Off-grid DOA estimation method for coherent gas leakage sources based on covariance fitting

Abstract

The present invention discloses a coherent gas leakage source off-grid DOA estimation method based on covariance fitting. Starting from the covariance matrix output by the leakage source, combined with the interference factors of the coherent signal source in the real leakage source environment, the norm is used as a constraint condition and the full-rank covariance matrix after covariance fitting is used for joint estimation in the off-grid model. The present invention restores the Toeplitz characteristic of the subspace vector after covariance fitting, on the one hand, uses it to correct the noise matrix in the off-grid algorithm model, and on the other hand, retains the angle information of the incident signal source under the coherent leakage source, which is more in line with engineering applications.

Description

Technical Field

[0001] The invention belongs to the technical field of gas leakage fault target parameter estimation, and in particular relates to a covariance fitting-based off-grid DOA estimation method for a coherent gas leakage source. Background Art

[0002] The storage and operation of chemical gases are an indispensable part of industrial production. Storage equipment (high-pressure containers, transmission pipelines, etc.) may accidentally rupture due to mechanical external forces, vibrations, etc., causing leakage accidents. This is not only extremely harmful to the surrounding environment, but also prone to fires and even explosions when encountering fire sources, seriously endangering people's lives and property safety. Various positioning methods suitable for complex gas leakage environments need to meet the requirements of high sensitivity, high precision, and low computational complexity. With the continuous development of sparse recovery algorithms in the field of array signal processing, it is crucial to use Direction of Arrival (DOA) estimation from an acoustic perspective to prevent and quickly deal with gas leakage problems.

[0003] Researchers have proposed a variety of acoustic gas DOA estimation techniques, such as the 2D-Multiple Signal Classification (2D-MUSIC) algorithm optimized by the whale algorithm, the ESPRIT algorithm, and so on. However, such subspace algorithms are only applicable to ideal situations with high signal-to-noise ratio and multiple blocks. Once the gas leakage environment deteriorates, the performance of such algorithms will be severely reduced. The continuous development of compressed sensing (CS) technology has provided new ideas for the problem of locating gas leak sources. The DOA estimation problem can be transformed into a solution under CS theory. norm minimization problem. However, the optimization of the objective function is a non-deterministic multinomial (NP-hard) problem and faces the optimal regularization parameter selection, so it is generally converted into The norm minimization problem is solved. However, the computational complexity is huge and it is not suitable for engineering applications. The l1-norm Singular ValueDecomposition (l1-SVD) algorithm model does not require iteration and has low computational complexity. It can still achieve accurate positioning in low snapshot and low signal-to-noise ratio environments. However, in a complex gas leakage environment, coherent signals generated by multipath effects are ubiquitous, and the rank of the array receiving data covariance matrix will degenerate, that is, the dimension of the signal subspace will be lower than the actual number of incident signal sources, and the algorithm performance will be seriously ineffective.

[0004] In a real leakage source environment, due to external noise interference and multipath effects, coherent sources will be generated, thus forming a non-full-rank source covariance matrix, and the sparse representation model will also be mismatched, thus de-grid. The algorithm cannot be applied to gas leak source DOA estimation.

[0005] The invention with the publication number CN113405736A discloses a leakage source positioning method and system based on the acoustic emission characteristics of gas leakage in a plate-like structure. The method collects the vibration leakage sound time domain signal propagating on the surface of the plate-like structure caused by gas leakage; then, based on the characteristics of the leakage acoustic emission signal, the leakage sound time domain signal is preprocessed; the effective signal in the intercepted time domain is extracted, and the noise and interference signal are removed as much as possible; the effective signal is then used as the signal input of the surround sensor array MUSIC algorithm, and other input parameters are obtained through the preprocessing method. Finally, the orientation result of the sensor array to the leakage source is obtained; using the relative position and orientation result of the sensor array, the positioning formula determines the distance of the leakage source relative to the sensor array. The invention effectively increases the positioning accuracy of the leakage point, realizes the automatic detection and precise positioning of the leakage point, improves the accuracy of leakage positioning, and further improves the accuracy of leakage source positioning. However, the invention does not consider the interference factors of coherent signal sources in the real leakage source environment. Summary of the invention

[0006] Technical problems solved: In view of the shortcomings of the background technology, a covariance fitting-based off-grid DOA estimation method for coherent gas leakage sources is proposed. Starting from the covariance matrix of the leakage source output, combined with the interference factors of the coherent signal source in the real leakage source environment, the off-grid model is used The norm is used as a constraint condition and the full-rank covariance matrix after covariance fitting is jointly estimated. After covariance fitting, the subspace vector restores the Toeplitz characteristic. On the one hand, it is used to correct the noise matrix in the off-grid algorithm model, and on the other hand, the angle information of the incident signal source under the coherent leakage source is retained, which is more in line with engineering applications.

[0007] Technical solution:

[0008] A method for estimating off-grid DOA of a coherent gas leakage source based on covariance fitting, the method comprising the following steps:

[0009] Step 1, constructing a gas leakage experimental platform, where the gas leakage experimental platform is used to generate and receive gas leakage source signals under different states;

[0010] Step 2: Receive the gas leakage source signal with a uniform linear array of 11 elements, and output the signal matrix according to the array. , calculate the maximum likelihood estimate of the covariance matrix ,in is an estimate of the leakage source covariance matrix, is the conjugate transpose operation, Represents the number of snapshots;

[0011] Step 3: Use the covariance fitting objective function to obtain the approximate equivalent of the covariance matrix and restore the signal covariance matrix The rank of while preserving the noise matrix; , is the array flow matrix, For the source The autocorrelation matrix of

[0012] Step 4: Establish the constraint model of the noise-free part: ,in is the number of far-field narrowband signals, is the leakage source signal matrix, is the array flow matrix expression in the constraint model, represents the transpose operation;

[0013] Step 5: Estimate the value of the array received signal Perform SVD decomposition: , we get the off-lattice semi-positive definite model under the coherent source, where SVD decomposition vector for the leakage source; yes The mutually orthogonal left singular vectors in ; is the adjoint matrix of the singular value diagonal matrix;

[0014] Step 6: Solve the semi-positive definite model to obtain the DOA of the leakage source.

[0015] Further, in step 1, the gas leakage experimental platform includes a fixed gas nitrogen cylinder, a gas pipeline opening and closing pressure relief valve, a movable gas cylinder, a broadband microphone and a MyDAQ acquisition card;

[0016] The fixed gas nitrogen cylinder is used to simulate the gas cylinder leakage source; the gas pipeline opening and closing pressure relief valve controls the opening and closing of gas leakage and the degree of leakage; the movable gas cylinder with adjustable pressure, aperture and position is used as a movable sound source to simulate the gas leakage source signal under different conditions; the wide-band microphone is used to receive the gas leakage source signal; the MyDAQ acquisition card is connected to the wide-band microphone to receive the analog signal sent by the wide-band microphone and convert it into a digital signal and store it in the computer.

[0017] Furthermore, in step 2, the maximum likelihood estimate of the covariance matrix is ​​calculated The process consists of the following sub-steps:

[0018] Assumptions The far-field narrowband leakage source signal is expressed in degrees Incident to The incident angle is ; The wavelength of the coherent leakage source signal is , the array element spacing is And satisfy relationship; in the snapshot number In sufficient cases, The vector form of the data received by the array element at the moment can be summarized as:

[0019] (1)

[0020] Where: A signal matrix for receiving the array; is the array flow matrix; is the signal matrix; is Gaussian white noise;

[0021] According to the array receiving signal matrix, when the signal and noise are independent of each other, the covariance matrix of the array output is obtained:

[0022] (2)

[0023] Where: It means to find the mathematical expectation; is the conjugate transpose operation; For the source The autocorrelation matrix of is the autocorrelation matrix of Gaussian white noise;

[0024] Use the maximum likelihood estimate of the array covariance matrix as an approximation:

[0025] (3)

[0026] Output the estimated value of the covariance matrix as an array; for two stationary signals and , using their correlation coefficient As the basis for determining the relevant:

[0027] (4)

[0028] ,when When defining two signals as independent signals, is the relevant signal, When all signals are independent, the source The autocorrelation matrix of is the incident signal power When the incident signal source is a coherent signal source, the rank of its autocorrelation matrix will degenerate and no longer meet the diagonal matrix condition, so it cannot be sparsely represented.

[0029] Furthermore, in step 3, the covariance fitting objective function is used to obtain the approximate equivalent of the covariance matrix and restore the signal covariance matrix The process of finding the rank of the noise matrix while preserving the rank of the noise matrix consists of the following sub-steps:

[0030] Assume that the number of snapshots satisfies , the objective function based on covariance fitting is expressed as:

[0031] (5)

[0032] Where: is an estimate of the array covariance matrix; represents the Frobenius norm; represents the trace operation; when the leakage source signal and the noise are uncorrelated, construct dimensional leakage source signal power vector , dimensional noise power vector and unknown angle of incidence Correction to the covariance matrix:

[0033] (6)

[0034] Where: is the leakage source covariance matrix; is the noise power vector The diagonal matrix formed by

[0035] According to the covariance fitting criterion:

[0036] (7)

[0037] Where: for The estimated value of is taken when the covariance fitting objective function is minimized;

[0038] Substituting equation (6) and equation (7) into equation (5), we can obtain the approximate equivalence of the three unknown parameters:

[0039] (8);

[0040] Transforming equation (8) into a semi-positive definite programming problem yields:

[0041] (9)

[0042] Where: represents a positive semidefinite matrix; the matrix About The unknown matrix is ​​decomposed into:

[0043] (10)

[0044]

[0045] The convex optimization toolkit is used to solve equation (10) to obtain the estimated value of the leakage source covariance matrix: .

[0046] Furthermore, in step 4, for the noise-free part, the constraint model is transformed into a scalar form:

[0047] (11)

[0048] Where: The direction of arrival angle of the leakage source satisfies , using the atomic norm represents the global optimal solution in model (11);

[0049] Assumptions for The first column of the dimensional identity matrix is ​​defined as , To satisfy hour The closed form solution set of The following model is met:

[0050] (12)

[0051] If you continue to decompose And meet , , model (12) is equivalent to model (11), Y, Q is the solution of model (12), expressed as:

[0052] (13)

[0053] Where: , are the decomposition amounts, Q Contains the angle information;

[0054] Consider the array aperture function , Indicates the first category Bessel function of order, Defined as:

[0055] (14)

[0056] when When , we can get approximately:

[0057] (15)

[0058] Where: Indicated in The positive measure on ; combined with formula (14), we can further obtain:

[0059] (16)

[0060] Where: , Indicates that All conditions are met The smallest positive integer of Represents a block matrix Column vector of .

[0061] Furthermore, in step 5, the off-lattice semi-positive definite model under the coherent source is expressed as:

[0062] (17)

[0063] st .

[0064] Furthermore, in step 6, the DOA of the leakage source is obtained by solving the SDTP3 toolkit.

[0065] Beneficial effects:

[0066] (1) Starting from the covariance matrix of the leakage source output, combined with the interference factors of the coherent signal source in the real leakage source environment, the off-grid model is used The norm is used as a constraint condition and the full-rank covariance matrix after covariance fitting is jointly estimated. After covariance fitting, the subspace vector restores the Toeplitz characteristic, which is used to correct the noise matrix in the off-grid algorithm model, and on the other hand, the angle information of the incident signal source under the coherent signal is retained.

[0067] (2) Compared with traditional Compared with the norm as a constraint condition, the algorithm proposed in the present invention does not require grid division and has higher accuracy. Similar to the greedy algorithm, it does not require iteration, which improves the real-time performance of the algorithm.

[0068] (3) Compared with the general off-grid algorithm, the algorithm of the present invention uses covariance fitting to accurately restore the rank of the signal covariance matrix, and can also perform high-resolution estimation under coherent leakage sources, which has strong engineering practicality. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 This is a flow chart of a method for estimating off-grid DOA of a coherent gas leakage source based on covariance fitting according to an embodiment of the present invention;

[0070] Figure 2 It is a structural schematic diagram of the data acquisition system of the present invention;

[0071] Figure 3 Schematic diagram of a uniform linear array consisting of 11 array elements;

[0072] Figure 4a The DOA estimation spatial spectrum comparison chart corresponding to the signal-to-noise ratio of 15. Figure 4b The DOA estimation spatial spectrum comparison chart corresponding to the signal-to-noise ratio of 10. Figure 4c Comparison diagram of DOA estimation spatial spectrum corresponding to the signal-to-noise ratio of 5;

[0073] Figure 5 It is the spatial spectrum comparison diagram under the coherent signal source;

[0074] Figure 6 This is a comparison chart of the relationship between root mean square error and signal-to-noise ratio;

[0075] Figure 7 This is a comparison chart of the relationship between the root mean square error and the number of snapshots. DETAILED DESCRIPTION

[0076] The following examples will enable those skilled in the art to more fully understand the present invention, but are not intended to limit the present invention in any way.

[0077] The embodiment of the present invention mentions a method for estimating the off-grid DOA of a coherent gas leakage source based on covariance fitting. The specific flow chart is as follows: Figure 1 As shown,

[0078] Step 1: Use a nitrogen bottle with adjustable pressure, aperture and position as a movable sound source. For the fixed sound source experiment, use the gas pipeline to open and close the pressure relief valve to simulate the occurrence of gas pipeline leakage, and use a wide-band microphone to receive the gas leakage source signal. Build a gas leakage experimental platform;

[0079] Specifically:

[0080] The sound source localization signal is obtained from the data collected by the field experiment. The data collection system is as follows: Figure 2 As shown. In order to provide different sound source positions for the experiment, a nitrogen cylinder with adjustable pressure, aperture and position is used as a movable sound source, while the fixed sound source experiment uses a gas pipeline opening and closing pressure relief valve to simulate gas pipeline leakage. A microphone sensor is used to receive the leakage sound source of the fixed gas cylinder and the movable gas cylinder and upload it to the acquisition card. In the experimental platform of the present invention:

[0081] 1 is a fixed nitrogen gas cylinder, which is used to simulate the gas cylinder leakage source. 2 is a pressure relief valve, which controls the opening and closing of gas leakage and the degree of leakage. 3 is a movable gas cylinder, which is used to simulate the gas leakage source signal under different conditions. 4 is a microphone sensor, which is used to receive the gas leakage signal, and its performance indicators are shown in Table 1. 5 is a MyDAQ acquisition card, which is used to receive analog signals and convert them into digital signals for storage in the computer.

[0082] model Sensitivity ±3dB frequency response (Hz) Dynamic range (dB) Diaphragm CRY343 4mV / Pa 4~90,000 25~164 titanium

[0083] Step 2: Receive the gas leakage source signal with a uniform linear array of 11 elements, and output the signal matrix according to the array. , calculate the maximum likelihood estimate of the covariance matrix ,in is an estimate of the leakage source covariance matrix, is the conjugate transpose operation, Represents the number of snapshots;

[0084] Specifically:

[0085] consider The far-field narrowband leakage source signal is expressed in degrees Incident to The incident angle is Assume that the wavelength of the coherent leakage source signal is , the array element spacing is And satisfy Such as Figure 3 As shown in the snapshot number In sufficient cases, The vector form of the data received by the array element at the moment can be summarized as:

[0086]

[0087] Where: A signal matrix for receiving the array; is the array flow matrix; is the signal matrix; is Gaussian white noise.

[0088] According to the array receiving signal matrix, when the signal and noise are independent of each other, the covariance matrix of the array output can be obtained:

[0089] (2)

[0090] Where: It means to find the mathematical expectation; is the conjugate transpose operation; For the source The autocorrelation matrix of is the autocorrelation matrix of Gaussian white noise. Since the actual array receiving matrix is ​​of finite length, the maximum likelihood estimate of the array covariance matrix is ​​generally used as an approximation:

[0091] (3)

[0092] The estimated value of the array output covariance matrix. During the signal transmission process, the multipath effect will cause the independent signal to become a coherent signal. For two stationary signal numbers and , using their correlation coefficient As a basis for determining relevance.

[0093] (4)

[0094] According to Schwartz inequality, ,when When defining two signals as independent signals, is the relevant signal, When is a coherent signal.

[0095] When all signals are independent, the source The autocorrelation matrix of is the incident signal power When the incident signal source is a coherent signal source, the rank of its autocorrelation matrix will degenerate and no longer meet the diagonal matrix condition, and it cannot be sparsely represented. Algorithmic models can also be mismatched.

[0096] Since the gas leakage environment is changeable and prone to multipath effects, the covariance matrix of the signal can be reconstructed using the covariance fitting criterion while retaining noise-related information.

[0097] Step 3: Use the covariance fitting objective function to obtain the approximate equivalent of the covariance matrix and restore the signal covariance matrix The rank of while preserving the noise matrix; , is the array flow matrix, For the source The autocorrelation matrix of .

[0098] Specifically:

[0099] Assuming that the number of snapshots satisfies J>>M, the objective function based on covariance fitting can be expressed as:

[0100]

[0101] Where: is an estimate of the array covariance matrix; ||·|| F represents the Frobenius norm; tr(·) represents the trace operation. When the leakage source signal and the noise are uncorrelated, a 1×K-dimensional leakage source signal power vector {λ 1 ,λ 2 , ..., λ K}, 1×M-dimensional noise power vector {δ 1 , δ 2 , ..., δ M} and unknown incident angle θ to correct the covariance matrix:

[0102] R X(t) (θ, λ, δ) = D (θ, λ) + R N (δ) (6)

[0103] Where: D(θ,λ)=A(θ)R S(t) (λ)A H (θ) is the leakage source covariance matrix; R N (δ) is the diagonal matrix composed of the noise power vector δ, and when the non-ideal leakage source signal is incident, the diagonal matrix R composed of the signal power vector λ S(t) The rank of will be degraded and its sparse representation model cannot be established.

[0104] According to formula (6), the leakage source covariance matrix is Nonlinear functions of three unknown parameters, fitting according to the covariance criterion:

[0105] (7)

[0106] Where: for The estimated value of is taken when the covariance fitting objective function is minimized. At this time, substituting equation (6) and equation (7) into equation (5), the approximate equivalence of the three unknown parameters can be obtained:

[0107] (8);

[0108] Solving equation (8) is still a nonlinear problem, and it is difficult to find the global optimal solution. By converting it into a semi-positive programming problem, we can obtain:

[0109] (9)

[0110]

[0111] In the formula: the special greater than sign " " represents a semi-positive definite matrix; the matrix About The unknown matrix of . Further decomposition can be obtained:

[0112] (10)

[0113] .

[0114] At this point, the estimated value of the leakage source covariance matrix can be obtained by solving equation (10) using the convex optimization toolkit: , obviously the matrix is a Hermitian Toeplitz matrix, which is also related to the lattice The full parameter semidefinite programming method in the algorithm model is consistent. For a coherent source, the full rank matrix is a function that is closer to the true value.

[0115] Step 4: Establish the constraint model of the noise-free part: ,in is the number of far-field narrowband signals, is the leakage source signal matrix, is the array flow matrix expression in the constraint model, represents the transpose operation. The norm is used as a constraint model to avoid meshing and eliminate the influence of quantization error on the final result.

[0116] Specifically:

[0117] The noise subspace vector can be determined by solving the minimum singular value of the covariance matrix. For the noise-free part, the constraint model can be transformed into a scalar form:

[0118] (11)

[0119] Where: The direction of arrival angle of the leakage source satisfies . Using the atomic norm Represents the global optimal solution in model (11).

[0120] consider for The first column of the dimensional identity matrix is ​​defined as , To satisfy hour The closed form solution set of The following model is met:

[0121] (12)

[0122] If you continue to decompose And meet , , then model (12) will be equivalent to model (11). Y, Q is the solution of model (12), which can be expressed as:

[0123] (13)

[0124] Where: , are the decomposition amounts, Q Contains the angle information. Break it down further.

[0125] Consider the array aperture function , Indicates the first category Bessel function of order, Defined as:

[0126] (14).

[0127] Although Equation (14) is an infinite series expansion, since the aperture function obeys , whose number of nonzero entries depends on the array aperture function .when can be approximated with almost no loss of precision:

[0128] (15)

[0129] Where: Indicated in Combining formula (14), we can further obtain:

[0130] (16)

[0131] Where: , Indicates that All conditions are met The smallest positive integer of Represents a block matrix Column vector of

[0132] Step 5: Estimate the value of the array received signal Perform SVD decomposition: ,in, SVD decomposition vector for the leakage source; yes The mutually orthogonal left singular vectors in ; is the diagonal matrix of singular values. We get the off-lattice semi-positive definite model under the coherent source:

[0133] Specifically:

[0134] The noise matrix is ​​retained using the covariance fitting technique, and the array received signal estimate Perform SVD decomposition:

[0135] (17)

[0136] Where: SVD decomposition vector for the leakage source; yes The mutually orthogonal left singular vectors in ; is the adjoint matrix of the singular value diagonal matrix. Combining equations (12) to (17), according to Schur’s lemma, the off-lattice semi-positive definite model under coherent sources can be expressed as:

[0137] (18)

[0138] st .

[0139] Step 6: Use the SDTP3 toolkit to solve the DOA of the leakage source.

[0140] The technical effect of the present invention can be further illustrated by the following simulation results. In order to verify the resolution and estimation effect of the gas leakage source DOA estimation method proposed in the present invention on multiple signal sources under low signal-to-noise ratio, coherent source influence and other environments, a gas leakage source DOA estimation method is selected. Algorithms and The algorithm and the algorithm of the present invention were compared with it under different experimental conditions. The grid step size of the grid partitioning algorithm was set to 1°. The root mean square error (RMSE) between the true value and the estimated value is a key indicator for judging the performance of the algorithm. The Cramer-Rao Lower Bound (CRLB) was introduced for comparison. The closer the root mean square error is to the CRLB bound, the better the algorithm performance is. RMSE is defined as:

[0141] (19)

[0142] Where: represents the number of Monte Carlo experiments; For the The true angle value of the leakage source signal; The leakage source signal is The estimated value of a Monte Carlo experiment.

[0143] Simulation experiment 1: Figure 4a~Figure 4c The DOA estimation spatial spectrum comparison chart under different signal-to-noise ratios. The incident angle of the two gas leakage sources collected is set to [-30, 40], the signal-to-noise ratio varies between 5 and 15 dB, the amplitude of each change is 5 dB, the number of array elements is 11, and the array element spacing is , the noise is Gaussian white noise, and the number of snapshots J = 200. 100 Monte Carlo experiments are performed. Figure 4a~Figure 4c It can be seen that: Algorithms and The algorithms show the problems of the estimated spectrum peak blunting and the appearance of spatial spectrum pseudo peaks. Although a small pseudo peak appears when the signal-to-noise ratio is 5dB, the method of the present invention can still produce a clear spectrum peak at the real sound source position. It proves that the algorithm proposed by the present invention is suitable for low signal-to-noise ratio environments, and its DOA estimation anti-noise ability is significantly stronger than other algorithms.

[0144] Simulation experiment 2: Figure 5 The spatial spectrum comparison diagram under the coherent signal source is shown in Figure 2. The signal-to-noise ratio is set to 25dB, the number of snapshots is J=200, the number of array elements is 11, and the array element spacing is , the noise is Gaussian white noise, the coherent leakage source signal is incident on the array model at two angles [10,40], and 100 Monte Carlo experiments are performed. Figure 5 It can be seen that even in the case of high signal-to-noise ratio, Algorithms and All algorithms are unable to correctly estimate the direction of the angle of arrival in the case of aliased coherent signals, but the algorithm of the present invention can form an obvious sharp spectral peak at the real sound source position after covariance fitting processing, which proves that: when the signal-to-noise ratio is high, the algorithm of the present invention can use covariance fitting to restore the rank of the matrix and still have good positioning performance under coherent signal interference.

[0145] Simulation experiment 3: Figure 6 The figure is a comparison chart of the relationship between the root mean square error and the signal-to-noise ratio. Set the incident angle of the leakage source signal to [10,40], change the signal-to-noise ratio from 5dB to 30dB, and perform 100 Monte Carlo experiments. Figure 6 It can be seen that: in the case of low signal-to-noise ratio, the coefficient matrix is ​​used The performance of the algorithm is slightly better than algorithm, but due to Algorithm Utilization The algorithm of the present invention uses the norm as the condition for grid division, which has advantages under high signal-to-noise ratio. The norm is used as a constraint to avoid the quantization error caused by grid division, and the original matrix is ​​restored by covariance fitting. Its root mean square error is significantly smaller than that of the other two algorithms and is closer to the CRLB bound.

[0146] Simulation experiment 4: Figure 7 The comparison chart of the root mean square error and the number of snapshots is shown in Figure 2. The number of snapshots is set from 50 to 550, the signal-to-noise ratio is 10dB, and the incident angle of the leakage source signal is [10,40]. 100 Monte Carlo experiments are performed. Figure 7 It can be seen that: in the case of multiple snapshots, the root mean square error of the algorithm of the present invention is significantly smaller than that of the other two algorithms, and has a higher positioning capability. Insufficient snapshots will affect the performance of the three algorithms, and the impact on the algorithm of the present invention is greater. This is mainly because the algorithm of the present invention does not rely on grid division and cannot accurately restore the rank of the covariance matrix in the case of low snapshots. However, thanks to the lower root mean square error under multiple snapshots and the avoidance of quantization error, the algorithm of the present invention still has an accuracy advantage.

Claims

1. A method for estimating off-grid DOA of a coherent gas leakage source based on covariance fitting, characterized in that: The estimation method comprises the following steps: Step 1, constructing a gas leakage experimental platform, where the gas leakage experimental platform is used to generate and receive gas leakage source signals under different states; Step 2: Receive the gas leakage source signal with a uniform linear array of 11 elements, and calculate the maximum likelihood estimation of the covariance matrix based on the array output signal matrix X(t) in is the estimate of the leakage source covariance matrix, (·) H is the conjugate transpose operation, J represents the number of snapshots; Step 3: Use the covariance fitting objective function to obtain the approximate equivalent of the covariance matrix, restore the rank of the signal covariance matrix D(θ,λ) while retaining the noise matrix; where D(θ,λ)=A(θ)R S(t) (λ)A H (θ), A(θ) is the array flow matrix, R S(t) is the autocorrelation matrix of the source S; Step 4: Establish the constraint model of the noise-free part: Where K is the number of far-field narrowband signals, S K (t) is the leakage source signal matrix, A(θ K ) is the array flow matrix expression in the constraint model, (·) T represents the transpose operation; Step 5: Estimate the value of the array received signal Perform SVD decomposition: The off-lattice semi-positive definite model under the coherent source is obtained, where Z is the SVD decomposition vector of the leakage source; U is The mutually orthogonal left singular vectors in V * is the adjoint matrix of the singular value diagonal matrix; Step 6, solving the semi-positive definite model to obtain the DOA of the leakage source; In step 2, the maximum likelihood estimate of the covariance matrix is ​​calculated The process consists of the following sub-steps: Assume that K far-field narrowband leakage source signals are incident on a uniform linear array of M sensors at an angle θ, where the incident angle θ = [θ1, θ2, …, θ K ]; the wavelength of the coherent leakage source signal is λ, the array element spacing is d=λ / 2 and satisfies the relationship M>K; when the number of snapshots J is sufficient, The vector form of the data received by the array element at the moment can be summarized as: K(t)=A(θ)S(t)+N (1) Where: is the array receiving signal matrix; A(θ) is the array flow matrix; S(t)=[S(1),S(2),…,S(J)]∈C K×J is the signal matrix; N is Gaussian white noise; According to the array receiving signal matrix, when the signal and noise are independent of each other, the covariance matrix of the array output is obtained: R X(t) =E[X(t)X 1 (t)]=AR S(t) A H +R N (2) Where: E[·] means to find the mathematical expectation; (·) H is the conjugate transpose operation; R S(t) is the autocorrelation matrix of the source S; R N is the autocorrelation matrix of Gaussian white noise; Use the maximum likelihood estimate of the array covariance matrix as an approximation: Output the estimated value of the covariance matrix as an array; for two stationary signals s i (t) and s k (t), and use their correlation coefficient ρ as the basis for determining the correlation: |ρ|≤1, when ρ=0, the two signals are defined as independent signals, when 0<|ρ|<1, they are correlated signals, and when |ρ|=1, they are coherent signals; when all signals are independent, the autocorrelation matrix R of the source S is S(t) is the incident signal power {p1,…,p K }; When the incident signal source is a coherent signal source, the rank of its autocorrelation matrix will degenerate and no longer meet the diagonal matrix condition, and it cannot be sparsely represented; In step 3, the covariance fitting objective function is used to obtain the approximate equivalent of the covariance matrix. The process of restoring the rank of the signal covariance matrix D(θ,λ) while preserving the noise matrix includes the following sub-steps: Assuming that the number of snapshots satisfies J>>M, the objective function based on covariance fitting is expressed as: Where: is an estimate of the array covariance matrix; ||·|| F represents the Frobenius norm; tr(·) represents the trace operation; when the leakage source signal and the noise are uncorrelated, a 1×K-dimensional leakage source signal power vector {λ1,λ2,…,λ K }, 1×M-dimensional noise power vector {δ1,δ2,…,δ M } and unknown incident angle θ to correct the covariance matrix: R X(t) (θ,λ,δ)=D(θ,λ)+R N (d) (6) Where: D(θ,λ)=A(θ)R S(t) (λ)A H (θ) is the leakage source covariance matrix; R N (δ) is the diagonal matrix composed of the noise power vector δ; According to the covariance fitting criterion: Where: is the estimated value of (θ,λ,δ), which is approximated when the covariance fitting objective function is minimized; Substituting equation (6) and equation (7) into equation (5), we can obtain the approximate equivalence of the three unknown parameters: stD(θ,λ)≥0 Transforming equation (8) into a semi-positive programming problem yields: Where: > represents a semi-positive definite matrix; the matrix D is an unknown matrix about (θ, λ), which can be decomposed into: The convex optimization toolkit is used to solve equation (10) to obtain the estimated value of the leakage source covariance matrix:

2. The method for estimating off-grid DOA of a coherent gas leakage source based on covariance fitting according to claim 1, characterized in that: In step 1, the gas leakage experimental platform includes a fixed gas nitrogen cylinder, a gas pipeline opening and closing pressure relief valve, a movable gas cylinder, a broadband microphone and a MyDAQ acquisition card; Fixed nitrogen gas cylinders are used to simulate the source of gas cylinder leakage; the opening and closing of the gas pipeline pressure relief valve controls the opening and closing of gas leakage and the degree of leakage; the movable gas cylinder with adjustable pressure, aperture and position is used as a movable sound source to simulate the gas leakage source signal under different conditions; the wide-band microphone is used to receive the gas leakage source signal; the MyDAQ acquisition card is connected to the wide-band microphone to receive the analog signal sent by the wide-band microphone and convert it into a digital signal and store it in the computer.

3. The off-grid DOA estimation method for coherent gas leakage source based on covariance fitting according to claim 1, characterized in that: In step 4, for the noise-free part, the constraint model is transformed into a scalar form: Where: The direction of arrival angle of the leakage source satisfies Using the atomic norm || R X(t) || A represents the global optimal solution in model (11); Assume that e is the first column of the M×M dimensional identity matrix and define Γ(θ)=A(λ)A * (λ), φ satisfies The closed-form solution set of Γ(θ) when ||R X(t) || A The following model is met: If we continue to decompose R = ∑ K A(θ)a K ε K * And meet ||R X(t) || A =∑ K a K , model (12) is equivalent to model (11), Y and Q are the solutions of model (12), expressed as: Where: ε K , a K They are all decomposed quantities, and Q contains the information of angle θ; Consider the array aperture function η, η q represents the q-order Bessel function of the first kind, and Γ(θ) is defined as: When Q∈φ, we can get: Where: σ(θ) represents The positive measure on ; combined with formula (14), we can further obtain: Where: N * Indicates that The smallest positive integer that satisfies the condition |q|≤N, ξ=[ξ0,…,ξ N ] T Represents the column vector of the block matrix Q.

4. The method for estimating off-grid DOA of a coherent gas leakage source based on covariance fitting according to claim 3, characterized in that: In step 5, the off-lattice semi-positive definite model under the coherent source is expressed as:

5. The off-grid DOA estimation method for coherent gas leakage source based on covariance fitting according to claim 1, characterized in that: In step 6, the DOA of the leakage source is obtained by solving the SDTP3 toolkit.

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