High-precision surveying and mapping method based on multi-source data fusion

Abstract

The invention relates to the field of surveying and mapping and geographic information systems, and discloses a high-precision surveying and mapping method based on multi-source data fusion, and the method comprises the following steps: S1, obtaining data sources from a plurality of sensors, and carrying out the preprocessing of the data sources; s2, constructing a sparse representation model for each preprocessed data source, and obtaining a sparse coefficient and a dictionary through an optimization method; s3, estimating posterior distribution of the sparse representation model by using a variational inference technology; s4, fusing the sparse coefficients of the plurality of data sources based on a multi-task sparse coding method; s5, enhancing the relevance among the data sources through a graph theory regularization method; s6, optimizing the fusion result by using a semi-definite programming method to obtain a globally optimal solution; and S7, outputting an optimized surveying and mapping data result. Through efficient fusion and optimization of multi-source data, high precision, consistency and robustness improvement of surveying and mapping data are realized, and the method is suitable for wide surveying and mapping application scenes.

Description

Technical Field

[0001] The present invention relates to the technical field of surveying and mapping and geographic information system, and in particular to a high-precision surveying and mapping method based on multi-source data fusion. Background Art

[0002] In the field of modern surveying and mapping, with the development of sensor technology, it is becoming easier to obtain multi-source data from satellites, aviation, ground, etc. These data sources have different resolutions, accuracy and noise characteristics, providing rich geographic information. However, how to effectively fuse these multi-source heterogeneous data to generate high consistency and high accuracy surveying and mapping results is still a key technical challenge.

[0003] In the existing technology, multi-source data fusion usually relies on simple weighted average or interpolation methods. Although these methods can integrate information from different data sources to a certain extent, they often ignore the complex correlation and uncertainty between data sources, making the fusion results vulnerable to noise and data bias, thereby reducing the accuracy and consistency of surveying and mapping results. In addition, the existing optimization methods are mostly limited to local optimal solutions and lack a global perspective, making the fused data insufficiently robust in complex application scenarios and difficult to meet actual needs. Summary of the invention

[0004] In view of the shortcomings of the prior art, the present invention provides a high-precision surveying and mapping method based on multi-source data fusion, which realizes efficient fusion and global optimization in multi-source heterogeneous data to generate surveying and mapping results with high precision, strong consistency and good robustness.

[0005] To achieve the above objectives, the present invention is implemented through the following technical solutions: A high-precision surveying and mapping method based on multi-source data fusion, comprising the following steps:

[0006] Acquire data sources from multiple sensors and pre-process the data sources;

[0007] A sparse representation model is constructed for each preprocessed data source, and sparse coefficients and dictionaries are obtained through optimization methods;

[0008] estimating the posterior distribution of the sparse representation model using variational inference techniques;

[0009] The sparse coefficients of multiple data sources are fused based on the multi-task sparse coding method;

[0010] Enhance the correlation between data sources through graph theory regularization method;

[0011] The fusion results are optimized using the semidefinite programming method to obtain the global optimal solution;

[0012] Output optimized surveying and mapping data results.

[0013] Preferably, the step of acquiring data sources from a plurality of sensors and preprocessing the data sources comprises:

[0014] Collect data sources from multiple sensors, where each data source X i is a multidimensional data matrix;

[0015] De-noising the data source to suppress noise components in the data;

[0016] The data sources are scaled and normalized to the same scale. i Convert to Where min(X i ) and max(X i ) are data sources X i The minimum and maximum values ​​of

[0017] Extract features from the data source, perform dimensionality reduction on the data source through principal component analysis, calculate the covariance matrix of the data source, perform eigenvalue decomposition on it, retain the main eigenvectors to form a data representation X″ after dimensionality reduction i ;

[0018] Output pre-processed multiple data sources X″ i For subsequent sparse representation model construction.

[0019] Preferably, the step of constructing a sparse representation model for each preprocessed data source and obtaining sparse coefficients and a dictionary by an optimization method comprises:

[0020] For the preprocessed data source X″ i Perform sparse representation modeling and represent each data source as a dictionary matrix D i and the sparse coefficient matrix α i The linear combination of X″ i ≈D i α i , where D i For size d i ×k dictionary matrix, α i is a sparse coefficient matrix;

[0021] Initialize the dictionary matrix D i and the sparse coefficient matrix α i ;

[0022] Fixed dictionary matrix D i , the sparse coefficient matrix α is obtained by solving the following optimization problem i :

[0023]

[0024] Among them, λ is the regularization parameter that controls sparsity, which is solved by LASS0 or matching pursuit algorithm;

[0025] Fixed sparse coefficient matrix α i , optimize the dictionary matrix D by minimizing the reconstruction error i , that is, solved by the following objective function:

[0026]

[0027] Alternately iterate the optimization steps of the above sparse coefficient matrix and dictionary matrix until convergence to obtain the final sparse coefficient matrix α i and dictionary matrix D i ;

[0028] Output sparse coefficient matrix α i and dictionary matrix D i For subsequent data fusion processing.

[0029] Preferably, the step of estimating the posterior distribution of the sparse representation model using variational inference technology includes:

[0030] Set the generation hypothesis of the sparse representation model, assuming that the preprocessed data source X″ i By dictionary matrix D i and the sparse coefficient matrix α i Generated, and the noise of the data source has zero mean and variance σ 2 Gaussian distribution of:

[0031] X i =D i α i +∈ i

[0032] in,

[0033] is the sparse coefficient matrix α i and dictionary matrix D i Specify the prior distribution, assuming α i The prior distribution of is Laplace distribution, and the dictionary matrix D i The prior distribution of is a Gaussian distribution:

[0034]

[0035] Among them, λ and τ are hyperparameters that control sparsity and dictionary matrix distribution respectively;

[0036] Estimate the posterior distribution p(αi, Di|X″) through variational inference techniques i ), set the variational distribution q(αi, Di) to approximate the true posterior distribution;

[0037] Minimize the KL divergence between the variational distribution and the true posterior distribution:

[0038] KL(q(α i , D i )||p(α i , D i |X″ i ))

[0039] Among them, KL divergence is defined as:

[0040]

[0041] Optimize the variational distribution q(αi, Di) by the variational Bayesian method or the stochastic gradient descent method until convergence, and obtain the variational distribution parameters that approximate the true posterior distribution;

[0042] The output estimated sparse coefficient matrix αi and the posterior distribution of the dictionary matrix Di are used to improve the robustness and accuracy of data fusion.

[0043] Preferably, the step of fusing sparse coefficients of multiple data sources based on the multi-task sparse coding method includes:

[0044] Set each data source X″ i The sparse representation result αi is regarded as a task, and multiple tasks are jointly modeled through a multi-task sparse coding model to capture the shared information between different data sources;

[0045] Define the optimization objective function of multi-task sparse coding, where the sparse representation αi of each task is represented by its corresponding dictionary Di, and the optimization objective function is:

[0046]

[0047] Among them, λ i is the regularization parameter for controlling sparsity, and γ is the regularization parameter for controlling the consistency between the sparse coefficients of different tasks;

[0048] By optimizing this objective function, we first fix the sparse coefficients α of other tasks. j (j≠i), optimize the sparse coefficient αi of each task and use the gradient descent method or the alternating direction multiplier method to solve it;

[0049] The sparse coefficient αi of each task is updated alternately, gradually approaching the global optimal solution, ensuring that the sparse representations between different data sources can fully integrate shared information;

[0050] The fused sparse coefficient matrix αi is output as the final data fusion result for subsequent graph regularization processing and optimization.

[0051] Preferably, the step of enhancing the correlation between data sources by using a graph theory regularization method comprises:

[0052] Construct a graph model G = (V, E) representing the relationship between multiple data sources, where V represents the data source node and E represents the connection relationship between the nodes;

[0053] Define the weight matrix W of the graph, where each element W ij Indicates data source X″ i and data source X″ j The similarity between them, the calculation formula of the weight matrix W is:

[0054]

[0055] Among them, σ is a parameter that controls the sensitivity of similarity between data sources, ‖X″ i -X″ j ‖ represents data source X″ i and X″ j The Euclidean distance between

[0056] A graph regularization term is introduced to enhance the correlation between sparse coefficients of different data sources. The form of the graph regularization term is:

[0057]

[0058] Among them, α i and α j They are respectively data source X″ i and X″ j The sparse coefficient of

[0059] The graph regularization term is introduced into the optimization objective function of multi-task sparse coding to form a new optimization problem:

[0060]

[0061] The optimization problem is solved by using an optimization algorithm to ensure that the sparse coefficient matrix α i The similarity between them is matched with the weight matrix W of the graph model, thereby enhancing the correlation between data sources;

[0062] Output the sparse coefficient matrix α after graph theory regularization i , which is used for subsequent semidefinite programming optimization processing.

[0063] Preferably, the step of optimizing the fusion result by using a semidefinite programming method to obtain a global optimal solution comprises:

[0064] The sparse coefficient matrix α after graph theory regularization i It is introduced into the semidefinite programming model, and the optimization goal is set to maximize the correlation between data sources while ensuring the accuracy of sparse representation;

[0065] Construct the objective function of the semidefinite programming problem, which includes the sparse representation error term and the graph regularization term. The objective function form is:

[0066]

[0067] Among them, Z is a semidefinite positive matrix, Z ij Represents the sparse coefficient α i and α j The correlation between them, trace(Z) is the trace of the matrix Z, which represents the overall quality of the optimization objective;

[0068] The regularization term Z in the objective function ij Set to the squared Euclidean distance between sparse coefficients:

[0069]

[0070] The above optimization problem is solved by using the existing semidefinite programming solver. By solving the semidefinite programming problem, the optimal sparse coefficient matrix α is obtained. i and dictionary matrix D i , so that the fusion result is optimal globally;

[0071] In the solution process, the alternating direction multiplier method is used to gradually approach the global optimal solution to ensure the stability and accuracy of the solution;

[0072] Output the sparse coefficient matrix α after semidefinite programming optimization i and dictionary matrix D i , as the final surveying and mapping result, thus achieving high-precision fusion of multi-source data.

[0073] Preferably, the step of outputting the optimized surveying and mapping data results comprises:

[0074] The sparse coefficient matrix α after semidefinite programming optimization i and dictionary matrix D i Applied to original data source X″ i Reconstruction, calculate the reconstruction result of each data source

[0075]

[0076] in, For data source X″ i The optimized reconstruction result, D i is the optimized dictionary matrix, α i is the optimized sparse coefficient matrix;

[0077] Reconstruction results for all data sources The final surveying and mapping results are generated by integrating and using the weighted average method.

[0078] The present invention also provides a high-precision surveying and mapping device based on multi-source data fusion, comprising:

[0079] A data acquisition module is used to obtain data sources of multiple sensors;

[0080] The data processing module performs data preprocessing, sparse representation model construction, variational inference, sparse coding, graph regularization, and semidefinite programming operations;

[0081] The data output module is used to output the fused surveying and mapping results.

[0082] The present invention also provides a computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, the above method is implemented.

[0083] The present invention also provides a storage medium on which a computer program is stored. When the computer program is executed by a processor, the method described above is implemented.

[0084] The present invention provides a high-precision surveying and mapping method based on multi-source data fusion. It has the following beneficial effects:

[0085] 1. The present invention realizes efficient integration of different data sources through the fusion and optimization of multi-source data, especially by using sparse representation, variational inference, graph theory regularization and semidefinite programming technology. This method effectively reduces the impact of data noise and redundant information, thereby greatly improving the spatial accuracy and representation accuracy of surveying and mapping data, making the final surveying and mapping results more accurate and reliable.

[0086] 2. In the process of data fusion, the present invention enhances the correlation between different data sources through multi-task sparse coding and graph regularization methods. This method ensures that the sparse representations of similar data sources are closer, thereby maintaining data consistency on a global scale. This consistency is crucial to generating unified surveying and mapping results, especially when processing multi-source heterogeneous data.

[0087] 3. The present invention effectively handles the uncertainty in the data by using variational inference technology and accurately estimates the posterior distribution of the sparse representation model. This makes the model more robust in the face of noise, missing data or other uncertainties, thereby improving the reliability and stability of the final mapping results.

[0088] 4. The present invention uses a semidefinite programming method to globally optimize the fusion results to ensure that data processing reaches the optimal solution globally. By introducing efficient optimization algorithms, such as the alternating direction multiplier method (ADMM), the efficiency of data processing is significantly improved, and high-quality surveying and mapping results can be obtained in a shorter time, meeting the high-efficiency requirements in practical applications.

[0089] 5. In the process of data fusion, the present invention introduces weighted average and other methods, so that users can flexibly adjust the weight coefficient according to factors such as the quality of the data source and the signal-to-noise ratio. This adjustable fusion strategy allows users to make personalized settings in different application scenarios to ensure the adaptability and flexibility of the surveying and mapping results.

[0090] 6. The present invention can process multi-source heterogeneous data and improve the accuracy and consistency of the data through multiple optimizations, so its results are suitable for a wide range of surveying and mapping application scenarios. Whether it is urban planning, geographic information system (GIS) construction, or natural resource management, the surveying and mapping method of the present invention can provide high-quality data support and has broad application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0091] Figure 1 It is a schematic diagram of the method flow of the present invention;

[0092] Figure 2 It is a schematic diagram of the structure of the device of the present invention;

[0093] Figure 3 It is a schematic diagram of the computer device structure of the present invention.

[0094] Among them, 10, data acquisition module; 20, data processing module; 30, data output module; 40, computer equipment; 41, processor; 42, memory; 43, storage medium. DETAILED DESCRIPTION

[0095] The following will be combined with the drawings of the present invention specification to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0096] Please see attached Figure 1The embodiment of the present invention provides a high-precision surveying and mapping method based on multi-source data fusion, comprising the following steps:

[0097] S1. Obtain and preprocess data sources

[0098] The present invention first obtains heterogeneous data sources from multiple sensors and performs a series of preprocessing operations on these data sources to ensure the effectiveness and consistency of subsequent data fusion. The preprocessing steps include noise removal, scale standardization, and feature extraction. Through these processing steps, the data sources of different sensors are converted into a unified standardized form, laying the foundation for the subsequent sparse representation model construction.

[0099] In this embodiment, the specific steps are as follows:

[0100] 1. Data source collection:

[0101] In this embodiment, data sources are collected from multiple sensors, where each data source X i It is represented as a multi-dimensional data matrix. Sensor types may include satellite image sensors, aerial photography sensors, LiDAR, and ground measurement equipment. These data sources have different resolutions, scales, and noise characteristics, and are the basic data inputs of the method of the present invention.

[0102] 2. Noise Removal:

[0103] In this embodiment, for each data source X i Noise removal is performed to reduce noise interference in the data. This embodiment uses wavelet transform or median filtering technology to process the data. Wavelet transform can decompose the data into components of different scales, thereby separating the noise components; median filtering removes isolated noise points by performing median operations on the neighborhood pixels of the data to obtain a smoother data matrix.

[0104] 3. Scale standardization:

[0105] In this embodiment, since the data sources of different sensors may have different value ranges and resolutions, for each data source X i Perform scale normalization. This embodiment uses mean normalization or maximum and minimum normalization methods to convert each data source into a unified scale:

[0106]

[0107] Among them, min(X i ) and max(X i ) are data sources X iThrough scale standardization, data from different sources can be processed within the same numerical range, providing a consistent basis for subsequent fusion and analysis.

[0108] 4. Feature extraction:

[0109] In this embodiment, in order to reduce the data dimension and extract key feature information, each standardized data source X′ i Perform feature extraction. This embodiment uses principal component analysis (PCA) technology to calculate the covariance matrix of the data source, perform eigenvalue decomposition on it, retain the main eigenvectors, and form a reduced-dimensional data representation X″ i Specifically, feature extraction is achieved through the following steps:

[0110] Calculate the data source X′ i The covariance matrix of

[0111] Perform eigenvalue decomposition on the covariance matrix and select the principal component vector;

[0112] The data source X′ i Mapped to the principal component space, the reduced-dimensional data representation X″ is obtained i .

[0113] 5. Output preprocessing results:

[0114] In this embodiment, after the above preprocessing operation, multiple preprocessed data sources X" are output. i As the input for the subsequent sparse representation model construction, these preprocessed data sources have been subjected to noise removal, scale standardization, and feature extraction, and can better adapt to the subsequent complex calculation process.

[0115] S2. Sparse representation model construction

[0116] After completing the preprocessing of the data source, the present invention constructs a sparse representation model for each preprocessed data source. Through the sparse representation model, complex high-dimensional data can be represented as a sparse linear combination, thereby simplifying the representation and processing of the data. This step obtains sparse coefficients and dictionary matrices through an optimization method to achieve a concise representation of the data, providing a basis for subsequent data fusion.

[0117] In this embodiment, the specific steps are as follows:

[0118] 1. Sparse representation modeling:

[0119] In this embodiment, the preprocessed data source X″ i Sparse representation modeling is performed. Specifically, each data source is represented as a dictionary matrix D i and the sparse coefficient matrix α i A linear combination of:

[0120] X″ i ≈D i α i

[0121] Among them, the dictionary matrix D i The size is d i ×k, represents the basic characteristic mode of the data source, and the sparse coefficient matrix α i represents the combined weight of these feature patterns in the data. The purpose of this modeling step is to represent the data source as a combination of a few features, thereby achieving a sparse representation of the data.

[0122] 2. Initialization of dictionary and sparse coefficients:

[0123] In this embodiment, the dictionary matrix D i and the sparse coefficient matrix α i Initialize. Dictionary matrix D i It can be initialized randomly or by selecting typical samples after clustering the data; the sparse coefficient matrix α i It is usually initialized to a zero matrix or a small random value to ensure the stability and convergence of the subsequent optimization process.

[0124] 3. Optimization of sparse coefficients:

[0125] In this embodiment, after initialization is completed, the fixed dictionary matrix D i , optimize the sparse coefficient matrix α i The optimization is achieved by solving the following optimization problem:

[0126]

[0127] Where λ is a regularization parameter for controlling sparsity, which is used to adjust the sparsity of sparse coefficients. In order to solve the optimization problem, this embodiment adopts LASSO (least absolute shrinkage and selection operator) or matching pursuit algorithm to iteratively update the sparse coefficient matrix α i , so that it can be maximally sparsified while maintaining the accuracy of the model.

[0128] 4. Dictionary optimization:

[0129] In this embodiment, the sparse coefficient matrix α i After the optimization is completed, the sparse coefficient matrix α is fixed i , optimize the dictionary matrix D i The optimization of the dictionary matrix is ​​achieved by minimizing the reconstruction error. The specific optimization goal is:

[0130]

[0131] The purpose of this step is to adjust the dictionary matrix D given the sparse coefficient matrix i The original data is reconstructed to the greatest extent possible so that the dictionary can more accurately represent the basic characteristics of the data.

[0132] 5. Iterative optimization process:

[0133] In this embodiment, the optimization of the sparse coefficients and the dictionary matrix is ​​performed by alternating iterations. In each iteration, one variable is fixed and another variable is optimized, and the value of the objective function is gradually reduced until convergence. Through continuous iterations, a stable sparse coefficient matrix α is finally obtained. i and dictionary matrix D i , making the sparse representation model optimal.

[0134] 6. Output results:

[0135] In this embodiment, after the above optimization process, the sparse coefficient matrix α is finally output. i and dictionary matrix D i , these results will serve as the basic input for the subsequent data fusion step. These matrices not only simplify the representation of the data, but also retain the main feature information of the data, which is conducive to the efficient fusion of multi-source data in the subsequent steps.

[0136] S3. Variational inference to estimate the posterior distribution

[0137] After obtaining and optimizing the sparse coefficients and dictionary matrix, the present invention further estimates the posterior distribution of the sparse representation model using variational inference techniques. This step aims to process the uncertainty in the data through statistical methods, estimate the probability distribution of the sparse coefficients and dictionary matrix, and thus improve the robustness and accuracy of the model.

[0138] In this embodiment, the specific steps are as follows:

[0139] 1. Set the generation hypothesis of the sparse representation model:

[0140] In this embodiment, it is assumed that the preprocessed data source X″ i is the dictionary matrix D i and the sparse coefficient matrix α i Generated, and assuming that the noise in the data has zero mean and variance σ 2 The specific generation model is assumed to be:

[0141] X″ i =D i α i +∈ i

[0142] in, represents the noise term, which is assumed to be independent and identically distributed Gaussian noise.

[0143] 2. Specify the prior distribution of sparse coefficients and dictionary matrix:

[0144] In this embodiment, in order to estimate the posterior distribution of the sparse coefficients and the dictionary matrix by the Bayesian inference method, it is necessary to first specify the prior distribution for these variables. Assume that the sparse coefficient matrix α i The prior distribution of is a Laplace distribution, which reflects the sparsity characteristics:

[0145] p(α i )∝exp(-λ‖α i ‖1)

[0146] Among them, λ is a hyperparameter that controls sparsity.

[0147] At the same time, assuming that the dictionary matrix D i The prior distribution of is zero mean and variance τ 2 Gaussian distribution of:

[0148]

[0149] Among them, τ is a hyperparameter that controls the distribution of the dictionary matrix.

[0150] 3. Variational inference estimates the posterior distribution:

[0151] In this embodiment, the sparse coefficient matrix α is quantized using variational inference technology. i and dictionary matrix D i The core idea of ​​variational inference is to approximate the complex true posterior distribution p(αi, Di|X″) by setting a simple variational distribution q(αi, Di) i ), and make the two as close as possible through optimization methods.

[0152] Specifically, by minimizing the variance between the variational distribution q(αi, Di) and the true posterior distribution p(αi, Di|X″ i ) to achieve this approximation:

[0153] KL(q(α i , D i )||p(α i , D i |X″ i ))

[0154] The KL divergence is defined as:

[0155]

[0156] The variational distribution q(αi, Di) is optimized by the variational Bayesian method or the stochastic gradient descent method, gradually approaching the true posterior distribution until convergence.

[0157] 4. Output the posterior distribution results:

[0158] In this embodiment, after the optimization converges, the posterior distribution of the estimated sparse coefficient matrix αi and the dictionary matrix Di is output. The posterior distribution is used to represent the uncertainty of the sparse coefficients and the dictionary matrix in the sparse representation model, providing a more robust basis for the subsequent data fusion step.

[0159] Through the above steps, the posterior distribution of the sparse representation model is effectively estimated, which makes the model more adaptable when facing noise and data uncertainty, and further improves the effect of subsequent data fusion and optimization.

[0160] S4, multi-task sparse coding fusion

[0161] After estimating the posterior distribution of the sparse representation model using variational inference techniques, the present invention further fuses the sparse coefficients of multiple data sources based on a multi-task sparse coding method. This step aims to capture the shared information between different data sources by jointly optimizing the sparse representation of multiple data sources, thereby improving the overall consistency and accuracy of data fusion.

[0162] In this embodiment, the specific steps are as follows:

[0163] 1. Construction of multi-task sparse coding model:

[0164] In this embodiment, each data source X″ i The sparse representation result αi of αi is regarded as an independent task. The sparse coefficient matrices αi corresponding to multiple data sources are regarded as multiple tasks in the multi-task sparse coding model. By jointly modeling these tasks, the shared information between different data sources can be captured, so that the data sources can complement and strengthen each other in the fusion process.

[0165] 2. Define the optimization objective function of multi-task sparse coding:

[0166] In this embodiment, the optimization objective function is used to jointly optimize multiple tasks. The sparse representation αi of each task is obtained by its corresponding dictionary D i It means that the optimization objective function is defined as:

[0167]

[0168] Among them, λ iis the regularization parameter for controlling sparsity, which adjusts the sparsity of the sparse coefficient; γ is the regularization parameter for controlling the consistency between the sparse coefficients of different tasks, which adjusts the similarity and correlation between tasks.

[0169] 3. Optimization process:

[0170] In this embodiment, first fix the sparse coefficient α of other tasks j (j≠i), optimize the sparse coefficient αi of each task. The specific optimization process uses the gradient descent method or the alternating direction multiplier method (ADMM) to solve:

[0171] While fixing the sparse coefficients of other tasks, optimize the sparse coefficient αi of a single task to minimize the sparse representation error in the current task.

[0172] The optimization process is carried out alternately, and by gradually updating the sparse coefficients of each task, the sparse coefficient matrix αi of all tasks finally reaches the global optimal solution.

[0173] 4. Output of sparse coefficient matrix after fusion:

[0174] In this embodiment, after the optimization process converges, the fused sparse coefficient matrix αi is output, which represents the sparse representation results of each data source after being optimized by the multi-task sparse coding model. This fusion result is used as the final data fusion output, laying the foundation for subsequent graph regularization processing and further optimization.

[0175] Through the above steps, the present invention can effectively fuse the sparse representations of multiple data sources, while maintaining the independent characteristics of each data source, making full use of the shared information between different data sources, thereby enhancing the overall consistency and accuracy of data fusion.

[0176] S5. Graph Theory Regularization Enhances Relevance

[0177] After completing the fusion of the sparse coefficients of multiple data sources, the present invention further enhances the correlation between the data sources through a graph theory regularization method. This step constructs a graph model to represent the relationship between data sources, and uses a graph theory regularization term to enhance the similarity between the sparse coefficients of different data sources to achieve a more consistent data fusion effect.

[0178] In this embodiment, the specific steps are as follows:

[0179] 1. Build a graph model:

[0180] In this embodiment, a graph model G = (V, E) representing the relationship between multiple data sources is first constructed. In this graph model, the node set V represents the data source nodes, and each node corresponds to a data source; the edge set E represents the connection relationship between the nodes, reflecting the similarity or correlation between the data sources.

[0181] 2. Define the weight matrix of the graph:

[0182] In this embodiment, in order to quantify the similarity between data sources, a weight matrix W is defined in the graph model. Each element W of the weight matrix W ij Indicates data source X″ i and data source X″ j The specific calculation formula is:

[0183]

[0184] Among them, σ is a parameter that controls the similarity sensitivity between data sources, ‖X″ i -X″ j || indicates data source X″ i and X″ j In this way, the weight matrix can effectively reflect the similarity between different data sources.

[0185] 3. Introduce graph regularization term:

[0186] In this embodiment, in order to enhance the correlation between sparse coefficients of different data sources, a graph regularization term is introduced. The form of the graph regularization term is:

[0187]

[0188] Among them, α i and α j They are respectively data source X″ i and X″ j The regularization term penalizes the differences between sparse coefficients, making the sparse coefficients of similar data sources closer, thereby enhancing the correlation between data sources as a whole.

[0189] 4. Form a new optimization problem:

[0190] In this embodiment, the graph regularization term is introduced into the optimization objective function of multi-task sparse coding to form a new optimization problem. The specific form of the optimization problem is:

[0191]

[0192] By introducing the graph regularization term, the new optimization problem not only considers the reconstruction error of each data source, but also adjusts the similarity between the sparse coefficients of different data sources through the weight matrix W.

[0193] 5. Optimization algorithm solution:

[0194] In this embodiment, an optimization algorithm is used to solve the above optimization problem. Commonly used solution methods include gradient descent method, alternating direction multiplier method (ADMM), etc. Through the iterative solution of the optimization algorithm, the sparse coefficient matrix α is ensured to be i The similarity between them is matched with the weight matrix W of the graph model, thereby enhancing the correlation between the data sources.

[0195] 6. Output results:

[0196] In this embodiment, after the optimization process is completed, the sparse coefficient matrix α after graph theory regularization is output. i These sparse coefficient matrices will be used in subsequent semidefinite programming optimization processing to provide a more consistent and relevant information basis for the final surveying and mapping data output.

[0197] Through the above steps, the graph theory regularization method effectively enhances the correlation between various data sources, making the sparse representation after data fusion more consistent in structure, which helps to improve the overall effect of subsequent data processing and analysis.

[0198] S6. Semidefinite programming optimization to obtain the global optimal solution

[0199] After enhancing the correlation between data sources through graph regularization, the present invention further optimizes the fusion results using semidefinite programming methods to ensure that data fusion is optimal in the global scope. Through this step, the correlation between data sources can be maximized while ensuring the accuracy of sparse representation, thus achieving high-precision fusion of multi-source data.

[0200] In this embodiment, the specific steps are as follows:

[0201] 1. Introduce sparse coefficient matrix into the semidefinite programming model:

[0202] In this embodiment, the sparse coefficient matrix α after graph theory regularization is i Introduced into the semidefinite programming (SDP) model. The semidefinite programming model can effectively handle convex optimization problems with matrix variables, so it is very suitable for optimizing the overall structure of sparse representation.

[0203] 2. Set optimization goals:

[0204] In this embodiment, the optimization goal is set to maximize the correlation between data sources while ensuring the accuracy of sparse representation. Specifically, the optimization goal is to minimize the sparse representation error and the correlation deviation between data sources, so as to achieve the optimal solution in the global scope.

[0205] 3. Construct the objective function of the semidefinite programming problem:

[0206] In this embodiment, an objective function of a semidefinite programming problem is constructed, and the objective function includes a sparse representation error term and a graph regularization term. The objective function is in the form of:

[0207]

[0208] Among them, Z is a semidefinite positive matrix, Z ij Represents the sparse coefficient α i and α j The correlation between them, trace(Z) is the trace of matrix Z, which is used to measure the overall quality of the optimization objective.

[0209] 4. Define the regularization term:

[0210] In this embodiment, the regularization term Z in the objective function is ij It is set to the square form of the Euclidean distance between sparse coefficients to ensure that the correlation deviation is minimized. The specific formula is:

[0211]

[0212] Through this definition, it can be ensured that during the optimization process, the sparse coefficients of similar data sources are closer, thereby enhancing the consistency of data fusion.

[0213] 5. Solve semidefinite programming problems:

[0214] In this embodiment, the above optimization problem is solved using an existing semidefinite programming solver (such as CVX). The solution of the semidefinite programming problem can gradually approach the global optimal solution through the alternating direction multiplier method (ADMM), ensuring the stability and accuracy of the solution during the optimization process.

[0215] 6. Output optimization results:

[0216] In this embodiment, the optimal sparse coefficient matrix α is obtained by solving the semidefinite programming problem. i and dictionary matrix D i These optimized matrices represent the data fusion results after global optimization, ensuring that the surveying and mapping data achieves the best quality globally.

[0217] The final output sparse coefficient matrix α i and dictionary matrix D iAs the final surveying and mapping result, it provides a solid foundation for the high-precision fusion of multi-source data. Through this global optimization step, the present invention can significantly improve the accuracy and consistency of data fusion and is applicable to various complex surveying and mapping application scenarios.

[0218] S7. Output optimized surveying and mapping data results

[0219] After completing the semidefinite programming optimization, the present invention generates the final mapping information by outputting the optimized mapping data results. This step involves applying the optimized sparse coefficient matrix and dictionary matrix to the reconstruction of the original data source, and integrating the reconstruction results of all data sources to generate a unified mapping data result.

[0220] In this embodiment, the specific steps are as follows:

[0221] 1. Reconstruct the data source:

[0222] In this embodiment, the sparse coefficient matrix α after semidefinite programming optimization is i and dictionary matrix D i Applied to original data source X″ i The reconstruction process is carried out through the following formula:

[0223]

[0224] in, For data source X″ i The optimized reconstruction result, D i is the optimized dictionary matrix, α i is the optimized sparse coefficient matrix. Through this step, the optimized representation of each data source can be obtained.

[0225] 2. Integrate the reconstruction results:

[0226] In this embodiment, the reconstruction results of all data sources are The integration process is achieved through the weighted average method, and the specific formula is:

[0227]

[0228] Among them, w i The weight coefficient for each data source can be set according to the quality of the data source, signal-to-noise ratio and other indicators. Through weighted integration, a final mapping result X that comprehensively reflects the information of all data sources can be obtained. final .

[0229] 3. Evaluate and adjust:

[0230] In this embodiment, in order to ensure the accuracy and consistency of the output results, the integrated surveying and mapping results Xfinal Evaluation can be performed. The evaluation method can include calculating indicators such as mean square error (MSE) and peak signal-to-noise ratio (PSNR) to measure the reconstruction accuracy and consistency of the results. If the evaluation result does not meet the expected standard, the weight coefficient w can be adjusted. i Or re-optimize the sparse coefficients and dictionary matrix for further adjustment and optimization.

[0231] 4. Output the final surveying and mapping results:

[0232] In this embodiment, after completing the integration of the reconstruction results, the final surveying and mapping data result X is output. final The result is high-precision data after multiple optimization processes, with good spatial consistency and mapping accuracy.

[0233] Through the above steps, the present invention can effectively integrate and optimize the information of multiple data sources when generating the final surveying and mapping results, ensure the high accuracy and consistency of the output data, and meet the actual needs of high-precision surveying and mapping.

[0234] The high-precision surveying and mapping device based on multi-source data fusion described below and the high-precision surveying and mapping method based on multi-source data fusion described above can refer to each other.

[0235] Please see attached Figure 2 The present invention also provides a high-precision surveying and mapping device based on multi-source data fusion, comprising:

[0236] A data acquisition module 10 is used to obtain data sources of multiple sensors;

[0237] The data processing module 20 performs data preprocessing, sparse representation model construction, variational inference, sparse coding, graph regularization and semidefinite programming operations;

[0238] The data output module 30 is used to output the fused surveying and mapping results.

[0239] The device of this embodiment can be used to execute the above method embodiment, and its principles and technical effects are similar, which will not be repeated here.

[0240] Please see attached Figure 3 The present invention further provides a computer device 40, comprising: a processor 41 and a memory 42, wherein the memory 42 stores a computer program executable by the processor, and when the computer program is executed by the processor, the above method is executed.

[0241] The present invention further provides a storage medium 43 on which a computer program is stored. When the computer program is run by the processor 41, the above method is executed.

[0242] Among them, the storage medium 43 can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as static random access memory (SRAM), electrically erasable programmable read-only memory (EEPROM), erasable programmable read-only memory (EPROM), programmable red-only memory (PROM), read-only memory (ROM), magnetic storage, flash memory, disk or optical disk.

[0243] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A high-precision surveying and mapping method based on multi-source data fusion, characterized in that: The following steps are involved: Acquire data sources from multiple sensors and pre-process the data sources; A sparse representation model is constructed for each preprocessed data source, and sparse coefficients and dictionaries are obtained through optimization methods; estimating the posterior distribution of the sparse representation model using variational inference techniques; The sparse coefficients of multiple data sources are fused based on the multi-task sparse coding method; Enhance the correlation between data sources through graph theory regularization method; The fusion results are optimized using the semidefinite programming method to obtain the global optimal solution; Output optimized surveying and mapping data results.

2. The high-precision surveying and mapping method based on multi-source data fusion according to claim 1 is characterized in that: The step of obtaining data sources from a plurality of sensors and preprocessing the data sources comprises: Collect data sources from multiple sensors, where each data source X i is a multidimensional data matrix; De-noising the data source to suppress noise components in the data; The data sources are scaled and normalized to the same scale. i Convert to Where min(X i ) and max(X i ) are data sources X i The minimum and maximum values ​​of Extract features from the data source, perform dimensionality reduction on the data source through principal component analysis, calculate the covariance matrix of the data source, perform eigenvalue decomposition on it, retain the main eigenvectors to form a data representation X' after dimensionality reduction i '; Output preprocessed multiple data sources X' i 'For subsequent sparse representation model construction.

3. The high-precision surveying and mapping method based on multi-source data fusion according to claim 1 is characterized in that: The step of constructing a sparse representation model for each preprocessed data source and obtaining sparse coefficients and a dictionary by an optimization method comprises: For the preprocessed data source X' i 'Perform sparse representation modeling and represent each data source as a dictionary matrix D i and the sparse coefficient matrix α i The linear combination of X″ i ≈D i α i , where D i For size d i ×k dictionary matrix, α i is a sparse coefficient matrix; Initialize the dictionary matrix D i and the sparse coefficient matrix α i ; Fixed dictionary matrix D i , the sparse coefficient matrix α is obtained by solving the following optimization problem i : Among them, λ is the regularization parameter that controls sparsity, and is solved using LASSO or matching pursuit algorithm; Fixed sparse coefficient matrix α i , optimize the dictionary matrix D by minimizing the reconstruction error i , that is, solved by the following objective function: Alternately iterate the optimization steps of the above sparse coefficient matrix and dictionary matrix until convergence to obtain the final sparse coefficient matrix α i and dictionary matrix D i ; Output sparse coefficient matrix α i and dictionary matrix D i For subsequent data fusion processing.

4. The high-precision surveying and mapping method based on multi-source data fusion according to claim 1 is characterized in that: The step of estimating the posterior distribution of the sparse representation model using the variational inference technique comprises: Set the generation hypothesis of the sparse representation model, assuming that the preprocessed data source X' i 'From the dictionary matrix D i and the sparse coefficient matrix α i Generated, and the noise of the data source has zero mean and variance σ 2 Gaussian distribution of: X″ i =D i a i +∈ i in, is the sparse coefficient matrix α i and dictionary matrix D i Specify the prior distribution, assuming α i The prior distribution of is Laplace distribution, and the dictionary matrix D i The prior distribution of is a Gaussian distribution: Among them, λ and τ are hyperparameters that control sparsity and dictionary matrix distribution respectively; Estimate the posterior distribution p(αi,Di|X') through variational inference techniques i '), set the variational distribution q(αi,Di) to approximate the true posterior distribution; Minimize the KL divergence between the variational distribution and the true posterior distribution: KL(q(α i ,D i )||p(α i ,D i |X″ i )) Among them, KL divergence is defined as: Optimize the variational distribution q(αi,Di) by the variational Bayesian method or the stochastic gradient descent method until convergence, and obtain the variational distribution parameters that approximate the true posterior distribution; The output estimated sparse coefficient matrix αi and the posterior distribution of the dictionary matrix Di are used to improve the robustness and accuracy of data fusion.

5. The high-precision surveying and mapping method based on multi-source data fusion according to claim 1 is characterized in that: The step of fusing sparse coefficients of multiple data sources based on the multi-task sparse coding method includes: Set each data source X″ i The sparse representation result αi is regarded as a task, and multiple tasks are jointly modeled through a multi-task sparse coding model to capture the shared information between different data sources; Define the optimization objective function of multi-task sparse coding, where the sparse representation αi of each task is represented by its corresponding dictionary Di, and the optimization objective function is: Among them, λ i is the regularization parameter for controlling sparsity, and γ is the regularization parameter for controlling the consistency between the sparse coefficients of different tasks; By optimizing this objective function, we first fix the sparse coefficients α of other tasks. j (j≠i), optimize the sparse coefficient αi of each task and use the gradient descent method or the alternating direction multiplier method to solve it; The sparse coefficient αi of each task is updated alternately, gradually approaching the global optimal solution, ensuring that the sparse representations between different data sources can fully integrate shared information; The fused sparse coefficient matrix αi is output as the final data fusion result for subsequent graph regularization processing and optimization.

6. The high-precision surveying and mapping method based on multi-source data fusion according to claim 1 is characterized in that: The step of enhancing the correlation between data sources by using a graph theory regularization method includes: Construct a graph model G = (V, E) representing the relationship between multiple data sources, where V represents the data source node and E represents the connection relationship between the nodes; Define the weight matrix W of the graph, where each element W ij Indicates data source X″ i and data source X' j 'The similarity between them, the calculation formula of the weight matrix W is: Among them, σ is a parameter that controls the sensitivity of similarity between data sources, ||X″ i -X″ j || indicates data source X' i 'and X' j 'The Euclidean distance between A graph regularization term is introduced to enhance the correlation between sparse coefficients of different data sources. The form of the graph regularization term is: Among them, α i and α j They are respectively data source X″ i and X″ j The sparse coefficient of The graph regularization term is introduced into the optimization objective function of multi-task sparse coding to form a new optimization problem: The optimization problem is solved by using an optimization algorithm to ensure that the sparse coefficient matrix α i The similarity between them is matched with the weight matrix W of the graph model, thereby enhancing the correlation between data sources; Output the sparse coefficient matrix α after graph theory regularization i , which is used for subsequent semidefinite programming optimization processing.

7. The high-precision surveying and mapping method based on multi-source data fusion according to claim 1 is characterized in that: The step of optimizing the fusion result by using the semidefinite programming method to obtain the global optimal solution includes: The sparse coefficient matrix α after graph theory regularization i It is introduced into the semidefinite programming model, and the optimization goal is set to maximize the correlation between data sources while ensuring the accuracy of sparse representation; Construct the objective function of the semidefinite programming problem, which includes the sparse representation error term and the graph regularization term. The objective function form is: Among them, Z is a semidefinite positive matrix, Z ij Represents the sparse coefficient α i and α j The correlation between them, trace(Z) is the trace of the matrix Z, which represents the overall quality of the optimization objective; The regularization term Z in the objective function ij Set to the squared Euclidean distance between sparse coefficients: The above optimization problem is solved by using the existing semidefinite programming solver. By solving the semidefinite programming problem, the optimal sparse coefficient matrix α is obtained. i and dictionary matrix D i , so that the fusion result is optimal globally; In the solution process, the alternating direction multiplier method is used to gradually approach the global optimal solution to ensure the stability and accuracy of the solution; Output the sparse coefficient matrix α after semidefinite programming optimization i and dictionary matrix D i , as the final surveying and mapping result, thus achieving high-precision fusion of multi-source data.

8. The high-precision surveying and mapping method based on multi-source data fusion according to claim 1 is characterized in that: The step of outputting the optimized surveying and mapping data results comprises: The sparse coefficient matrix α after semidefinite programming optimization i and dictionary matrix D i Applied to the original data source X' i 'Reconstruction, calculate the reconstruction result of each data source in, For data source X″ i The optimized reconstruction result, D i is the optimized dictionary matrix, α i is the optimized sparse coefficient matrix; Reconstruction results for all data sources The final surveying and mapping results are generated by integrating and using the weighted average method.

9. A high-precision surveying and mapping device based on multi-source data fusion, used to implement the method according to any one of claims 1 to 8, characterized in that: include: A data acquisition module is used to obtain data sources of multiple sensors; The data processing module performs data preprocessing, sparse representation model construction, variational inference, sparse coding, graph regularization, and semidefinite programming operations; The data output module is used to output the fused surveying and mapping results.

10. A storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method according to any one of claims 1 to 8 is implemented.

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