Method for Locating Pipeline Turbulence Signal Source Based on MUSIC Spectrum Estimation Algorithm of Near-Field Turbulence Signal

Abstract

The present invention relates to the technical field of turbulence signal analysis, and provides a method for locating a pipeline turbulence signal source based on a near-field turbulence signal MUSIC spectrum estimation algorithm, comprising: constructing a signal model with a turbulence signal source in a pipeline as a point source to obtain a signal matrix; calculating the covariance matrix of the signal matrix; constructing an array manifold matrix based on the near-field signal model; based on the covariance matrix and the array manifold matrix, using the MUSIC spectrum estimation algorithm to perform spatial spectrum estimation on the signal source to obtain a two-dimensional spatial spectrum graph and perform a maximum point search; locating the signal source based on the maximum point in the spatial spectrum graph; and updating and optimizing the positioning of the signal source in real time by introducing a dynamic positioning method. By considering not only the incident angle of the signal source but also the distance from the signal source to the array reference point, the specific coordinates of the signal source in space can be determined more accurately, positioning deviation can be reduced, and the propagation characteristics of the near-field turbulence signal can be described more accurately.

Description

Technical Field

[0001] The present invention relates to the technical field of turbulence signal analysis, and in particular to a pipeline turbulence signal source positioning method based on a near-field turbulence signal MUSIC spectrum estimation algorithm. Background Art

[0002] Turbulence signals are common in pipeline flows, especially when conveying media. Turbulence can cause pressure and velocity fluctuations, which can generate signals in the near-field region of the pipeline. By analyzing the characteristics of these turbulence signals, the location, intensity, and changes of turbulence within the pipeline can be effectively monitored and located.

[0003] Traditional turbulence signal source localization methods are mostly based on far-field propagation models, which assume that the signal maintains the same propagation path during transmission. However, turbulence signals often exhibit strong non-uniformity and time-varying properties. 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 suffer from significant errors when locating near-field turbulence sources.

[0004] Furthermore, existing pipeline turbulence signal location methods typically use time-domain signal processing, but this method fails to fully utilize the signal's frequency-domain characteristics and cannot effectively cope with multi-source interference and complex signal environments. Therefore, a new MUSIC spectrum estimation algorithm based on near-field turbulence signals is urgently needed to improve the estimation accuracy of turbulence signal source locations and address the shortcomings of existing technologies. 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. The present invention achieves high-precision positioning of pipeline turbulence sources by combining near-field signal characteristics and the spatial dynamic characteristics of turbulence signals.

[0006] The present invention provides a pipeline turbulence signal source location method based on a near-field turbulence signal MUSIC spectrum estimation algorithm, comprising:

[0007] 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;

[0008] 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 arrays, and provides information for subsequent spectrum estimation and signal source localization.

[0009] S3, constructing the 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 spectrum estimation algorithm is used to estimate the spatial spectrum of the signal source, obtain a two-dimensional spatial spectrum map and perform maximum point search;

[0011] S5, locate the signal source based on the maximum point in the spatial spectrum;

[0012] S6, updates and optimizes the positioning of signal sources in real time by introducing dynamic positioning methods.

[0013] Furthermore, the construction process of the signal model in step S1 is:

[0014] 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:

[0015] X=A S+N;

[0016] in, represents the signal matrix received by the flexible film strip, = [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, reflecting the characteristics of the source signal, = [S 1 (t), S 2 (t),….. S M (t)] T ;

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

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

[0021] Indicates the sampling time;

[0022] T represents matrix transpose.

[0023] Furthermore, in step S2, the covariance matrix R is calculated as:

[0024] ;

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

[0026] Indicates the The flexible film strip of the sub-snapshot receives the signal vector;

[0027] for The conjugate transposed matrix of .

[0028] Furthermore, in step S3, the process of constructing 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 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:

[0030] ; 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:

[0031] ; Substitute into the phase formula to get:

[0032] ;

[0033] Using the Fresnel approximation and retaining the first-order and second-order terms, the phase difference can be approximated as:

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

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

[0036] ;

[0037] 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.

[0038] Furthermore, the MUSIC (Multiple Signal Classification) spectrum estimation algorithm is a classic spatial spectrum estimation algorithm. 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:

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

[0040] ;

[0041] 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;

[0042] S42, the eigenvectors of the covariance matrix R i By eigenvalue i Sort from large to small and select the eigenvectors corresponding to 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, constructing spatial spectrum function :

[0047] ;

[0048] in, 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 noise subspace matrix Conjugate transpose;

[0051] 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;

[0052] S45, by 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.

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

[0054] The horizontal coordinate of the signal source and the vertical axis They are:

[0055] = ;

[0056] = ;

[0057] in, , Respectively represent the coordinates of the initial observation points; Represents the distance from the signal source to the reference flexible film strip.

[0058] Furthermore, 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 observation 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:

[0059] ;

[0060] in, The signal source at time estimated location of For the moment Observation value; is the Kalman gain; is the measurement matrix.

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

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

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

[0064] (3) The present invention also optimizes the positioning of the signal source through dynamic filtering, so that the position of the turbulence source can be tracked in real time, which is suitable for complex environments such as pipeline monitoring and fault detection. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] Figure 1 This is a flow chart of pipeline turbulence positioning in the present invention.

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

[0067] Figure 3 The present invention is a flow chart of using a MUSIC spectrum estimation algorithm to perform spatial spectrum estimation on a signal source to obtain a two-dimensional spatial spectrum graph. DETAILED DESCRIPTION

[0068] The technical solution of the present invention is further described in detail below in conjunction with specific embodiments and accompanying drawings, but this embodiment is not intended to limit the present invention. All similar structures and similar variations of the present invention should be included in the scope of protection of the present invention. The semicolons in the present invention represent the relationship of and, and the English letters in the present invention are case-sensitive.

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

[0070] S1, construct a signal model with the turbulence signal source in the pipeline as the point source, and the piezoelectric film sensor receives the signal to obtain the signal matrix X. The construction process of the signal model is:

[0071] Assume that the turbulence signal source in the pipeline is a point source, and a piezoelectric film sensor 1 is provided on the outer wall of the pipeline. The piezoelectric film sensor includes M flexible film strips 12, and the spacing between the flexible film strips is ,like Figure 2As shown in the figure, since the piezoelectric film sensor is a flexible film strip, it can seamlessly fit the outer pipe wall surface. When the signal sent by 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 strip is expressed as:

[0072] X=A S+N;

[0073] in, represents the signal matrix received by the flexible film strip, = [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, reflecting the characteristics of the source signal, = [S 1 (t), S 2 (t),….. S M (t)] T ;

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

[0077] represents the incident angle from the signal source to the flexible film strip, and its subscripts correspond to the flexible film strips respectively; represents the sampling time; T represents the 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 arrays, and provides information for subsequent spectrum estimation and signal source localization.

[0079] The flexible film strip converts the time domain information of the turbulence signal in the pipeline into a discrete signal vector by sampling N times (i.e. N snapshots). ;

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

[0081] ;

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

[0083] Indicates the The flexible film strip of the sub-snapshot receives the signal vector;

[0084] for The conjugate transposed matrix of .

[0085] S3, constructing the 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 suitable for narrowband signals. The time domain signal is used to calculate the covariance matrix because narrowband signals have a high signal-to-noise ratio and the larger the snapshot number, the better. Secondly, the far-field signal is a parallel wave by default, and the angle when hitting the array does not change. The phase difference between arrays is completely determined by the spacing between the piezoelectric film sensors. However, most pipeline turbulence signals are near-field signals, and the distance and angle with each array are different. At the same time, the angle of the far-field model does not change, while the turbulence signal moves rapidly and the angle changes with time. The spatial spectrum 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 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:

[0088] ;

[0089] 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:

[0090] ;

[0091] Substituting into the phase formula we get:

[0092] ;

[0093] Using the Fresnel approximation and retaining the first-order and second-order terms, the phase difference can be approximated as:

[0094] =A*i+B* , where A=- ; B= ;

[0095] Therefore, the array manifold matrix based on the near-field signal model is for:

[0096] ;

[0097] 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.

[0098] 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 maximum point search;

[0099] The MUSIC (Multiple Signal Classification) spectrum estimation algorithm is a classic spatial spectrum estimation algorithm. 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. ,

[0100] like Figure 3 As shown, the specific implementation process is:

[0101] S41, performing eigenvalue decomposition on the covariance matrix R to obtain the eigenvalues and eigenvectors of the matrix R;

[0102] ;

[0103] 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;

[0104] S42, the eigenvectors of the covariance matrix R i By eigenvalue i Sort from large to small and select the eigenvectors corresponding to small eigenvalues to construct the noise subspace matrix :

[0105] ;

[0106] Among them, the dimension of the noise subspace matrix is ;

[0107] is the number of signal sources;

[0108] S43, constructing spatial spectrum function :

[0109] ;

[0110] in, is the array manifold matrix, which reflects the propagation characteristics of the signal source;

[0111] is the conjugate transpose of the array manifold matrix;

[0112] is the noise subspace matrix Conjugate transpose;

[0113] 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;

[0114] S45, by 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.

[0115] S5, locate the signal source based on the maximum point in the spatial spectrum;

[0116] The horizontal coordinate of the signal source and the vertical axis They are:

[0117] = ;

[0118] = ;

[0119] in, , Respectively represent the coordinates of the initial observation points; Indicates the distance from the signal source to the reference flexible film strip;

[0120] S6, by introducing a dynamic positioning method to update and optimize the positioning of the signal source in real time, specifically by using Kalman filtering to update the position estimate of the signal source 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; the horizontal coordinate of the signal source after Kalman filtering k Updated to , the vertical axis is not updated:

[0121] ;

[0122] in, The signal source at time estimated location of For the moment Observation value; is the Kalman gain; is the measurement matrix.

[0123] The specific steps of updating the position estimate of the signal source based on the estimated value of the current signal source position and the new observation value through Kalman filtering are:

[0124] Building a nonlinear measurement model

[0125] Based on the signal receiving characteristics of the flexible film strip, the measurement model is determined as: ;in, Phase information (position-related quantity) measured for the flexible film strip, is a nonlinear measurement function (including the signal source position parameters, such as the incident angle θ from the signal source to the flexible film strip, the distance from the signal source to the reference flexible film strip ), For measuring noise, the reference flexible film strip is any flexible film strip of the piezoelectric film sensor, which is used as a reference point;

[0126] Constructing nonlinear measurement functions (near-field models)

[0127] For the i-th flexible film strip, a measurement value function is constructed based on the near-field signal propagation characteristics:

[0128] , 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, ).

[0129] Linearize the measurement function and calculate the observation matrix Hk

[0130] because is nonlinear, and the current state estimation At, right Perform a first-order Taylor expansion;

[0131] If the state vector is:

[0132] , calculate the partial derivative of the measurement function with respect to the state variable ,

[0133] Arrange the partial derivatives of all flexible film strips into a matrix to obtain the observation matrix :

[0134]

[0135] Observation Matrix In the current state For each measurement equation About state variables The matrix obtained after partial derivative calculation has each element reflecting the effect of state change on the output of the flexible film strip;

[0136] Calculate Kalman gain

[0137] Using the prediction covariance matrix and the measurement noise covariance R k , calculate the Kalman gain , the formula is:

[0138] ;

[0139] Update the signal source position estimate

[0140] Horizontal coordinate update: combined with the current estimated position , observations , Kalman gain and the measurement matrix , update the horizontal coordinate for: ;

[0141] Vertical axis hold: vertical axis No update is performed; the original estimate is used.

[0142] 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 positioning accuracy.

[0143] Although the preferred embodiments of the present application have been described, those skilled in the art may make additional changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall 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; The signal model is constructed as follows: Assume that the turbulence signal source in the pipeline is a point source. A piezoelectric film sensor is provided on the outer wall of the pipeline. The piezoelectric film sensor includes M flexible film strips. The spacing between the flexible film strips is d. When the signal emitted by 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 flexible film strips receiving the signal source is expressed as: X = A′·S+N; Where X represents the signal matrix received by the flexible film strip, X=[x1(t),x2(t),…x M (t)] T ; A′ is the array manifold matrix, which describes the propagation characteristics of the signal source; A′=[a′(θ1),a′(θ2),.....a′(θ M )] T , S is the incident signal matrix of the signal source, S=[S1(t),S2(t),.....S M (t)] T ; N is the array noise matrix, N=[n1(t),n2(t),.....n M (t)] T ; θ represents the direction angle from the signal source to the flexible film strip, and its subscripts correspond to the flexible film strips; t represents the sampling time; T represents matrix transpose; S2, calculate the covariance matrix R of the signal matrix X; S3, constructing the array manifold matrix based on the near-field signal model; In the near-field model, the phase difference is not only related to the directional angle θ from the signal source to the flexible film strip, but also 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: in, Therefore, the array manifold matrix A(θ i , r i )for: 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; 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 maximum point search; S5, locate the signal source based on the maximum point in the spatial spectrum; S6, updates and optimizes the positioning of signal sources in real time by introducing dynamic positioning methods.

2. The pipeline turbulence signal source location method based on the near-field turbulence signal MUSIC spectrum estimation algorithm according to claim 1 is characterized in that: In step S2, the covariance matrix R is calculated as: Where N is the number of signal snapshots, i.e. the number of sampling points; X(n) represents the flexible film strip receiving signal vector of the nth snapshot; X H (n) is the conjugate transposed matrix of X(n).

3. The pipeline turbulence signal source location method based on the near-field turbulence signal MUSIC spectrum estimation algorithm according to claim 1 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 P(θ,r) based on the noise subspace. The specific implementation process of step S4 is as follows: S41, performing eigenvalue decomposition on the covariance matrix R to obtain the eigenvalues and eigenvectors of the matrix R; For example i =λ i v i ; Among them, λ i is the characteristic value of the i-th flexible film strip, v i is the characteristic vector of the i-th flexible film strip; S42, the eigenvector v of the covariance matrix R i By eigenvalue λ i Sort from large to small and select the eigenvectors corresponding to small eigenvalues to construct the noise subspace matrix E N : E N =[v p+1 ,v p+2 ,...,v M ]; Among them, the dimension of the noise subspace matrix is (Mp); p is the number of signal sources; S43, construct the spatial spectrum function P(θ,r): Where A(θ,r) is the array manifold matrix; A H (θ, r) is the conjugate transpose of the array manifold matrix; is the noise subspace matrix E N Conjugate transpose; S44, calculating the values of the spatial spectrum function P(θ, r) at different incident angles θ and distances r from the signal source to the reference flexible film strip, to form a two-dimensional spatial spectrum graph; S45, by performing a peak search on the spatial spectrum function P(θ, r), a maximum point in the spatial spectrum is determined. The angle and distance corresponding to the maximum point are the angle and distance between the turbulence signal and the reference film strip.

4. The pipeline turbulence signal source location method based on the near-field turbulence signal MUSIC spectrum estimation algorithm according to claim 1 is characterized in that: The calculation formula of the signal source in step S5 is: The horizontal coordinate x of the signal source k and the vertical coordinate y k They are: x k =x0+r s cos(θ); y k =y0+r s sin(θ); Among them, x0 and y0 represent the coordinates of the initial observation point respectively; r s Represents the distance from the signal source to the reference flexible film strip.

5. The pipeline turbulence signal source location method based on the near-field turbulence signal MUSIC spectrum estimation algorithm according to claim 4 is characterized in that: In step S6, the position estimate of the signal source is updated based on 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; the horizontal coordinate x of the signal source after Kalman filtering is k Updated to The vertical axis is not updated: in, is the estimated position of the signal source at time k; z k is the observation value at time k; K k is the Kalman gain; H k is the measurement matrix.

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