Multi-dimensional adaptive streaming reconstruction method of spectrum situation tensor for space-based dynamic incomplete observation

Abstract

The application discloses a kind of multi-dimensional self-adaptive streaming reconstruction methods of spectrum situation tensor for space-based dynamic incomplete observation, comprising: based on spectrum measurement data, construct dynamic tensor and determine dimension evolution mode by the spatial coverage dimension variation of dynamic tensor;When dimension evolution mode is expansion or invariable, using historical factor matrix as prior constraint to process current observation tensor, obtain the factor matrix of current time slot;When dimension evolution mode is short, using time series prediction method to pre-fill blind area, obtain the factor matrix of current time slot;Based on factor matrix, reconstruct spectrum situation tensor, and separate abnormal interference from reconstruction residual using soft threshold operator;Based on the reconstruction residual after separating abnormal interference, calculate relative change rate, update tensor rank in combination with sliding window regression trend;Based on the tensor rank after updating, adjust factor matrix structure, use the adjusted factor matrix for the processing of next time slot, iterate until the reconstruction result converges.

Description

Technical Field

[0001] This invention belongs to the field of aerospace dynamic information flow processing and multidimensional adaptive reconstruction technology, and particularly relates to a multidimensional adaptive streaming reconstruction method of spectrum situation tensor for space-based dynamic incomplete observation. Background Technology

[0002] With the rapid development of 6G communication technology, the continuous expansion of the user base, and the ongoing advancement of integrated land, sea, air, and space network construction, establishing an electromagnetic spectrum monitoring system that is spatiotemporally continuous, has wide-area coverage, and possesses high dynamic sensing capabilities has become an important trend. Low Earth Orbit (LEO) satellite constellations, with their unique advantages such as wide-area coverage, free-view observation, and lack of geographical limitations, provide crucial support for constructing a full-time, multi-dimensional space-based dynamic spectrum sensing system.

[0003] However, space-based spectrum situational awareness faces extremely complex observation environment constraints in practical applications. To achieve continuous spatiotemporal spectrum monitoring, relay observations from low-Earth orbit constellations are typically required. However, due to the continuous switching of coverage areas and payload types among different satellite formations during transit, this heterogeneous relay observation causes drastic time-varying changes in the spatial dimensions of the acquired spectrum data. Simultaneously, limited by the predetermined satellite orbits and harsh space-to-ground transmission environments, not only are the observation data spatially non-uniformly missing, but they are also frequently mixed with anomalous interference. More seriously, the electromagnetic spectrum itself has highly dynamic evolutionary characteristics, with measurements arriving continuously as data streams. Therefore, how to reconstruct a complete spectrum situational awareness in real time and accurately based on such incomplete, anomalous, and dimensionally drastically changing streaming data, to comprehensively and holistically display the current state, correlations, and development trends of the electromagnetic environment, and thus significantly improve key capabilities such as spectrum monitoring, spectrum resource allocation, radiation source location, and spectrum interference identification, constitutes a significant technical challenge.

[0004] Existing methods for completing and reconstructing spectral situations can be broadly categorized into model-driven and data-driven approaches. Model-driven methods primarily utilize prior information about space transmission channels and radiation sources for position estimation, but they are prone to evolutionary model mismatch in low-Earth orbit, highly dynamic, and non-cooperative environments. Among data-driven methods, traditional spatial interpolation relies on fixed spatial statistical models, making it difficult to adapt to the complex and ever-changing space-based environment; deep learning-based methods excessively depend on massive and complete training samples, resulting in poor generalization ability; and traditional tensor completion methods mainly target static offline data, employing batch processing for global optimization calculations. Faced with continuously arriving streaming spectral measurements from space-based systems, traditional batch processing methods are insufficient in terms of storage space and computational overhead, failing to meet the demands of online real-time reconstruction of dynamic situations.

[0005] To address the computational timeliness issue, current research has shifted towards developing online dynamic tensor completion methods. However, existing technologies still have many limitations and are difficult to directly apply to complex space-based observation scenarios: First, single-dimensional streaming tensor completion methods (such as dynamic completion methods based on online stochastic gradient descent or higher-order CP decomposition) typically assume that the data changes in only one dimension (e.g., time). However, in actual space-based observations, multiple dimensions of tensor data may change dynamically over time. Furthermore, some single-dimensional tracking algorithms lack anomaly detection capabilities, resulting in slow convergence and low reconstruction accuracy when interference is introduced. Second, while multi-dimensional streaming tensor completion methods expand the processing dimensions, they generally suffer from insufficient adaptability. On the one hand, existing methods for tracking tensor dimensions are often unidirectional (only supporting dimensional increases), failing to adapt to the complex situation of drastic time-varying spatial dimensions (i.e., dimensions may increase or decrease at any time) caused by heterogeneous relay observations of low-Earth orbit constellations. On the other hand, existing methods rely on prior information about the spectral tensor rank, or their tracking of the spectral tensor rank is mostly limited to unidirectional increases, unable to make bidirectional adaptive adjustments based on the time-varying low-rank nature of the actual spectral environment. Furthermore, most lack robust detection mechanisms for multidimensional complex anomalies.

[0006] In summary, facing the dynamic and incomplete observation environment of space-based systems, existing situation generation methods cannot simultaneously handle real-time processing of multidimensional data streams, robust suppression of complex anomalies, and adaptive mechanisms for drastic time-varying spatial dimensions. Therefore, this invention proposes a multidimensional adaptive streaming spectral tensor incremental reconstruction method that supports dimensional elastic scaling to overcome existing technical bottlenecks and achieve spatiotemporal continuous spectrum situational awareness in complex space-based environments. Summary of the Invention

[0007] To address the aforementioned technical problems, this invention proposes a multidimensional adaptive streaming reconstruction method for spectral situation tensor based on space-based dynamic incomplete observations, thereby resolving the issues present in the existing technologies.

[0008] To achieve the above objectives, this invention provides a multidimensional adaptive streaming cytometry reconstruction method for spectral situation tensor based on space-based dynamic incomplete observations, comprising: S1. Construct a dynamic tensor based on spectrum measurement data received in continuous time slots; S2. Determine the dimension evolution mode based on the spatial coverage dimension change of the dynamic tensor in adjacent time slots; S3. When the dimensionality evolution mode is expanding or remaining unchanged, an optimization model based on the historical factor matrix as a prior constraint is used to process the current observation tensor to obtain the factor matrix of the current time slot; when the dimensionality evolution mode is shrinking, a time series prediction method is used to pre-fill the blind zone, and the factor matrix of the current time slot is obtained by solving the observation tensor that is aligned with the dimension of the previous time step after filling. S4. Reconstruct the spectral situation tensor based on the factor matrix, and use a soft threshold operator to separate abnormal interference from the reconstruction residual; S5. Calculate the relative rate of change based on the reconstructed residual after separating abnormal interference, and update the tensor rank by combining the relative rate of change with the sliding window regression trend; S6. Based on the updated tensor rank adjustment factor matrix structure, the adjusted factor matrix is ​​used for the processing of the next time slot. S2-S6 are executed iteratively until the reconstruction result converges.

[0009] Optionally, the process of constructing a dynamic tensor based on spectrum measurement data received in consecutive time slots includes: Based on the spectrum measurement data received in continuous time slots, a dynamic tensor with three dimensions—longitude grid number, latitude grid number, and channel frequency point number—is constructed. The dynamic tensor is constrained at the element level using a binary observation tensor, and the dynamic tensor is represented as the Hadamard product of the sum of the true spectral situation tensor, the anomalous interference tensor, and the noise tensor and the binary observation tensor.

[0010] Optionally, the process of determining the dimensionality evolution mode based on the spatial coverage dimensionality change of the dynamic tensor in adjacent time slots includes: Based on the difference in the number of dimensions of the dynamic tensor between the current time slot and the previous time slot in the longitude grid dimension and the latitude grid dimension, the change in spatial coverage dimension is calculated. Based on the comparison between the change in spatial coverage dimension and zero, the dimension evolution mode is determined, which includes expansion, contraction, and invariance.

[0011] Optionally, when the dimensionality evolution mode is either expanding or remaining unchanged, the process of obtaining the factor matrix of the current time slot includes: Based on the spatial coverage dimension of the previous moment, the current observation tensor is divided into overlapping region subtensors and newly added region subtensors; Based on CP decomposition, the spatial factor matrix of the current time slot is divided into known sub-blocks corresponding to the historical dimensions and incremental sub-blocks corresponding to the newly added dimensions; Using the historical situation reconstructed based on the factor matrix of the previous moment, soft constraints are applied to the overlapping region subtensors of the known sub-blocks participating in the reconstruction, and the newly added region subtensors of the incremental sub-blocks participating in the reconstruction are fitted with the current observation data, and a joint optimization objective is constructed by combining the nuclear norm regularization term; The joint optimization objective is solved using the alternating direction multiplier method to obtain the factor matrix of the current time slot.

[0012] Optionally, the process of solving the joint optimization objective using the alternating direction multiplier method to obtain the factor matrix of the current time slot includes: S7. Introduce auxiliary variables and Lagrange multipliers, and construct an augmented Lagrange function based on the joint optimization objective; S8. The known sub-blocks of the current time slot are updated using the spatial factor matrix of the previous time step. The incremental sub-blocks of the current time slot are solved based on the updated known sub-blocks, and the frequency factor matrix and time factor vector are updated. S9. Based on the updated known sub-blocks, incremental sub-blocks, frequency factor matrix and time factor vector, the auxiliary variables are updated using the singular value shrinkage thresholding algorithm, and the Lagrange multipliers are updated using the dual ascent method. Execute S8 and S9 alternately until convergence is obtained to obtain the factor matrix of the current time slot.

[0013] Optionally, when the dimensionality evolution mode is shrinking, the process of obtaining the factor matrix of the current time slot includes: The blind zone index set is determined based on the difference between the spatial coverage at the previous moment and the actual observation range at the current moment; The predictability of each position in the blind zone index set is evaluated using approximate entropy, and a preset number of positions with the lowest approximate entropy value are selected to form a set to be filled. The set to be filled is predicted using a time-series prediction method, and an observation tensor aligned with the dimension of the previous time step is constructed based on the predicted value and the current observation data. Based on the aligned observation tensor and the factor matrix of the previous time slot, the factor matrix of the current time slot is obtained.

[0014] Optionally, the process of calculating the relative rate of change based on the reconstructed residuals after separating abnormal disturbances, and updating the tensor rank by combining the relative rate of change with the sliding window regression trend, includes: The relative rate of change is calculated based on the current time slot reconstruction residual after separating abnormal interference and the previous time slot reconstruction residual. The slope representing the error trend is obtained by performing least squares linear regression using the relative rate of change over several consecutive time slots within a sliding window. Based on the comparison results of the relative rate of change and the first threshold, and the comparison results of the slope and the second threshold, the rank adjustment direction is determined; The rank adjustment step size is determined based on the absolute value of the slope; The tensor rank is updated based on the rank adjustment direction and the rank adjustment step size.

[0015] Optionally, the process of determining the rank adjustment direction includes: When the relative rate of change is greater than the first threshold and the absolute value of the slope is greater than the second threshold, the rank adjustment direction is determined to be increasing; When the relative rate of change is greater than the first threshold and the absolute value of the slope is less than or equal to the second threshold, the rank adjustment direction is determined to be decreasing.

[0016] Optionally, the process based on the updated tensor rank adjustment factor matrix structure includes: When the rank adjustment direction is increasing, a randomly initialized column is generated and concatenated with the current factor matrix to obtain the factor matrix after structural adjustment. When the rank adjustment direction is to decrease, singular value decomposition is performed on the current factor matrix, and the first specified number of singular values ​​and the corresponding right singular matrix are truncated to obtain the structurally adjusted factor matrix.

[0017] The present invention also provides a computer, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements the method as described.

[0018] Compared with the prior art, the present invention has the following advantages and technical effects: This invention adapts to the elastic scaling of spatial dimensions caused by heterogeneous relay observations from low-Earth orbit constellations through dynamic tensor representation and dimensional evolution pattern determination. When the dimension expands, the historical factor matrix is ​​reused as a priori constraint to accelerate convergence; when the dimension shrinks, time-series prediction pre-filling overcomes structural deficiencies, and soft-threshold operators robustly suppress anomalous interference. Furthermore, bidirectional adaptive adjustment of the tensor rank is achieved based on reconstruction residual feedback to avoid underfitting and overfitting. The synergistic operation of these techniques enables high-precision, low-latency online streaming reconstruction of the spectral situation under dynamic incomplete observation environments on space-based systems. Attached Figure Description

[0019] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings: Figure 1 This is a scene diagram of spectrum situational awareness based on multi-satellite relay observation according to an embodiment of the present invention; Figure 2 This is a framework diagram of the dynamic tensor decomposition and completion technology according to an embodiment of the present invention; Figure 3 This is a comparison curve of the completion performance when the spectral situation dimension is expanded according to an embodiment of the present invention; Figure 4 This is a comparison curve of the completion performance when the spectral situation dimension is reduced according to an embodiment of the present invention; Figure 5 This is a visualization analysis image for spectrum situation completion in an embodiment of the present invention. Detailed Implementation

[0020] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0021] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0022] This invention proposes a multidimensional adaptive streaming reconstruction method for spectrum situation tensor in space-based dynamic incomplete observation, which is used to address the problem of generating a wide-area spatiotemporally continuous spectrum situation in space-based spectrum monitoring systems.

[0023] To address the issues of drastic time-varying tensor dimensions and high computational overhead associated with traditional batch processing in heterogeneous relay observations of low-Earth orbit constellations, this invention first constructs a dynamic tensor representation of the streaming spectral situation. Second, based on spatiotemporal-frequency correlation, a streaming incremental processing mechanism is employed, combined with nuclear norm constraints, to achieve missing data completion and abnormal interference filtering under a tensor space dimension elastic scaling (dynamic expansion or contraction) mode. Finally, based on real-time detection of reconstruction errors and bidirectional adaptive updating of the tensor rank, the low-rank subspace is reconstructed. This invention overcomes the limitations of fixed or unidirectionally changing dimensions and ranks in traditional models, enabling robust generation of online spectral situations with high precision and low latency in complex space-based incomplete observation environments. Specifically: (1) A streaming incremental reconstruction mechanism based on spectral tensors is proposed, breaking through the computational and storage bottlenecks of traditional batch processing. Addressing the problem that existing static batch processing methods are ill-suited to the highly dynamic environment of space-based applications, this invention constructs a dynamic tensor and introduces an online incremental processing mechanism. When a new observation data stream arrives, only the incremental data at the current moment needs to be updated and reconstructed incrementally, without repeatedly calculating historical global data. This mechanism significantly reduces the time complexity and storage overhead of the algorithm, achieving efficient online real-time generation of spectral situations.

[0024] (2) Supports flexible scaling of spatial dimensions, effectively overcoming the bottleneck of drastic time-varying dimensions caused by heterogeneous relay observations of low-Earth orbit constellations. Most existing streaming tensor processing methods rely on the assumption of fixed spatial dimensions, which cannot handle the dimensional mutations that occur over time. However, in actual space-based heterogeneous relay observations, the alternating passage of different payloads leads to irregular dynamic scaling of the effective spatial sensing range. In the face of the uncertainty changes in the sensing area caused by alternating observations of space-based constellations, this invention delves into the spatiotemporal-frequency multidimensional correlation of the spectral situation at continuous moments and innovatively proposes a tensor decomposition model that supports "flexible scaling of dimensions (i.e., dynamic expansion or contraction)". This model can effectively characterize the incremental pattern of newly added spectral situation tensor data, track the low-rank subspace in real time, and achieve dynamic completion of missing data and detection and removal of abnormal information through nuclear norm constraints.

[0025] (3) Achieves bidirectional adaptive dynamic optimization of the spectral tensor rank, significantly improving reconstruction accuracy under complex situations. Addressing the shortcomings of existing online completion methods that rely on "fixed rank" or "unidirectional rank increase" assumptions to accurately depict the dynamic evolution (appearance, disappearance, or movement) of radiation sources, this invention introduces a tensor rank detection and update mechanism based on reconstruction error feedback. This mechanism can perceive the intrinsic changes in the time-varying low-rank structure of the spectrum in real time, perform bidirectional adaptive adjustment of the tensor rank, and thus accurately update the low-rank subspace, maximizing the restoration of the true electromagnetic spectrum situational evolution process.

[0026] In addition, the English abbreviations and their corresponding full English and Chinese names involved in the accompanying drawings are shown in Table 1.

[0027] Table 1 Example 1 This invention proposes a multi-aspect Robust Adaptive Streaming Tensor (MA-RAST) method for generating wide-area spatiotemporally continuous spectrum situations in complex space-based spectrum monitoring environments.

[0028] A multidimensional adaptive streaming reconstruction method for spectral situation tensor based on space-based dynamic incomplete observations includes the following steps: S1, constructing a dynamic tensor based on spectral measurement data received in consecutive time slots; S2, determining the dimensional evolution mode based on the spatial coverage dimension change of the dynamic tensor in adjacent time slots; S3, when the dimensional evolution mode is expanding or remaining unchanged, processing the current observation tensor using an optimization model based on historical factor matrices as prior constraints to obtain the factor matrix of the current time slot; when the dimensional evolution mode is shrinking, using a time-series prediction method to... The blind zone is pre-filled, and the factor matrix of the current time slot is obtained by solving the observation tensor that is aligned with the dimension of the previous time step after filling; S4, the spectral situation tensor is reconstructed based on the factor matrix, and the abnormal interference is separated from the reconstruction residual using a soft threshold operator; S5, the relative rate of change is calculated based on the reconstruction residual after separating the abnormal interference, and the tensor rank is updated in combination with the sliding window regression trend; S6, the factor matrix structure is adjusted based on the updated tensor rank, and the adjusted factor matrix is ​​used for the processing of the next time slot. S2-S6 are iteratively executed until the reconstruction result converges.

[0029] As described in the background art and Figure 1 As shown, multiple LEO satellites work in formation to continuously observe and collect information about the target area, thus achieving continuous spatiotemporal coverage. However, due to limitations in onboard computing and storage capabilities, the satellites periodically transmit the collected data to a ground fusion center after completing spectrum measurements. At the ground fusion center, the spectrum measurement data is aggregated in real time as a continuous data stream and, through fusion with geographic information, a multi-domain spectrum situation map (SSM) covering space, frequency, and time is constructed to visually present the spatial distribution, spectrum occupancy, and temporal variation characteristics of radiated signals within the target area.

[0030] During this process, due to the constraints of the satellite's predetermined orbit, the complex space-to-ground transmission environment, and heterogeneous relay observations, the spectrum measurement data stream faces three major challenges: incomplete observations, inclusion of anomalous interference, and drastic changes in spatial dimension over time. Based on this, the core technical steps of the MA-RAST method of this invention are as follows: 1. Dynamic tensor representation for multidimensional heterogeneous data streams.

[0031] To characterize the incremental characteristics of spectrum data collected by sensing satellites in continuous time slots and to depict multi-dimensional information such as space, frequency, and field strength, this invention models the spectrum measurement data stream as a dynamic tensor.

[0032] Due to the transit characteristics of satellite formations, the spatial coverage dimension of spectral observation data in adjacent time slots will dynamically change. Therefore, in the... At any given moment, the observation data received by the ground fusion center can be characterized as a tensor. ,in This is called the spectral situation in the time slot. The incomplete observation tensor of the flow cytometry, the set of observation tensors at different time slots can be represented as , These represent the number of effective longitude grids, latitude grids, and channel frequency points sensed by the low-Earth orbit satellite at each moment, respectively.

[0033] In the complex space-based spectral situation observation environment It is incomplete and has abnormal pollution effects, which can be specifically described as follows: (1) in, Indicates at time The true spectral state tensor, Represents the anomalous disturbance tensor. This represents the Hadamard product, which is element-wise multiplication. Is with A binary observation tensor of the same size, where each element represents whether the element at the corresponding position has been observed (a value of 1 indicates that the position has been observed, and a value of 0 indicates that the data is missing), can be represented as follows: (2) 2. Adapting to dynamic tensor decomposition and completion for spatial dimension scaling.

[0034] Addressing the spatial coverage dimension caused by heterogeneous relay observation To address the problem that traditional static tensor methods fail due to the uncertainty of changes over time, this invention proposes a dynamic tensor decomposition scheme.

[0035] This scheme effectively addresses the problem of rapidly changing dimensions by adaptively matching the factor matrix of the elastic dimension. During streaming processing, subspace tracking technology is used to update the factor matrix of tensor decomposition in real time; simultaneously, robust penalty mechanisms such as soft-thresholding are introduced to effectively isolate and eliminate sparse anomalies. This allows for the acquisition of a preliminarily complete clean spectral state tensor under non-stationary observations.

[0036] 3. A bidirectional adaptive rank update strategy based on error feedback.

[0037] Due to the dynamic characteristics of the actual space-based spectrum environment, the state of radiation sources within the target area (appearance, disappearance, or movement) will continuously evolve. Traditional spectrum tensor generation methods usually presuppose a fixed tensor rank or only use a one-way rank-increasing strategy, which is difficult to adapt to this dynamic and non-stationary scenario and is prone to reconstruction distortion.

[0038] To address this, this invention proposes a bidirectional adaptive rank update strategy based on reconstruction error feedback. The mechanism captures the time-varying patterns of the low-rank structure of the spectrum by real-time monitoring of the fitting residual: when a new signal source appears, increasing the information content, an adaptive "rank increase" operation is triggered; when the signal source disappears or to avoid overfitting noise, a "rank decrease" operation is triggered. This strategy achieves bidirectional adaptive adjustment of the tensor rank, thereby accurately iterating the low-rank subspace and maximally reproducing the evolution of the real electromagnetic spectrum.

[0039] In summary, the overall design concept of this invention can be summarized as follows: modeling heterogeneous spectrum measurement data streams through "dynamic tensor representation," adapting to the uncertainties and abnormal interference of spatial dimensions using a "dynamic tensor decomposition and completion scheme," and finally capturing the spectrum evolution pattern through a "bidirectional adaptive rank update strategy." These three elements work synergistically to successfully achieve high-precision, spatiotemporally continuous spectrum situation reconstruction in complex space-based environments.

[0040] Furthermore, the MA-RAST architecture comprises the following two key modules: I. Dynamic Tensor Decomposition and Completion Module.

[0041] like Figure 2 As shown, this module, based on the multidimensional correlation and low-rank structure of the spectral situation in time, space, and frequency, and the smooth characteristics of situation evolution under continuous time slots, adaptively coordinates the dimensional uncertainty change patterns of the streaming tensor sequence caused by satellite relay observations. Specifically, this can be divided into two cases (dimensional expansion or dimensional reduction): 1) such as Figure 2 As shown in (a), when the effective spatial coverage of satellite sensing expands, it means continuous The tensor of spectral situation observation within a time slot expands along the spatial dimension, that is, for =1,2, therefore... .

[0042] Input: Ground fusion center at Incomplete observational spectral situational data received at any time (The initial state is denoted as) ), the moment before Reconstructed spectral state tensor (Green square) and its CP decomposition space factor matrix Frequency factor matrix Time factor vector .

[0043] Output: The spectral state tensor at the current time, preliminarily completed and with outliers removed. and its CP decomposition space factor matrix Frequency factor matrix Time factor vector sparse outlier data .

[0044] Objective: To address the challenge of sudden increases in spatial coverage caused by heterogeneous satellite relay observations, and to accelerate the completion and convergence process of the current spectral tensor by maximizing the reuse of historical decoupling factors.

[0045] As a specific implementation of this embodiment, the first step is: incremental dimensional coordination based on tensor partitioning. The continuously arriving spectral data stream is modeled as a dynamic tensor. To handle the scaling of spatial dimensions, a tensor partitioning strategy is adopted, based on... The dimensional benchmark of time is the current measurement spectrum state tensor. Divided into A subtensor, introducing a binary index set. Sub-tensor is denoted as ,in .here The corresponding space region overlaps with the satellite coverage at the previous moment. The remaining subtensors represent the spatial regions that newly enter the field of view as the satellite formation moves.

[0046] Step 2: Dynamic partitioning of the CP factor matrix. Based on the block partitioning property of CP decomposition, each sub-block of the tensor can be approximated by a sub-matrix of its corresponding factor matrix. Specifically, if at time... Spatial dimension of the observation tensor Expanded Then the CP space factor to be solved It can be divided into two submatrices: Corresponding to the unchanged historical spatial dimension, This corresponds to the increase in the spatial dimension. Therefore, each subtensor... It can be approximated as .

[0047] Step 3: Dynamic tensor completion joint optimization model. Utilizing... Prior information of CP decomposition at time step and This is combined with nuclear norm constraints to update the current spectral status. Specifically, it is expressed as follows: (3) Equation (3) is the overall objective expression, which means that the observed spectral data in the current time slot should be fitted as closely as possible to the low-rank tensor model estimated by CP decomposition, so as to minimize the error between the observed data and the estimated model, and complete the initial tensor completion. Simultaneously, it utilizes... Regularization terms constrain model complexity, eliminate abnormal noise, and ensure low-rank structure.

[0048] To incorporate historical priors, the overlapping and newly added regions in the above formula are separated, and then... Historical models of moments Alternative As a soft constraint, it is equivalent to the final optimization expression: (4) in, , Forgetting factor, It is the Frobenius norm, representing the square root of the sum of the squares of all elements in the array.

[0049] The first and second rows of equation (4) indicate that the effective observation area of ​​the satellite is divided into a common overlapping area. (The portion overlapping with satellite coverage from the previous moment) and newly added / changed areas This lays the groundwork for the subsequent introduction of historical priors.

[0050] The third and fourth lines of equation (4) indicate: introducing historical prior regularization for overlapping regions. Historical trends are used as priors to ensure the temporal continuity of the spectral trends; for newly added areas of change, only current observation data is used for fitting to cope with the dynamic scaling of spatial dimensions brought about by satellite relay observations. Used to balance the weights of historical priors and current observations, The larger the spectrum, the more dependent it is on historical spectrum trends.

[0051] Factor initialization strategy: To ensure rapid convergence of the algorithm, the following differentiated initialization mechanism is adopted: Spatial factor: Known dimension sub-blocks fully inherit historical state ( ); Incremental sub-blocks with added dimensions ( Random initialization is used.

[0052] Frequency and Time Factor: Due to the continuity of frequency bands and time sequences, the state of the previous moment is directly inherited, i.e. , .

[0053] The dimensions have not changed. When this occurs, it can be considered a special case where the space in this framework expands to 0. In this case, a new sub-block is added. Directly initialize the global factor. This allows for dynamic updates and iterations, thereby estimating the current complete state tensor. .

[0054] 2) such as Figure 2 As shown in (b), when the effective spatial coverage area sensed by the satellite shrinks, it means that continuous Within a time slot, the spectral situation observation tensor decreases along the spatial dimension, that is, for =1,2, therefore... .

[0055] To address the issue of structurally missing rows and columns of space-based spectrum data due to coverage blind spots, traditional online completion methods struggle to effectively recover these missing spectral regions. This invention introduces a pre-filling strategy based on temporal predictability assessment to complete the spectral data in unobserved areas.

[0056] Input: Ground Fusion Center Observational spectrum situation data received at any time The spectrum state tensor that was reconstructed in the previous moment ( Figure 2 (b) the green square and its CP decomposition space factor matrix Frequency factor matrix Time factor vector .

[0057] Output: The preliminary estimated spectral situation tensor after structural pre-filling and dynamic updating. and its updated CP decomposition space factor matrix Frequency factor matrix Time factor vector and the sparse anomaly of separation .

[0058] Objective: To address the large-scale structural gaps caused by the reduced effective spatial coverage resulting from satellite relay observations. While ensuring accuracy in the completion process, strict control must be exercised over the accumulation and cascading spread of prediction errors.

[0059] As a specific implementation of this embodiment, the first step is: Prophet structural prefilling based on temporal continuity. Addressing the problem that traditional methods cannot effectively fill in large structural gaps, this method first utilizes the inherent temporal continuity of the electromagnetic spectrum situation and introduces the multivariate time series prediction method, Prophet. By performing forward prediction along the temporal dimension on the missing regions, the missing regions are... Spatial dimensions aligned to the previous time slot This scale provides the necessary data support for subsequent tensor decomposition.

[0060] Step 2: Error Accumulation Resistance Optimization Strategy Based on Approximate Entropy (ApEn). Since direct prediction over large areas inevitably introduces computational errors, relying entirely on Prophet prediction for blind zone data and directly using it as the true observation value would lead to severe error accumulation. To overcome this bottleneck, this invention utilizes approximate entropy theory to quantitatively evaluate the signal complexity of unobserved regions. The lower the entropy value, the stronger the spectral evolution pattern and the higher the predictability at that location.

[0061] Define the previous moment The set of all spatial-frequency grid index tuples covered is ,current Observation tensor at all times The actual set of indexes used is The set of blind spots that cannot be observed at the current moment due to spatial contraction is: .

[0062] For blind spots Each grid position ( Figure 2 Calculate the approximate entropy of the white square marked with a question mark in (b) of the image. Then from Choose the one with the lowest entropy value. The positions (i.e., those with the strongest regularity and highest prediction confidence) constitute the set to be filled in for prediction. : (5) The third step is to address the dual limitations of traditional pure time series forecasting being susceptible to the accumulation of historical errors and pure tensor completion being unable to cope with large-scale structural defects, and to construct a framework of "time series forecast pre-filling + observation-based collaborative correction".

[0063] By using the current time slot spectrum observation data With time series prediction pre-filled items ( Figure 2 By combining the yellow square portion in (b) of the above, we obtain an observation tensor with the same dimension as the previous time step. That is, after filling Its expression is as follows: (6) Based on the newly constructed spectral state tensor after alignment Using the CP decomposition factor information obtained at the previous time step, the matrix is ​​iteratively updated to estimate the factor matrix at the new time step. and time vector Finally, the complete spectral state tensor is restored. .

[0064] In summary, the dynamic tensor decomposition and completion module can adaptively select the appropriate processing scheme based on the change in spatial dimension of the effective satellite sensing area within consecutive time slots. This architecture not only effectively solves the problem of wide-area dynamic time-varying conditions caused by heterogeneous relay observations from low-Earth orbit constellations, but also fills the technical gap in traditional online tensor completion methods, which cannot achieve high-precision streaming reconstruction in non-stationary, structurally missing scenarios.

[0065] To achieve the above objectives, the present invention employs the Alternating Direction Multiplier Method (ADMM) to solve the non-convex optimization objective and obtain the factor matrix of the current time slot. The process includes: S7, introducing auxiliary variables and Lagrange multipliers, and constructing an augmented Lagrange function based on the joint optimization objective; S8, updating the known sub-blocks of the current time slot using the spatial factor matrix from the previous time step, solving for the incremental sub-blocks of the current time slot based on the updated known sub-blocks, and updating the frequency factor matrix and time factor vector; S9, updating the auxiliary variables using the singular value shrinkage thresholding algorithm based on the updated known sub-blocks, incremental sub-blocks, frequency factor matrix, and time factor vector, and updating the Lagrange multipliers using the dual ascent method; S8 and S9 are executed alternately until convergence is obtained to obtain the factor matrix of the current time slot.

[0066] The specific steps for this module are as follows: 1. Dimensional Change Monitoring and Adaptive Decision Making: By calculating the change in spatial coverage dimension between adjacent time slots. ， Determine the dimensional evolution pattern of the current measurement spectrum data: when When the dimension increases or remains the same, the ADMM algorithm is directly applied to solve the reconstructed model in a streaming manner.

[0067] when (Time-dimension reduction) Using the "temporal series prediction pre-filling" scheme, the Prophet model is called to fill in structural gaps, so that the filled gaps are... .

[0068] 2. Constructing the augmented Lagrangian function: To achieve variable decoupling, an auxiliary variable is introduced. , , and the corresponding Lagrange multipliers , , for =1,2. Then the augmented Lagrangian function of the optimization model (3) can be expressed as: (7) in , is the penalty parameter. Let f(x) represent the constraint function of the original problem (3).

[0069] 3. Update the spatial spectrum state tensor factor and By fixing other variables Alternately update the space factor matrix , , First, based on the results of the previous time step. renew ,Then Used to update the incremental part The update rules are as follows: (8a) (8b) in , , They represent the following respectively: (9) and It is the spectral state tensor A specific set of indices for a subtensor. The product of Khatri-Rao, Subtensor Along the first The matrix after dimensional expansion.

[0070] 4. Update the frequency spectrum situation tensor factor and time vector factor : (10a) (10b) in, , , as well as The specific definitions are as follows: (11) in, This represents the corresponding subtensor Row vectorization, operator Indicates except the first Apart from the first factor, the remaining factors are multiplied sequentially using the Hadamard product operator. Indicates except the first Apart from the first factor, the remaining factors are multiplied by Khatri-Rao in sequence.

[0071] 5. Complete the full spectrum situation : Utilizing the updated factor matrix at the current time step and Get the time Spectral state subtensor: (12) 6. Update sparse anomaly interference Using a soft threshold operator, abnormal disturbances in the environment are stripped away and updated. (13) in, , It is a symbolic function. and These represent the operators for finding the maximum value and the absolute value, respectively. These represent arbitrary tensors, tensors consisting entirely of 1s, and tensors consisting entirely of 0s, respectively, and they are all the same size. The soft thresholding operator sets a threshold value. For input tensors where the absolute value of an element is greater than a threshold Defined as an anomaly, and then detected. .

[0072] 7. Update auxiliary variables , :Using the Singular Value Shrinking Thresholding (SVT) algorithm to constrain the low-rank property of the matrix, update the auxiliary variables: (14) Finally, the Lagrange multipliers are updated using the dual ascent method: (15) in, , It is an arbitrary matrix The singular value decomposition operation, .

[0073] II. Bidirectional Adaptive Rank Update Module.

[0074] Considering the highly time-varying characteristics of complex electromagnetic spectrum environments, radiation sources within the target region will continuously evolve dynamically. To maintain optimal reconstruction performance of tensor decomposition, this module monitors the dynamic changes in reconstruction errors in real time, and adaptively adjusts and updates the tensor rank bidirectionally, thereby achieving high-precision and robust recovery of the tensor of the true spectral situation.

[0075] Input: Preliminary completion results obtained from the dynamic tensor decomposition and completion module. Initial observation tensor Abnormal data tensors The current initial rank .

[0076] Output: Updated spectral state tensor rank The updated initial CP factor, i.e., the space factor. Frequency factor and time factor vector .

[0077] Objective: To overcome the limitations of traditional methods that rely on unidirectional rank increase or fixed rank, this method uses error trend to perceive the dimensionality change of the tensor quantum space, and then adaptively adjusts the tensor rank in both directions while simultaneously reconstructing the factor matrix. This aims to improve the accuracy and robustness of the spectral state tensor recovery while suppressing the risks of overfitting (too high rank) and underfitting (too low rank).

[0078] As a specific implementation of this embodiment, (a) the relative rate of change of the reconstruction residuals of adjacent time slots is calculated. (a) Real-time capture of rank changes caused by radiation source evolution. (b) Bidirectional adaptive rank adjustment based on error trend. A sliding window mechanism is introduced, combined with least squares linear regression to quantify the error evolution trend. The rate of change of residuals Error Trend (c) Rank-aware spectral tensor factor matrix synchronous update. When the rank dimension changes, the tensor factor matrix is ​​synchronously expanded in dimension or truncated based on singular value decomposition (SVD), avoiding the model mismatch problem after rank adjustment and ensuring the optimal reconstruction performance of tensor decomposition.

[0079] The implementation steps of the bidirectional adaptive rank update module are as follows: 1. Rank Change Detection. After each dynamic tensor decomposition and completion module, the rate of change of the error between the initially estimated spectral situation tensor and the true value is calculated to detect and update the tensor rank. The relative rate of change is specifically expressed as follows: (16) in, If the tensor rank remains unchanged, the residual will be small enough, typically. If the rank changes, the residual will increase significantly.

[0080] 2. Adaptive Rank Adjustment: If a change in rank is detected in step (1) above, the rank is adjusted accordingly. To determine the direction of the rank change, a sliding window is used. The data within the dataset is used to quantify the error trend through linear least squares regression. Specifically, Corresponding to the slope of the regression line fitted by minimizing the sum of squared residuals within this window index range, the formula is expressed as: (17) The rate of error change was quantified. By comprehensively considering the above two indicators, the direction of rank change was determined as follows: (18) in and Indicates the empirical threshold. The first threshold, This is the second threshold. The formula captures the fundamental trade-off in dynamic rank adaptation: an excessively large rank leads to a stable reconstruction error, i.e., overfitting, corresponding to... Conversely, insufficient rank leads to persistently large errors, i.e., underfitting, corresponding to... That is, when the relative rate of change is greater than the first threshold and the absolute value of the slope is greater than the second threshold, the rank adjustment direction is determined to be increasing; when the relative rate of change is greater than the first threshold and the absolute value of the slope is less than or equal to the second threshold, the rank adjustment direction is determined to be decreasing.

[0081] Furthermore, through dynamic step size The magnitude of each rank update is controlled by the following calculation method: (19) in Used to scale error trend The range, This represents the floor function. This is the maximum allowed step size, which helps to balance response speed and update stability.

[0082] Finally, according to the direction and step length , old rank The following formula can be used to update and crop: (20) in The function defines a preset rank allowable range. make sure .

[0083] 3. Synchronous update of the spectral tensor factor matrix. Based on the new rank. and its adjustment direction tensor factor Perform adaptive updates in the following manner: (twenty one) Among them, for (Rank increases), random initialization step size A new column (denoted as) ), and with Stitching to capture emerging features in a dynamically evolving spectral environment; for (Rank decreases), then from In singular value decomposition, retain the first singular values ​​( ) and the corresponding right singular matrix This allows for the elimination of redundant features while retaining the most important spectral components. It is worth noting that for the vector case... Singular value decomposition adaptive truncation is replaced by a variance-based truncation method, which selects the top truncation methods with the highest cumulative variance proportions. The elements are used to obtain the updated time vector. .

[0084] In summary, the MA-RAST method for multidimensional adaptive streaming reconstruction of spectral situation tensors for space-based dynamic incomplete observations proposed in this invention alternates between the dynamic tensor decomposition and completion module and the bidirectional adaptive rank update module until the spectral situation tensor is completed in two consecutive iterations. The relative change is less than the threshold tolerance.

[0085] The proposed spectral situation completion method is compared with other advanced methods.

[0086] The simulation settings are as follows, with a size of In the space region, seven radiation sources are deployed to transmit wireless signals, and the frequency domain range sensed by the satellite is [missing information]. MHz, divided into Each sub-band has equal bandwidth. Continuous monitoring. Each time slot has a different effective sensing area due to orbital limitations, meaning... As time changes, a third-order spectral situation tensor is constructed using the received power spectral density (PSD) of each spatial grid point in each frequency band within each time slot. The antenna transmit and receive gains are: dBi, path loss index of 2. The orbital altitude of the monitoring satellite is set at 340km, and the minimum elevation angle is [missing information]. 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.

[0087] like Figure 3 The graphs show a comparison of spectral situation completion performance under different missing rates, anomalies, and time slots with increased spatial dimensionality. The proposed MA-RAST algorithm consistently outperforms all online streaming baseline methods, including RACP, OR-MATC, and T-MUST, while achieving performance comparable to batch-based methods SPC and STDC. Furthermore, Figure 2 It can be observed that the rank change occurs in the time slot. , and None of the above algorithms have the ability to adaptively update the rank, resulting in a gradual decline in the performance of the spectrum situation map reconstruction over time.

[0088] at the same time, Figure 4 This study demonstrates a scenario where spatial dimensionality shrinkage occurs in measurements with structural missing data. Since other algorithms do not have the ability to dynamically handle dimensionality changes, the same time series prediction mechanism used in the comparison process is integrated into all baseline algorithms to ensure fair comparison.

[0089] The results clearly demonstrate that the proposed MA-RAST algorithm outperforms other online methods.

[0090] from Figure 5 It is also clear that MA-RAST successfully tracked the changes in the spectral dynamics over time. To visually compare the construction performance of different online algorithms, Figure 5 They respectively show the expansion of dimensions When stages and dimensions are reduced The 13th (constructed at that time) The spectrum situation of the narrowband channel is shown in the figure. It can be seen that the proposed MA-RAST is superior to OR-MAST and T-MUST, achieving the best visualization performance in both cases.

[0091] The present invention also provides a computer, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements the method as described.

[0092] The above are merely preferred embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A multidimensional adaptive streaming cytometry reconstruction method based on spectral situation tensor for space-based dynamic incomplete observations, characterized in that, Includes the following steps: S1. Construct a dynamic tensor based on spectrum measurement data received in continuous time slots; S2. Determine the dimension evolution mode based on the spatial coverage dimension change of the dynamic tensor in adjacent time slots; S3. When the dimensionality evolution mode is expanding or remaining unchanged, an optimization model based on the historical factor matrix as a prior constraint is used to process the current observation tensor to obtain the factor matrix of the current time slot; when the dimensionality evolution mode is shrinking, a time series prediction method is used to pre-fill the blind zone, and the factor matrix of the current time slot is obtained by solving the observation tensor that is aligned with the dimension of the previous time step after filling. S4. Reconstruct the spectral situation tensor based on the factor matrix, and use a soft threshold operator to separate abnormal interference from the reconstruction residual; S5. Calculate the relative rate of change based on the reconstructed residual after separating abnormal interference, and update the tensor rank by combining the relative rate of change with the sliding window regression trend; S6. Based on the updated tensor rank adjustment factor matrix structure, the adjusted factor matrix is ​​used for the processing of the next time slot. S2-S6 are executed iteratively until the reconstruction result converges.

2. The spectral situation tensor multidimensional adaptive streaming cytometry reconstruction method for space-based dynamic incomplete observation as described in claim 1, characterized in that, The process of constructing a dynamic tensor based on spectrum measurement data received in continuous time slots includes: Based on the spectrum measurement data received in continuous time slots, a dynamic tensor with three dimensions—longitude grid number, latitude grid number, and channel frequency point number—is constructed. The dynamic tensor is constrained at the element level using a binary observation tensor, and the dynamic tensor is represented as the Hadamard product of the sum of the true spectral situation tensor, the anomalous interference tensor, and the noise tensor and the binary observation tensor.

3. The spectral situation tensor multidimensional adaptive streaming cytometry reconstruction method for space-based dynamic incomplete observation as described in claim 1, characterized in that, The process of determining the dimensional evolution pattern based on the spatial coverage dimension change of the dynamic tensor in adjacent time slots includes: Based on the difference in the number of dimensions of the dynamic tensor between the current time slot and the previous time slot in the longitude grid dimension and the latitude grid dimension, the change in spatial coverage dimension is calculated. Based on the comparison between the change in spatial coverage dimension and zero, the dimension evolution mode is determined, which includes expansion, contraction, and invariance.

4. The spectral situation tensor multidimensional adaptive streaming cytometry reconstruction method for space-based dynamic incomplete observation as described in claim 3, characterized in that, When the dimensionality evolution mode is either expanding or remaining unchanged, the process of obtaining the factor matrix of the current time slot includes: Based on the spatial coverage dimension of the previous moment, the current observation tensor is divided into overlapping region subtensors and newly added region subtensors; Based on CP decomposition, the spatial factor matrix of the current time slot is divided into known sub-blocks corresponding to the historical dimensions and incremental sub-blocks corresponding to the newly added dimensions; Using the historical situation reconstructed based on the factor matrix of the previous moment, soft constraints are applied to the overlapping region subtensors of the known sub-blocks participating in the reconstruction, and the newly added region subtensors of the incremental sub-blocks participating in the reconstruction are fitted with the current observation data, and a joint optimization objective is constructed by combining the nuclear norm regularization term; The joint optimization objective is solved using the alternating direction multiplier method to obtain the factor matrix of the current time slot.

5. The spectral situation tensor multidimensional adaptive streaming cytometry reconstruction method for space-based dynamic incomplete observation as described in claim 4, characterized in that, The process of solving the joint optimization objective using the alternating direction multiplier method to obtain the factor matrix of the current time slot includes: S7. Introduce auxiliary variables and Lagrange multipliers, and construct an augmented Lagrange function based on the joint optimization objective; S8. The known sub-blocks of the current time slot are updated using the spatial factor matrix of the previous time step. The incremental sub-blocks of the current time slot are solved based on the updated known sub-blocks, and the frequency factor matrix and time factor vector are updated. S9. Based on the updated known sub-blocks, incremental sub-blocks, frequency factor matrix and time factor vector, the auxiliary variables are updated using the singular value shrinkage thresholding algorithm, and the Lagrange multipliers are updated using the dual ascent method. Execute S8 and S9 alternately until convergence is obtained to obtain the factor matrix of the current time slot.

6. The spectral situation tensor multidimensional adaptive streaming cytometry reconstruction method for space-based dynamic incomplete observation as described in claim 1, characterized in that, When the dimensionality evolution mode is reduced, the process of obtaining the factor matrix of the current time slot includes: The blind zone index set is determined based on the difference between the spatial coverage at the previous moment and the actual observation range at the current moment; The predictability of each position in the blind zone index set is evaluated using approximate entropy, and a preset number of positions with the lowest approximate entropy value are selected to form a set to be filled. The set to be filled is predicted using a time-series prediction method, and an observation tensor aligned with the dimension of the previous time step is constructed based on the predicted value and the current observation data. Based on the aligned observation tensor and the factor matrix of the previous time slot, the factor matrix of the current time slot is obtained.

7. The spectral situation tensor multidimensional adaptive streaming cytometry reconstruction method for space-based dynamic incomplete observation as described in claim 1, characterized in that, The process of calculating the relative rate of change based on the reconstructed residual after separating abnormal disturbances, and updating the tensor rank by combining the relative rate of change with the sliding window regression trend, includes: The relative rate of change is calculated based on the current time slot reconstruction residual after separating abnormal interference and the previous time slot reconstruction residual. The slope representing the error trend is obtained by performing least squares linear regression using the relative rate of change over several consecutive time slots within a sliding window. Based on the comparison results of the relative rate of change and the first threshold, and the comparison results of the slope and the second threshold, the rank adjustment direction is determined; The rank adjustment step size is determined based on the absolute value of the slope; The tensor rank is updated based on the rank adjustment direction and the rank adjustment step size.

8. The spectral situation tensor multidimensional adaptive streaming cytometry reconstruction method for space-based dynamic incomplete observation as described in claim 7, characterized in that, The process of determining the direction of rank adjustment includes: When the relative rate of change is greater than the first threshold and the absolute value of the slope is greater than the second threshold, the rank adjustment direction is determined to be increasing; When the relative rate of change is greater than the first threshold and the absolute value of the slope is less than or equal to the second threshold, the rank adjustment direction is determined to be decreasing.

9. The spectral situation tensor multidimensional adaptive streaming cytometry reconstruction method for space-based dynamic incomplete observation as described in claim 1, characterized in that, The process based on the updated tensor rank adjustment factor matrix structure includes: When the rank adjustment direction is increasing, a randomly initialized column is generated and concatenated with the current factor matrix to obtain the factor matrix after structural adjustment. When the rank adjustment direction is to decrease, singular value decomposition is performed on the current factor matrix, and the first specified number of singular values ​​and the corresponding right singular matrix are truncated to obtain the structurally adjusted factor matrix.

10. A computer comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the method as described in claim 1.

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