Pipeline turbulence signal source positioning method based on near-field turbulence signal MUSIC spectrum estimation algorithm

Abstract

The invention relates to the technical field of turbulence signal analysis, and provides a pipeline turbulence signal source positioning method based on a near-field turbulence signal MUSIC spectrum estimation algorithm, and the method comprises the steps: constructing a signal model employing a turbulence signal source in a pipeline as a point source, and obtaining a signal matrix; calculating a covariance matrix of the signal matrix; constructing an array manifold matrix based on a near-field signal model; based on the covariance matrix and the array manifold matrix, adopting a MUSIC spectrum estimation algorithm to carry out spatial spectrum estimation on the signal source to obtain a two-dimensional spatial spectrogram, and carrying out maximum value point search; positioning the signal source based on a maximum value point in the spatial spectrogram; and positioning of a signal source is updated and optimized in real time by introducing a dynamic positioning method. The method not only considers the incident angle of the signal source, but also introduces the distance from the signal source to the array reference point, can more accurately determine the specific coordinates of the signal source in the space, reduces the positioning deviation, and more accurately describes the propagation characteristics of the near-field turbulence signal.

Description

Technical Field

[0001] The present invention relates to the technical field of turbulent signal analysis, and particularly to a method for locating a pipeline turbulent signal source based on a MUSIC spectral estimation algorithm for near-field turbulent signals. Background Art

[0002] Turbulent signals widely exist in pipeline flows. Especially during the process of pipeline transporting media, turbulence can cause pressure fluctuations and flow velocity fluctuations, and these fluctuations can generate signals in the near-field region of the pipeline. By analyzing the characteristics of these turbulent signals, the position, intensity, and their changes of the turbulence in the pipeline can be effectively monitored and located.

[0003] Traditional methods for locating turbulent signal sources are mostly based on far-field propagation models. This method assumes that the signal maintains the same propagation path during transmission. However, turbulent signals often exhibit strong non-uniformity and time-variability, and these signal sources are often near-field signals, and their propagation characteristics are affected by the distance between the signal source and the receiving array. Therefore, traditional far-field signal localization methods have large errors in locating near-field turbulent sources.

[0004] In addition, existing methods for locating pipeline turbulent signals usually adopt time-domain signal processing, but this method cannot fully utilize the frequency-domain characteristics of the signals and cannot effectively cope with the interference of multi-source signals and complex signal environments. Therefore, there is an urgent need for a new MUSIC spectral estimation algorithm based on near-field turbulent signals, which can improve the estimation accuracy of the position of the turbulent signal source and solve the deficiencies in the prior art. Summary of the Invention

[0005] In order to solve the above technical problems, the present invention mainly solves the limitations of traditional positioning methods based on far-field signal models. By combining the characteristics of near-field signals and the spatial dynamic characteristics of turbulent signals, the present invention realizes high-precision positioning of pipeline turbulent sources.

[0006] The present invention provides a method for locating a pipeline turbulent signal source based on a MUSIC spectral estimation algorithm for near-field turbulent signals, including:

[0007] S1, constructing a signal model with the turbulent signal source in the pipeline as a point source, receiving the signal by a piezoelectric film sensor, and obtaining a signal matrix X;

[0008] S2, calculating the covariance matrix R of the signal matrix X; the covariance matrix R reflects the correlation between the signals received by the array and is the basis for subsequent spatial spectral estimation; the covariance matrix R captures the spatial characteristics of the signal source and the correlation between the arrays, and provides information for subsequent spectral estimation and signal source localization.

[0009] S3, constructing an array manifold matrix based on the near-field signal model;

[0010] S4. Based on the covariance matrix R and the array manifold matrix, the MUSIC spectral estimation algorithm is used to perform spatial spectral estimation on the signal source, obtain a two-dimensional spatial spectrogram, and search for the maximum points.

[0011] S5. Locate the signal source based on the maximum points in the spatial spectrogram.

[0012] S6. Introduce a dynamic positioning method to update and optimize the positioning of the signal source in real time.

[0013] Further, the construction process of the signal model in step S1 is as follows:

[0014] Assume that the turbulent signal source in the pipeline is a point source. Piezoelectric film sensors are provided on the outer wall of the pipeline. The piezoelectric film sensors include M flexible film strips, and the spacing between the flexible film strips is . When the signal emitted by the signal source reaches the piezoelectric film sensor, the phase difference of the signals received between the flexible film strips changes with the position of the turbulent source. The signal matrix received by the flexible film strips from the signal source is expressed as:

[0015] X = A S + N;

[0016] where represents the signal matrix received by the flexible film strips, = [x 1 (t), x 2 (t),….. x M (t)] T ;

[0017] is the array manifold matrix, which describes the propagation characteristics of the signal source; = [a' ( θ 1 ),a'( θ 2 ),…..a'( θ M )] T ,

[0018] is the incident signal matrix of the signal source, which reflects the characteristics of the source signal, = [S 1 (t), S 2 (t),….. S M (t)] T ;

[0019] is the array noise matrix, which reflects the noise interference of the signal, = [n 1 (t), n 2 (t),….. n M (t)] T ;

[0020] represents the incident angle of the signal source to the flexible film strip, and its subscripts correspond to the flexible film strips respectively;

[0021] represents the sampling time;

[0022] T represents the matrix transpose.

[0023] Further, in step S2, the calculation formula for the covariance matrix R is:

[0024] ;

[0025] where N is the number of signal snapshots, i.e., the number of sampling points;

[0026] represents the th snapshot's flexible thin film strip received signal vector;

[0027] is 's conjugate transpose matrix.

[0028] Further, in step S3, the construction process of the array manifold matrix based on the near-field signal model is as follows:

[0029] In the near-field model, the phase difference is related not only to the direction angle from the signal source to the flexible thin film strip,

[0030] ; where r i is the distance from the signal source to the i-th flexible thin film strip, r 0 is the distance from the signal source to the reference flexible thin film strip. Taking any one of the flexible thin film strips of the piezoelectric film sensor as the reference point, i.e., the reference flexible thin film strip, then the distance r i from the signal source to the i-th flexible thin film strip is:

[0031] ; Substituting into the phase formula gives:

[0032] ;

[0033] Using the Fresnel approximation and retaining the first-order and second-order terms, the approximate value of the phase difference is:

[0034] =A*i + B* , where A = - ; B = ;

[0035] Therefore, the array manifold matrix based on the near-field signal model is:

[0036] ;

[0037] where j represents the imaginary unit; λ represents the wavelength of the signal source; Indicates the phase difference; A and B are meaningless and are used to simplify the parameters of the formula; i represents the index of the flexible film strip.

[0038] Furthermore, the MUSIC (Multiple Signal Classification) spectral estimation algorithm is a classical spatial spectral estimation algorithm. The core idea of the MUSIC spectral estimation algorithm is to decompose the covariance matrix into a signal subspace and a noise subspace through eigenvalue decomposition, and then calculate the spatial spectral function based on the noise subspace. The specific implementation process of step S4 is as follows:

[0039] S41, perform eigenvalue decomposition on the covariance matrix R to obtain the eigenvalues and eigenvectors of matrix R;

[0040] ;

[0041] Among them, i is the eigenvalue of the i-th flexible film strip, i is the eigenvector of the i-th flexible film strip;

[0042] S42, sort the eigenvectors i of the covariance matrix R in descending order of eigenvalues i and select the eigenvectors corresponding to the small eigenvalues to construct the noise subspace matrix :

[0043] ;

[0044] Among them, the dimension of the noise subspace matrix is ;

[0045] is the number of signal sources;

[0046] S43, construct the spatial spectral function :

[0047] ;

[0048] Among them, is the array manifold matrix, which reflects the propagation characteristics of the signal source;

[0049] is the conjugate transpose of the array manifold matrix;

[0050] is the conjugate transpose of the noise subspace matrix ;

[0051] S44. Calculate the spatial spectrum function at different incident angles and the distance from the signal source to the reference flexible film strip to form a two-dimensional spatial spectrum diagram;

[0052] S45. By performing peak search on the spatial spectrum function to determine the maximum value point in the spatial spectrum diagram, the angles and distances corresponding to the maximum value point are the angles and distances between the turbulent signal and the reference film strip.

[0053] Further, the calculation formula of the signal source in step S45 is:

[0054] The abscissa of the signal source and the ordinate are respectively:

[0055] = ;

[0056] = ;

[0057] Wherein, , respectively represent the coordinates of the initial observation point; represents the distance from the signal source to the reference flexible film strip.

[0058] Further, in step S6, the position estimate of the signal source is updated by Kalman filtering according to the estimated value of the current signal source position and the new observation value, so as to obtain a more accurate position at each moment; after Kalman filtering, the abscissa k is updated to , and the ordinate is not updated:

[0059] ;

[0060] Wherein, is the estimated position of the signal source at time ; is the observation value at time ; is the Kalman gain; is the measurement matrix.

[0061] The present invention has the following beneficial effects:

[0062] (1) The present invention uses MUSIC spectral estimation to estimate the direction and position of the signal source, considering not only the incident angle of the signal source, but also introducing the distance from the signal source to the reference flexible film strip , compared with the traditional method that only considers a single angle, it greatly improves the accuracy of signal source position estimation, can more accurately determine the specific coordinates of the signal source in space, and reduces the positioning deviation;

[0063] (2) The pipeline turbulence source localization method based on the MUSIC spectrum estimation algorithm of near-field turbulence signals provided by the present invention can more accurately describe the propagation characteristics of turbulence signals compared with the traditional far-field model. Especially in the near-field case, it can significantly improve the positioning accuracy;

[0064] (3) The present invention also optimizes the positioning of the signal source through dynamic filtering, enabling real-time tracking of the position of the turbulence source, and is applicable to complex environments such as pipeline monitoring and fault detection. Description of the Drawings

[0065] Figure 1 is the pipeline turbulence localization flowchart in the present invention.

[0066] Figure 2 is the plan view of the piezoelectric thin film sensor in the present invention.

[0067] Figure 3 is the schematic flowchart of obtaining a two-dimensional spatial spectrum diagram by performing spatial spectrum estimation on the signal source using the MUSIC spectrum estimation algorithm in the present invention. Detailed Embodiments

[0068] The technical solutions of the present invention will be further described in detail below in conjunction with specific embodiments and the accompanying drawings. However, these embodiments do not limit the present invention. Any similar structures and similar changes using the present invention should be included in the protection scope of the present invention. The commas in the present invention all represent the relationship of "and". The English letters in the present invention are case-sensitive.

[0069] As Figure 1 shown, the present invention provides a pipeline turbulence signal source localization method based on the MUSIC spectrum estimation algorithm of near-field turbulence signals, including:

[0070] S1, constructing a signal model with the turbulence signal source in the pipeline as a point source, receiving the signal by a piezoelectric thin film sensor to obtain a signal matrix X; the process of constructing the signal model is as follows:

[0071] Assume that the turbulence signal source in the pipeline is a point source. There is a piezoelectric thin film sensor 1 on the outer wall of the pipeline. The piezoelectric thin film sensor includes M flexible film strips 12, and the distance between the flexible film strips is , as Figure 2As shown, since the piezoelectric film sensor is a flexible film strip, it can be seamlessly attached to the outer wall surface. When the signal sent by the signal source reaches the piezoelectric film sensor, the phase difference of the signals received between the flexible film strips changes with the position of the turbulence source. The signal matrix received by the flexible film strips generated by the signal source is expressed as:

[0072] X = A S + N;

[0073] Wherein, represents the signal matrix received by the flexible film strips, = [x 1 (t), x 2 (t),….. x M (t)] T ;

[0074] is the array manifold matrix, which describes the propagation characteristics of the signal source; = [a' ( θ 1 ),a'( θ 2 ),…..a'( θ M )] T ;

[0075] is the incident signal matrix of the signal source, which reflects the characteristics of the source signal, = [S 1 (t), S 2 (t),….. S M (t)] T ;

[0076] is the array noise matrix, which reflects the noise interference of the signal, = [n 1 (t), n 2 (t),….. n M (t)] T ;

[0077] represents the incident angle of the signal source to the flexible film strip, and its subscripts correspond to the flexible film strips respectively; represents the sampling time; T represents matrix transpose.

[0078] S2, calculate the covariance matrix R of the signal matrix X; the covariance matrix R reflects the correlation between the signals received by the array and is the basis for subsequent spatial spectrum estimation; the covariance matrix R captures the spatial characteristics of the signal source and the correlation between the arrays, and provides information for subsequent spectrum estimation and signal source localization.

[0079] The flexible film strip converts the time-domain information of the turbulent signal in the pipeline into a discrete signal vector through N samplings (i.e., N snapshots) ;

[0080] The calculation formula of the covariance matrix R is:

[0081] ;

[0082] Wherein, N is the number of signal snapshots, i.e., the number of sampling points;

[0083] denote the received signal vector of the flexible film strip for the -th snapshot;

[0084] is the conjugate transpose matrix of.

[0085] S3. Construct an array manifold matrix based on the near-field signal model;

[0086] In traditional signal processing methods, the array manifold matrix is generally based on the far-field signal model. The far-field signal model is applicable to narrowband signals. The covariance matrix is calculated using time-domain signals. Since narrowband signals have a high signal-to-noise ratio, the larger the number of snapshots, the better. Secondly, the far-field signal is defaulted to a parallel wave, and the angle when hitting the array remains unchanged. The phase difference between arrays is completely determined by the spacing between piezoelectric film sensors. However, most pipeline turbulence signals are near-field signals, with different distances and angles from each array. At the same time, the angle of the far-field model remains unchanged, while the turbulence signal is fast-moving and the angle changes with time. The spatial spectral function is a two-dimensional output and cannot be converted into a three-dimensional frequency-wavenumber spectrum. Therefore, it is necessary to construct an array manifold matrix based on the near-field signal model. The construction process of the array manifold matrix based on the near-field signal model is as follows:

[0087] In the near-field model, the phase difference is related to not only the direction angle from the signal source to the flexible film strip, but also the distance from the signal source to each array element. The phase difference is expressed as:

[0088] ;

[0089] where r i is the distance from the signal source to the i-th flexible film strip, and r 0 is the distance from the signal source to the reference flexible film strip. Taking any one of the flexible film strips of the piezoelectric film sensor as the reference point, i.e., the reference flexible film strip, then the distance r i from the signal source to the i-th flexible film strip is:

[0090] ; Substituting into the phase formula, we can get:

[0091] ;

[0092] Using the Fresnel approximation and retaining the first-order and second-order terms, the approximate value of the phase difference can be obtained as:

[0093] =A*i + B* , where A = - ; B = ;

[0094] Therefore, the array manifold matrix based on the near-field signal model is as follows:

[0095] ;

[0096] where j represents the imaginary unit; λ represents the wavelength of the signal source; represents the phase difference; A and B are meaningless and are used to simplify the parameters of the formula; i represents the index of the flexible film strip.

[0097] S4. Based on the covariance matrix R and the array manifold matrix, use the MUSIC spectral estimation algorithm to perform spatial spectral estimation on the signal source, obtain a two-dimensional spatial spectrogram, and perform a maximum point search;

[0098] The MUSIC (Multiple Signal Classification) spectral estimation algorithm is a classic spatial spectral estimation algorithm. The core idea of the MUSIC spectral estimation algorithm is to decompose the covariance matrix into a signal subspace and a noise subspace through eigenvalue decomposition, and then calculate the spatial spectral function according to the noise subspace ,

[0099] As Figure 3 shown, the specific implementation process is as follows:

[0100] S41. Perform eigenvalue decomposition on the covariance matrix R to obtain the eigenvalues and eigenvectors of the matrix R;

[0101] ;

[0102] where, i is the eigenvalue of the i-th flexible film strip, i is the eigenvector of the i-th flexible film strip;

[0103] S42. Arrange the eigenvectors i of the covariance matrix R in descending order of eigenvalues i , and select the eigenvectors corresponding to the small eigenvalues to construct the noise subspace matrix :

[0104] ;

[0105] where the dimension of the noise subspace matrix is ;

[0106] is the number of signal sources;

[0107] S43, Construct the spatial spectrum function :

[0108] ;

[0109] wherein, is the array manifold matrix, which reflects the propagation characteristics of the signal source;

[0110] is the conjugate transpose of the array manifold matrix;

[0111] is the noise subspace matrix conjugate transpose;

[0112] S44, Calculate the spatial spectrum function at different incident angles and the distance from the signal source to the reference flexible film strip to form a two-dimensional spatial spectrum diagram;

[0113] S45, By performing peak search on the spatial spectrum function to determine the maximum value point in the spatial spectrum diagram, the angle and distance corresponding to the maximum value point are the angle and distance between the turbulent signal and the reference film strip.

[0114] S5, Locate the signal source based on the maximum value point in the spatial spectrum diagram;

[0115] The abscissa of the signal source and the ordinate are respectively:

[0116] = ;

[0117] = ;

[0118] wherein, , respectively represent the coordinates of the initial observation point; represents the distance from the signal source to the reference flexible film strip;

[0119] S6, By introducing a dynamic positioning method, the positioning of the signal source is updated and optimized in real time. Specifically, the position estimate of the signal source is updated according to the estimated value of the current signal source position and the new observation value through Kalman filtering, so as to obtain a more accurate position at each moment; After Kalman filtering, the abscissa k is updated to , and the ordinate remains unchanged:

[0120] ;

[0121] Among them, is the estimated position of the signal source at time ; is the observed value at time ; is the Kalman gain; is the measurement matrix.

[0122] The specific steps to update the position estimate of the signal source through Kalman filtering based on the estimated value of the current signal source position and the new observed value are as follows:

[0123] Establish a non - linear measurement model

[0124] Based on the signal reception characteristics of the flexible film strip, determine the measurement model as: ; Among them, is the phase information (quantity related to position) measured by the flexible film strip, is the non - linear measurement function (including signal source position parameters, such as the incident angle θ of the signal source to the flexible film strip, the distance from the signal source to the reference flexible film strip), is the measurement noise, where the reference flexible film strip is any one of the flexible film strips of the piezoelectric film sensor, and it is used as the reference point;

[0125] Construct a non - linear measurement function (near - field model)

[0126] For the i - th flexible film strip, according to the near - field signal propagation characteristics, construct the measured value function:

[0127] , is the distance from the signal source to the reference flexible film strip, λ is the signal wavelength, contains signal source position parameters (such as θ, ).

[0128] Linearize the measurement function and calculate the observation matrix Hk

[0129] Since is non - linear, at the current state estimate , perform a first - order Taylor expansion on ;

[0130] If the state vector is:

[0131] , calculate the partial derivative of the measurement function with respect to the state variable ,

[0132] Arrange the partial derivatives of all flexible film strips into a matrix to obtain an observation matrix :

[0133]

[0134] Observation matrix is at the current state for each measurement equation with respect to the state variable The matrix obtained after taking the partial derivative, and each element of it reflects the influence of the state change on the output of the flexible film strip;

[0135] Calculate the Kalman gain

[0136] Use the predicted covariance matrix and the measurement noise covariance R k , calculate the Kalman gain , and its formula is:

[0137] ;

[0138] Update the estimated position of the signal source

[0139] Update of the abscissa: Combine the current estimated position , the observed value , the Kalman gain and the measurement matrix , update the abscissa as: ;

[0140] Keep the ordinate: The ordinate is not updated and the original estimated value is used.

[0141] The pipeline turbulence source localization method based on the MUSIC spectrum estimation algorithm of near-field turbulence signals provided by the present invention can more accurately describe the propagation characteristics of turbulence signals compared with the traditional far-field model, especially in the near-field case, and can significantly improve the localization accuracy.

[0142] Although the preferred embodiments of the present application have been described, those skilled in the art can make additional changes and modifications to these embodiments once they learn the basic creative concept. Therefore, the appended claims are intended to be interpreted to include the preferred embodiments as well as all changes and modifications falling within the scope of the present application.

Claims

1. A pipeline turbulence signal source location method based on near-field turbulence signal MUSIC spectrum estimation algorithm, characterized in that: include: S1, construct a signal model with the turbulence signal source in the pipeline as the point source, and receive the signal from the piezoelectric film sensor to obtain the signal matrix X; S2, calculate the covariance matrix R of the signal matrix X; S3, constructing an array manifold matrix based on a near-field signal model; S4, based on the covariance matrix R and the array manifold matrix, the MUSIC spectrum estimation algorithm is used to estimate the spatial spectrum of the signal source, obtain a two-dimensional spatial spectrum map and perform a maximum point search; S5, locating the signal source based on the maximum point in the spatial spectrum; S6, updates and optimizes the positioning of the signal source in real time by introducing a dynamic positioning method.

2. According to claim 1, a pipeline turbulence signal source positioning method based on near-field turbulence signal MUSIC spectrum estimation algorithm is characterized in that: The construction process of the signal model in step S1 is: Assume that the turbulence signal source in the pipeline is a point source, and a piezoelectric film sensor is provided on the outer wall of the pipeline. The piezoelectric film sensor includes M flexible film strips, and the spacing between the flexible film strips is , when the signal from the signal source reaches the piezoelectric film sensor, the phase difference of the received signal between the flexible film strips changes with the position of the turbulence source. The signal matrix generated by the signal source received by the flexible film strips is expressed as: X=A S+N; in, Represents the matrix of signals received by the flexible film strip, = ; is the array manifold matrix, which describes the propagation characteristics of the signal source; = , is the incident signal matrix of the signal source, = ; is the array noise matrix, = ; represents the direction angle from the signal source to the flexible film strip, and its subscripts correspond to the flexible film strips respectively; Indicates sampling time; T stands for matrix transpose.

3. According to claim 2, a pipeline turbulence signal source positioning method based on near-field turbulence signal MUSIC spectrum estimation algorithm is characterized in that: In step S2, the calculation formula of the covariance matrix R is: ； Where N is the number of signal snapshots, i.e. the number of sampling points; Indicates The sub-snapshot flexible film strip receives the signal vector; for The conjugate transposed matrix of .

4. According to claim 2, a pipeline turbulence signal source positioning method based on near-field turbulence signal MUSIC spectrum estimation algorithm is characterized in that: In step S3, the process of constructing the array manifold matrix based on the near-field signal model is as follows: In the near-field model, the phase difference is related to the direction angle from the signal source to the flexible film strip. , is also related to the distance from the signal source to each array element. The phase difference is expressed as: ； Among them, r i is the distance from the signal source to the i-th flexible film strip, r0 is the distance from the signal source to the reference flexible film strip, and any flexible film strip of the piezoelectric film sensor is used as a reference point, that is, the reference flexible film strip. Then the distance r from the signal source to the i-th flexible film strip is i for: ； Substituting into the phase formula we get: ； Using the Fresnel approximation and retaining the first-order and second-order terms, the phase difference can be approximated as: =A*i+B* , therein, A=- ;B= ; Therefore, the array manifold matrix based on the near-field signal model is for: ； Where, j represents the imaginary unit; λ represents the wavelength of the signal source; represents the phase difference; A and B are meaningless in order to simplify the parameters of the formula; i represents the index of the flexible film strip.

5. According to claim 4, a pipeline turbulence signal source location method based on near-field turbulence signal MUSIC spectrum estimation algorithm is characterized in that: The core idea of ​​the MUSIC spectrum estimation algorithm is to decompose the covariance matrix into signal subspace and noise subspace through eigenvalue decomposition, and then calculate the spatial spectrum function based on the noise subspace. , the specific implementation process of step S4 is: S41, performing eigenvalue decomposition on the covariance matrix R to obtain eigenvalues ​​and eigenvectors of the matrix R; ； in, i is the characteristic value of the i-th flexible film strip, i is the characteristic vector of the i-th flexible film strip; S42, the eigenvectors of the covariance matrix R i By feature value i Sort from large to small, select the eigenvectors corresponding to small eigenvalues ​​to construct the noise subspace matrix : ； Among them, the dimension of the noise subspace matrix is ; is the number of signal sources; S43, constructing spatial spectrum function : ； in, is the array manifold matrix; is the conjugate transpose of the array manifold matrix; is the noise subspace matrix Conjugate transpose; S44, calculate the spatial spectrum function At different incident angles and the distance from the signal source to the reference flexible film strip The values ​​on form a two-dimensional spatial spectrum; S45, through the spatial spectrum function Perform peak search to determine the maximum point in the spatial spectrum. The angle and distance corresponding to the maximum point are the angle and distance between the turbulence signal and the reference film strip.

6. According to claim 4, a pipeline turbulence signal source location method based on near-field turbulence signal MUSIC spectrum estimation algorithm is characterized in that: The calculation formula of the signal source in step S5 is: The horizontal coordinate of the signal source and the vertical coordinate They are: = ； = ； in, , Respectively represent the coordinates of the initial observation points; Represents the distance from the signal source to the reference flexible film strip.

7. The pipeline turbulence signal source location method based on the near-field turbulence signal MUSIC spectrum estimation algorithm according to claim 6 is characterized in that: In step S6, the position estimate of the signal source is updated according to the estimated value of the current signal source position and the new observed value through Kalman filtering, so as to obtain a more accurate position at each moment; the horizontal coordinate of the signal source after Kalman filtering is k Updated to , the vertical axis is not updated: ； in, is the signal source at time The estimated location of For the moment Observation value; is the Kalman gain; is the measurement matrix.

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