A space-based spectrum situation online robust completion and prediction method, system, terminal and storage medium based on subspace tracking

Abstract

The present application relates to the technical field of signal processing, and especially relates to a space-based spectrum situation online robust completion and prediction method, system, terminal and storage medium based on subspace tracking; the method first acquires a current spectrum observation tensor and a non-time factor matrix of a last time spectrum situation, and then generates a current time factor vector and an abnormal tensor; clean observation data is obtained by eliminating the abnormal part, and then the non-time factor matrix and the time factor vector are updated; finally, a complete spectrum situation tensor is reconstructed through tensor operation. The present application supports online real-time updating processing of the spectrum situation, avoids repeated calculation of a large amount of historical data in the traditional method, significantly reduces the calculation complexity and storage requirement, and is suitable for efficient and robust situation awareness and prediction in space-based spectrum monitoring.

Description

Technical Field

[0001] This invention relates to the field of signal processing technology, and in particular to a method, system, terminal, and storage medium for online robust completion and prediction of space-based spectral situation based on subspace tracking. Background Technology

[0002] The space-based electromagnetic spectrum monitoring system can achieve continuous spatiotemporal wide-area spectrum perception through the continuous coverage of low-orbit satellites in the time, space, and frequency domains. By comprehensively monitoring and analyzing the space electromagnetic spectrum, it can construct a wireless environment map that characterizes the electromagnetic spectrum situation. It can depict the electromagnetic spectrum status from multiple dimensions such as the spatial domain, time domain, and frequency domain, and comprehensively display the current status, correlation forms, and development trends of the wide-area electromagnetic environment.

[0003] However, due to limitations imposed by satellite orbits and payload power consumption, space-based observation data suffers from non-uniform gaps, and the long-distance transmission via satellite-to-ground links makes the data susceptible to noise and interference signals. Therefore, it is urgent to supplement and restore the desired spectrum based on incomplete sensing data to reconstruct a complete electromagnetic spectrum situation.

[0004] Existing methods for generating spectral situations are based on batch processing and static completion methods, which do not consider the dynamic changes of spatial spectral situations over time. Moreover, each batch processing operation requires calculations based on a large amount of historical observation data, resulting in high computational complexity and low situation completion efficiency. Summary of the Invention

[0005] The main objective of this invention is to provide a robust online completion and prediction method for space-based spectral situation based on subspace tracking. This method aims to solve the problems of existing batch-based static completion methods that do not consider the dynamic changes of space spectral situation over time, and the high computational complexity caused by each batch calculation based on a large amount of historical observation data.

[0006] The objective of this invention can be achieved through the following technical solutions: A robust online completion and prediction method for space-based spectral situation based on subspace tracking includes the following steps: Obtain the non-temporal factor matrix of the current spectrum observation tensor and the spectrum situation tensor at the previous moment; based on the current spectrum observation tensor and the non-temporal factor matrix, generate the current temporal factor vector and the current anomaly tensor; remove the current anomaly tensor to obtain the current target spectrum observation tensor. The non-time factor matrix is ​​updated based on the current target spectrum observation tensor and the current time factor vector to obtain the current non-time factor matrix. The current time factor vector is then updated based on the current target spectrum observation tensor and the current non-time factor matrix. Based on the current non-time factor matrix and the updated current time factor vector, the current spectral situation tensor is obtained through tensor synthesis operation.

[0007] Furthermore, the step of generating the current time factor vector and the current anomaly tensor based on the current spectral observation tensor and the non-time factor matrix specifically includes: The non-temporal factor matrix of the spectrum situation tensor at the previous moment is fixed, and an optimization problem about the current time factor vector and the current anomaly tensor is constructed by combining the current spectrum observation tensor with the current spectrum observation tensor. The optimization problem is solved using the alternating direction multiplier method to obtain the current time factor vector and the current anomaly matrix; The current anomaly tensor is obtained by performing tensor synthesis operation on the current anomaly matrix.

[0008] Furthermore, the step of updating the non-time factor matrix based on the current target spectrum observation tensor and the current time factor vector to obtain the current non-time factor matrix specifically includes: The recursive least squares method is used to update the non-time factor matrix incrementally using the current target spectrum observation tensor and the non-time factor matrix of the previous time step; The updated non-time factor matrix is ​​column-normalized to obtain the current non-time factor matrix.

[0009] Furthermore, the step of obtaining the non-time factor matrix of the current spectrum observation tensor and the spectrum situation tensor at the previous time step also includes: Obtain the observation data for the initial time window and construct the initial spectral observation tensor set; Based on the initial set of spectral observation tensors, the initial factor matrix, rank, and spectral situation tensor are estimated, wherein the initial factor matrix includes an initial time factor matrix and an initial non-time factor matrix.

[0010] Furthermore, the step of estimating the initial factor matrix, rank, and spectral situation tensor based on the initial set of spectral observation tensors specifically includes: The data completion and denoising problem of the initial batch is transformed into an optimization problem. The objective function of the optimization problem includes: reconstruction error term, abnormal sparsity constraint term and time smoothing constraint term. The objective function is solved using the soft threshold operator and the alternating least squares method to obtain the initial factor matrix and rank; Tensor synthesis operations are performed on the initial factor matrix to obtain the initial spectral situation tensor.

[0011] Furthermore, the step of obtaining the current spectral situation tensor through tensor synthesis based on the current non-time factor matrix and the updated current time factor vector, further includes: Obtain the future time step; Based on the future time step, the future time factor is calculated using a time series prediction model. Tensor synthesis operations are performed on the future time factor and the current non-time factor matrix to obtain the future spectral situation tensor.

[0012] Furthermore, the construction steps of the time series prediction model include: Obtain the time factor vector of the most recent time points; The horizontal component, trend component, and periodic component of the time factor vector are extracted as training data. The Holt-Winters model is trained using the training data to obtain a time series prediction model.

[0013] This invention also provides a robust online space-based spectral situational awareness completion and prediction system based on subspace tracking, comprising: The tensor construction module is used to obtain the non-time factor matrix of the current spectrum observation tensor and the spectrum situation tensor at the previous time step, generate the current time factor vector and the current anomaly tensor based on the current spectrum observation tensor and the non-time factor matrix, remove the current anomaly tensor, and obtain the current target spectrum observation tensor. The matrix update module is used to update the non-time factor matrix according to the current target spectrum observation tensor and the current time factor vector to obtain the current non-time factor matrix, and update the current time factor vector according to the current target spectrum observation tensor and the current non-time factor matrix. The tensor generation module is used to obtain the current spectral situation tensor through tensor synthesis operation based on the current non-time factor matrix and the updated current time factor vector.

[0014] The present invention also provides a terminal, the terminal comprising: a memory, a processor, and a subspace tracking-based space-based spectrum situation online robust completion and prediction program stored in the memory and executable on the processor, wherein when the subspace tracking-based space-based spectrum situation online robust completion and prediction program is executed by the processor, it implements the steps of the subspace tracking-based space-based spectrum situation online robust completion and prediction method described above.

[0015] The present invention also provides a computer-readable storage medium storing a subspace tracking-based online robust completion and prediction program for space-based spectrum situation, wherein when the subspace tracking-based online robust completion and prediction program for space-based spectrum situation is executed by a processor, it implements the steps of the subspace tracking-based online robust completion and prediction method for space-based spectrum situation as described above.

[0016] The beneficial effects of this invention are as follows: This invention transforms the batch processing problem into an online incremental update problem. It only requires computation based on the non-temporal factor matrix of the spectral situation tensor from the previous time step and the observation data from the current time step to obtain the complete, anomaly-free spectral situation tensor for the current time step, thus completing the online completion of the current spectral situation. This process eliminates the need to repeatedly calculate large amounts of historical data, greatly reducing computational complexity and storage requirements, and meeting the high real-time requirements of space-based applications.

[0017] Furthermore, this invention, by generating a current anomaly tensor and removing it from the observation tensor, can accurately filter out interference, noise, and other abnormal information in the spectrum data, obtaining a clean spectrum observation tensor. This provides a high-quality data foundation for subsequent situational analysis and avoids misleading situational judgments due to anomalies. The time factor vector captures the dynamic changes in the spectrum over time, while the non-time factor matrix accurately reflects non-time-dimensional spectrum characteristics such as frequency and space, thereby improving the accuracy of the matrix's representation of the spectrum situation. The current spectrum situation tensor is generated based on the clean observation tensor and the optimized factor matrix, ensuring that the situation tensor truly and accurately reflects the actual state of the current spectrum environment. Attached Figure Description

[0018] To facilitate understanding by those skilled in the art, the present invention will be further described below with reference to the accompanying drawings.

[0019] Figure 1 This is a flowchart of the novel online robust completion and prediction of space-based spectral situation based on subspace tracking according to the present invention. Figure 2 This is a schematic diagram illustrating the online dynamic updating of the spectrum situation according to an embodiment of the present invention; Figure 3 This is a schematic diagram of spectrum situation prediction according to an embodiment of the present invention; Figure 4 This is a comparison curve of completion performance under different spatial missing rates in the simulation experiment process of this invention embodiment; Figure 5 This is a comparison curve of completion performance under different anomaly ratios in the simulation experiment process of this invention embodiment; Figure 6 This is a schematic diagram of the spectrum situation visualization analysis image in the simulation experiment process of this invention embodiment; Figure 7 This is a comparison curve of prediction performance under different missing rates in the simulation experiment process of this invention embodiment; Figure 8 This is a framework diagram of the space-based spectral situation online robust completion and prediction system based on subspace tracking according to the present invention; Figure 9 This is a structural diagram of a preferred embodiment of the terminal of the present invention. Detailed Implementation

[0020] To further illustrate the technical means and effects of the present invention in achieving its intended purpose, the following detailed description of the specific implementation methods, structures, features, and effects of the present invention, in conjunction with the accompanying drawings and preferred embodiments, is provided.

[0021] To address the characteristics of space-based sensing data, such as non-uniform missing data, strong noise interference, dynamic changes, and streaming input, specifically the low-rank nature of the spectral situation tensor in long-term time series, its correlation in short-term time series, and the sparsity of anomalous interference, this invention constructs an online completion and prediction mechanism for the spatiotemporal streaming spectral tensor and proposes a robust online completion and prediction method for space-based spectral situation based on subspace tracking, such as... Figure 1 and Figure 2 As shown, this method aims to achieve accurate generation of spatiotemporally continuous space-based electromagnetic spectrum situation, comprehensively displaying the current status, correlation patterns, and development trends of the wide-area electromagnetic environment. The online robust completion and prediction method for space-based spectrum situation based on subspace tracking includes a time-aware online robust spectrum situation generation method (Robust Time-Aware Streaming Tensor, R-TAST), used for generating wide-area spatiotemporally continuous spectrum situation under space-based spectrum monitoring systems; it also includes a space-based spectrum situation prediction method for predicting future trends in the spectrum situation.

[0022] A robust online completion and prediction method for space-based spectral situation based on subspace tracking is available in the following document: Figure 1 and Figure 2 This includes the following steps: S10. Obtain the non-time factor matrix of the current spectrum observation tensor and the spectrum situation tensor of the previous moment. Based on the current spectrum observation tensor and the non-time factor matrix, generate the current time factor vector and the current anomaly tensor. Remove the current anomaly tensor to obtain the current target spectrum observation tensor. It should be noted that the time factor vector described in this invention refers to a row vector, rather than the more common column vector.

[0023] In the above scheme, the non-time factor matrix includes a latitude factor matrix, a longitude factor matrix, and a frequency factor matrix.

[0024] It should be noted that step S10 is a robust online space-based spectrum situational awareness completion process. Before the system is deployed, an initialization estimation process is required to obtain the original data.

[0025] Initial estimation includes: Acquire observation data from multiple moments within the initial time window and construct an initial spectral observation tensor set; Based on the initial set of spectral observation tensors, the initial factor matrix, rank, and spectral situation tensor are estimated, wherein the initial factor matrix includes an initial time factor matrix and an initial non-time factor matrix.

[0026] Furthermore, the step of estimating the initial factor matrix, rank, and spectral situation tensor based on the initial set of spectral observation tensors specifically includes: The initial batch data completion and denoising problem is transformed into a batch optimization problem. The objective function of the optimization problem includes: a reconstruction error term, an abnormally sparse constraint term, and a time smoothing constraint term. The expression of the objective function is as follows: ; in, This indicates that this is a minimization problem, the goal of which is to find an optimal set of factor matrices that minimizes the value of the entire objective function; This represents the decision variables to be solved, i.e., the four factor matrices; The index variable represents different dimensions. In this invention, its value range is {1,2,3,4}, which correspond to the four physical dimensions of the tensor: latitude, longitude, frequency, and time, respectively. The subscript 0 indicates that this is the initial value estimated during the initialization phase. This represents the reconstruction error term, used to ensure that the reconstructed tensor is as close as possible to the true observation value at locations where observation data is available; It is the F-norm, which is the square root of the sum of the squares of all elements in the array; Indicates from time 1 to A set of binary mask tensors (where 1 indicates a valid value and 0 indicates a missing value). This indicates element-wise multiplication (Hadamard product), used to ensure that errors are calculated only for locations with observed data; Indicates from time 1 to The set of observed tensors (including missing and outliers); This indicates that the time to be estimated is from time 1 to... The true complete tensor (i.e., the initial spectral state tensor). This indicates that the time to be estimated is from time 1 to... Anomalous tensors; This represents an anomalous sparsity constraint term, used to make the anomalous tensor sparse, since anomalous tensors are usually sudden, isolated, and appear sporadically in time and space. This represents the sparsity control parameter; the larger the value, the more likely the residuals are to be judged as outliers. L1 norm (i.e., the sum of the absolute values ​​of all elements) represents the tensor. Minimizing the L1 norm will effectively cause a large number of elements in the tensor to become zero. This represents a time smoothing constraint term, used to ensure that the changes in the time factor matrix are smooth, avoiding unreasonable abrupt changes, and thus reflecting the characteristic of the spectrum trend evolving steadily over time. and These represent regularization parameters (hyperparameters), which control the strength of continuous smoothing and periodic smoothing, respectively. Represents a first-order difference matrix; This represents the initial time factor matrix, where each row represents the eigenvector of a time moment. Represents a periodic difference matrix; It is an abbreviation for "subject to", which indicates a constraint. Represents the initial spectral state tensor; For tensor composition operators, it means that the true spectral tensor must be reconstructed from these four factor matrices through the CP decomposition model (usually with the help of operations such as the Khatri-Rao product). This is a hard constraint that transforms the problem of estimating high-dimensional tensors into the problem of estimating several low-dimensional factor matrices. Represents the initial latitude factor matrix; Represents the initial longitude factor matrix; Represents the initial frequency factor matrix; This represents the initial time factor matrix.

[0027] As can be seen, the objective function of the optimization problem clearly defines the problem to be solved in the initialization phase: assuming the true spectral tensor is low-rank (decomposable into four factor matrices) and changes smoothly over time, find an optimal set of factor matrices and sparse outlier tensors such that the reconstructed data approximates the true values ​​as closely as possible to the observed values. By solving this optimization problem, the algorithm can simultaneously achieve: data completion: recovering missing data; denoising: separating Gaussian noise (using the Frobenius norm term); anomaly detection: identifying and separating sparse anomalies (using the L1 norm term); and feature extraction: obtaining an initial factor matrix representing the intrinsic structure of the data, laying the foundation for subsequent online updates and predictions.

[0028] The objective function is solved using the soft thresholding operator and the alternating least squares (ALS) method to obtain the initial factor matrix and rank; The expression for the soft threshold operator is as follows: ; in, This represents the soft threshold operator. Represents a symbolic function. and These represent the operators for taking the maximum value and the absolute value, respectively. These represent the action tensor, the all-1 tensor, and the all-0 tensor, respectively, and they are all the same size; This represents the sparsity control parameter.

[0029] In this scheme, the soft thresholding operator detects elements in the input tensor whose absolute value is greater than the set sparsity control parameter, thus obtaining anomaly vectors. These anomaly vectors are then used to synthesize tensors to obtain the anomaly tensor. Then, based on the initial spectral observation tensor and the initial anomaly tensor, a relatively "clean" initial target spectral observation tensor is obtained; the calculation formula is as follows: ; Based on this, the factor matrix is ​​estimated using ALS. Alternately use ALS and the soft thresholding operator until the residual change between two adjacent iterations is less than the threshold, indicating that the optimal optimization result has been reached, thus obtaining the initial factor matrix and rank.

[0030] Tensor synthesis operations are performed on the initial factor matrix to obtain the initial spectral situation tensor.

[0031] The expression for the initial spectral state tensor is: ; in, Represents the initial spectral state tensor. This is a tensor composition operator. Represents the initial latitude factor matrix. Represents the initial longitude factor matrix. Represents the initial frequency factor matrix. This represents the initial time factor matrix.

[0032] It should be noted that the expression for tensor composition is: ; in, Represents the spectral state tensor. This is a tensor composition operator. Represents the latitude factor matrix. Represents the longitude factor matrix. Represents the frequency factor matrix, This represents the time factor matrix. For the rank of the tensor, For matrix The column vectors, It is the outer product of vectors.

[0033] In step S10, generating the current time factor vector and the current anomaly tensor based on the current spectral observation tensor and the non-time factor matrix specifically includes: The non-temporal factor matrix of the previous time-space situation tensor is fixed, and an optimization problem is constructed about the current time factor vector and the current anomaly tensor in combination with the current spectral observation tensor. The expression for the optimization problem concerning the current time factor vector and the current anomaly tensor is as follows: ; in, This represents a minimization problem, the goal of which is to find an optimal set of variables that minimizes the value of the entire expression. Represents the current time factor vector (to be optimized); This indicates the current abnormal tensor (to be optimized). Indicates the current moment; The square of the F-norm represents the sum of squares of all elements in the matrix, used to measure the magnitude of the overall reconstruction error. Represents the current spectral observation tensor; This is the tensor composition operator; This represents the latitude factor matrix at the previous time step; This represents the longitude factor matrix at the previous moment; This represents the frequency factor matrix at the previous time step; Indicates the continuous smoothness intensity parameter; This represents the square of the L2 norm (minimizing this term means forcing the time factor changes between adjacent time points to be as small as possible, thereby ensuring that the spectral situation evolves continuously and smoothly over time, avoiding abrupt changes). This represents the difference between the current time factor and the time factor at the previous moment; This represents the periodic smoothing strength parameter; This represents the difference between the current time factor and the time factor of the previous period (m time ago); This represents the sparsity control parameter; the larger the value, the more likely the residuals are to be judged as outliers. This represents the L1 norm, used to calculate the sum of the absolute values ​​of all elements in the current anomalous tensor.

[0034] The optimization problem is solved using the alternating direction multiplier method to obtain the current time factor vector and the current anomaly matrix; The current anomaly tensor is obtained by performing tensor synthesis operation on the current anomaly matrix.

[0035] S20. Update the non-time factor matrix based on the current target spectrum observation tensor and the current time factor vector to obtain the current non-time factor matrix; update the current time factor vector based on the current target spectrum observation tensor and the current non-time factor matrix; specifically including: S21. Using the recursive least squares method, the non-time factor matrix is ​​updated incrementally using the current target spectrum observation tensor and the non-time factor matrix of the previous time step. The updated non-time factor matrix is ​​then column-normalized to obtain the current non-time factor matrix. .

[0036] In the above scheme, the non-time factor matrix is ​​updated incrementally by recursive least squares (RLS). The optimal estimate for the current time is calculated recursively by using the observation data at the current time and the estimated state at the previous time, thereby avoiding batch repetitive calculations on a large amount of historical data.

[0037] The specific implementation process of S21 is as follows: 1. Parameter initialization: Before starting the online update process, initialize two key state variables for each row in every non-time factor matrix: Covariance matrix: Initialized as a very small positive definite matrix (e.g., an identity matrix multiplied by a very small positive number), which represents the uncertainty of the initial estimate.

[0038] Cross-correlation vector: initialized as a zero vector.

[0039] The parameter value of the forgetting factor (a number between 0 and 1) is set to control the weight of historical information in the current estimate. The closer the value is to 1, the longer the historical information is remembered; the smaller the value, the more sensitive the algorithm is to changes in recent data.

[0040] Phase Two: Iterative Update Loop For each new observation data that arrives at each time step, perform the following iterative steps to update all non-time factor matrices: 2. Start dimensional loop: Process each non-time dimension in turn (e.g., latitude, longitude, frequency domain). For the current dimension, begin updating its corresponding factor matrix.

[0041] 3. Start the row vector loop: For the current factor matrix, process it row by row. For each row, perform the following operations: 4. Construct the auxiliary projection matrix: Calculate an auxiliary matrix that is the specific matrix product (Khatri-Rao product) of all other non-time factor matrices (excluding the one currently being updated); used to project high-dimensional tensor data into a low-dimensional row vector space.

[0042] 5. Recursively update the covariance matrix: Read the covariance matrix stored at the previous time step, corresponding to the current row.

[0043] Calculate the information matrix derived from the new observation data. This calculation involves the auxiliary projection matrix and the observation mask matrix for the current row.

[0044] Weighted fusion: Multiply the covariance matrix from the previous time step by a forgetting factor (for decay), and then add the new information matrix. The result is the updated covariance matrix for the current time step.

[0045] Store this updated covariance matrix for use in the next time step.

[0046] 6. Recursively update the cross-correlation vector: Read the cross-correlation vector corresponding to the current row stored in the previous time step.

[0047] Calculate the projection results of the new observation data and the auxiliary projection matrix.

[0048] Weighted fusion: Multiply the cross-correlation vector of the previous time step by the forgetting factor (to decay it), and add the new projection result; the result is the cross-correlation vector updated at the current time step.

[0049] Store the updated cross-correlation vector for use in the next time step.

[0050] Calculate the optimal estimate for the current row: Read the current covariance matrix and cross-correlation vector that were just updated in this step.

[0051] Solving the linear equation system: The optimal estimate of the current row vector is obtained by calculating the inverse of the updated covariance matrix and multiplying it by the updated cross-correlation vector.

[0052] Assign this estimate to the current row of the current factor matrix.

[0053] End the row vector loop: Check if all rows of the current factor matrix have been updated. If not, move to the next row and jump back to step 3 to continue.

[0054] 9. Column normalization: After all rows of a factor matrix have been updated, each column of the matrix is ​​normalized (e.g., the modulus of each column is adjusted to 1). This step aims to ensure the stability of the numerical computation and satisfy the model constraints.

[0055] 10. End the dimensional loop and output: Check if all non-time factor matrices across all dimensions have been updated. If not, move to the factor matrix of the next dimension and jump back to step 2 to continue execution.

[0056] After all the factor matrices in all dimensions have been updated and normalized, the final updated set of current non-time factor matrices is output.

[0057] The above process cleverly avoids repeatedly processing historical data by recursively updating the covariance matrix and cross-correlation vector, greatly reducing computational and storage overhead and meeting the high real-time requirements of space-based applications. The entire process is an efficient, incremental, online learning loop that progressively refines the estimation of non-time factor matrices.

[0058] S22. Based on the current non-time factor matrix and the current target spectrum observation tensor, the current time factor vector is obtained by constructing a regularized projection matrix and fusing anomaly correction terms and historical smoothing constraints, and by solving the linear system through pseudo-inverse. The specific update process is as follows: Step 1: Construct the core projection matrix Using the current non-time factor matrix, a core projection matrix is ​​constructed through Khatri-Rao product operations. This core projection matrix maps high-dimensional tensor observation data to a low-dimensional factor space, serving as a bridge connecting the observed values ​​and the time factor to be determined, thus enabling subspace tracking.

[0059] Step 2: Construct the regularized information matrix Calculate the regularized projection information matrix to ensure the numerical stability of subsequent inversion operations.

[0060] Step 3: Synthesize the comprehensive target vector A target vector is calculated that integrates observation information, anomaly correction, and historical trends. This vector represents the projection of the anomaly-corrected observation data onto the subspace; the solution is also guided towards the historical time factors of "previous time" and "previous cycle time" to ensure the continuous smoothness and periodicity of the temporal evolution.

[0061] Step 4: Solve the linear system Solve the constructed linear system. In practical numerical computation, the Moore-Penrose pseudoinverse or other stable linear system solutions (such as Cholesky decomposition) are often used. The use of pseudoinverses ensures a robust numerical solution even when the matrix is ​​not full rank.

[0062] Step 5: Transpose to obtain the time factor matrix The solution obtained in row vector form is transposed to obtain the current time factor matrix in column vector form; this current time factor matrix is ​​the optimal estimate of the time dimension feature at the current time.

[0063] As can be seen from the above process, this invention integrates a highly efficient computational process that combines subspace projection, anomaly robust handling, temporal dynamic modeling, and numerical stability guarantees. It fully utilizes historical states and current observations to achieve accurate and robust online updates of the time factor matrix.

[0064] S30. Based on the current non-time factor matrix and the updated current time factor vector, the current spectral situation tensor is obtained through tensor synthesis operation.

[0065] The expression for the current spectral situation tensor is as follows: ; in, express, This represents the tensor composition operator. This represents the feature vector of the current time dimension. This represents the feature matrix of the current dimension. This represents the current longitude dimension feature matrix. This represents the current frequency domain dimension feature matrix.

[0066] Please see Figure 3 The process of obtaining the current spectral situation tensor through tensor synthesis based on the current non-time factor matrix and the updated current time factor vector, further includes: Obtain the future time step; Based on the future time step, the future time factor is calculated using a time series prediction model. It should be noted that the future time factor can be a future time factor vector or a future time factor matrix.

[0067] The expression for the future time factor is as follows: ; in, This represents the predicted future time factor. Indicates the future time step. Indicates the current time step. The horizontal component represents the baseline level of the sequence at the current time T; The trend component represents the estimated trend slope per unit time at time T. The seasonal (periodic) component represents the seasonal or periodic effect corresponding to the next h time points; Indicates rounding down. It indicates the length of a complete seasonal cycle.

[0068] Tensor synthesis operations are performed on the future time factor and the current non-time factor matrix to obtain the future spectral situation tensor.

[0069] The expression for the future spectral situation tensor is as follows: ; in, The tensor representing the future spectrum trend. This is a tensor composition operator. This represents the predicted future time factor. Indicates the current time T The latitudinal factor matrix, Indicates the current time T The longitude factor matrix, Indicates the current time T The frequency factor matrix.

[0070] Furthermore, the construction steps of the time series prediction model include: Obtain the time factor vector of the most recent time points; The horizontal component, trend component, and periodic component of the time factor vector are extracted as training data. The Holt-Winters model is trained using the training data to obtain a time series prediction model.

[0071] The expression for the horizontal component of the time factor vector is as follows: ; in, This represents the horizontal component of the current time factor vector. Indicates the horizontal smoothing parameter. This indicates element-wise multiplication. Represents the current time factor vector. This represents the periodic component from the previous cycle (m time ago). This represents the horizontal component of the time factor vector from the previous time step. This represents the trend component of the time factor vector at the previous moment.

[0072] The expression for the trend component of the time factor vector is as follows: ; in, This represents the trend component of the current time factor vector. This represents the trend smoothing parameter.

[0073] The expression for the periodic component of the time factor vector is as follows: ; in, This represents the periodic component of the current time factor vector. This represents the periodic smoothing parameter.

[0074] As can be seen, this embodiment utilizes a trained Holt-Winters time series prediction model to predict the time factors for the next h moments (from T+1 to T+h) based on the time factor vector completed from historical time periods. The Holt-Winters model captures the baseline level, trend, and periodicity of the time series through horizontal, trend, and periodic components, respectively, thereby more accurately describing and predicting the changing patterns of the spectral landscape over time. It also reuses the non-time factor matrix from the dynamically updated phase to generate future spectral landscape prediction results.

[0075] The performance verification process is as follows: Set up the scenario: Generate a simulation spectrum tensor of a realistic size (e.g., 70x70x20x1000) to simulate radiation sources, satellite orbits, path loss, and satellite-to-ground link noise and anomalies.

[0076] Missing data and anomalies were introduced: The complete simulation data was processed according to the set missing rate and anomaly ratio to simulate the observation data with problems.

[0077] Comparative experiment: The algorithm (R-TAST) was tested on the same data with other advanced online algorithms (such as OLSTEC, SOFIA, RACP, etc.) and offline algorithms (such as ALS).

[0078] Evaluation indicators: Completion accuracy: Using metrics such as A-NMSE, the error between the data recovered by the algorithm and the true complete data is measured.

[0079] Visual comparison: Directly compare the spectrum diagrams completed by different algorithms.

[0080] Prediction accuracy: The error between the predicted result and the actual future value.

[0081] Results Analysis: By plotting performance curves (such as...) Figure 4 and 5 ) and spectrum situation diagram (such as Figure 6 and 7 This demonstrates that the R-TAST algorithm outperforms other online comparison algorithms in terms of completion accuracy, anomaly robustness, and prediction performance, and achieves accuracy similar to offline batch processing algorithms while meeting the efficiency requirements of online processing.

[0082] In other words, The proposed spectral situation completion and prediction method is compared with other advanced methods. Consider a spectral situation tensor of size "70×70×20×1000" with 5 radiation sources. The antenna transmit and receive gain is 43.3 dBi, and the path loss exponent is 2. The orbital altitude of the LEO monitoring satellite is set to 340 km, with a minimum elevation angle of 20°. The satellite-to-ground link comprehensively considers ionospheric attenuation, shadow fading, multipath effects, and noise interference. Shadow fading and multipath effects can be modeled as following a log-normal distribution with a variance of 4 dB and a Rayleigh distribution with a variance of 1, respectively, and the average received signal-to-noise ratio (SNR) is assumed to be 10 dB.

[0083] like Figure 4 and 5 As shown, the completion accuracy curves of A-NMSE under different missing rates and outlier proportions are compared. The proposed R-TAST outperforms other online tensor completion algorithms, including OLSTEC, SOFIA, ACP, RACP, and BRST, in the completion accuracy experiments, and achieves performance comparable to the batch-based ALS algorithm; simultaneously... Figure 6 Column (c) clearly shows that R-TAST successfully tracked the spectral dynamics changes over time. To visually compare the construction performance of different online algorithms, Figure 6 The spectral status diagrams of the fifth sub-narrowband channel constructed during the initialization t="50" (first row) and the dynamic update t="350,850" (second and third rows) are shown respectively. It can be seen that the proposed R-TAST outperforms RACP and SOFIA, achieving the best visualization performance in both the initial and subsequent dynamic tracking phases. Figure 7 The spectral prediction performance of the proposed R-TAST algorithm and SOFIA was compared. SOFIA also used the Holt-Winters model to predict future values ​​under different missing rate and outlier percentage settings. Compared with SOFIA, R-TAST's spectral prediction results were more accurate despite the presence of missing and corrupted measurements.

[0084] In summary, this invention addresses the issues of non-uniform gaps and abnormal interference caused by the predetermined orbit constraints of low-Earth orbit satellites and long-distance satellite-to-ground transmission. Based on the multidimensional correlation of the spatial spectrum situation, it combines multivariate temporal analysis and subspace tracking to achieve joint completion and prediction of the spatial spectrum situation. First, for large-scale spatiotemporal dynamic scenarios, based on continuously collected high-dimensional spectrum measurement data over time, this invention dynamically generates the spatial spectrum situation in a continuous spatiotemporal-frequency dimension through dynamic tensor modeling and online optimization learning, combined with tensor decomposition and subspace tracking, using incremental updates. On this basis, through comprehensive analysis of the spatiotemporal-frequency multidimensional spectrum situation, and based on the multidimensional correlation of the spatial spectrum situation, multivariate temporal analysis is used to capture the evolution law of the multidimensional spectrum over time, further realizing the joint completion and prediction of the spatial spectrum situation. This achieves real-time, accurate, and comprehensive completion of the spatial spectrum situation across the entire domain, and reliable prediction of future evolution trends.

[0085] In summary, the beneficial effects of the present invention are as follows: (1) A space-based wide-area dynamic spectrum situational awareness architecture was constructed; by utilizing the wide-area continuous coverage, periodic rapid access and multi-source data fusion of low-orbit satellites, spatiotemporal continuous wide-area spatial spectrum situational awareness was realized. (2) An online robust completion scheme for the spatial spectrum situation is proposed. In view of the non-uniform missing and abnormal interference caused by the predetermined orbit limitation of low-orbit satellites and long-distance transmission between satellite and ground, the spectrum situation is completed and abnormal interference is removed based on the multidimensional correlation and time series analysis of the spectrum situation. (3) An online spectrum situation generation scheme was proposed. In the case of large-scale spatiotemporal dynamic scenarios, the high-dimensional spectrum measurement data increases with time and the spatial spectrum changes dynamically. Based on subspace tracking, the online dynamic completion of the spectrum situation is realized, and the dynamic generation of multi-dimensional spectrum situation is realized in the form of incremental update. (4) A time-series prediction scheme for the spectrum situation was proposed. Through comprehensive analysis of the multi-dimensional spectrum situation in time, space and frequency, based on the multi-dimensional correlation of the spatial spectrum situation, and by capturing the development law of the spectrum time, the joint completion and prediction of the spatial spectrum situation was further realized, which promoted the practical application of space-based electromagnetic spectrum monitoring in electromagnetic control, frequency guarantee and electromagnetic protection.

[0086] like Figure 8 As shown, the present invention also provides a robust online space-based spectral situational awareness completion and prediction system based on subspace tracking, comprising: Tensor construction module 51 is used to obtain the non-time factor matrix of the current spectrum observation tensor and the spectrum situation tensor at the previous moment, generate the current time factor vector and the current anomaly tensor based on the current spectrum observation tensor and the non-time factor matrix, remove the current anomaly tensor, and obtain the current target spectrum observation tensor. The matrix update module 52 is used to update the non-time factor matrix according to the current target spectrum observation tensor and the current time factor vector to obtain the current non-time factor matrix, and update the current time factor vector according to the current target spectrum observation tensor and the current non-time factor matrix. Tensor generation module 53 is used to obtain the current spectral situation tensor through tensor synthesis operation based on the current non-time factor matrix and the updated current time factor vector.

[0087] It should be noted that the working principle and technical effect of the subspace tracking-based space-based spectrum situation online robust completion and prediction system correspond one-to-one with the subspace tracking-based space-based spectrum situation online robust completion and prediction method described above, so they will not be repeated here.

[0088] Furthermore, such as Figure 9 As shown, based on the above-mentioned method and system for online robust completion and prediction of space-based spectrum situation based on subspace tracking, the present invention also provides a terminal, which includes a processor 10, a memory 20 and a display 30. Figure 9 Only some of the terminal components are shown; however, it should be understood that it is not required to implement all of the components shown, and more or fewer components may be implemented instead.

[0089] In some embodiments, the memory 20 may be an internal storage unit of the terminal, such as a hard disk or memory. In other embodiments, the memory 20 may be an external storage device of the terminal, such as a plug-in hard disk, smart media card (SMC), secure digital card (SD), flash card, etc. Further, the memory 20 may include both internal and external storage devices. The memory 20 is used to store application software and various types of data installed on the terminal, such as the program code installed on the terminal. The memory 20 can also be used to temporarily store data that has been output or will be output. In one embodiment, the memory 20 stores a subspace tracking-based space-based spectrum situation online robust completion and prediction program 40, which can be executed by the processor 10 to implement the subspace tracking-based space-based spectrum situation online robust completion and prediction method of this application.

[0090] In some embodiments, the processor 10 may be a central processing unit (CPU), a microprocessor, or other data processing chip, used to run program code stored in the memory 20 or process data, such as executing the online robust completion and prediction method for space-based spectral situation based on subspace tracking.

[0091] In some embodiments, the display 30 may be an LED display, a liquid crystal display, a touch-sensitive liquid crystal display, or an OLED (Organic Light-Emitting Diode) touchscreen. The display 30 is used to display information on the terminal and to display a visual user interface. The terminal's processor 10, memory 20, and display 30 communicate with each other via a system bus.

[0092] In one embodiment, when the processor 10 executes the subspace-based tracking-based space-based spectral situation online robust completion and prediction program 40 in the memory 20, it implements the steps of the subspace-based tracking-based space-based spectral situation online robust completion and prediction method as described above.

[0093] The present invention also provides a computer-readable storage medium storing a subspace tracking-based online robust completion and prediction program for space-based spectrum situation, wherein when the subspace tracking-based online robust completion and prediction program for space-based spectrum situation is executed by a processor, it implements the steps of the subspace tracking-based online robust completion and prediction method for space-based spectrum situation as described above.

[0094] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the scope of the present invention.

Claims

1. A robust online completion and prediction method for space-based spectral situation based on subspace tracking, characterized in that, Includes the following steps: Obtain the non-temporal factor matrix of the current spectrum observation tensor and the spectrum situation tensor at the previous moment; based on the current spectrum observation tensor and the non-temporal factor matrix, generate the current temporal factor vector and the current anomaly tensor; remove the current anomaly tensor to obtain the current target spectrum observation tensor. The non-time factor matrix is ​​updated based on the current target spectrum observation tensor and the current time factor vector to obtain the current non-time factor matrix. The current time factor vector is then updated based on the current target spectrum observation tensor and the current non-time factor matrix. Based on the current non-time factor matrix and the updated current time factor vector, the current spectral situation tensor is obtained through tensor synthesis operation; Obtain the future time step; Based on the aforementioned future time step, the future time factor is calculated using a time series prediction model: ； in, This represents the predicted future time factor. Indicates the future time step. Indicates the current time step. The horizontal component represents the baseline level of the sequence at the current time T; The trend component represents the estimated trend slope per unit time at time T. The seasonal component represents the seasonal or cyclical effect corresponding to the next h time points. Indicates rounding down. Indicates the length of a complete seasonal cycle; Tensor synthesis operations are performed on the future time factor and the current non-time factor matrix to obtain the future spectral situation tensor: ； in, The tensor representing the future spectrum trend. This is a tensor composition operator. This represents the predicted future time factor. Indicates the current time T The latitudinal factor matrix, Indicates the current time T The longitude factor matrix, Indicates the current time T The frequency factor matrix; The steps for constructing the time series prediction model include: Obtain the time factor vector of the most recent time points; The horizontal component, trend component, and periodic component of the time factor vector are extracted as training data. The Holt-Winters model is trained using the training data to obtain a time series prediction model.

2. The method for online robust completion and prediction of space-based spectral situation based on subspace tracking according to claim 1, characterized in that, The process of generating the current time factor vector and the current anomaly tensor based on the current spectral observation tensor and the non-time factor matrix specifically includes: The non-temporal factor matrix of the previous time-space situation tensor is fixed, and an optimization problem is constructed about the current time factor vector and the current anomaly tensor in combination with the current spectral observation tensor. The optimization problem is solved using the alternating direction multiplier method to obtain the current time factor vector and the current anomaly matrix; The current anomaly tensor is obtained by performing tensor synthesis operation on the current anomaly matrix.

3. The method for online robust completion and prediction of space-based spectral situation based on subspace tracking according to claim 1, characterized in that, The step of updating the non-time factor matrix based on the current target spectrum observation tensor and the current time factor vector to obtain the current non-time factor matrix specifically includes: The recursive least squares method is used to update the non-time factor matrix incrementally using the current target spectrum observation tensor and the non-time factor matrix of the previous time step; The updated non-time factor matrix is ​​column-normalized to obtain the current non-time factor matrix.

4. The method for online robust completion and prediction of space-based spectral situation based on subspace tracking according to claim 1, characterized in that, The process of obtaining the non-time factor matrix of the current spectrum observation tensor and the spectrum situation tensor at the previous moment also includes: Obtain the observation data for the initial time window and construct the initial spectral observation tensor set; Based on the initial set of spectral observation tensors, the initial factor matrix, rank, and spectral situation tensor are estimated, wherein the initial factor matrix includes an initial time factor matrix and an initial non-time factor matrix.

5. The method for online robust completion and prediction of space-based spectral situation based on subspace tracking according to claim 4, characterized in that, The step of estimating the initial factor matrix, rank, and spectral situation tensor based on the initial spectral observation tensor set specifically includes: The data completion and denoising problem of the initial batch is transformed into an optimization problem. The objective function of the optimization problem includes: reconstruction error term, abnormal sparsity constraint term and time smoothing constraint term. The objective function is solved using the soft threshold operator and the alternating least squares method to obtain the initial factor matrix and rank; Tensor synthesis operations are performed on the initial factor matrix to obtain the initial spectral situation tensor.

6. A robust online space-based spectral situational awareness completion and prediction system based on subspace tracking, characterized in that, The subspace tracking-based online robust completion and prediction system for space-based spectrum situation is used to implement the subspace tracking-based online robust completion and prediction method for space-based spectrum situation as described in any one of claims 1-5. The subspace tracking-based online robust completion and prediction system for space-based spectrum situation comprises: The tensor construction module is used to obtain the non-time factor matrix of the current spectrum observation tensor and the spectrum situation tensor at the previous time step, generate the current time factor vector and the current anomaly tensor based on the current spectrum observation tensor and the non-time factor matrix, remove the current anomaly tensor, and obtain the current target spectrum observation tensor. The matrix update module is used to update the non-time factor matrix according to the current target spectrum observation tensor and the current time factor vector to obtain the current non-time factor matrix, and update the current time factor vector according to the current target spectrum observation tensor and the current non-time factor matrix. The tensor generation module is used to obtain the current spectral situation tensor through tensor synthesis operation based on the current non-time factor matrix and the updated current time factor vector.

7. A terminal, characterized in that, The terminal includes: a memory, a processor, and a subspace tracking-based space-based spectrum situation online robust completion and prediction program stored in the memory and executable on the processor. When the subspace tracking-based space-based spectrum situation online robust completion and prediction program is executed by the processor, it implements the steps of the subspace tracking-based space-based spectrum situation online robust completion and prediction method as described in any one of claims 1-5.

8. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a subspace tracking-based online robust completion and prediction program for space-based spectrum situation, which, when executed by a processor, implements the steps of the subspace tracking-based online robust completion and prediction method for space-based spectrum situation as described in any one of claims 1-5.

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