] The beneficial effects of this invention are as follows: This invention discloses a lightweight remote sensing image geometric localization method, system, and device, mainly solving the problems of computational complexity and accuracy in remote sensing image localization. This invention acquires remote sensing images and creates a coordinate dataset, uses orthogonal random projection to generate an input weight matrix and random bias vector, adaptively determines the hidden layer dimension, generates the hidden layer output, and uses regularized least squares to optimize the output weights. This invention also introduces a cross-validation mechanism to optimize the regularization parameters and improve the model's generalization ability. Through this method, this invention improves the training speed and inference efficiency of remote sensing image coordinate prediction, effectively handles large-scale data, and is suitable for real-time and resource-constrained remote sensing scenarios. Simultaneously, this invention maintains good prediction accuracy and stability while operating efficiently, adapts to various complex data distributions, achieves accurate and reliable coordinate calculation, and has good practical application value. Attached Figure Description

[0016] Figure 1 This is a flowchart illustrating the overall steps of a lightweight remote sensing image geometric positioning method. Figure 2 This is a schematic diagram of the basic network structure; Figure 3 This is a schematic diagram of a lightweight remote sensing image geometric positioning system; Figure 4 This is a schematic diagram of a lightweight remote sensing image geometric positioning device. Detailed Implementation

[0017] In this embodiment, the present invention includes a lightweight remote sensing image geometric positioning method, system, and device.

[0018] like Figure 1 As shown in the figure, the specific process of a lightweight remote sensing image geometric positioning method in this embodiment is as follows: S1. Acquire remote sensing images and create a coordinate dataset; S2. Initialize the parameters of the remote sensing image geometric positioning model, generate the input weight matrix using orthogonal random projection, generate a random bias vector, and adaptively determine the hidden layer dimension based on the statistical characteristics of the input feature data. S3. Train a geometric localization model for remote sensing images based on the coordinate dataset, generate hidden layer output through nonlinear feature mapping, and construct the output weight matrix based on regularized least squares method combined with multi-level solution strategy; S4. Evaluate model performance based on cross-validation, optimize regularization parameters, retrain the model, and save all key parameters of the final model in a unified standardized file format. S5. Based on the trained model parameters, input the test data into the trained remote sensing image geometric positioning model to perform regression calculation. The model outputs the predicted coordinate data, which is compared with the coordinates calculated by the satellite sensor model. The running time of the lightweight remote sensing image geometric positioning model and the satellite sensor model on the test data is recorded to verify the efficiency and accuracy of the model.

[0019] The more specific process of this implementation method is as follows: S1. Acquiring remote sensing imagery and creating a coordinate dataset involves using a satellite sensor model to calculate the three-dimensional spatial coordinates of virtual grid points, creating a dataset containing image pixel coordinates and object space coordinates, and normalizing the remote sensing image coordinate data. The specific steps are as follows: S101. Determine the width and height values ​​of the image, and divide it into grid points at certain intervals to form a two-dimensional planar grid; S102. Several discrete height layers are set in the elevation direction according to the elevation range; S103. Using a satellite sensor model, the two-dimensional planar coordinates of the grid points are back-projected onto the ground space to obtain the correspondence between the geographic coordinates and image coordinates of each grid point, and to obtain a coordinate dataset; S104. Normalize the coordinate data using the following formula: ,

[0020] in, These are the normalized coordinate values; Coordinate data; These are translation parameters; The number of coordinate points; This is a proportional parameter; The maximum value of the coordinate data; The minimum value of the coordinate data; S105. Generate a normalized coordinate matrix ,in, The number of coordinate points. The dimension of the coordinates. Representing dimensions including longitude, latitude, and elevation, and constructing training and testing datasets; S2. Initialize the parameters of the remote sensing image geometric positioning model, generate the input weight matrix using orthogonal random projection, generate a random bias vector, and adaptively determine the hidden layer dimension based on the statistical characteristics of the input feature data.

[0021] The specific steps for initializing the input weights and biases are as follows: S201. Generate a random matrix. For a given coordinate dataset, randomly generate a temporary matrix. Where R represents the set of real numbers, For the hidden layer dimension, Let be the dimension of the coordinates, and let its elements follow a standard normal distribution. Independent sampling in the middle.

[0022] S202. Generate the orthogonalized input weight matrix using the QR decomposition method. .right Performing QR matrix decomposition yields: , in It is an orthogonal matrix. column vectors satisfy , It is an upper triangular matrix. elements for , yes The List; Take orthogonal matrix transpose matrix The construction dimension is Input weight matrix: , S203. Bias Initialization. Generate a random bias vector, with elements following a standard normal distribution. Sampling.

[0023] The specific steps for adaptively determining the hidden layer dimension are as follows: S204. Based on the standardized coordinate matrix The complexity of calculating the input coordinate data is as follows: The variance of each coordinate dimension is: , In the above formula, Indicates the first The variance of the 3D coordinates; Representation matrix The Middle line, number Column elements; For the first The mean of the dimensional coordinates; S205. The total variance is used to characterize the feature space complexity. The expression for the total variance is: , S206. Calculate the hidden layer dimension based on the input feature variance. : ,

[0024] In the above formula, For constant terms; This is the variance scaling factor; and These are the upper and lower limits of the number of neurons; This is a truncation function.

[0025] S207. Determine whether a hidden layer dimension is specified. If the hidden layer dimension is not explicitly specified (i.e., the specified value is empty), then use the dimension calculated based on the features of the input data. If a preset dimension value is explicitly provided, that value will be directly used as the hidden layer dimension. In resource-constrained environments, lightweight models adapted to current hardware conditions can be quickly generated.

[0026] The initialization phase also includes pre-compiling Numba functions to accelerate inference. During the model initialization phase, the core computation steps are pre-compiled, which enables the rapid generation of hidden layer outputs and prediction results during the prediction process.

[0027] S3. Train a geometric localization model for remote sensing images based on the coordinate dataset, generate hidden layer output through nonlinear feature mapping, and construct the output weight matrix based on regularized least squares method combined with multi-level solution strategy.

[0028] The specific steps are as follows: S301. Network architecture design. For example... Figure 2 As shown, a single-hidden-layer feedforward neural network architecture is adopted. The model structure consists of three main parts: an input layer, a hidden layer, and an output layer. The input layer has a dimension of 3 and receives the normalized coordinate data. The output of the hidden layer performs a non-linear transformation on the input data through an activation function to generate a high-dimensional feature representation. The output layer has a dimension of 2 and directly outputs the calculated coordinate values.

[0029] S302. Calculate the hidden layer output matrix With the target value matrix The linear relationship between them is used to construct the output weight matrix. The solution form is as follows: , in, For regularization parameters; To optimize the operator; This represents the Frobenius norm.

[0030] The analytical solution for regularized least squares is: , in, To output the weight matrix; This is the output matrix of the hidden layer; for The transpose of the matrix; For regularization parameters; For unit array; Inverse operator for a matrix; This is the target value matrix.

[0031] S303. Calculation by batch and The dataset is divided into several batches, and calculations are performed on each batch. and Sum the results of all batches , , This represents the total number of batches.

[0032] S304. Calculate the result of adding a regularization term to the hidden layer output covariance matrix. When the matrix is ​​positive definite, a linear equation based on Cholesky decomposition is used to solve it; when the matrix is ​​non-positive definite but symmetrical, a linear equation based on LU decomposition is used to solve it; when the matrix is ​​ill-conditioned, the SVD pseudo-inverse is used as a degenerate strategy. , in, Let be a right singular vector matrix, satisfying ; It is a diagonal matrix, and its diagonal elements are: , It is a singular value. The set threshold is used to filter out outliers that are too small. Let be a left singular vector matrix, satisfying .

[0033] S305. Construct the output of the geometric positioning model of the remote sensing image, and use the model to predict the data: , in, For the first The first sample Dimensional prediction output value; For sample index; To define the dimensions of the output data; For hidden layer index; For the hidden layer dimension; This is for the accumulation of neurons in the hidden layer; For activation functions; Index the dimensions of the input data; The coordinate dimension; For the first The first sample 3D coordinate values; For the first Dimensional input coordinates and the first The weights of each neuron; For the first The bias vectors of each hidden layer neuron; For the first The hidden layer neuron and the first The output weights of the dimension. S306. Evaluation Indicators. Calculate the root mean square error (RMSE), mean absolute error (MAE), and coefficient of determination. The formula used to quantify the accuracy and reliability of the model output is: , S4. Evaluate model performance based on cross-validation, optimize regularization parameters, retrain the model, and save all key parameters of the final model in a unified standardized file format. The cross-validation and model tuning utilize K-fold cross-validation to improve the model's generalization ability and determine the optimal regularization parameters. .

[0034] The specific steps are as follows: S401. Data Partitioning. The data is randomly divided into K subsets using the KFold method. The KFold method is a cross-validation technique commonly used in machine learning and model evaluation. It is used to divide the dataset into K mutually exclusive subsets (called "folds"), and to more robustly evaluate model performance through multiple rounds of training and validation. S402. Model Retraining. Each time, select one subset as the validation set and the rest as the training set, repeat the model training process, and record the evaluation metrics each time.

[0035] S403. Indicator Statistics. Statistics for each fold. MAE The mean and standard deviation of training time and condition number are used to evaluate model stability.

[0036] S404. Search for the optimal regularization parameter. Searching for the optimal parameter in the logarithmic space. By traversing the preset Range, for each Cross-validation is performed to minimize the model's prediction error on the validation set, as shown in the formula: , Based on the cross-validation results, select the minimum... of As hyperparameters of the final model.

[0037] S405. Determine the optimal hyperparameters through the aforementioned optimization process. The model is then retrained. After training, key model parameters are saved, including hidden layer dimensions, regularization parameters, input weights, biases, and output weights. These parameters are then combined with other relevant model configurations and saved into a single model file for easy loading and application later.

[0038] S5. Based on the trained model parameters, input the test data into the trained remote sensing image geometric positioning model to perform regression calculation. The model outputs the predicted coordinate data, which is compared with the coordinates calculated by the satellite sensor model. The running time of the lightweight remote sensing image geometric positioning model and the satellite sensor model on the test data is recorded to verify the efficiency and accuracy of the model.

[0039] Experiment 1 To verify the fitting accuracy of the method proposed in this invention, five remote sensing images from two satellites were first selected as test data. The fitting accuracy of the method in the X-direction, Y-direction, and in-plane on the test dataset was calculated. The root mean square error (RMSE) and maximum error (MAX) were used as evaluation indicators to reflect the positioning accuracy and error distribution characteristics of this invention. The results are shown in Table 1.

[0040] Table 1. Fitting accuracy of the present invention (unit: pixels)

[0041] The experimental results show that the lightweight remote sensing image geometric localization method proposed in this invention has high fitting accuracy. In all test images, the RMSE remains at 10. -4 Level, MAE remains at 10 -3 The level meets the measurement requirements, verifying the effectiveness of the invention.

[0042] Experiment 2 To evaluate the computational efficiency advantages of this invention, a comparative experiment was designed to examine the computation time of the method and the rational function model under different computational modes. Two satellite images were selected for the experiment, and the computation time was tested at data volumes of 100,000, 500,000, and 1,000,000 data points, respectively. The time required to complete the computation was statistically analyzed by iteratively processing each point. Simultaneously, the data normalization and denormalization processes in the method of this invention were included in the overall time statistics. The results are shown in Table 2.

[0043] Table 2 Comparison of Predicted Times (Unit: Seconds)

[0044] The experimental results show that the method of this invention has a faster inference speed. This invention exhibits stable and efficient computational performance in both computation modes, with a shorter computation time compared to the rational function model. In orthographic projection computation, the computation time of the rational function model increases approximately linearly with the amount of data. In backprojection computation, the computation time of the rational function model increases significantly due to the need for iterative computation. These experimental results demonstrate the computational efficiency advantage of this invention.

[0045] Based on the comparative experimental results of fitting accuracy and prediction time, this invention achieves relatively fast computational efficiency while maintaining prediction accuracy. This verifies the technical feasibility of the invention.

[0046] like Figure 3As shown, this embodiment further provides a lightweight remote sensing image geometric positioning system, including: a data acquisition module, a data preprocessing module, a data training module, an inference module, and a result processing and output module, wherein: The data acquisition module is used to acquire remote sensing image data and its corresponding coordinate information; The data preprocessing module is used to perform preliminary processing on the acquired remote sensing image data and standardize the remote sensing image data; The data training module is used to execute the model training process, calculate the hidden layer output based on the preprocessed dataset, and optimize the weight output layer. The inference module is used to quickly predict the coordinates of new input data using pre-trained model weights. The results processing and output module is used to de-standardize and convert the inference results, and output them in a suitable format for use by users or other systems.

[0047] like Figure 4 As shown, this embodiment further provides a lightweight remote sensing image geometric positioning device. The device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the lightweight remote sensing image geometric positioning method described above.

[0048] In summary, this invention successfully solves the following two problems: (1) When performing back projection calculations on rational function models, iterative solutions are required, which has a convergence delay. However, the method of this invention exhibits stable and efficient computational performance in both forward and back projection calculation modes.

[0049] (2) Existing neural network models are usually complex in structure and redundant in parameters, resulting in low training and inference efficiency, making it difficult to meet real-time requirements for geometric localization calculations. An effective balance needs to be achieved between model complexity, computational efficiency, and accuracy. The method of this invention achieves relatively fast computational efficiency while maintaining prediction accuracy.

[0050] Although the embodiments of the present invention are described with reference to actual solutions, they do not constitute a limitation on the meaning of the present invention. Modifications to the embodiments and combinations with other solutions based on this specification will be obvious to those skilled in the art.

Claims

1. A lightweight remote sensing image geometric positioning method, characterized in that, It includes the following steps: Step 1: Acquire remote sensing imagery and create a coordinate dataset; Step 2: Initialize the parameters of the remote sensing image geometric positioning model, generate the input weight matrix using orthogonal random projection, generate a random bias vector, and adaptively determine the hidden layer dimension based on the statistical characteristics of the input feature data; Step 3: Train a geometric localization model for remote sensing images based on the coordinate dataset, generate hidden layer output through nonlinear feature mapping, and solve the output weight matrix using a multi-level solution strategy based on regularized least squares. Step 4: Evaluate model performance based on cross-validation, optimize regularization parameters, retrain the model, and save all key parameters of the final model in a unified standardized file format. Step 5: Based on the trained model parameters, input the test data into the trained remote sensing image geometric positioning model to perform regression calculation. The model outputs the predicted coordinate data, which is compared with the coordinates calculated by the satellite sensor model. The running time of the lightweight remote sensing image geometric positioning model and the satellite sensor model on the test data is recorded to verify the efficiency and accuracy of the model. The specific steps for generating the input weight matrix and the random bias vector using orthogonal random projection in step 2 are as follows: Step 201: Generate a random matrix. For the given coordinate dataset, randomly generate a temporary matrix. Where R represents the set of real numbers, For the hidden layer dimension, Let be the dimension of the coordinates, and let its elements follow a standard normal distribution. Independent sampling in the middle; Step 202: Generate the orthogonalized input weight matrix using the QR decomposition method. ,right Performing QR matrix decomposition yields: ， in It is an orthogonal matrix. column vectors satisfy , It is an upper triangular matrix. elements for , yes The List; Take orthogonal matrix transpose matrix The construction dimension is Input weight matrix: ， Step 203: Generate a random bias vector, with elements following a standard normal distribution. Mid-sampling; The specific steps for adaptively determining the hidden layer dimension in step 2 are as follows: Step 204: Based on the standardized coordinate matrix The complexity of calculating the input coordinate data, and the variance of each coordinate dimension are: ， In the above formula, Indicates the first The variance of the 3D coordinates; Representation matrix The Middle line, number Column elements; For the first The mean of the dimensional coordinates; Step 205: Use the total variance to characterize the feature space complexity. The expression for the total variance is: ， Step 206: Calculate the hidden layer dimension based on the input feature variance : ， In the above formula, For constant terms; This is the variance scaling factor; and These are the upper and lower limits of the number of neurons; This is a truncation function.

2. The lightweight remote sensing image geometric positioning method according to claim 1, characterized in that: The step 1 of acquiring remote sensing images and creating a coordinate dataset involves using a satellite sensor model to calculate the three-dimensional coordinates of virtual grid points, creating a dataset containing image pixel coordinates and object space coordinates, and then normalizing the remote sensing image coordinate data.

3. The lightweight remote sensing image geometric positioning method according to claim 1, characterized in that: The specific steps for generating the hidden layer output in step 3 are as follows: Step 301: Network architecture design. The model structure is divided into three main parts: input layer, hidden layer, and output layer. The input layer is set to have a dimension of 3 to receive the normalized coordinate data. The output of the hidden layer performs a non-linear transformation on the input data through an activation function to generate a high-dimensional feature representation. The output layer is set to have a dimension of 2 and directly outputs the calculated coordinate values. Step 302: Calculate the hidden layer output matrix With the target value matrix The linear relationship between them is used to construct the output weight matrix. The solution form is as follows: ， in, For regularization parameters; To optimize the operator; Denotes the Frobenius norm; The analytical solution for regularized least squares is: ， in, To output the weight matrix; This is the output matrix of the hidden layer; for The transpose of the matrix; For regularization parameters; For unit array; Inverse operator for a matrix; The target value matrix; Step 303: Calculate in batches and The dataset is divided into several batches, and calculations are performed on each batch. and Sum the results of all batches , , Total number of batches; Step 304: Calculate the result of adding a regularization term to the hidden layer output covariance matrix. When the matrix is ​​positive definite, a linear equation based on Cholesky decomposition is used to solve it; when the matrix is ​​non-positive definite but symmetrical, a linear equation based on LU decomposition is used to solve it; when the matrix is ​​ill-conditioned, the SVD pseudo-inverse is used as a degenerate strategy. ， in, Let be a right singular vector matrix, satisfying ; It is a diagonal matrix, and its diagonal elements are: , It is a singular value. The set threshold is used to filter out outliers that are too small. Let be a left singular vector matrix, satisfying ; Step 305: Construct the output of the geometric positioning model of the remote sensing image, and use the model to predict the data: ， in, For the first The first sample Dimensional prediction output value; For sample index; To define the dimensions of the output data; For hidden layer index; For the hidden layer dimension; This is for the accumulation of neurons in the hidden layer; For activation functions; Index the dimensions of the input data; The coordinate dimension; For the first The first sample 3D coordinate values; For the first Dimensional input coordinates and the first The weights of each neuron; For the first The bias vectors of each hidden layer neuron; For the first The hidden layer neuron and the first Dimensional output weights; Step 306: Evaluation metrics, calculate root mean square error (RMSE), mean absolute error (MAE), and coefficient of determination. The formula used to quantify the accuracy and reliability of the model output is: 。 4. The lightweight remote sensing image geometric positioning method according to claim 1, characterized in that: The specific steps of step 4 are as follows: Step 401: Data partitioning. Use the KFold method to randomly divide the data into K subsets; Step 402: Model retraining. Each time, select one subset as the validation set and the rest as the training set. Repeat the model training process and record the evaluation metrics each time. Step 403: Indicator statistics, statistics for each discount MAE The mean and standard deviation of training time and condition number are used to evaluate model stability. Step 404: Search for the optimal regularization parameter, searching for the optimal parameter in the logarithmic space. By traversing the preset Range, for each Cross-validation is performed to minimize the model's prediction error on the validation set, as shown in the formula: ； Step 405: Determine the optimal hyperparameters through the aforementioned optimization process. The model is then retrained, and key model parameters are saved after training, including hidden layer dimensions, regularization parameters, input weights, biases, and output weights. These parameters, along with other relevant model configurations, are combined and saved into a single model file for easy loading and application later.

5. A lightweight remote sensing image geometric positioning system, characterized in that, The system is applied to a lightweight remote sensing image geometric positioning method according to any one of claims 1 to 4, the system comprising: The data acquisition module is used to acquire remote sensing image data and its corresponding coordinate information; The data preprocessing module is used to perform preliminary processing on the acquired remote sensing image data and standardize the remote sensing image data; The data training module is used to execute the model training process, calculate the hidden layer output based on the preprocessed dataset, and optimize the weight output layer. The inference module is used to quickly predict the coordinates of new input data using pre-trained model weights. The results processing and output module is used to de-standardize and convert the inference results, and output them in a suitable format for use by users or other systems.

6. A lightweight remote sensing image geometric positioning device, characterized in that, It includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement a lightweight remote sensing image geometric positioning method according to any one of claims 1 to 4.

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