Water conservancy application unmanned aerial vehicle positioning method based on CSI and machine learning

Abstract

The application discloses a water conservancy application unmanned plane positioning method based on CSI and machine learning, relates to the technical field of wireless positioning and intelligent water conservancy monitoring, and first divides a target three-dimensional space into multiple subspaces, collects CSI data and constructs a preliminary fingerprint map; further, a CSI tensor containing amplitude and phase information is constructed, and a representative feature is extracted by using a HOSVD decomposition method; subsequently, a UMAP algorithm is used for visual analysis and structure discovery of the feature, a feature set is optimized in combination with a feature selection strategy based on mutual information, and a refined fingerprint map is reconstructed; finally, a RNN network with a BiLSTM module is used for coding and learning of the optimized space-time feature, and the position of the unmanned plane in the three-dimensional space is recognized and tracked through the dynamic change of the CSI. The application can effectively overcome signal interference caused by strong reflection on the water surface and dam shielding, and realize high-precision unmanned plane positioning in a water conservancy complex environment.

Description

Technical Field

[0001] This invention relates to the field of water conservancy engineering monitoring and wireless communication sensing technology, and in particular to a UAV positioning method for water conservancy applications based on CSI and machine learning. Background Technology

[0002] With the advancement of smart water conservancy construction, drones are increasingly widely used in areas such as reservoir dam safety inspections, river sewage outlet inspections, hydrological station inspections, and flood disaster emergency monitoring. Their efficient inspection operations rely on precise autonomous positioning and navigation. While GNSS (Global Navigation Satellite System) can provide meter-level positioning in open areas, water conservancy scenarios typically have unique characteristics. For example, large areas of calm water can cause strong specular reflections, leading to severe multipath effects; concrete structures such as dams and sluices can obstruct GNSS signals; and in long-distance river inspections, traditional visual positioning is easily affected by lighting and water mist.

[0003] Wireless signal-based sensing and positioning technology offers a new approach to solving the aforementioned problems. Traditional RSSI (Received Signal Strength Indication) methods exhibit significant fluctuations and poor stability in aquatic environments. CSI (Channel State Information) contains finer-grained physical layer information, better characterizing multipath propagation environments. While CSI provides fine-grained information, extracting location-related features from the unique high-reflectivity and high-humidity environment of waterways, and adapting to spatiotemporal changes brought about by UAV movement, remains a key challenge for achieving high-precision positioning. Summary of the Invention

[0004] To address the above technical problems, this invention provides a method for unmanned aerial vehicle (UAV) positioning in water conservancy applications based on CSI and machine learning, comprising the following steps: Step S1: Divide the target area into multiple three-dimensional subspaces, and collect Channel State Information (CSI) data from multiple WiFi links by traversing all subspaces; Step S2: Preprocess the acquired CSI data, including noise filtering, phase correction, outlier removal, and data normalization. Step S3: Integrate the amplitude and phase information of all OFDM subcarriers to construct the CSI tensor and form a preliminary wireless fingerprint map containing the original fingerprint features; use the HOSVD decomposition method to decompose the CSI tensor into low-dimensional tensors and extract representative features. Step S4: Use the UMAP algorithm to perform visual analysis of the features to discover hidden structures, and combine it with an information theory-based feature selection method to optimize the feature set and reconstruct the fingerprint map; Step S5: Using a recurrent neural network (RNN) with a long short-term memory (BiLSTM) module, referred to as the RNN-BiLSTM model, time-dependent encoding and abstract representation learning are performed on the optimized features. The specific location of the UAV in the perceived three-dimensional space is identified by CSI changes.

[0005] The technical solution further defined in this invention is: Furthermore, step S1 specifically includes the following sub-steps: Step S1.1: Based on the MIMO-OFDM system architecture, the target area is divided into multiple three-dimensional subspaces, with at least one fixed access point (AP) set in each subspace. The UAV, acting as a mobile receiver, is equipped with an M-element uniform linear array antenna and establishes a communication link with the AP. Analyzing a single subspace, we assume there are L signal propagation paths, and the spacing between the receiving antenna elements is d. For the l-th signal path, the corresponding angle of arrival (AoA) is expressed as... It is the azimuth angle of the l-th signal. and pitch angle The function, that is, in three-dimensional space The attenuation experienced by the WiFi signal reaching the antenna array along the l-th propagation path is represented as: Each signal path is associated with two parameters, including attenuation and AoA; the phase offset of the m-th antenna relative to the first receiving antenna in the array is expressed as... , where c is the speed of light in air and f is the carrier frequency; For the l-th propagation path, the phase difference is expressed as a complex exponential function of the angle of arrival: ; Where j is the imaginary unit; For the l-th signal path, the AoA vector at the antenna array is expressed by the above formula as follows: ; Where T represents the transpose operation. The steering vector is represented by: For all signal propagation paths, the overall steering matrix of the antenna array is expressed as: ; The received signal vector s is formed by superimposing the signals from each path. ,in It is a complex decay vector along all paths. Let L be the complex attenuation vector of the Lth path; in a MIMO-OFDM system, there are a total of The nth subcarrier has several subcarriers of different frequencies; the received vector on the nth subcarrier contains not only path attenuation and AoA information, but also a superimposed Doppler phase term; assuming the radial velocity of the UAV is v, the additional Doppler phase of the l-th path on the nth subcarrier is: ; in, Let λ be the wavelength of the nth subcarrier, and k be the current sampling time; diagonalize the Doppler phase to construct the Doppler compensation matrix. ;according to and Then the actual received vector of the nth subcarrier after Doppler frequency offset for: ; Construct a measurement matrix for all subcarriers of the antenna array. As shown in the following formula: ; in, It is the vector received on all subcarriers, and It is the complex attenuation matrix of L signal paths on all subcarriers; therefore, receiving signals from M antennas via a MIMO-OFDM system... The CSI matrix of each subcarrier is expressed as follows: ; in, This represents the CSI value on the nth subcarrier of the m-th antenna; when the moving target is in different positions in three-dimensional space, the propagation paths are different from each other, thus distinguishing AoA and attenuation; Step S1.2: Combine the amplitude and phase information of the CSI matrix at K consecutive time points, and collect CSI measurements by traversing each target area to initially realize a radio map; use all CSI measurements from all subcarriers on the antenna array to construct a tensor. For a set of CSI measurements, the CSI tensor is represented as: ; in, It includes amplitude attenuation and phase shift, both of which are real values; This is the measurement matrix for all subcarriers of the antenna array.

[0006] As described above, in a method for UAV positioning in water conservancy applications based on CSI and machine learning, in step S3, the CSI tensor is denoted as... M represents the number of receiving antennas, N represents the number of subcarriers in the MIMO-OFDM system, and K represents the number of time sampling points; HOSVD decomposition is used to extract features from the CSI tensor, the specific process of which includes: The third-order CSI tensor Modal expansion is performed along the three dimensions of antenna, subcarrier, and time, resulting in three mode matrices: ; Perform singular value decomposition (SVD) on each pattern matrix to obtain the left singular vector matrix, which serves as the orthogonal basis matrix for the corresponding dimension. ; in, , , Let f be a left singular matrix, and f be three orthogonal basis matrices in three dimensions; , , It is a diagonal matrix, and the diagonal elements are singular values; , , , where is a right singular matrix, and are orthogonal basis matrices for the three input dimensions respectively; The core tensor is obtained by multiplying the CSI tensor. : ; in, This represents the product operation of the e-th modulus tensor. Represents the core tensor; Singular value sequence for each pattern matrix Calculate the cumulative energy percentage Choose the smallest r such that r is a preset threshold, and the truncation rank is determined accordingly. , and Preserve the core tensor Center front , and The components corresponding to the maximal singular values ​​yield the truncated core tensor. and the corresponding truncated orthogonal basis matrix , , ; the truncated spatial dimension factor matrix As a representative feature, it is used to construct the initial localization fingerprint map.

[0007] As described above, in a method for UAV positioning in water conservancy applications based on CSI and machine learning, step S4 involves constructing a fuzzy topological structure in a high-dimensional space. Specifically, this involves: for the factor matrix... The feature set obtained First, for each data point Find its z nearest neighbors in the high-dimensional space; then calculate Its j-th nearest neighbor Distance between ; Define high-dimensional space and Weight of connected edges This weight is modeled using an adaptive exponential kernel function based on local connectivity: ; in, yes The distance to its nearest neighbor; It is a scale parameter, determined through binary search, such that each point... The sum of the locally fuzzy simplexes is a constant. ; ; in, for The j-th nearest neighbor, For local density estimation; To ensure symmetry and obtain a joint probability representation in high-dimensional space, a fuzzy simplex is constructed: ; in, Representation of features and Similarity in high-dimensional manifold structures.

[0008] As described above, in a UAV localization method for water conservancy applications based on CSI and machine learning, step S4 defines the similarity of the low-dimensional embedding space. Specifically, in a low-dimensional embedding space with a target dimension of 2 or 3, for corresponding points... and The similarity between the two is defined using a smooth family of piecewise functions. This is used to capture the global topology of a manifold, and is specifically defined as follows: ; Among them, parameters and The fuzzy simplex is set by fitting nonlinear least squares to a high-dimensional distance to maintain adjacency relationships at different scales in the low-dimensional space.

[0009] As described above, in a UAV localization method for water conservancy applications based on CSI and machine learning, step S4 optimizes the low-dimensional embedding to minimize topological differences. Specifically, UMAP minimizes the high-dimensional fuzzy simplex. Low-dimensional representation The cross-entropy between them is used to optimize the low-dimensional embedding, and the objective function is: ; The attraction term encourages connected edges in P to remain adjacent in Q, while the repulsion term drives non-adjacent points in P to move away from each other in Q, thus preserving both the local and global topology of the data. This objective function, with respect to low-dimensional coordinates... The gradient is used for gradient-based optimization, and its gradient calculation formula is: ; When using When the gradient is simplified to its simplified form, it further simplifies to: .

[0010] As described above, in a method for locating unmanned aerial vehicles (UAVs) for water conservancy applications based on CSI and machine learning, step S4 involves the feature set from factor matrix A. The entropy is expressed as: ; in, This indicates a feature belonging to X. yes The probability of X among all values; the conditional entropy of X given a category label Y is expressed by the following formula: ; Where Y represents the location label in three-dimensional space. express The prior probability; This represents conditional probability, used to show the uncertainty of X given Y; based on the preliminary clustering visualization analysis of the feature dataset using UMAP, the Euclidean distance is used to obtain the cluster centers, corresponding to different category labels. Cluster center Given features With cluster center The distance between them is further transformed into information about The probability problem of Y, for The probability that a value belongs to a certain category label is expressed by the following formula: ; The information gain between features and category labels is used to calculate the specific information shared by X and Y: ; in, Indicates about and The joint probability, and due to symmetry, is known. When they are independent, their mutual information will be zero.

[0011] As described above, in a method for UAV localization in water conservancy applications based on CSI and machine learning, step S4 employs a forward sequential search strategy to continuously add dominant features to the optimized feature dataset; the selected feature dataset is denoted as... Initially, it is an empty set, and Y is the category label of the position in 3D space; express A specific feature; assumption As a decision-making standard, among which The larger the value, the stronger the feature The more meaningful it is, the more meaningful it becomes; in feature selection based on the unified conditional likelihood maximization framework, given features... The specific decision criteria are mathematically defined as follows: ; in, Representing mutual information, Y is the location category label. For the currently selected feature subset, Represents two variables and The function; assuming If a function is represented as a linear function, then it is called a decision criterion or decision standard based on a linear combination of Shannon information items. Used to evaluate features Its importance is defined as: ; in, and The parameter is a non-negative parameter between 0 and 1; the maximum value is selected through iterative selection. Based on the characteristics, an optimized feature set is obtained.

[0012] As described above, a method for locating unmanned aerial vehicles (UAVs) in water conservancy applications based on CSI and machine learning includes the following sub-steps in step S5: Step S5.1: Take the optimized feature sequence from step S4 as input. The input vector of the model is represented as: ; Where T represents the transpose operation. These are the features being optimized; Step S5.2: The RNN-BiLSTM model utilizes P sets of optimized features to make decisions. The BiLSTM consists of a forward LSTM layer and a backward LSTM layer. This represents the input of the RNN-BiLSTM model at step p. and These represent the hidden layers of the forward and backward RNN-BiLSTM models at the p-th step, respectively, with corresponding sizes of... The RNN-BiLSTM model also includes an additional unit state. It is used to control the flow of meaningful information through input gates, forget gates, and output gates; at each time step p, the forward LSTM unit computes the input gate. Forgotten Gate Output gate : ; For backward LSTM unit calculation of input gate Forgotten Gate Output gate : ; in, , , , and Here are the weight matrices, with sizes of [sizes to be filled in]. and ; and The bias vector has a size of ; The sigmoid functions associated with the three gates, In the RNN-BiLSTM model, both the cell state and the hidden layer are initialized to zero. Step S5.3, Forward LSTM Cell Status and hidden state The update is as follows: ; LSTM cell states before and after and hidden state The update is as follows: ; in, It represents the Hadamardi (or Hadama) stack; and They are all activation functions; Step S5.4: Concatenate the forward and backward hidden states to obtain the bidirectional hidden state: ; The bidirectional hidden state at the last time step P is taken as the representation of the entire sequence and mapped to the UAV's 3D coordinates through a fully connected layer: ; in, The size is is the weight matrix of the fully connected output layer, which represents the bidirectional hidden state of the BiLSTM at the last time step. Linear mapping to 3D spatial coordinates output; For bias, It includes all available parameters in the RNN-BiLSTM model.

[0013] As described above, a UAV positioning method for water conservancy applications based on CSI and machine learning is used. In step S5, all locations within the water conservancy facility area to be inspected are numbered according to the regional division. A training dataset (X, Y) is constructed using optimized features and category labels, where X represents the obtained feature set, which serves as the input to the BiLSTM model, and Y is the corresponding real 3D location coordinate label. As a dataset for training and validating neural networks, it contains There are 1000 sample pairs; all available parameters are optimized along the direction of minimizing the cost function, which is defined as the mean squared error of all samples. ; in, It is the number of elements in the dataset. The true three-dimensional position coordinates of the g-th sample; This is the prediction output of the BiLSTM model for the g-th sample, i.e. ; Denotes the square of the Euclidean norm, i.e. .

[0014] The beneficial effects of this invention are: (1) In this invention, high-order singular value decomposition (HOSVD) is used to perform multilinear algebraic decomposition on the CSI tensor, decoupling the coupled information of the three dimensions of antenna, subcarrier and time into mutually orthogonal basis matrices and core tensors. Compared with traditional Tucker and CP decomposition, HOSVD directly performs standard singular value decomposition after modulus expansion, avoiding the local optimum problem that may be introduced by alternating least squares iteration. The decomposition result is more stable and reliable. At the same time, it can dynamically retain the dominant singular components according to the channel complexity of different water conservancy scenarios. The method of this invention effectively suppresses the noise interference caused by strong water surface reflection and dam blockage, extracts the most discriminative spatial features, and retains location-related information while reducing the feature dimension, providing a high-quality feature dataset for subsequent positioning, and reducing the computational complexity and accuracy of feature extraction. (2) In this invention, the soft membership degree of UMAP fuzzy clustering is used as the conditional probability estimate. The conditional mutual information (CMI) forward search strategy is introduced to construct a comprehensive evaluation function that takes into account both relevance and redundancy. UMAP constructs a fuzzy simplex representation of a high-dimensional manifold based on fuzzy topology theory. By minimizing cross-entropy, the local and global topological structures of the data are preserved. The CMI criterion optimizes the relevance between features and location labels and the redundancy between features during the iteration process, and accurately selects the most discriminative and independent feature subsets. The deep integration of the two can efficiently remove redundant features introduced by water surface reflection and multipath interference, significantly reduce the dimension of the fingerprint database, reduce the risk of model overfitting, improve the robustness of localization and training efficiency, and is suitable for complex water conservancy environments such as rivers and reservoirs with severe multipath interference. (3) In this invention, a bidirectional long short-term memory network (BiLSTM) is used to perform time-series modeling on the optimized CSI feature sequence. The forward LSTM and backward LSTM capture the forward evolution trend and backward backtracking information of the signal, respectively. The hidden states in the two directions are spliced ​​together to obtain a bidirectional hidden representation containing the complete context. The gating mechanism and cell state update rules of BiLSTM can selectively remember long-term useful location-related information and forget instantaneous noise interference, thus achieving effective signal-noise separation in the time dimension. In the water conservancy inspection scenario, this method can effectively cope with complex situations such as continuous changes in water surface reflection angle, gradual changes in dam obstruction, and Doppler frequency shift fluctuations, and achieve sub-meter level three-dimensional positioning accuracy. Attached Figure Description

[0015] Figure 1 This is a schematic diagram of the overall process of the present invention; Figure 2 This is a schematic diagram of the structure of the RNN-BiLSTM model in an embodiment of the present invention. Detailed Implementation

[0016] This embodiment provides a UAV positioning method for water conservancy applications based on CSI and machine learning, such as... Figure 1 As shown, it includes the following steps: Step S1: Divide the target area to be inspected into multiple three-dimensional subspaces, and collect CSI (Channel State Information) data from multiple WiFi links by traversing all subspaces.

[0017] Step S1 specifically includes the following sub-steps: Step S1.1: Wireless signal propagation in a hydrological environment exhibits significant multipath effects and complex spatial scattering characteristics. To accurately capture these physical layer characteristics, this embodiment employs a MIMO-OFDM (Multiple-Input Multiple-Output) technology. MIMO utilizes the spatial diversity capability of multi-antenna arrays to resolve the angle of arrival (AoA) and phase difference of signals along different spatial paths. OFDM divides the broadband channel into multiple orthogonal narrowband subcarriers, effectively combating frequency-selective fading caused by water reflection. The combination of these two technologies enables the receiver to acquire CSI containing rich spatial, frequency, and temporal information.

[0018] Based on the aforementioned MIMO-OFDM architecture, the target positioning area is divided into multiple three-dimensional subspaces. Analyzing a single subspace, we assume there are L signal propagation paths and M receiving antennas arranged in an array with a spacing of d. For the l-th signal path, the corresponding angle of arrival (AoA) is expressed as... It is the azimuth angle of the l-th signal. and pitch angle The function, that is, in three-dimensional space .

[0019] Furthermore, the attenuation experienced by the WiFi signal reaching the antenna array along the l-th propagation path is expressed as: In particular, each signal path is closely related to two important parameters: attenuation and AoA; the phase offset of the m-th antenna relative to the first receiving antenna in the array can be mathematically expressed as... , where c is the speed of light in air and f is the carrier frequency.

[0020] Therefore, for the l-th propagation path, the phase offset is defined as a function of AoA, expressed in complex exponential form: ; Where j is the imaginary unit, This is represented by phase offset; For the l-th signal path, the phase difference is expressed as a complex exponential function of the angle of arrival: ; in, denoted as the guide vector, and T represents the transpose operation.

[0021] Furthermore, for all signal propagation paths, the overall steering matrix of the antenna array is expressed as: ; The received signal vector s is formed by superimposing the signals from each path. ,in It is a complex decay vector along all paths. Let be the complex decay vector of the Lth path.

[0022] In MIMO-OFDM systems, there are a total of The system consists of subcarriers of different frequencies. Considering the Doppler shift caused by the UAV's motion, the received vector on the nth subcarrier not only includes path attenuation and AoA information but also needs to be superimposed with a Doppler phase term. Let the radial velocity of the UAV be v, then the additional Doppler phase of the l-th path on the nth subcarrier is: ; in Let be the wavelength of the nth subcarrier, and k be the current sampling time. Diagonalize the Doppler phase to construct the Doppler compensation matrix. .according to and Then the actual received vector of the nth subcarrier after Doppler frequency offset is: ; in, , and Let be the actual received vector, complex attenuation vector, and Doppler compensation matrix of the nth subcarrier after Doppler frequency offset.

[0023] Construct a measurement matrix for all subcarriers of the antenna array. As shown in the following formula: in, It is the vector received on all subcarriers, and It is the complex attenuation matrix of L signal paths on all subcarriers.

[0024] Therefore, receiving signals from M antennas via a MIMO-OFDM system The CSI matrix of each subcarrier is expressed as follows: ; in, This represents the CSI value on the nth subcarrier of the m-th antenna; when the moving target is in different positions in three-dimensional space, the propagation paths are different from each other, thus distinguishing AoA and attenuation.

[0025] Step S1.2: Combine the amplitude and phase information of the CSI matrix at K consecutive time points, and collect enough CSI measurements by traversing each target area to initially realize the radio map; use all CSI measurements from all subcarriers on the antenna array to construct a tensor, which helps to retain meaningful information and characterize the contour of the moving target's position.

[0026] For a set of CSI measurements, the CSI tensor is represented as: ; in, It includes amplitude attenuation and phase shift, both of which are real values; This is the measurement matrix for all subcarriers of the antenna array.

[0027] Step S2: Preprocess the acquired CSI data, including noise filtering, phase correction, outlier removal, and data normalization.

[0028] Step S3: Integrate the amplitude and phase information of all OFDM (Orthogonal Frequency Division Multiplexing) subcarriers to construct a CSI tensor, forming a preliminary wireless fingerprint map containing the original fingerprint features; use the HOSVD (High Order Singular Value Decomposition) method to decompose the CSI tensor into low-dimensional tensors and extract representative features.

[0029] Since the CSI tensor is a multilinear mapping defined as the Cartesian product over some vector space and its dual space, the CSI tensor is denoted as... N represents the number of subcarriers in the MIMO-OFDM system, K represents the number of time sampling points, and M represents the number of receiving antennas; HOSVD decomposition is used to extract features from the CSI tensor, the specific process of which includes: The third-order CSI tensor Modal expansion is performed along the three dimensions of antenna, subcarrier, and time, resulting in three mode matrices: ; Perform Singular Value Decomposition (SVD) on each pattern matrix to obtain the left singular vector matrix, which serves as the orthogonal basis matrix for the corresponding dimension. ; in, , , The left singular matrix is ​​divided into three orthogonal basis matrices for output in three dimensions. , , It is a diagonal matrix, and the diagonal elements are singular values; , , , where is a right singular matrix, and are orthogonal basis matrices for the three input dimensions.

[0030] The core tensor is obtained by multiplying the CSI tensor. : ; in, This represents the product operation of the e-th modulus tensor. This represents the core tensor.

[0031] Singular value sequence for each pattern matrix Calculate the cumulative energy percentage Choose the smallest r such that r is a preset threshold, and the truncation rank is determined accordingly. and Preserve the core tensor Center front and The components corresponding to the maximal singular values ​​yield the truncated core tensor. and the corresponding truncated orthogonal basis matrix , , The truncated spatial dimension factor matrix As a representative feature, it is used to construct the initial localization fingerprint map.

[0032] Step S4: Use the UMAP algorithm to perform visual analysis of the features to discover hidden structures, and combine it with an information theory-based feature selection method to optimize the feature set and reconstruct a refined fingerprint map.

[0033] The specific process of using UMAP for feature visualization analysis includes: 1. Constructing fuzzy topological structures in high-dimensional space: For from the factor matrix The feature set obtained First, for each data point Find its z nearest neighbors in the high-dimensional space; then calculate Its j-th nearest neighbor Distance between ; Define high-dimensional space and Weight of connected edges This weight is modeled using an adaptive exponential kernel function based on local connectivity: ; in, yes Distance to its nearest neighbor (used to ensure local connectivity); It is a scale parameter, determined through binary search, such that each point... The sum of the weights of the local fuzzy simplex (i.e., the sum of the weights of all its nearest neighbors) is a constant. : ; in, for The j-th nearest neighbor, This is for local density estimation.

[0034] To ensure symmetry and obtain a joint probability representation in high-dimensional space, a fuzzy simplex is constructed: ; in, Representation of features and Similarity in high-dimensional manifold structures.

[0035] 2. Define the similarity of the low-dimensional embedding space: In a low-dimensional embedding space (the target dimension is typically 2 or 3), for the corresponding point and Their similarity We use a smooth family of piecewise functions to effectively capture the global topology of the manifold, as defined below: ; Among them, parameters and Typically, a fuzzy simplex is fitted to a high-dimensional distance using nonlinear least squares to maintain adjacency relationships at different scales in a low-dimensional space. In this embodiment, to simplify computation and encourage a wider range of clustering structures, a t-distribution kernel function with 1 degree of freedom is often used as an approximation.

[0036] 3. Optimize low-dimensional embeddings to minimize topological differences: UMAP minimizes the high-dimensional fuzzy simplex. Low-dimensional representation The low-dimensional embedding is optimized using the cross-entropy (CE) between the nodes, with the objective function being: ; The attraction term encourages edges connected in P to remain adjacent in Q, while the repulsion term drives non-adjacent points in P to move away from each other in Q, thus preserving both the local and global topology of the data.

[0037] The objective function is about low-dimensional coordinates The gradient is used for gradient-based optimization, and its gradient calculation formula is: .

[0038] When using When the gradient is simplified to its simplified form, it further simplifies to: ; The feature selection method based on mutual information is as follows: The feature set from factor matrix A The entropy is expressed as: ; in, This indicates a feature belonging to X. yes The probability among all values.

[0039] Furthermore, the conditional entropy of X given category label Y is expressed by the following formula: ; Where Y represents the location label in three-dimensional space. express The prior probability; This represents conditional probability, used to show the uncertainty of X given Y.

[0040] Based on preliminary clustering visualization analysis of the feature dataset using UMAP, cluster centers were obtained using Euclidean distance, corresponding to different category labels. Cluster center Given features With cluster center The distance between them is further transformed into information about The probability problem of Y; based on this viewpoint, for The probability that a value belongs to a certain category label is expressed by the following formula: ; Furthermore, the information gain between features and category labels is used to calculate the specific information shared by X and Y: ; in, Indicates about and The joint probability, and due to symmetry, is known. When they are independent, their mutual information will be zero.

[0041] A forward sequential search strategy is employed to continuously add dominant features to the optimized feature dataset; to achieve this goal, the currently selected feature dataset is denoted as... Initially, it is an empty set, and Y is the category label of the position in 3D space; specifically, express A specific feature; furthermore, it is assumed As a decision-making standard, among which The larger the value, the stronger the feature The more meaningful it is, the more meaningful it becomes.

[0042] In feature selection based on a unified conditional likelihood maximization framework, given features The specific decision criteria are mathematically defined as follows: ; in, Representing mutual information, Y is the location category label. For the currently selected feature subset, Represents two variables and The function.

[0043] Assumption If a function is represented as a linear function, then it is called a decision criterion or decision standard based on a linear combination of Shannon information items. Used to evaluate features Its importance is defined as: ; in, and The parameter is a non-negative parameter between 0 and 1; the maximum value is selected through iterative selection. Based on the characteristics, an optimized feature set is obtained.

[0044] Step S5, as follows Figure 2As shown, an RNN (Recurrent Neural Network) with a BiLSTM (Bi-directional Long Short-Term Memory) module, denoted as the RNN-BiLSTM model, is used to perform time-dependent encoding and high-level abstract representation learning on the optimized features. The specific location of the UAV in the perceived three-dimensional space is identified by CSI changes.

[0045] The processing of RNN-LSTM models includes the following steps: Step S5.1: Take the optimized feature sequence as input. The input vector of the model is represented as: ; Where T represents the transpose operation. These are the features that are being optimized.

[0046] Step S5.2: The RNN-BiLSTM model utilizes P sets of optimized features to make decisions, where... This represents the input of the RNN-BiLSTM model at step p. and These represent the hidden layers of the forward and backward RNN-BiLSTM models at the p-th step, respectively, with corresponding sizes of... The RNN-BiLSTM model also includes an additional unit state. It is used to control the flow of meaningful information through input gates, forget gates, and output gates; at each time step p, the forward LSTM unit computes the input gate. Forgotten Gate Output gate : ; For backward LSTM unit calculation of input gate Forgotten Gate Output gate : ; in, , , , and Here are the weight matrices, with sizes of [sizes to be filled in]. and ; and It is the bias vector; The sigmoid functions associated with the three gates, In the RNN-LSTM model, both the cell state and the hidden layer are initialized to zero.

[0047] Step S5.3, Forward LSTM Cell Status and hidden state The update is as follows: ; LSTM cell states before and after and hidden state The update is as follows: ; in, It represents the Hadamardi (or Hadama) stack; and They are all activation functions.

[0048] Step S5.4: Concatenate the forward and backward hidden states to obtain the bidirectional hidden state: The bidirectional hidden state at the last time step P is taken as the representation of the entire sequence and mapped to the UAV's 3D coordinates through a fully connected layer: ; in, The size is b For bias, It includes all available parameters in the RNN-BiLSTM model.

[0049] Based on the regional division, all locations of the water conservancy facilities in the area requiring inspection are numbered; a training dataset (X,Y) is constructed using optimized features and category labels, where X represents the obtained feature set, which serves as the input to the BiLSTM model, and Y is the corresponding real 3D location coordinate label.

[0050] Introduction This dataset serves as the training and validation dataset for the neural network, where all parameters are optimized along the direction of minimizing the cost function. ; in, It is the number of elements in the dataset. The true three-dimensional position coordinates of the g-th sample; This represents the prediction output of the BiLSTM model for the g-th sample, i.e. ; Denotes the square of the Euclidean norm, i.e. .

[0051] In this embodiment, a water conservancy facility area requiring high-precision UAV positioning is selected, such as a mixed area of ​​river channel and dam with a length, width, and height of 1000m, 200m, and 50m, respectively. This three-dimensional space is divided into multiple uniform grid subspaces as positioning reference points. For example, the subspace is divided at intervals of 5m, 2m, and 1m along the length, width, and height directions, resulting in approximately 10,000 reference points. At the center of each reference point, a mobile terminal device supporting CSI acquisition (such as a microcomputer equipped with an Intel 5300 network card) is placed and fixed on a ground tripod or buoy to simulate the airborne receiver signal characteristics of the UAV at specific three-dimensional coordinates (x, y, z).

[0052] Several commercial Wi-Fi routers were installed as fixed signal transmitters (APs) on both sides of the river and on the top of the dam, and their locations were ensured to be known and fixed.

[0053] Data Collection: The mobile terminal is sequentially placed at each reference point. At each reference point, the control terminal establishes connections with all APs and continuously collects CSI data from all APs. During collection, the terminal should remain stationary and continuously collect data for K consecutive time intervals to cover channel diversity caused by minor environmental disturbances. For each AP, at time k, the terminal acquires a dimension... CSI complex matrix Where M=3 (number of receiving antennas). (Number of subcarriers).

[0054] Constructing a local CSI tensor: For a single reference point l, and for a specific AP link, the amplitude and phase information of the CSI matrix at consecutive K time points are separated and combined to construct a third-order local CSI tensor. : ; in, This tensor captures the complete temporal, frequency, and spatial characteristics of the channel at that reference point along that link.

[0055] Integrating multi-link data: Repeat the above process for all APs. To synthesize all link information, local tensors obtained from different APs can be stacked on the newly added dimension (AP link dimension) to form a higher-dimensional tensor structure, or they can be processed separately and then their features fused. For simplicity, this embodiment takes processing a single strongest AP link as an example, i.e. This represents the fingerprint tensor of reference point l on the optimal AP link.

[0056] Initial fingerprint feature extraction based on HOSVD decomposition: fingerprint tensor for each reference point l Perform HOSVD decomposition to extract low-dimensional, representative feature vectors.

[0057] Execution decomposition: Solving the HOSVD decomposition model: Obtaining the core tensor ,in, This represents the product operation of the nth modulus tensor. Represents the core tensor. Obtain the truncated core tensor. and the corresponding truncated orthogonal basis matrix , , The truncated spatial dimension factor matrix As a representative feature.

[0058] Feature acquisition: Select factor matrix A (whose dimensions correspond to the receiving antenna mode) from the tensor Representative features are extracted to construct a preliminary fingerprint.

[0059] Feature visualization analysis and optimization selection: The initial feature dimensions are still high and may be redundant, so optimization is required.

[0060] UMAP Visualization Analysis: Expanding the features of all reference points into vectors and forming a set. The UMAP algorithm is used to reduce the dimensionality to 2D or 3D for visualization. The discriminative power of the features is evaluated by observing the clustering and separation of reference points at different spatial locations in the visualization.

[0061] Feature selection based on mutual information: First, a location category label Y is assigned to the reference point based on its true 3D coordinates. Then, a forward search strategy based on conditional mutual information maximization (CMI) as defined in the claims is employed. (From the empty set...) Initially, features are iteratively selected from the initial feature set X. This feature makes the criteria maximum: ; in, Representing mutual information, Y is the location category label. For the currently selected feature subset, , is a non-negative parameter between 0 and 1. This criterion aims to select features that are highly relevant to the location label Y and have low redundancy with the already selected features.

[0062] The process iterates until the preset number of features is reached, resulting in the optimal feature index set. This index set is then used to filter all feature vectors, yielding optimized feature vectors after dimensionality reduction and redundancy removal.

[0063] Constructing a refined fingerprint map: Associate the optimized features of each reference point with its true 3D coordinates (x, y, z) to form the final refined fingerprint database.

[0064] Training the RNN-LSTM localization model: A recurrent neural network model based on LSTM is trained using the constructed fingerprint database DB.

[0065] Data preparation: To learn the time-series dynamics, the optimized features corresponding to the continuous CSI data collected at each reference point are... As input to the model.

[0066] Model Construction and Training: Construct an RNN-BiLSTM network. The input layer receives the feature sequence; the middle layer may contain 1-2 LSTM layers, each containing several (e.g., 128) hidden units to capture the temporal dependencies of the features; finally, a fully connected layer is connected to output the probability of 3D coordinates (for regression tasks) or location class.

[0067] Model optimization: using mean squared error (MSE) as the loss function The model is trained using the Adaptive Moment Estimator (Adam) optimizer, and an early stopping strategy is used on the validation set to prevent overfitting. After training, the model parameters are saved. .

[0068] This embodiment first divides the target 3D space into multiple subspaces and collects CSI data to construct a preliminary fingerprint map. Then, it constructs a CSI tensor containing amplitude and phase information and extracts representative features using the HOSVD decomposition method. Subsequently, it employs the UMAP algorithm for feature visualization analysis and structure discovery, and combines a feature selection strategy based on mutual information to optimize the feature set and reconstruct a refined fingerprint map. Finally, it uses an RNN network with a BiLSTM module to encode and learn the optimized spatiotemporal features, identifying and tracking the UAV's position in 3D space through dynamic changes in CSI. This invention effectively overcomes signal interference caused by strong water surface reflection and dam obstruction, achieving high-precision UAV positioning in complex water conservancy environments, providing support for efficient flight path planning for dam safety inspections, river sewage outlet investigations, and hydrological and water quality emergency monitoring.

[0069] In addition to the embodiments described above, the present invention may have other implementations. All technical solutions formed by equivalent substitution or equivalent transformation fall within the protection scope claimed by the present invention.

Claims

1. A method for locating unmanned aerial vehicles (UAVs) in water conservancy applications based on CSI and machine learning, characterized in that: Includes the following steps: Step S1: Divide the target area into multiple three-dimensional subspaces, and collect Channel State Information (CSI) data from multiple WiFi links by traversing all subspaces; Step S2: Preprocess the acquired CSI data, including noise filtering, phase correction, outlier removal, and data normalization. Step S3: Integrate the amplitude and phase information of all OFDM subcarriers to construct the CSI tensor and form a preliminary wireless fingerprint map containing the original fingerprint features; use the HOSVD decomposition method to decompose the CSI tensor into low-dimensional tensors and extract representative features. Step S4: Use the UMAP algorithm to perform visual analysis of the features to discover hidden structures, and combine it with an information theory-based feature selection method to optimize the feature set and reconstruct the fingerprint map; Step S5: Using a recurrent neural network (RNN) with a long short-term memory (BiLSTM) module, referred to as the RNN-BiLSTM model, time-dependent encoding and abstract representation learning are performed on the optimized features. The specific location of the UAV in the perceived three-dimensional space is identified by CSI changes.

2. The method for locating unmanned aerial vehicles (UAVs) in water conservancy applications based on CSI and machine learning according to claim 1, characterized in that: Step S1 specifically includes the following sub-steps: Step S1.1: Based on the MIMO-OFDM system architecture, the target area is divided into multiple three-dimensional subspaces, and at least one fixed access point (AP) is set in each subspace; the UAV, as a mobile receiver, is equipped with an M-element uniform linear array antenna and establishes a communication link with the AP; the single subspace is analyzed, assuming there are L signal propagation paths and the spacing between the receiving antenna elements is d. For the l-th signal path, the corresponding angle of arrival AoA is expressed as: It is the azimuth angle of the l-th signal. and pitch angle The function, that is, in three-dimensional space The attenuation experienced by the WiFi signal reaching the antenna array along the l-th propagation path is expressed as: Each signal path is associated with two parameters, including attenuation and AoA; the phase offset of the m-th antenna relative to the first receiving antenna in the array is expressed as... , where c is the speed of light in air and f is the carrier frequency; For the l-th propagation path, the phase difference is expressed as a complex exponential function of the angle of arrival: ； Where j is the imaginary unit; For the l-th signal path, the AoA vector at the antenna array is expressed by the above formula as follows: ； Where T represents the transpose operation. The steering vector is represented by: For all signal propagation paths, the overall steering matrix of the antenna array is expressed as: ； The received signal vector s is formed by superimposing the signals from each path. ,in It is a complex decay vector along all paths. Let L be the complex attenuation vector of the Lth path; in a MIMO-OFDM system, there are a total of The nth subcarrier has several subcarriers of different frequencies; the received vector on the nth subcarrier contains not only path attenuation and AoA information, but also a superimposed Doppler phase term; assuming the radial velocity of the UAV is v, the additional Doppler phase of the l-th path on the nth subcarrier is: ； in, Let λ be the wavelength of the nth subcarrier, and k be the current sampling time; diagonalize the Doppler phase to construct the Doppler compensation matrix. ;according to and Then the actual received vector of the nth subcarrier after Doppler frequency offset for: ； Construct a measurement matrix for all subcarriers of the antenna array. As shown in the following formula: ； in, It is the vector received on all subcarriers, and It is the complex attenuation matrix of L signal paths on all subcarriers; therefore, receiving signals from M antennas via a MIMO-OFDM system... The CSI matrix of each subcarrier is expressed as follows: ； in, This represents the CSI value on the nth subcarrier of the m-th antenna; when the moving target is in different positions in three-dimensional space, the propagation paths are different from each other, thus distinguishing AoA and attenuation; Step S1.2: Combine the amplitude and phase information of the CSI matrix at K consecutive time points, and collect CSI measurements by traversing each target area to initially realize a radio map; use all CSI measurements from all subcarriers on the antenna array to construct a tensor. For a set of CSI measurements, the CSI tensor is represented as: ； in, It includes amplitude attenuation and phase shift, both of which are real values; This is the measurement matrix for all subcarriers of the antenna array.

3. The method for locating unmanned aerial vehicles (UAVs) in water conservancy applications based on CSI and machine learning according to claim 2, characterized in that: In step S3, the CSI tensor is denoted as M represents the number of receiving antennas, N represents the number of subcarriers in the MIMO-OFDM system, and K represents the number of time sampling points; The specific process of using HOSVD decomposition to extract features from the CSI tensor includes: The third-order CSI tensor Modular expansion is performed along the three dimensions of antenna, subcarrier, and time, resulting in three mode matrices: ； Perform singular value decomposition (SVD) on each pattern matrix to obtain the left singular vector matrix, which serves as the orthogonal basis matrix for the corresponding dimension. ； in, , , Let f be a left singular matrix, and f be three orthogonal basis matrices in three dimensions; , , It is a diagonal matrix, and the diagonal elements are singular values; , , , where is a right singular matrix, and are orthogonal basis matrices for the three input dimensions respectively; The core tensor is obtained by multiplying the CSI tensor. : ； in, This represents the product operation of the e-th modulus tensor. Represents the core tensor; Singular value sequence for each pattern matrix Calculate the cumulative energy percentage Choose the smallest r such that r is a preset threshold, and the truncation rank is determined respectively. , and Preserve the core tensor Center front , and The components corresponding to the maximal singular values ​​yield the truncated core tensor. and the corresponding truncated orthogonal basis matrix , , ; the truncated spatial dimension factor matrix As a representative feature, it is used to construct the initial localization fingerprint map.

4. The method for locating unmanned aerial vehicles (UAVs) in water conservancy applications based on CSI and machine learning according to claim 3, characterized in that: In step S4, constructing the fuzzy topological structure in the high-dimensional space specifically involves: for the factor matrix... The feature set obtained First, for each data point Find its z nearest neighbors in the high-dimensional space; then calculate Its j-th nearest neighbor Distance between ; Define high-dimensional space and Weight of connected edges This weight is modeled using an adaptive exponential kernel function based on local connectivity: ； in, yes The distance to its nearest neighbor; It is a scale parameter, determined through binary search, such that each point... The sum of the locally fuzzy simplexes is a constant. ; ； in, for The j-th nearest neighbor, For local density estimation; To ensure symmetry and obtain a joint probability representation in high-dimensional space, a fuzzy simplex is constructed: ； in, Representation of features and Similarity in high-dimensional manifold structures.

5. The method for locating unmanned aerial vehicles (UAVs) in water conservancy applications based on CSI and machine learning according to claim 4, characterized in that: In step S4, the similarity of the low-dimensional embedding space is defined, specifically: in the low-dimensional embedding space with a target dimension of 2 or 3, for the corresponding points... and The similarity between the two is defined using a smooth family of piecewise functions. This is used to capture the global topology of a manifold, and is specifically defined as follows: ； Among them, parameters and The fuzzy simplex is set by fitting nonlinear least squares to a high-dimensional distance to maintain adjacency relationships at different scales in the low-dimensional space.

6. The method for locating unmanned aerial vehicles (UAVs) in water conservancy applications based on CSI and machine learning according to claim 5, characterized in that: In step S4, optimizing the low-dimensional embedding to minimize topological differences specifically involves: UMAP minimizing the high-dimensional fuzzy simplex. Low-dimensional representation The cross-entropy between them is used to optimize the low-dimensional embedding, and the objective function is: ； The attraction term encourages connected edges in P to remain adjacent in Q, while the repulsion term drives non-adjacent points in P to move away from each other in Q, thus preserving both the local and global topology of the data. This objective function, with respect to low-dimensional coordinates... The gradient is used for gradient-based optimization, and its gradient calculation formula is: ； When using When the gradient is simplified to its simplified form, it further simplifies to: 。 7. The method for locating unmanned aerial vehicles (UAVs) in water conservancy applications based on CSI and machine learning according to claim 6, characterized in that: In step S4, the feature set from factor matrix A is... The entropy is expressed as: ； in, This indicates a feature belonging to X. yes The probability of X among all values; the conditional entropy of X given a category label Y is expressed by the following formula: ； Where Y represents the location label in three-dimensional space. express The prior probability; This represents conditional probability, used to show the uncertainty of X given Y; based on the preliminary clustering visualization analysis of the feature dataset using UMAP, the Euclidean distance is used to obtain the cluster centers, corresponding to different category labels. Cluster center Given features With cluster center The distance between them is further transformed into information about The probability problem of Y, for The probability that a value belongs to a certain category label is expressed by the following formula: ； The information gain between features and category labels is used to calculate the specific information shared by X and Y: ； in, Indicates about and The joint probability, and due to symmetry, is known. When they are independent, their mutual information will be zero.

8. The method for locating unmanned aerial vehicles (UAVs) in water conservancy applications based on CSI and machine learning according to claim 7, characterized in that: In step S4, a forward sequential search strategy is used to continuously add dominant features to the optimized feature dataset; the selected feature dataset is denoted as... Initially, it is an empty set, and Y is the category label of the position in 3D space; express A specific feature; assumption As a decision-making standard, among which The larger the value, the stronger the feature The more meaningful it is, the more meaningful it becomes; in feature selection based on the unified conditional likelihood maximization framework, given features... The specific decision criteria are mathematically defined as follows: ； in, Representing mutual information, Y is the location category label. For the currently selected feature subset, Represents two variables and The function; assuming If a function is represented as a linear function, then it is called a decision criterion or decision standard based on a linear combination of Shannon information items. Used to evaluate features Its importance is defined as: ； in, and The parameter is a non-negative parameter between 0 and 1; the maximum value is selected through iterative selection. Based on the characteristics, an optimized feature set is obtained.

9. A method for locating unmanned aerial vehicles (UAVs) in water conservancy applications based on CSI and machine learning, as described in claim 8, is characterized in that: In step S5, the processing of the RNN-BiLSTM model includes the following sub-steps: Step S5.1: Take the optimized feature sequence from step S4 as input. The input vector of the model is represented as: ； Where T represents the transpose operation. These are the features being optimized; Step S5.2: The RNN-BiLSTM model uses P groups of optimized features to make decisions. The BiLSTM consists of a forward LSTM layer and a backward LSTM layer. This represents the input of the RNN-BiLSTM model at step p. and These represent the hidden layers of the forward and backward RNN-BiLSTM models at the p-th step, respectively, with corresponding sizes of... The RNN-BiLSTM model also includes an additional cell state. It is used to control the flow of meaningful information through input gates, forget gates, and output gates; at each time step p, the forward LSTM unit computes the input gate. Forgotten Gate Output gate : ； For backward LSTM unit calculation of input gate Forgotten Gate Output gate : ； in, , , , and Here are the weight matrices, with sizes respectively. and ; and The bias vector has a size of ; The sigmoid functions associated with the three gates, In the RNN-BiLSTM model, both the cell state and the hidden layer are initialized to zero. Step S5.3, Forward LSTM Cell Status and hidden state The update is as follows: ； LSTM cell states before and after and hidden state The update is as follows: ； in, It represents the Hadamardi (or Hadama) stack; and They are all activation functions; Step S5.4: Concatenate the forward and backward hidden states to obtain the bidirectional hidden state: ； The bidirectional hidden state at the last time step P is taken as the representation of the entire sequence and mapped to the UAV's 3D coordinates through a fully connected layer: ； in, The size is is the weight matrix of the fully connected output layer, which represents the bidirectional hidden state of the BiLSTM at the last time step. Linear mapping to 3D spatial coordinates output; For bias, It includes all available parameters in the RNN-BiLSTM model.

10. A method for locating unmanned aerial vehicles (UAVs) in water conservancy applications based on CSI and machine learning, as described in claim 9, characterized in that: In step S5, all locations within the water conservancy facility area requiring inspection are numbered according to the regional division; a training dataset (X, Y) is constructed using optimized features and category labels, where X represents the obtained feature set, serving as the input to the BiLSTM model, and Y is the corresponding real 3D location coordinate label; [The text then abruptly shifts to a different topic:] As a dataset for training and validating neural networks, it contains There are 1000 sample pairs; all available parameters are optimized along the direction of minimizing the cost function, which is defined as the mean squared error of all samples. ； in, It is the number of elements in the dataset. The true three-dimensional position coordinates of the g-th sample; This represents the prediction output of the BiLSTM model for the g-th sample, i.e. ; Denotes the square of the Euclidean norm, i.e. .

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