Electromagnetic spectrum map construction method based on tdoa / aod data supplement

Abstract

The application relates to a TDOA / AOA data supplemented electromagnetic spectrum map construction method. The method comprises the following steps: a measurement point collects a received signal to determine the received signal strength of the measurement point to obtain TDOA measurement data and AOA measurement data, a probability model is constructed to probabilistically update an electromagnetic spectrum map of a target region, a posterior probability distribution of a signal source position is obtained, a signal source position corresponding to a maximum value of the posterior probability distribution is taken as a candidate signal source position, and the received signal strength of the candidate signal source position and the received signal strength at other non-measurement point positions are estimated; a candidate point set is randomly generated in the target region, a candidate point with the maximum target function value is selected as a target point and is added to an accurate data set; after adaptive mixed kernel function optimization parameters are constructed, a Bayesian Kriging method is used to interpolate and output an electromagnetic spectrum map of the target region after supplement, and the electromagnetic spectrum map construction precision is improved.

Description

Technical Field

[0001] This application relates to the field of electromagnetic spectrum technology, and in particular to a method for constructing an electromagnetic spectrum map based on TDOA / AOA data supplementation. Background Technology

[0002] Electromagnetic spectrum maps are tools for systematically dividing and visualizing electromagnetic waves within different wavelength or frequency ranges. They visualize and describe invisible electromagnetic waves, helping people better understand and utilize electromagnetic spectrum resources. The electromagnetic spectrum, similar to land resources, is finite. Signals such as 4G, 5G, and broadcasting all rely on specific frequency bands; therefore, proper planning and avoidance of signal interference are necessary to better utilize spectrum resources.

[0003] Currently, electromagnetic spectrum map construction methods are mainly divided into three categories: direct construction methods (i.e., spatial interpolation methods), indirect construction methods (i.e., parametric construction methods), and hybrid construction methods. Direct construction methods (such as inverse distance weighted (IDW) and kriging methods) rely solely on measurement data from discrete monitoring points, generating continuous data surfaces through spatial interpolation. Among them, kriging, as an optimal unbiased estimation method, models spatial correlation based on variograms and covariance functions, exhibiting high interpolation accuracy when data is abundant. However, when monitoring points are unevenly distributed or insufficient in number, direct construction methods are prone to misestimating the center location of signal sources, especially when multiple signal sources exist, failing to accurately capture global spectrum distribution characteristics. For example, the IDW method relies excessively on local measurement extrema, while ordinary kriging may merge multiple signal sources into a single region when data is sparse, leading to severe distortion.

[0004] Indirect construction methods estimate spectral distribution by combining prior information such as transmitter location and radiated power with radio wave propagation models. While this method can compensate for the shortcomings of direct construction methods, it requires extremely high accuracy of the channel model and struggles to adapt to complex environmental changes such as multipath effects and shadowing fading. Especially in scenarios with multiple signal sources, indirect construction methods lack effective multi-source separation capabilities, resulting in limited estimation accuracy.

[0005] Furthermore, existing transmitter position estimation methods typically assume a single signal source and rely on accurate modeling of the path loss exponent and shadowing fading parameters. These methods suffer from model mismatch issues in real-world testing environments and cannot effectively handle spectral overlap when multiple signal sources coexist.

[0006] In summary, existing electromagnetic spectrum map construction methods have low accuracy. Summary of the Invention

[0007] Therefore, it is necessary to provide an electromagnetic spectrum map construction method based on TDOA / AOA data supplementation that can improve the accuracy of electromagnetic spectrum map construction, addressing the aforementioned technical problems.

[0008] A method for constructing an electromagnetic spectrum map based on TDOA / AOA data supplementation, the method comprising:

[0009] Step S1: Collect the received signals at each measurement point, determine the received signal strength at each measurement point, and perform parameter estimation on the collected received signals to obtain TDOA measurement data and AOA measurement data.

[0010] Step S2: Based on the TDOA measurement data and the AOA measurement data, construct a probability model, update the electromagnetic spectrum map of the target area according to the probability model, and normalize the updated probability distribution to obtain the posterior probability distribution of the signal source location.

[0011] Step S3: Based on the posterior probability distribution of the signal source location, the signal source location corresponding to the maximum value of the posterior probability distribution is taken as the candidate signal source location, and the candidate signal source location is taken as the center location of the intensity peak. Then, combined with the received signal intensity at each measurement point, the received signal intensity at the candidate signal source location and the received signal intensity at other non-measurement point locations are estimated using the log-normal shadowing fading model to generate fuzzy data. The fuzzy data includes the estimated received signal intensity at the candidate signal source location and the estimated received signal intensity at other non-measurement point locations.

[0012] Step S4: The data hierarchical recursive algorithm is used to analyze the precise data and the fuzzy data to determine the recursive prediction formula and its conditional variance formula for the point to be predicted. The precise data includes the received signal strength of each measurement point.

[0013] Step S5: A set of candidate points is uniformly and randomly generated within the target area. The prediction variance of each candidate point in the set is analyzed under precise data and under fuzzy data. The weighted sum of the prediction variances of each candidate point under precise data and fuzzy data is used as the objective function. The candidate point with the largest objective function value is selected as the target point. The precise predicted value and prediction variance of the target point are calculated using the recursive prediction formula and conditional variance formula of the point to be predicted. The target point and its precise predicted value are added to the precise dataset. When the reduction in the overall prediction variance of the target points due to the addition of a new target point is less than a set threshold... When the target point addition is stopped, the precise dataset includes the location information of each measurement point and its received signal strength, and the location information of each target point and its precise predicted value.

[0014] Step S6: Construct an adaptive hybrid kernel function consisting of a quadratic exponential kernel, a Matern 3 / 2 kernel, and a rational quadratic kernel. Using points in the precise data as sample points, maximize the logarithmic marginal likelihood as the optimization objective, and iteratively optimize the weight parameters using the gradient ascent method. , and And kernel function hyperparameters, to obtain the adaptive hybrid kernel function after optimization parameters;

[0015] Step S7: Using the optimized parameters of the adaptive hybrid kernel function, the Bayesian skrygian method is used to interpolate the unknown coordinate points in the target area space, and output the supplemented electromagnetic spectrum map of the target area.

[0016] In one embodiment, the probability model includes an AOA probability model and a TDOA probability model;

[0017] The AOA probability model is a von Mises distribution, and the probability density function of the AOA probability model is... Represented as:

[0018] ;

[0019] in, For the AOA probability model, the first i The probability density value corresponding to each measurement point Here, is the concentration parameter, controlling the degree of concentration of the distribution; e is the natural constant. Let be the AOA observation value at the i-th measurement point in the AOA measurement data; The true angle of arrival of the signal source; To correct the zeroth-order Bessel function and ensure the normalization condition;

[0020] The TDOA probability model follows a Gaussian distribution, and the probability density function of the TDOA probability model is... Represented as:

[0021] ;

[0022] in, For the TDOA probability model i The probability density value corresponding to each measurement point Let be the TDOA observation value at the i-th measurement point in the TDOA measurement data; exp represents the natural exponential function; This represents the theoretical distance difference corresponding to the location of the candidate signal source; This represents the standard deviation of the TDOA measurement error. The variance of the TDOA measurement error; It is the speed of light.

[0023] In one embodiment, the expression for the probability update is:

[0024] ;

[0025] in, This represents the number of groups of AOA measurement data; The number of groups of TDOA measurement data; An index for AOA measurement data; An index for TDOA measurement data; For coordinates in two-dimensional space The probability value of the arrival angle observation at the grid point of the i-th group; For coordinates in two-dimensional space The probability value of reaching the time difference observation after passing through the j-th group at the grid point; This indicates that the coordinates in two-dimensional space are The unnormalized posterior probability value is obtained at the grid point after joint probability update of multiple sets of arrival angle and arrival time difference observations.

[0026] In one embodiment, the two-dimensional spatial coordinates in the posterior probability distribution of the signal source location are: Normalized posterior probability values ​​at grid points for:

[0027] ;

[0028] in, To be on all grid points in the target area The maximum value.

[0029] In one embodiment, the log-normal shadowing fading model is: ,in, Let n be the signal strength to be estimated, and n be the path loss exponent. The distance between the receiving point and the signal source. For shadow fading terms; This is the received signal strength vector.

[0030] In one embodiment, the step of using a data hierarchical recursive algorithm to analyze precise data and fuzzy data to determine the recursive prediction formula and its conditional variance formula for the point to be predicted includes:

[0031] The precise data and the fuzzy data are integrated to construct an autoregressive expression;

[0032] Assuming that the fuzzy data and the residual stochastic process of the autoregressive expression both follow Gaussian processes, a joint distribution of the measurement points and the points to be predicted is constructed. Based on the conditional distribution properties of the Gaussian process, the recursive prediction formula and its conditional variance formula for the points to be predicted are determined. The recursive prediction formula for the points to be predicted is as follows:

[0033] ;

[0034] in, Indicates the point to be predicted Accurate prediction value; Indicates the point to be predicted The correlation coefficient function between precise predicted values ​​and fuzzy data; Represents the points to be predicted under fuzzy data. The predicted value at that location; This represents the mean function of the residual random process at the point to be predicted. This represents the transpose of the correlation vector between the point to be predicted and the known point in the residual stochastic process. The matrix representing the inverse of the covariance matrix of a stochastic process with known residuals; Represents known point data Subtract the corresponding mean The residual vector after;

[0035] The conditional variance formula for the point to be predicted is:

[0036] ;

[0037] in, Indicates the point to be predicted The predicted variance at the location; Indicates the point to be predicted The square of the correlation coefficient function between the precise predicted value and the fuzzy data; Represents the points to be predicted under fuzzy data. The predicted variance at the location; This indicates that the residual stochastic process is at the point to be predicted. The autocovariance at a given point is used to characterize the uncertainty introduced by the residual stochastic process itself; This indicates that the residual stochastic process is at the point to be predicted. The correlation vector between the known points, for transpose, It represents the inverse matrix of the covariance matrix of a random process with known residuals.

[0038] In one embodiment, the regression expression is:

[0039] ;

[0040] in, For accurate data, For fuzzy data, It is the correlation coefficient between precise data and fuzzy data. It is a residual random process that follows a Gaussian process.

[0041] In one embodiment, the objective function for:

[0042] ;

[0043] in, The prediction variance for accurate data; The prediction variance for fuzzy data; For weighting coefficients, through Adjust the weights of precise and fuzzy data.

[0044] In one embodiment, the adaptive hybrid kernel function for:

[0045] ;

[0046] In the formula, and These represent any two spatial locations within the target area. , and These are the weighting coefficients. It is a squared exponent kernel. It uses the Matern 3 / 2 core. For rational quadratic kernels, the expressions are as follows:

[0047] ,

[0048] ;

[0049] ;

[0050] in, , and For length scale parameters, , and These are used to control the smoothness of the function, the frequency of the function's fluctuations, and the multi-scale mixing weights, respectively. For shape parameters.

[0051] In one embodiment, the expression for the logarithmic marginal likelihood is:

[0052] ;

[0053] In the formula, z is the observation vector, representing the number of observations in the exact dataset. Received signal strength data at each sample point; X is the precise dataset, containing... The location information of each sample point; θ is a parameter set, which includes weight parameters. , and Length scale parameter , and and shape parameters Where K is the covariance matrix generated by the kernel function. It is the noise variance, and I is the identity matrix. This represents finding the inverse of a matrix. Represents a determinant; Indicates transpose; π is the constant of pi. For the given input Given the parameter set θ, the probability distribution of the observed vector z;

[0054] The iterative formula for optimizing hyperparameters using the gradient ascent method is as follows:

[0055] ;

[0056] in, Indicates the first The parameter set at the next iteration For the first The parameter set at the next iteration; It is the learning rate; It is a set of parameters gradient operator, For the given input The probability distribution of the observed vector z under the given condition.

[0057] The aforementioned electromagnetic spectrum map construction method based on TDOA / AOA data supplementation determines the received signal strength at each measurement point by collecting received signals at each measurement point and performing parameter estimation on the collected received signals to obtain TDOA and AOA measurement data. Based on the TDOA and AOA measurement data, a probability model is constructed, and the electromagnetic spectrum map of the target area is updated probabilistically according to the probability model. The updated probability distribution is then normalized to obtain the posterior probability distribution of the signal source location. Based on the posterior probability distribution of the signal source location, the signal source location corresponding to the maximum value of the posterior probability distribution is selected as the candidate signal source location, and this candidate signal source location is used as the intensity peak center location. Then, combined with the received signal strength at each measurement point, a log-normal shadowing fading model is used to estimate the received signal strength at the candidate signal source location. Signal strength and received signal strength at other non-measurement point locations are used to generate fuzzy data. A data hierarchical recursive algorithm is employed to analyze the precise and fuzzy data, determining the recursive prediction formula and its conditional variance formula for the points to be predicted. A set of candidate points is uniformly and randomly generated within the target area. The prediction variance of each candidate point under precise and fuzzy data is analyzed, and the weighted sum of the prediction variances of each candidate point under precise and fuzzy data is used as the objective function. The candidate point with the largest objective function value is selected as the target point. The precise predicted value and its prediction variance of the target point are calculated using the recursive prediction formula and its conditional variance formula for the points to be predicted, and the target point and its precise predicted value are added to the precise dataset. If the reduction in the overall target point prediction variance due to the addition of a new target point is less than a set threshold... When the target point addition stops, an adaptive hybrid kernel function consisting of a quadratic exponential kernel, a Matern 3 / 2 kernel, and a rational quadratic kernel is constructed. Using points in the precise data as sample points, the optimization objective is to maximize the logarithmic marginal likelihood, and the gradient ascent method is used to iteratively optimize the weight parameters. , and The hyperparameters of the kernel function are obtained to obtain an adaptive hybrid kernel function with optimized parameters. Using the optimized adaptive hybrid kernel function, the Bayesian skrygian method is used to interpolate the unknown coordinates of each unknown coordinate point in the target area space, and output the electromagnetic spectrum map of the target area. This solves the problem of not being able to handle multiple signal sources well and the low estimation accuracy, and improves the accuracy of electromagnetic spectrum map construction. Attached Figure Description

[0058] Figure 1 This is a flowchart illustrating a method for constructing an electromagnetic spectrum map based on TDOA / AOA data supplementation in one embodiment.

[0059] Figure 2 This is a schematic diagram of the adaptive sample selection algorithm in one embodiment;

[0060] Figure 3 Error comparison chart for electromagnetic spectrum map construction methods;

[0061] Figure 4 An error comparison chart is constructed before and after parameter optimization of the adaptive Bayesian skewkin method in this application;

[0062] Figure 5 A comparison chart showing the electromagnetic spectrum map construction results of three methods: IDW method, ordinary Kriging method, and adaptive Bayesian Kriging method. Detailed Implementation

[0063] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0064] In one embodiment, such as Figure 1 As shown, a method for constructing an electromagnetic spectrum map based on TDOA / AOA data supplementation is provided, including the following steps:

[0065] Step S1: Collect the received signals at each measurement point, determine the received signal strength at each measurement point, and perform parameter estimation on the collected received signals to obtain TDOA (Time Difference of Arrival) measurement data and AOA (Angle of Arrival) measurement data.

[0066] It should be understood that the location information (i.e., spatial coordinates) of each measurement point is known, based on the received signals collected by the antennas at each measurement point.

[0067] Step S2: Based on the TDOA measurement data and AOA measurement data, construct a probability model, update the electromagnetic spectrum map of the target area according to the probability model, and normalize the updated probability distribution to obtain the posterior probability distribution of the signal source location.

[0068] In one embodiment, the probability model includes the AOA probability model and the TDOA probability model;

[0069] The AOA probability model follows a von Mises distribution, and the probability density function of the AOA probability model is... Represented as:

[0070] ;

[0071] in, For the AOA probability model, the first iThe probability density value corresponding to each measurement point Here, is the concentration parameter, controlling the degree of concentration of the distribution; e is the natural constant. Let be the AOA observation value at the i-th measurement point in the AOA measurement data; The true angle of arrival of the signal source; To correct the zeroth-order Bessel function and ensure the normalization condition;

[0072] The TDOA probability model follows a Gaussian distribution, and the probability density function of the TDOA probability model is... Represented as:

[0073] ;

[0074] in, For the TDOA probability model i The probability density value corresponding to each measurement point Let be the TDOA observation value at the i-th measurement point in the TDOA measurement data; exp represents the natural exponential function; This represents the theoretical distance difference corresponding to the candidate signal source location. Specifically, it represents the distance from the candidate signal source location to the reference measurement point and the distance to the [missing information] point, assuming that the candidate signal source location is the actual signal source location. The difference in propagation distance between measurement points; This represents the standard deviation of the TDOA measurement error. The variance of the TDOA measurement error; It is the speed of light.

[0075] In one embodiment, the expression for probability update is:

[0076] ;

[0077] in, This represents the number of sets of AOA measurement data; each measurement point's AOA measurement data constitutes one set. This represents the number of sets of TDOA measurement data; each measurement point's TDOA measurement data constitutes one set. An index for AOA measurement data; An index for TDOA measurement data; For coordinates in two-dimensional space The probability value of the arrival angle observation at the grid point of the i-th group; For coordinates in two-dimensional space The probability value of reaching the time difference observation after passing through the j-th group at the grid point; This indicates that the coordinates in two-dimensional space are The unnormalized posterior probability value is obtained at the grid point after joint probability update of multiple sets of arrival angle and arrival time difference observations.

[0078] In one embodiment, after multiple sets of data updates are completed and normalization is performed, the two-dimensional spatial coordinates in the posterior probability distribution of the signal source location are: Normalized posterior probability values ​​at grid points for:

[0079] ;

[0080] in, To be on all grid points in the target area The maximum value.

[0081] Step S3: Based on the posterior probability distribution of the signal source location, the signal source location corresponding to the maximum value of the posterior probability distribution is taken as the candidate signal source location, and the candidate signal source location is taken as the center location of the intensity peak. Then, combined with the received signal intensity at each measurement point, the received signal intensity at the candidate signal source location and the received signal intensity at other non-measurement point locations are estimated using the log-normal shadowing fading model, generating fuzzy data. The fuzzy data includes the estimated received signal intensity at the candidate signal source location and the estimated received signal intensity at other non-measurement point locations.

[0082] Given the received signal strengths at M measurement points, these signals are combined to form a received signal strength vector. for:

[0083] ;

[0084] in, For the first The received signal strength at each measurement point .

[0085] Then, a log-normal shadowing fading model of the received signal strength is constructed, and its formula is:

[0086] ;

[0087] in, Let n be the signal strength to be estimated, and n be the path loss exponent. The distance between the receiving point and the signal source. For shadow fading terms; This is the received signal strength vector.

[0088] Construct the probability density based on the log-normal shadowing fading model of the received signal strength. Its formula is:

[0089] ;

[0090] in, Indicates the distance between the receiving point and the signal source. The variance of the measurement error for received power. This is the shadow fading correction factor. Indicates the number of measurement points.

[0091] The path loss index is as follows:

[0092] .

[0093] It should be understood that shadow fading reflects the random attenuation of a signal during propagation caused by factors such as obstacles, terrain, or buildings. This random attenuation is characterized by a shadow fading term, which follows a zero-mean Gaussian distribution. After obtaining the path loss exponent, the received signal strength at candidate locations and other non-measurement locations can be estimated based on the signal propagation model, thereby generating fuzzy data.

[0094] In one embodiment, the log-normal shadowing fading model is: ,in, Let n be the signal strength to be estimated, and n be the path loss exponent. The distance between the receiving point and the signal source. For shadow fading terms; This is the received signal strength vector.

[0095] Step S4: The data hierarchical recursive algorithm is used to analyze the precise data and fuzzy data to determine the recursive prediction formula and its conditional variance formula for the point to be predicted. The precise data includes the received signal strength of each measurement point.

[0096] Among them, the precise data obtained directly With the estimated fuzzy data Integrate and construct the autoregressive expression:

[0097] ;

[0098] in, For accurate data, For fuzzy data, It is the correlation coefficient between precise data and fuzzy data. It is a residual random process that follows a Gaussian process.

[0099] Assume that the random error process of the fuzzy data and the autoregressive expression follows a Gaussian process:

[0100] ,

[0101] ;

[0102] in, It is an abbreviation for Gaussian Process; and For any two spatial locations within the target area, The mean function for fuzzy data; For the location point A random process at a given location; It is a mean function. For fuzzy data, the covariance function is... For error random process The covariance function. The predicted point is derived using known precise and fuzzy data. accurate predicted value .

[0103] Based on the aforementioned autoregressive relationship and Gaussian process assumption, a joint distribution of the measurement points and the points to be predicted can be constructed, and the points to be predicted can be obtained using the conditional distribution properties of the Gaussian process. The conditional mean and conditional variance of the precise data are given. The conditional mean of the point to be predicted can be written as a recursive prediction formula:

[0104] ;

[0105] Among them, among them, Indicates the point to be predicted Precise prediction value; Indicates the point to be predicted The correlation coefficient function between precise predicted values ​​and fuzzy data; Represents the points to be predicted under fuzzy data. The predicted value at that location; This represents the mean function of the residual random process at the point to be predicted. This represents the transpose of the correlation vector between the point to be predicted and the known point in the residual stochastic process. The matrix representing the inverse of the covariance matrix of a stochastic process with known residuals; Represents known point data Subtract the corresponding mean The residual vector after the recursive prediction formula can be used with known precise data. and fuzzy data Derive the point to be predicted accurate predicted value .

[0106] Meanwhile, the point to be predicted The conditional variance at point is:

[0107] ;

[0108] in, Indicates the point to be predicted The predicted variance at the location; Indicates the point to be predicted The square of the correlation coefficient function between the precise predicted value and the fuzzy data; Represents the points to be predicted under fuzzy data. The predicted variance at the location; This indicates that the residual stochastic process is at the point to be predicted. The autocovariance at a given point is used to characterize the uncertainty introduced by the residual stochastic process itself; This indicates that the residual stochastic process is at the point to be predicted. The correlation vector between the known points, for transpose, It represents the inverse matrix of the covariance matrix of a random process with known residuals.

[0109] In one embodiment, a data hierarchical recursive algorithm is used to analyze precise and fuzzy data to determine the recursive prediction formula and its conditional variance formula for the point to be predicted, including:

[0110] accurate data With fuzzy data Integrate the data and construct an autoregressive expression;

[0111] Assuming that the residual stochastic processes of the fuzzy data and the autoregressive expression both follow Gaussian processes, a joint distribution of the measured points and the points to be predicted is constructed. Based on the properties of the conditional distribution of the Gaussian process, the recursive prediction formula and its conditional variance formula for the points to be predicted are determined. The recursive prediction formula for the points to be predicted is as follows:

[0112] ;

[0113] in, Indicates the point to be predicted Precise prediction value; Indicates the point to be predicted The correlation coefficient function between precise predicted values ​​and fuzzy data; Represents the points to be predicted under fuzzy data. The predicted value at that location; This represents the mean function of the residual random process at the point to be predicted. This represents the transpose of the correlation vector between the point to be predicted and the known point in the residual stochastic process. The matrix representing the inverse of the covariance matrix of a stochastic process with known residuals; Represents known point data Subtract the corresponding mean The residual vector after;

[0114] The formula for the conditional variance of the point to be predicted is:

[0115] ;

[0116] in, Indicates the point to be predicted The predicted variance at the location; Indicates the point to be predicted The square of the correlation coefficient function between the precise predicted value and the fuzzy data; Represents the points to be predicted under fuzzy data. The predicted variance at the location; This indicates that the residual stochastic process is at the point to be predicted. The autocovariance at a given point is used to characterize the uncertainty introduced by the residual stochastic process itself; This indicates that the residual stochastic process is at the point to be predicted. The correlation vector between the known points, for transpose, It represents the inverse matrix of the covariance matrix of a random process with known residuals.

[0117] In one embodiment, the regression expression is:

[0118] ;

[0119] in, For accurate data, For fuzzy data, It is the correlation coefficient between precise data and fuzzy data. It is a residual random process that follows a Gaussian process.

[0120] Step S5: Generate a set of candidate points uniformly and randomly within the target area. Analyze the prediction variance of each candidate point in the set under precise data and the prediction variance under fuzzy data. Use the weighted sum of the prediction variances of each candidate point under precise data and the prediction variances under fuzzy data as the objective function. The candidate point with the largest objective function value is selected as the target point. The recursive prediction formula and its conditional variance formula for the points to be predicted are used to calculate the accurate predicted value and prediction variance of the target points, and the target points and their accurate predicted values ​​are added to the accurate dataset; when the reduction in the overall prediction variance of the newly added target points is less than a set threshold... When the target point addition is stopped, the accurate dataset includes the location information of each measurement point and its received signal strength, as well as the location information of each target point and its accurate predicted value.

[0121] The reduction in the overall target variance due to the addition of a new target point refers to the change between the average of the prediction variances of all target points in the accurate dataset (excluding the newly added target point) and the average of the prediction variances of all target points in the accurate dataset.

[0122] Among them, such as Figure 2 As shown, a set of candidate points is uniformly and randomly generated within the target area. The prediction variance of each candidate point under precise data and the prediction variance under fuzzy data are calculated using the following formula:

[0123] ,

[0124] ;

[0125] in, Indicates precise data at candidate points The predicted variance at that location Indicates fuzzy data at candidate points The prediction variance; and Representing the sets of precise data coordinate points and fuzzy data coordinate point set The covariance matrix; and These are the covariance functions for precise data and fuzzy data, respectively. and For row vectors, overall quantization and , The correlation, Indicates transpose; For noise variance; It is the identity matrix. This represents finding the inverse of a matrix.

[0126] And use its weighted sum as the objective function. for:

[0127] ;

[0128] in, The prediction variance for accurate data; The prediction variance for fuzzy data; For weighting coefficients, through Adjust the weights of precise and fuzzy data.

[0129] The candidate point with the largest objective function value is selected as the target point. A hierarchical recursive algorithm is used to calculate the accurate predicted value, and the target point and its accurate predicted value are added to the accurate dataset; when the reduction in the prediction variance of the newly added target point on the overall target point is less than a set threshold... When that happens, stop adding new target points.

[0130] In one embodiment, the objective function for:

[0131] ;

[0132] in, The prediction variance for accurate data; The prediction variance for fuzzy data; For weighting coefficients, through Adjust the weights of precise and fuzzy data.

[0133] Step S6: Construct an adaptive hybrid kernel function consisting of a quadratic exponential kernel, a Matern 3 / 2 kernel, and a rational quadratic kernel. Using points in the precise data as sample points, maximize the logarithmic marginal likelihood as the optimization objective, and iteratively optimize the weight parameters using the gradient ascent method. , and And kernel function hyperparameters, to obtain the adaptive hybrid kernel function after optimization parameters.

[0134] In one embodiment, the adaptive hybrid kernel function for:

[0135] ;

[0136] In the formula, and These represent any two spatial locations within the target area; , and These are the weighting coefficients; It is a squared exponent kernel; It uses a Matern 3 / 2 core; For rational quadratic kernels, the expressions are as follows:

[0137] ,

[0138] ;

[0139] ;

[0140] in, , and For length scale parameters, , and These are used to control the smoothness of the function, the frequency of the function's fluctuations, and the multi-scale mixing weights, respectively. For shape parameters.

[0141] In one embodiment, the expression for the log-marginal likelihood is:

[0142] ;

[0143] In the formula, z is the observation vector, representing the number of observations in the exact dataset. Received signal strength data at each sample point; X is the precise dataset, containing... The location information of each sample point; θ is a parameter set, which includes weight parameters. , and Length scale parameter , and and shape parameters Where K is the covariance matrix generated by the kernel function. It is the noise variance, and I is the identity matrix. This represents finding the inverse of a matrix. Represents a determinant; Indicates transpose; π is the constant of pi. For the given input Given the parameter set θ, the probability distribution of the observed vector z; The larger the value, the better the kernel function.

[0144] The iterative formula for optimizing hyperparameters using the gradient ascent method is as follows:

[0145] ;

[0146] in, Indicates the first The parameter set at the next iteration (i.e., the current iteration). For the first The parameter set for the next iteration; It is the learning rate; It is a set of parameters gradient operator, For the given input The probability distribution of the observed vector z under the given condition.

[0147] Among them, the kernel function hyperparameters include the length scale parameter. , and and shape parameters .

[0148] It should be understood that after the iteration is completed, the convergence condition of the iteration is checked. If the condition is met, the iteration is stopped. Then, the Kriging method is used to interpolate and complete the electromagnetic spectrum map of the target area to generate the electromagnetic spectrum map.

[0149] Step S7: Using the optimized adaptive hybrid kernel function, the Bayesian skrygian method is used to interpolate the unknown coordinates of each point in the target area space, and output the supplemented electromagnetic spectrum map of the target area.

[0150] Specifically, using an adaptive hybrid kernel function with optimized parameters, the Bayesian skrygian method is employed to interpolate and predict the received signal intensity at each unknown coordinate point within the target area, obtaining the predicted received signal intensity value corresponding to each unknown coordinate point. Then, the predicted value is fused with the measured received signal intensity at each measurement point and the accurate predicted value of the target point already included in the accurate dataset, and mapped according to the grid coordinates of the target area to form the received signal intensity distribution matrix corresponding to each grid point within the target area, thereby obtaining the supplemented electromagnetic spectrum map of the target area.

[0151] The electromagnetic spectrum map construction method based on TDOA / AOA data supplementation described above determines the received signal strength at each measurement point by collecting received signals at each measurement point and performing parameter estimation on the collected received signals to obtain TDOA and AOA measurement data. Based on the TDOA and AOA measurement data, a probability model is constructed, and the electromagnetic spectrum map of the target area is updated probabilistically according to the probability model. The updated probability distribution is then normalized to obtain the posterior probability distribution of the signal source location. Based on the posterior probability distribution of the signal source location, the signal source location corresponding to the maximum value of the posterior probability distribution is selected as the candidate signal source location, and this candidate signal source location is used as the intensity peak center location. Combining the received signal strength at each measurement point, a log-normal shadowing fading model is used to estimate the received signal strength at the candidate signal source location and the received signal strength at other non-measurement point locations. The process involves generating fuzzy data, including estimated received signal strength at candidate signal source locations and estimated received signal strength at other non-measurement point locations. A hierarchical recursive algorithm is used to analyze both precise and fuzzy data to determine the recursive prediction formula and its conditional variance formula for the points to be predicted. A set of candidate points is uniformly and randomly generated within the target area. The prediction variance of each candidate point under precise and fuzzy data is analyzed, and the weighted sum of these variances is used as the objective function. The candidate point with the largest objective function value is selected as the target point. The precise predicted value and its prediction variance of the target point are calculated using the recursive prediction formula and its conditional variance formula, and the target point and its precise predicted value are added to the precise dataset. The process continues until the reduction in the overall target point prediction variance due to the addition of a new target point is less than a set threshold. When the target point addition stops, an adaptive hybrid kernel function consisting of a quadratic exponential kernel, a Matern 3 / 2 kernel, and a rational quadratic kernel is constructed. Using points in the precise data as sample points, the optimization objective is to maximize the logarithmic marginal likelihood, and the gradient ascent method is used to iteratively optimize the weight parameters. , and The hyperparameters of the kernel function are obtained to obtain an adaptive hybrid kernel function with optimized parameters. Using the optimized adaptive hybrid kernel function, the Bayesian skrygian method is used to interpolate the unknown coordinates of each unknown coordinate point in the target area space, and output the electromagnetic spectrum map of the target area. This solves the problem of not being able to handle multiple signal sources well and the low estimation accuracy, and improves the accuracy of electromagnetic spectrum map construction.

[0152] The electromagnetic spectrum map construction method based on TDOA / AOA data supplementation described above first performs probability updates based on the measured TDOA and AOA data to find the extreme points of existing signal sources and estimate the signal strength value at these points, thereby obtaining probability-based signal strength data. Then, it constructs the map using the adaptive Bayesian Skrigin method (the adaptive Bayesian Skrigin method is the spatial interpolation method in this application that deeply integrates the Bayesian Skrigin method with the adaptive kernel function selection mechanism). It performs hierarchical recursion based on precise and fuzzy data, adaptively selects sample points, adds the estimated data of the selected sample points to the precise dataset, and then uses the optimized adaptive hybrid kernel function and the Bayesian Skrigin method to interpolate and predict the received signal strength at unknown locations within the target area, thereby obtaining a complete electromagnetic spectrum map.

[0153] In one embodiment, simulation results demonstrate that, for the IDW method, ordinary kriging method, and the electromagnetic spectrum map construction method based on TDOA / AOA data supplementation of this application, three signal sources are simulated in space, and the impact of the number of supplementary location points used to generate fuzzy data on the accuracy of electromagnetic spectrum map construction is examined under the condition that the number of actual measured accurate data points is the same. When the number of supplementary location points changes from 5 to 15, 1000 simulations are performed on each method and the root mean square error (RMSE) is calculated. Figure 3 The error comparison chart of the magnetic spectrum map construction methods shown in the figure demonstrates that the adaptive Bayesian Kriging method of this application can improve the construction accuracy by 45.66% compared to the IDW method and by 10.33% compared to the ordinary Kriging method. This application optimizes the parameters in the adaptive Bayesian Kriging method, and the results are as follows... Figure 4 The comparison chart of construction errors before and after parameter optimization using the adaptive Bayesian Skrigin method of this application shows that the construction accuracy can be further improved by 2.37% compared to the original method. These results demonstrate that the method of this application can effectively improve the construction accuracy of the electromagnetic spectrum map. The method of this application achieves higher mapping accuracy by first using TDOA and AOA measurement data to perform joint probability updates on the target area to more accurately determine the signal source center region; secondly, generating fuzzy data based on the probability update results to supplement spatial information of non-measurement areas; thirdly, through hierarchical recursion and adaptive sample selection, only the supplementary location points that are most effective in improving the overall model accuracy are added to the accurate dataset, thereby controlling error propagation; finally, an adaptive hybrid kernel function is constructed, and the kernel function weights and hyperparameters are optimized using logarithmic marginal likelihood. Using the optimized adaptive hybrid kernel function, the Bayesian Skrigin method is used to interpolate the unknown coordinates in the target area space to complete the magnetic spectrum map of the target area, improving the global electromagnetic spectrum map completion accuracy.

[0154] The specific electromagnetic spectrum map construction results are as follows: Figure 5 As shown, the electromagnetic spectrum map construction method based on TDOA / AOA data supplementation proposed in this application, employing the adaptive Bayesian Kriging method, can more accurately reflect the true electromagnetic spectrum distribution compared to the other two methods. The IDW method and ordinary Kriging method cannot accurately describe the information of each signal source. These two methods rely on the extreme points of signal intensity at actual measurement points, leading to incorrect estimation of the signal source center and resulting in information loss and misjudgment of the signal. In contrast, the adaptive Bayesian Kriging method used in the electromagnetic spectrum map construction method based on TDOA / AOA data supplementation proposed in this application can better cover as many signal distribution areas as possible and effectively identify the approximate distribution of the three signal sources.

[0155] It should be understood that, although Figure 1 The steps in the flowchart are shown sequentially as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified herein, there is no strict order in which these steps are executed, and they can be performed in other orders. Figure 1 At least some of the steps in the process may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least some of the sub-steps or stages of other steps.

[0156] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0157] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. A method for constructing an electromagnetic spectrum map based on TDOA / AOA data supplementation, characterized in that, The method for constructing an electromagnetic spectrum map based on TDOA / AOA data supplementation includes: Step S1: Collect received signals at each measurement point, determine the received signal strength at each measurement point, and perform parameter estimation on the collected received signals to obtain TDOA measurement data and AOA measurement data. Step S2: Based on the TDOA measurement data and the AOA measurement data, construct a probability model, update the electromagnetic spectrum map of the target area according to the probability model, and normalize the updated probability distribution to obtain the posterior probability distribution of the signal source location. Step S3: Based on the posterior probability distribution of the signal source location, the signal source location corresponding to the maximum value of the posterior probability distribution is taken as the candidate signal source location, and the candidate signal source location is taken as the center location of the intensity peak. Then, combined with the received signal intensity at each measurement point, the received signal intensity at the candidate signal source location and the received signal intensity at other non-measurement point locations are estimated using the log-normal shadowing fading model to generate fuzzy data. The fuzzy data includes the estimated received signal intensity at the candidate signal source location and the estimated received signal intensity at other non-measurement point locations. Step S4: The data hierarchical recursive algorithm is used to analyze the precise data and the fuzzy data to determine the recursive prediction formula and its conditional variance formula for the point to be predicted. The precise data includes the received signal strength of each measurement point. Step S5: A set of candidate points is uniformly and randomly generated within the target area. The prediction variance of each candidate point in the set is analyzed under precise data and under fuzzy data. The weighted sum of the prediction variances of each candidate point under precise data and fuzzy data is used as the objective function. The candidate point with the largest objective function value is selected as the target point. The precise predicted value and prediction variance of the target point are calculated using the recursive prediction formula and conditional variance formula of the point to be predicted. The target point and its precise predicted value are added to the precise dataset. When the reduction in the overall prediction variance of the target points due to the addition of a new target point is less than a set threshold... When the target point addition is stopped, the precise dataset includes the location information of each measurement point and its received signal strength, and the location information of each target point and its precise predicted value. Step S6: Construct an adaptive hybrid kernel function consisting of a quadratic exponential kernel, a Matern 3 / 2 kernel, and a rational quadratic kernel. Using each point in the precise data as sample points, maximize the logarithmic marginal likelihood as the optimization objective, and iteratively optimize the weight parameters using the gradient ascent method. , and And kernel function hyperparameters, to obtain an adaptive hybrid kernel function with optimized parameters, wherein the adaptive hybrid kernel function for: ； In the formula, and These represent any two spatial locations within the target area. , and For weight parameters, It is a squared exponent kernel. It uses the Matern 3 / 2 core. It is a rational quadratic kernel; Step S7: Using the optimized parameters of the adaptive hybrid kernel function, the Bayesian skrygian method is used to interpolate the unknown coordinate points in the target area space, and output the supplemented electromagnetic spectrum map of the target area.

2. The electromagnetic spectrum map construction method based on TDOA / AOA data supplementation according to claim 1, characterized in that, The probability models include the AOA probability model and the TDOA probability model; The AOA probability model is a von Mises distribution, and the probability density function of the AOA probability model is expressed as: ； in, For the AOA probability model, the first i The probability density value corresponding to each measurement point Here, is the concentration parameter, controlling the degree of concentration of the distribution; e is the natural constant. Let be the AOA observation value at the i-th measurement point in the AOA measurement data; The true angle of arrival of the signal source; To correct the zeroth-order Bessel function and ensure the normalization condition; The TDOA probability model follows a Gaussian distribution, and the probability density function of the TDOA probability model is... Represented as: ； in, For the TDOA probability model i The probability density value corresponding to each measurement point Let be the TDOA observation value at the i-th measurement point in the TDOA measurement data; exp represents the natural exponential function; This represents the theoretical distance difference corresponding to the location of the candidate signal source; This represents the standard deviation of the TDOA measurement error. The variance of the TDOA measurement error; It is the speed of light.

3. The electromagnetic spectrum map construction method based on TDOA / AOA data supplementation according to claim 2, characterized in that, The expression for the probability update is: ； in, This represents the number of groups of AOA measurement data; The number of groups of TDOA measurement data; An index for AOA measurement data; An index for TDOA measurement data; For coordinates in two-dimensional space The probability value of the arrival angle observation at the grid point of the i-th group; For coordinates in two-dimensional space The probability value of reaching the time difference observation after passing through the j-th group at the grid point; This indicates that the coordinates in two-dimensional space are The unnormalized posterior probability value is obtained at the grid point after joint probability update of multiple sets of arrival angle and arrival time difference observations.

4. The electromagnetic spectrum map construction method based on TDOA / AOA data supplementation according to claim 3, characterized in that, The two-dimensional spatial coordinates in the posterior probability distribution of the signal source location are: Normalized posterior probability values ​​at grid points for: ； in, To be on all grid points in the target area The maximum value.

5. The electromagnetic spectrum map construction method based on TDOA / AOA data supplementation according to claim 1, characterized in that, The log-normal shadowing fading model is as follows: ,in, Let n be the signal strength to be estimated, and n be the path loss exponent. The distance between the receiving point and the signal source. For shadow fading terms; This is the received signal strength vector.

6. The electromagnetic spectrum map construction method based on TDOA / AOA data supplementation according to claim 1, characterized in that, The step of using a data hierarchical recursive algorithm to analyze precise data and fuzzy data to determine the recursive prediction formula and its conditional variance formula for the point to be predicted includes: The precise data and the fuzzy data are integrated to construct an autoregressive expression; Assuming that the fuzzy data and the residual stochastic process of the autoregressive expression both follow Gaussian processes, a joint distribution of the measurement points and the points to be predicted is constructed. Based on the conditional distribution properties of the Gaussian process, the recursive prediction formula and its conditional variance formula for the points to be predicted are determined. The recursive prediction formula for the points to be predicted is as follows: ； in, Indicates the point to be predicted Precise prediction value; Indicates the point to be predicted The correlation coefficient function between precise predicted values ​​and fuzzy data; Represents the points to be predicted under fuzzy data. The predicted value at that location; This represents the mean function of the residual random process at the point to be predicted. This represents the transpose of the correlation vector between the point to be predicted and the known point in the residual stochastic process. The matrix representing the inverse of the covariance matrix of a stochastic process with known residuals; Represents known point data Subtract the corresponding mean The residual vector after; The conditional variance formula for the point to be predicted is: ； in, Indicates the point to be predicted The predicted variance at the location; Indicates the point to be predicted The square of the correlation coefficient function between the precise predicted value and the fuzzy data; Represents the points to be predicted under fuzzy data. The predicted variance at the location; This indicates that the residual stochastic process is at the point to be predicted. The autocovariance at a given point is used to characterize the uncertainty introduced by the residual stochastic process itself; This indicates that the residual stochastic process is at the point to be predicted. The correlation vector between the known points, for transpose, It represents the inverse matrix of the covariance matrix of a random process with known residuals.

7. The electromagnetic spectrum map construction method based on TDOA / AOA data supplementation according to claim 6, characterized in that, The regression expression is: ； in, For accurate data, For fuzzy data, It is the correlation coefficient between precise data and fuzzy data. It is a residual random process that follows a Gaussian process.

8. The method for constructing an electromagnetic spectrum map based on TDOA / AOA data supplementation according to claim 1, characterized in that, The objective function for: ； in, The prediction variance for accurate data; The prediction variance for fuzzy data; For weighting coefficients, through Adjust the weights of precise and fuzzy data.

9. The electromagnetic spectrum map construction method based on TDOA / AOA data supplementation according to claim 1, characterized in that, The squared exponent kernel Matern 3 / 2 core Rational quadratic nuclei The expressions are as follows: ， ； ； in, , and For length scale parameters, , and These are used to control the smoothness of the function, the frequency of the function's fluctuations, and the multi-scale mixing weights, respectively. For shape parameters.

10. The electromagnetic spectrum map construction method based on TDOA / AOA data supplementation according to claim 9, characterized in that, The expression for the logarithmic marginal likelihood is: ； In the formula, z is the observation vector, representing the number of observations in the exact dataset. Received signal strength data at each sample point; X is the precise dataset, containing... The location information of each sample point; θ is a parameter set, which includes weight parameters. , and Length scale parameter , and and shape parameters Where K is the covariance matrix generated by the kernel function. It is the noise variance, and I is the identity matrix. This represents finding the inverse of a matrix. Represents a determinant; Indicates transpose; π is the constant of pi. For the given input Given the parameter set θ, the probability distribution of the observed vector z; The iterative formula for optimizing hyperparameters using the gradient ascent method is as follows: ； in, Indicates the first The parameter set at the next iteration For the first The parameter set at the next iteration; It is the learning rate; It is a set of parameters gradient operator, For the given input The probability distribution of the observed vector z under the given condition.

Images