Spectral map construction method based on dynamic window tensor ring low rank factor

Abstract

The application relates to the technical field of electromagnetic spectrum management and control, in particular to a spectrum map construction method based on a dynamic window tensor ring low-rank factor, which comprises the following steps: modeling missing spectrum data by using a tensor; introducing a dynamic window mechanism based on the correlation of space-time spectrum data; solving a target function of the model by using an alternating direction multiplier method; and realizing the completion of the missing spectrum data and the real-time construction of a spectrum map. The application solves the target function of the DW-TRLRF model by using ADMM, converts the optimization problem of the target function into a plurality of sub-problems for solving, outputs target spectrum tensor data after multiple iteration convergences of all observed spectrum data when the motion time of a radiation source is less than or equal to the length of the dynamic window, and only needs to take the observed spectrum data of the length of the dynamic window as the input of the DW-TRLRF algorithm when the motion time of the radiation source is greater than the length of the dynamic window, and the iteration number of the algorithm is 1, so that the spectrum map reconstruction can be quickly realized.

Description

Technical Field

[0001] This invention relates to the field of electromagnetic spectrum management technology, specifically to a method for constructing a spectrum map based on a low-rank factor of a dynamic window tensor ring. Background Technology

[0002] With the widespread adoption of smart terminals and the emergence of various new services, spectrum scarcity and low utilization have become bottlenecks hindering the sustainable development of the wireless communication industry. Real-time monitoring and analysis of the radio spectrum environment are the foundation and prerequisite for achieving optimal allocation and management of spectrum resources. Spectrum maps, as a visual tool for describing spectrum resources, map the received signal strength within a region of interest to corresponding geographical coordinates, describing the spatial distribution of received signal strength. They can provide information on spectrum resource occupancy in the electromagnetic environment and the activity distribution of signal sources, providing crucial support for spectrum monitoring, spectrum management, and signal identification. Therefore, the construction of spectrum maps has received widespread attention from both academia and industry.

[0003] Currently, the algorithms used in constructing spectrum maps include alternating least square tensor ring completion (TR-ALS), tensor ring weighted optimization (TR-WOPT), tensor ring low-rank factors (TRLRF), and Kriging.

[0004] Chinese patent CN116754849A discloses a method and apparatus for constructing an electromagnetic spectrum map based on multi-precision monitoring data. The method includes: firstly, collecting monitoring data of different precisions using different types of sensors, and then using this data to perform trend surface fitting through a generalized regression neural network to obtain an estimate of the path attenuation component of radio wave propagation; then, subtracting the path attenuation component estimate from the monitoring data at the corresponding location to obtain residual monitoring data. Next, fitting a variogram function based on a small amount of high-precision residual monitoring data, and using only the high-precision variogram function when constructing the co-kriging system; then, supplementing the small amount of high-precision monitoring residual data with a large amount of low-precision monitoring residual data, and obtaining an estimate of the shadow attenuation component through co-kriging interpolation; finally, adding the two component estimates to obtain the overall electromagnetic spectrum map construction result.

[0005] Currently, when using the TR-ALS, TR-WOPT, TRLRF, and Kriging algorithms to construct spectrum maps, the Regression Sequence (RSE) is high, and the reconstructed spectrum map runs slowly. Therefore, there is an urgent need for a spectrum map construction method that can reduce RSE and improve the speed of spectrum map reconstruction. Summary of the Invention

[0006] To address the aforementioned problems, the present invention aims to provide a method and apparatus for constructing a spectrum map based on a low-rank factor of a dynamic window tensor ring.

[0007] The technical solution provided by this invention is as follows:

[0008] Firstly, a method for constructing a spectral map based on a low-rank factor of a dynamic window tensor ring includes the following steps:

[0009] S1. Model the missing spectral data using tensors;

[0010] S2. Based on the correlation of spatiotemporal spectrum data, a dynamic window mechanism is introduced;

[0011] S3. Solve the objective function of the model using the alternating direction multiplier method;

[0012] S4. Complete missing spectrum data and build spectrum maps in real time.

[0013] As an optional technical solution in the first aspect, in step S1, the tensor ring factor corresponding to the tensor ring decomposition representation is found from the observation items of the incomplete spectral tensor data in order to recover the missing items of the spectral tensor data.

[0014] Furthermore, in step S1, the specific modeling is as follows:

[0015]

[0016] Among them, ||·|| F Let P represent the Frobenius norm of the tensor, Ω represent the set of spectral data observations, and P represent the tensor's Frobenius norm. Ω (·) denotes the mapping under Ω, T denotes the incomplete spectral tensor data, [G] denotes the set of tensor ring factors, and Ψ([G]) denotes the approximate spectral tensor data generated by [G].

[0017] Furthermore, in step S2, based on the correlation of spatiotemporal spectral data, a dynamic window mechanism is introduced, and a spectral map generation model based on the low-rank factor of the dynamic window tensor ring is proposed:

[0018]

[0019] stP Ω (X)=P Ω(T);

[0020] Among them, ||·|| * denoted as nuclear norm regularization in the form of the sum of singular values ​​of a matrix, where X represents the target spectral tensor data.

[0021] Furthermore, by imposing low-rank constraints on the two rank moduli of the tensor ring factor, the tensor ring factor is expanded along modulo-1 and modulo-3 as follows:

[0022]

[0023] The spectrum map generation model based on the low-rank factor of the dynamic window tensor ring is ultimately represented as:

[0024]

[0025] stP Ω (X)=P Ω (T).

[0026] Furthermore, by adding the auxiliary variable [M], the optimization problem of the objective function can be expressed as:

[0027]

[0028]

[0029] P Ω (X)=P Ω (T);

[0030] gather Let represent the tensor sequence, which is an auxiliary variable of [G].

[0031] By adding equality constraints to the auxiliary variables into the Lagrange equation, we obtain the augmented Lagrange function of the objective function:

[0032] stP Ω (X)=P Ω (T);

[0033] in, Let μ be the set of Lagrange multipliers, μ be the penalty parameter, and μ > 0;

[0034] n = 1, ..., N, i = 1, 2, 3, G (n) M (n,i) Y (n,i) They are independent of each other.

[0035] Optionally, G (n) The update plan is as follows:

[0036]

[0037] Among them, C G It is a constant, which is composed of the other parts of the Lagrange function;

[0038] When n = 1, ..., N, G (n) Can be updated to:

[0039]

[0040] in, It is an identity matrix.

[0041] Optionally, M (n,i) The update plan is as follows:

[0042] When i = 1, 2, 3, the augmented Lagrangian function of [M] is expressed as:

[0043]

[0044] Among them, C M It is a constant, which is composed of the other parts of the Lagrange function;

[0045] Further updates to:

[0046]

[0047] Among them, D β (·) is a singular value thresholding operation.

[0048] Alternatively, the update scheme for X is as follows:

[0049]

[0050] stP Ω (X)=P Ω (T);

[0051] Among them, C X It is a constant, which is composed of the other parts of the Lagrange function;

[0052] The target tensor X is updated by inputting observed spectral data, and in each iteration, the missing terms of the tensor circumference factor [G] approximate the spectral data are updated, i.e.:

[0053]

[0054] Among them, P Ω (T) represents all observations of the incomplete spectral data. It is a collection of missing items in the spectrum data. This represents all missing terms in the approximate spectral tensor data generated by the TR factor [G].

[0055] Optionally, when n = 1, ..., N and i = 1, 2, 3, the Lagrange multiplier Y (n,i) Updated to:

[0056]

[0057] Furthermore, the penality of the Lagrange function is constrained by μ, and each iteration passes through μ + =max{ρμ,μ max Update, where ρ is a tuning hyperparameter, and 1 < ρ < 1.5; μ max This represents the upper limit of μ, max{ρμ,μ max} represents taking ρμ and μ max The larger one is taken as the current μ value;

[0058] When the radiation source's motion time is less than or equal to the length of the dynamic window, each variable is updated alternately through multiple iterations. Two convergence conditions are set: the maximum number of iterations maxiter and the relative error threshold tol between two iterations. When both convergence conditions are met simultaneously, i.e., the maximum number of iterations maxiter is reached and the relative error between two iterations is less than the threshold tol, the iteration ends, and the target spectral tensor data X is obtained.

[0059] When the radiation source's motion time is greater than the length of the dynamic window, the observed spectral data of the dynamic window length only needs to be used as the input of the DW-TRLRF algorithm, and the algorithm iteration count is 1, to obtain the target spectral tensor data X, which can quickly realize the reconstruction of the spectral map.

[0060] In a second aspect, a computer device includes 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 spectrum map construction method of the first aspect or any of the technical solutions of the first aspect.

[0061] Compared with the prior art, the technical solution provided by this invention has the following advantages:

[0062] Compared with existing technologies, this invention first utilizes tensors to model missing spatiotemporal spectral data, developing a spectral map construction model based on tensor ring decomposition. Based on the correlation of spatiotemporal spectral data, a dynamic window mechanism is introduced, with a window length of β. t The spectral data at the relevant time points are put into β. t In the observed spectral data X t-βt+1 , ..., X t-1 X tThis model exhibits strong correlation, therefore a spectrum map generation model based on the low-rank factor of the dynamic window tensor ring is proposed. The objective function of the DW-TRLRF model is solved using ADMM. By constructing the augmented Lagrangian form of the objective function, the optimization problem is transformed into multiple sub-problems to be solved separately. Intermediate variables are iteratively updated by solving each sub-problem sequentially. When the radiation source motion time t ≤ β... t When the observed spectral data at all times needs to be iterated and converged multiple times to output the target spectral tensor data, and when the radiation source's motion time t>β t Only t-β is needed t ,t-β t The spectral data at times +1,…t-1 are used as input to the DW-TRLRF algorithm, and the algorithm has only one iteration. This enables rapid reconstruction of the spectral map and improves the accuracy of the spectral map construction. Attached Figure Description

[0063] Figure 1 This is a schematic diagram showing the arrangement of mobile radiation sources and monitoring sensors within the area in an embodiment of this application;

[0064] Figure 2 This is a schematic diagram illustrating the modeling of missing spectral tensor data in an embodiment of this application;

[0065] Figure 3 This is a diagram of the tensor ring decomposition model in the embodiments of this application;

[0066] Figure 4 This is a flowchart of the spectrum map construction method based on the low-rank factor of the dynamic window tensor ring in an embodiment of the present invention;

[0067] Figure 5 This is the distribution of singular values ​​of the spectral matrix at different spatial locations in this embodiment of the invention;

[0068] Figure 6 This is the distribution of singular values ​​of the spectral matrix under different shadow fading standard deviations in this embodiment of the invention;

[0069] Figure 7 This describes the spectrum map construction process based on the DW-TRLRF algorithm in this embodiment of the invention.

[0070] Figure 8 (a) is the initial spatial location of the radiation source in the embodiment of the present invention;

[0071] Figure 8 (b) is the spatial position of the radiation source after 100 seconds of movement in this embodiment of the invention;

[0072] Figure 8 (c) is the spatial position of the radiation source after 200 seconds of movement in this embodiment of the invention;

[0073] Figure 9 (a) is the third-order spectral tensor data in an embodiment of the present invention;

[0074] Figure 9 (b) is the spectral tensor data with a missing rate of 70% in the embodiment of the present invention;

[0075] Figure 9 (c) is the spectral tensor data completed by the DW-TRLRF algorithm in the embodiment of the present invention;

[0076] Figure 10 (a) Comparison of the performance of constructing a spectrum map with the data missing rate when the standard deviation of shadow fading is 3dB in an embodiment of the present invention;

[0077] Figure 10 (b) Comparison of the performance of constructing a spectrum map with the data missing rate when the standard deviation of shadow fading is 5dB in the embodiment of the present invention;

[0078] Figure 10 (c) A comparison of the performance of constructing a spectrum map with the data missing rate when the standard deviation of shadow fading is 7dB in the embodiment of the present invention;

[0079] Figure 11 This is a comparison of the runtime of constructing a spectrum map when the standard deviation of shadow fading is 3dB in an embodiment of the present invention. Detailed Implementation

[0080] To further understand the content of this invention, a detailed description of the invention will be provided in conjunction with the accompanying drawings and embodiments.

[0081] The structures, proportions, and sizes illustrated in the accompanying drawings are merely for illustrative purposes and to aid those skilled in the art in understanding and reading the invention. They are not intended to limit the scope of the invention and therefore have no substantial technical significance. Any modifications to the structure, changes in proportions, or adjustments to size, without affecting the effectiveness and purpose of the invention, should still fall within the scope of the technical content disclosed herein. Furthermore, terms such as "upper," "lower," "left," "right," and "middle" used in this specification are merely for clarity and not intended to limit the scope of implementation. Changes or adjustments to their relative relationships, without substantially altering the technical content, should also be considered within the scope of the invention's implementation.

[0082] In one embodiment, the problem scenario provided by this application is as follows:

[0083] A set of monitoring sensors and multiple mobile radiation sources are randomly deployed within the target area, where the initial location and emission power of the radiation sources are unknown. Figure 1 As shown.

[0084] The position of sensor i is monitored using m i The strength of the received signal is represented by P(m). i If ) indicates that:

[0085]

[0086] In the formula, Let m be the emission power of a certain radiation source, K be the free-space path loss factor, ε be the path loss exponent, and m be the path loss index. p Let ||·|| represent the location of a radiation source, and ||·|| represent the Euclidean distance between two vectors. It is m i The shadow fading at a location follows a log-normal distribution and has a standard deviation of σ.

[0087] For dynamic spectrum situational awareness scenarios, monitoring sensors are deployed on a uniformly spaced grid of size a×b in a two-dimensional geographic region. These sensors monitor the surrounding spectrum situation. At time t, the spectrum data is represented by matrix X. t ∈R a×b This is represented as a three-dimensional spectral tensor, such as... Figure 2 As shown in the figure. The X and Y axes represent spatial positions, and the Z axis represents the time of motion of the radiation source.

[0088] Accurate construction of a spectrum map requires the use of a large number of sensors. In order to reduce time and cost, tensor completion algorithms need to be applied to recover spectrum data from a limited number of sensors.

[0089] Tensor ring (TR) decomposition is a model for processing high-dimensional spectral tensors. It decomposes the complexity of high-dimensional spectral data into a series of easily processed low-dimensional spectral data structures using a ring structure, which is highly valuable for extracting useful features and information. When n = 1, ..., N, the TR factor is used... This indicates that each factor consists of two rank moduli (modulo-1 and modulo-3) and a one-dimensional moduli (modulo-2). {R1,R2,…,R N+1} represents the rank of the tensor ring, and the rank of the tensor ring controls the model complexity of tensor ring decomposition. Therefore, for tensor rings... The tensor ring decomposition is defined as:

[0090]

[0091] Trace{·} is the matrix trace operation. G represents the nth TR factor. (n) The i-th n A modulo-2 slice matrix can also be used with G. (n) (:,i n ,:) represents the rank of a tensor ring.TR (X)=(R1,R2,…,R N ), where R1 = R N+1 .like Figure 3 As shown.

[0092] Based on this, in this embodiment, as Figure 4 As shown, this application proposes a method for constructing a spectrum map based on the low-rank factor of a dynamic window tensor ring, including the following steps:

[0093] S1. Model the missing spectral data using tensors;

[0094] S2. Based on the correlation of spatiotemporal spectrum data, a dynamic window mechanism is introduced; a spectrum map generation model based on dynamic window size tensor ring low-rank factors (DW-TRLRF) is proposed.

[0095] S3. Solve the objective function of the DW-TRLRF model using the alternating direction method of multipliers (ADMM). By constructing the augmented Lagrangian form of the objective function, the optimization problem of the objective function is transformed into multiple sub-problems to be solved separately. The intermediate variables are updated iteratively by solving each sub-problem in turn. After the function converges after multiple iterations, the completed spectrum data is output.

[0096] S4. Complete missing spectrum data and build spectrum maps in real time.

[0097] In this embodiment, in step S1, a spectrum map construction model based on tensor ring decomposition is developed to find the tensor ring (TR) factor corresponding to the tensor ring decomposition representation from the observations of incomplete spectrum tensor data, so as to recover the missing items of the spectrum tensor data. The specific modeling is as follows:

[0098]

[0099] Among them, ||·|| F Let Ω represent the Frobenius norm of the tensor, Ω represent the set of spectral data observations, and P represent the tensor's Frobenius norm. Ω (·) denotes the mapping under Ω, T denotes the incomplete spectral tensor data, [G] denotes the set of tensor ring factors, and Ψ([G]) denotes the approximate spectral tensor data generated by [G].

[0100] To describe the characteristics of the rank of the spectral tensor data, the spectral data is first preprocessed and expanded into a matrix in the time dimension. Singular value decomposition is then used to analyze the distribution of the rank at the spatial location of the radiation source as it moves over time and the distribution of the rank at the initial position under different shadow fading label differences. Figure 5 The paper presents the singular value distribution in descending order after normalization. When the standard deviation of shadow fading is 3dB, the three lines represent the singular value analysis curves of the spectrum map matrix of the radiation source at the initial moment, after 100s of motion, and after 200s of motion.

[0101] Figure 6 The image shows the normalized singular values ​​arranged in descending order. The three lines represent the spectral map matrix at the initial position with shadow fading standard deviations of 3dB, 5dB, and 7dB, respectively.

[0102] from Figure 5 and Figure 6 It can be seen that the distribution of singular values ​​of the received signal strength matrix after the spectral tensor expansion is always concentrated in the first few singular values, which indicates that the spectral data has an approximately low-rank structure.

[0103] The length of the window is β t The spectral data at the relevant time points are put into β. t In the observed spectral data X t-βt+1 , ..., X t-1 X t It has a strong correlation, such as Figure 7 As shown. β t It can be set to 10.

[0104] In step S2, based on the correlation of spatiotemporal spectral data, a dynamic window mechanism is introduced to apply low-rank constraints to each TR factor. Figure 5 and Figure 6 To address the low-rank nature of the exhibited spectral tensor data, a spectral map generation model based on the low-rank factor of the dynamic window tensor ring is proposed.

[0105]

[0106] stP Ω (X)=P Ω (T);

[0107] Among them, ||·|| * denoted as nuclear norm regularization in the form of the sum of singular values ​​of a matrix, where X represents the target spectral tensor data.

[0108] In this embodiment, a low-rank constraint is applied to the two rank moduli of the tensor ring factor, and the tensor ring factor is expanded along modulo-1 and modulo-3 as follows:

[0109]

[0110] The spectrum map generation model based on the low-rank factor of the dynamic window tensor ring is ultimately represented as:

[0111]

[0112] stP Ω (X)=P Ω (T).

[0113] In step S3, ADMM is used to solve the objective function of the DW-TRLRF model. Since the variables in the DW-TRLRF model are interdependent, an auxiliary variable [M] is added. The optimization problem of the objective function is then expressed as:

[0114]

[0115]

[0116] P Ω (X)=P Ω (T);

[0117] gather Let represent a tensor sequence, which is an auxiliary variable of [G].

[0118] By adding equality constraints to the auxiliary variables into the Lagrange equation, we obtain the augmented Lagrange function of the objective function:

[0119]

[0120] stP Ω (X)=P Ω (T);

[0121] in, Let μ be the set of Lagrange multipliers, μ be the penalty parameter, and μ > 0.

[0122] n = 1, ..., N, i = 1, 2, 3, G (n) M (n,i) Y (n,i) Since they are independent of each other, the update scheme for each variable is as follows:

[0123] G (n) The update plan is as follows:

[0124]

[0125] Among them, C G It is a constant, composed of the other parts of the Lagrange function, which is related to the update of G. (n)Irrelevant. This is a least squares problem, when n = 1, ..., N, G (n) Can be updated to:

[0126]

[0127] in, It is an identity matrix.

[0128] M (n,i) The update plan is as follows:

[0129] When i = 1, 2, 3, the augmented Lagrangian function of [M] is expressed as:

[0130]

[0131] Among them, C M It is a constant, which is composed of the other parts of the Lagrange function;

[0132] Further updates to:

[0133]

[0134] Among them, D β (·) is a singular value thresholding operation.

[0135] The update scheme for X is as follows:

[0136]

[0137] stP Ω (X)=P Ω (T);

[0138] Among them, C X It is a constant, which is composed of the other parts of the Lagrange function;

[0139] The target tensor X is updated by inputting observed spectral data, and in each iteration, the missing terms of the tensor circumference factor [G] approximate the spectral data are updated, i.e.:

[0140]

[0141] Among them, P Ω (T) represents all observations of the incomplete spectral data. It is a collection of missing items in the spectrum data. This represents all missing terms in the approximate spectral tensor data generated by the TR factor [G].

[0142] When n = 1, ..., N and i = 1, 2, 3, the Lagrange multiplier Y (n,i) Updated to:

[0143] Y+ (n,i) =Y (n,i) +μ(M (n,i) -G (n) ).

[0144] The penality of the Lagrange function is constrained by μ, and each iteration passes through μ. + =max{ρμ,μ max Update, where ρ is a tuning hyperparameter, and 1 < ρ < 1.5; μ max This represents the upper limit of μ, max{ρμ,μ max} represents taking ρμ and μ max The larger one is taken as the current μ value.

[0145] In one embodiment, ρ can be set to 1.01.

[0146] When the radiation source's motion time is less than or equal to the length of the dynamic window, each variable is updated alternately through multiple iterations. Two convergence conditions are set: a maximum number of iterations (maxiter) and a relative error threshold (tol) between two iterations. The iteration ends when both conditions are met simultaneously (maxiter = 300) and the relative error between two iterations is less than the threshold (tol), yielding the target spectral tensor data X. In this embodiment, each variable is updated alternately through multiple iterations, with two convergence conditions: a maximum number of iterations (maxiter) = 300 and a relative error threshold (tol) between two iterations = 10. -6 The formula for calculating the relative error between two iterations is ||XX|. last || F / ||X|| F X represents the current value of X. last This represents the value of X in the previous iteration. The maximum number of iterations (300) is reached when both of the above convergence conditions are met simultaneously, and the relative error between two iterations is less than a threshold of 10. -6 The iteration ends, and the target spectral tensor data X is obtained.

[0147] When the radiation source's motion time is greater than the length of the dynamic window, the observed spectral data of the dynamic window length only needs to be used as the input of the DW-TRLRF algorithm, and the algorithm iteration count is 1, to obtain the target spectral tensor data X, which can quickly realize the reconstruction of the spectral map.

[0148] To verify that the proposed method achieves higher accuracy in constructing spectrum maps compared to existing methods, this embodiment will evaluate the performance of the proposed spectrum map construction scheme using simulation data. Figure 8(a) shows a 1000m × 1000m simulation environment with three radiation sources. Their initial coordinates are (500m, 900m), (900m, 900m), and (900m, 500m). The radiation sources move at a speed of 5m / s along a fixed direction. The spatial position matrices after 100 seconds and 200 seconds of movement are shown below. Figure 8 As shown in (b), Figure 8 As shown in (c).

[0149] Considering the motion time of the radiation source, it is modeled as a third-order spectral tensor, such as... Figure 9 As shown in (a), the spectral tensor data has a size of 100×100×200. The three dimensions represent the location (X-axis and Y-axis) and the radiation source's motion time (Z-axis), respectively. The received signal intensity is displayed in different colors. Then, it is randomly missing data, assuming a missing rate of 70%. The missing spectral tensor data is as follows. Figure 9 As shown in (b). After the radiation source has moved for 200 seconds, the missing spectral tensor data is completed using the DW-TRLRF algorithm, as follows: Figure 9 As shown in (c).

[0150] The parameter settings for the simulation data are shown in the table below:

[0151] parameter numerical values target area 1000m×1000m Radiation source movement time 200s Radiation source velocity 5m / s Radiation source emission power [30dBm, 26dBm, 24dBm] Initial position of radiation source (500m,900m), (900m,900m), (900m,500m) Path loss index 2 Path loss factor 10dB Shadow fading standard deviation 3dB, 5dB, 7dB <![CDATA[Dynamic window size β t > 10

[0152] To quantify the performance of the tensor completion algorithm, the root square error (RSE) criterion is used:

[0153]

[0154] In the formula H is the completed spectral tensor data, while H is the original spectral tensor data from the simulation.

[0155] Figure 10To compare and analyze the accuracy of five different algorithms for constructing spectrogram maps based on different standard deviations of shadow fading in simulation data, including the DW-TRLRF algorithm, the tensor ring completion by alternating least square (TR-ALS) algorithm, the tensor ring weighted optimization (TR-WOPT) algorithm, the tensor ring low-rank factors (TRLRF) algorithm, and the Kriging algorithm. It can be seen that when the missing spectral data rate is 0.2 to 0.8 and the standard deviation of shadow fading is 3 dB, 5 dB, and 7 dB, the average RSE of the DW-TRLRF algorithm for constructing the spectrogram map is reduced by 15.27%, 15.67%, 1.88%, and 12.97% compared to the TR-ALS, TR-WOPT, TRLRF, and Kriging algorithms, respectively.

[0156] like Figure 11 As shown, time tests were conducted on an i9-12900H CPU with 16GB RAM. With a spectrum data missing rate of 0.2-0.8 and a shadow fading standard deviation of 3dB, DW-TRLRF reduced the average runtime for spectrum map reconstruction by 39.85%, 94.1%, 86.75%, and 99.67% compared to TR-ALS, TR-WOPT, TRLRF, and Kriging, respectively.

[0157] This invention proposes a spectrum map construction method based on the low-rank factor of a dynamic window tensor ring, which can quickly reconstruct the spectrum map and improve its construction accuracy. Simulation results show that, with a spectrum data missing rate of 0.2-0.8 and a shadow fading standard deviation of 3dB, the proposed algorithm reduces the average RSE by 12.41% compared to the Kriging algorithm, indicating that it can effectively improve the spectrum map construction capability under conditions of incomplete spectrum data.

[0158] In one embodiment, this application also proposes a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the above-described spectrum map construction method.

[0159] The present invention and its embodiments have been described above illustratively. This description is not restrictive, and the figures shown are only one embodiment of the present invention; the actual structure is not limited thereto. Therefore, if those skilled in the art are inspired by this description and design similar structures and embodiments without departing from the spirit of the present invention, such designs should fall within the protection scope of the present invention.

Claims

1. A method for constructing a spectral map based on a low-rank factor of a dynamic window tensor ring, characterized in that, Includes the following steps: S1. Model the missing spectral data using tensors; S2. Based on the correlation of spatiotemporal spectrum data, a dynamic window mechanism is introduced; S3. Solve the objective function of the model using the alternating direction multiplier method; S4. Complete missing spectrum data and build spectrum maps in real time; In step S1, the specific modeling is as follows: ； in, The Frobenius norm of a tensor is represented by... Represents the set of spectral data observations. Indicates in The following mapping, Represents incomplete spectral tensor data. Represents the set of tensor ring factors. Indicates by The generated approximate spectral tensor data; In step S2, based on the correlation of spatiotemporal spectrum data, a dynamic window mechanism is introduced, and a spectrum map generation model based on the low-rank factor of the dynamic window tensor ring is proposed: ； in, This represents nuclear norm regularization in the form of the sum of the singular values ​​of a matrix. Represents the target spectrum tensor data; When the radiation source's motion time is less than or equal to the length of the dynamic window, each variable is updated alternately through multiple iterations. Two convergence conditions are set: the maximum number of iterations (maxiter) and the relative error threshold (tol) between two iterations. When both convergence conditions are met simultaneously (i.e., the maximum number of iterations (maxiter) is reached and the relative error between two iterations is less than the threshold (tol), the iteration ends, and the target spectral tensor data is obtained. ; When the radiation source's motion time exceeds the length of the dynamic window, only the observed spectral data of the dynamic window length needs to be used as input to the DW-TRLRF algorithm, with the algorithm iteration count being 1, to obtain the target spectral tensor data. It can quickly reconstruct the spectrum map.

2. The spectrum map construction method according to claim 1, characterized in that: In step S1, the tensor ring factor corresponding to the tensor ring decomposition representation is found from the observations of the incomplete spectral tensor data in order to recover the missing items of the spectral tensor data.

3. The spectrum map construction method according to claim 2, characterized in that: Applying low-rank constraints to the two rank moduli of the tensor ring factor, the tensor ring factor is expanded along modulo-1 and modulo-3 as follows: ； The spectrum map generation model based on the low-rank factor of the dynamic window tensor ring is ultimately represented as: 。 4. The spectrum map construction method according to claim 3, characterized in that: Add auxiliary variables The optimization problem of the objective function is expressed as: ； gather Representing a tensor sequence, as Auxiliary variables; By adding equality constraints to the auxiliary variables into the Lagrange equation, we obtain the augmented Lagrange function of the objective function: ； in, Let μ be the set of Lagrange multipliers, μ be the penalty parameter, and μ > 0; n =1,…, N , i =1,2,3 , , They are independent of each other.

5. The spectrum map construction method according to claim 4, characterized in that, The update plan is as follows: ； in, It is a constant, which is composed of the other parts of the Lagrange function; when n =1,…, N , Can be updated to: ； in, It is an identity matrix.

6. The spectrum map construction method according to claim 4, characterized in that, The update plan is as follows: when i When =1,2,3 The augmented Lagrange function is expressed as: ； in, C M It is a constant, which is composed of the other parts of the Lagrange function; Further updates to: ； in, This is a threshold operation for singular values.

7. The spectrum map construction method according to claim 4, characterized in that, The update scheme for X is as follows: ； in, C X It is a constant, which is composed of the other parts of the Lagrange function; The target tensor X is updated by inputting observed spectral data, and the tensor circumfactor is updated in each iteration. The missing terms in the approximate spectral data, namely: ； in, This represents all observations in incomplete spectral data. It is a collection of missing items in the spectrum data. Indicated by TR factor All missing terms in the generated approximate spectral tensor data.

8. The spectrum map construction method according to claim 4, characterized in that, when n =1,…, N and i When =1,2,3, the Lagrange multipliers Updated to: 。 9. The spectrum map construction method according to any one of claims 5-8, characterized in that: The penalized effect of the Lagrange function μ Limitation: Each iteration passes Update, in which ρ It is a tuning hyperparameter, and 1 < ρ <1.5; Indicates setting upper limit Indicates taking and One of the larger ones as the current value.

10. A computer device 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 spectrum map construction method as described in any one of claims 1-9.

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