An Improved DOA Method and System for Underwater Acoustic Localization

Abstract

This invention belongs to the field of target localization technology, specifically relating to an improved Direction of Arrival (DOA) method and system for underwater acoustic localization. The method includes: preprocessing the received signal from a linear array; the linear array comprising n primitives with an adjacent distance of d; calculating the covariance matrix of the preprocessed received signal; de-ambiguously adjusting the phase difference between primitive 1 and primitive n based on the covariance matrix of the received signal to obtain the de-ambigued phase; performing phase correction on the covariance matrix of the preprocessed received signal based on the de-ambigued phase; performing Toeplitz correction on the phase-corrected covariance matrix; and estimating the incident angle using the DOA algorithm on the covariance matrix after phase correction and Toeplitz correction. By using the method of this invention to correct the covariance matrix of the array with the covariance of two relatively distant primitives, the accuracy of direction of arrival estimation can be effectively improved.

Description

Technical Field

[0001] This invention belongs to the field of target localization technology, specifically relating to an improved DOA method and system for underwater acoustic localization. Background Technology

[0002] Direction of Arrival (DOA) estimation is one of the fundamental problems in array signal processing and an important task in many fields such as radar and sonar.

[0003] Because the signal subspace and noise subspace of a coherent signal source interpenetrate each other, and there are errors in the array installation, the spatial covariance matrix is ​​rank-deficient. Traditional DOA algorithms such as the MUSIC algorithm and ESPRIT algorithm cannot effectively distinguish and determine the direction of the signal. Therefore, a smoothing algorithm is needed to restore the rank of the spatial covariance matrix.

[0004] The Toeplitz algorithm only considers that the distance between adjacent hydrophones is equal, so the phase difference of the received signal is also equal. However, for linear arrays with multiple hydrophones, the Toeplitz algorithm does not consider the multiple relationship of their distances. Summary of the Invention

[0005] To address the problem that existing direction-of-arrival (DOA) estimation algorithms cannot effectively distinguish and determine signals when the spatial covariance matrix is ​​rank-deficient, this invention aims to overcome the shortcomings of existing technologies by proposing an improved DOA method and system for underwater acoustic localization, based on phase correction and Toeplitz correction.

[0006] To achieve the above objectives, this invention proposes an improved DOA (Depth of Orientation) method for underwater acoustic localization, the method comprising:

[0007] Step 1) Preprocess the received signal of the linear array; the linear array includes n primitives with an adjacent distance of d;

[0008] Step 2) Calculate the covariance matrix of the preprocessed received signal;

[0009] Step 3) Based on the covariance matrix of the received signal, the phase difference between the first and nth primitives is de-blurred to obtain the de-blurred phase.

[0010] Step 4) Perform phase correction on the covariance matrix of the preprocessed received signal based on the deblurred phase;

[0011] Step 5) Perform Toeplitz correction on the phase-corrected covariance matrix;

[0012] Step 6) Estimate the incident angle using the DOA algorithm on the covariance matrix after phase correction and Toeplitz correction.

[0013] As an improvement to the above method, step 1) specifically includes:

[0014] Step 1-1) Determine if the received signal is a beacon transmission signal. If yes, proceed to step 1-2); if no, re-receive the signal.

[0015] Step 1-2) Perform matched filtering on the received signal x(t) to obtain the signal X(t);

[0016] Steps 1-3) perform signal correlation on X(t) to obtain the received signal delay difference TimeDelay of n primitives:

[0017]

[0018] Among them, timedelay ab Let be the received signal delay difference between the a-th primitive and the b-th primitive, where a∈[1,n], b∈[1,n].

[0019] As an improvement to the above method, step 2) specifically includes:

[0020] The covariance matrix of the signal X(t) is calculated using the following formula:

[0021]

[0022] Where E(·) represents the expectation, (·) H r represents the conjugate transpose of a matrix. ab Let be the covariance of the received signals between the a-th and b-th primitives.

[0023] As an improvement to the above method, step 3) specifically includes:

[0024] Step 3-1) Based on the covariance r between primitive 1 and primitive n 1n The phase difference θ between primitive 1 and primitive n is calculated using the following formula. 1n :

[0025]

[0026] Where j represents the imaginary part; abs(·) represents taking the absolute value;

[0027] Step 3-2) Based on the time delay difference (timedelay) obtained in Step 1-3) 1n Converted to the corresponding phase difference θ 1n ′:

[0028]

[0029] Where c is the speed of sound and λ is the wavelength;

[0030] Step 3-3) Obtain the maximum absolute value of the phase difference |θ| according to the following formula. max :

[0031]

[0032] Steps 3-4) at (θ) 1n +2kπ)∈[-|θ| max ,|θ| max Within the range of θ, k = ±1, ±2, ..., find abs(θ) 1n +2kπ-θ 1n The minimum value of θ') corresponds to the value of k, then θ'') 1n "=θ 1n +2kπ represents the phase after deblurring.

[0033] As an improvement to the above method, step 4) includes:

[0034] Based on the defuzzified phase θ 1n "The covariance matrix R of the preprocessed received signal" XX Phase correction is performed, and the covariance matrix R after phase correction is obtained by the following formula. XX ′:

[0035] R XX ′=γ×R XX

[0036]

[0037] Where γ is a phase correction coefficient between 0 and 1.

[0038] As an improvement to the above method, step 5) specifically includes:

[0039] The covariance matrix R obtained after phase correction XX Perform Toeplitz correction to obtain the Toeplitz-corrected covariance matrix T(R). XX ′):

[0040]

[0041] Among them, T(R) XX The i-th element of ′) m represents the m-th primitive. It is r i Complex conjugate.

[0042] As an improvement to the above method, step 6) specifically includes:

[0043] Step 6-1) Apply the power method to the Toeplitz-corrected covariance matrix T(R) XX Find the eigenvalues ​​by performing eigenvalue decomposition.

[0044] Step 6-2) Take the eigenvector U corresponding to the largest eigenvalue. x Constructing the first sub-signal space U x1 With the second sub-signal space U x2 :

[0045] U x1 =U x (1:n-1)

[0046] U x2 =U x (2:n)

[0047] Among them U x (1:n-1) represents taking the eigenvector U x The first n-1 elements, U x (2:n) represents taking the eigenvector U x U y The last n-1 elements;

[0048] The angle θ between the ultra-short baseline received signal and the coordinate axis normal is obtained from the following formula, thus enabling the estimation of the incident angle:

[0049]

[0050] In this context, the upper right "+" indicates finding the pseudo-inverse of a matrix, angle(·) indicates finding the phase of a complex number, c represents the speed of sound, and f... c The center frequency of the received signal is denoted by d, and the element spacing of the ultra-short baseline is denoted by d.

[0051] On the other hand, the present invention proposes an improved DOA system for underwater acoustic localization, the system comprising:

[0052] A preprocessing module is used to preprocess the received signal of the linear array; the linear array includes n primitives with an adjacent distance of d.

[0053] The covariance matrix calculation module is used to calculate the covariance matrix of the preprocessed received signal.

[0054] The deblurring module is used to deblur the phase difference between the first and nth primitives based on the covariance matrix of the received signal, and obtain the deblurred phase.

[0055] The phase correction module is used to perform phase correction on the covariance matrix of the preprocessed received signal based on the deblurred phase.

[0056] The Toeplitz correction module is used to perform Toeplitz correction on the phase-corrected covariance matrix; and

[0057] The DOA module is used to estimate the incident angle using the DOA algorithm on the covariance matrix after phase correction and Toeplitz correction.

[0058] Compared with the prior art, the advantages of the present invention are:

[0059] 1. The Toeplitz correction only considers that the distance between adjacent uniform linear array elements is equal, so the phase difference of the received signal is also equal. However, for multi-element linear arrays, the Toeplitz correction does not consider the phase difference multiple caused by the multiple relationship of their distance. The method of this invention considers the phase difference multiple caused by the multiple relationship of their distance for multi-element linear arrays.

[0060] 2. When there are errors in the array installation, the relative error decreases as the spacing between the elements increases, and the impact of the error is reduced. The method of this invention can be used to correct the covariance matrix of the array using the covariance of two elements that are far apart, which can effectively improve the accuracy of direction of arrival estimation. Attached Figure Description

[0061] Figure 1 This is a schematic flowchart of the improved DOA method for underwater acoustic localization according to Embodiment 1 of the present invention;

[0062] Figure 2 This is a schematic diagram of the element distribution of a linear array. Detailed Implementation

[0063] This invention proposes an improved DOA (Depth of Orientation) method for underwater acoustic localization, the method comprising:

[0064] Step 1) Preprocess the received signal of the linear array; the linear array includes n primitives with an adjacent distance of d;

[0065] Step 2) Calculate the covariance matrix of the preprocessed received signal;

[0066] Step 3) Based on the covariance matrix of the received signal, the phase difference between the first and nth primitives is de-blurred to obtain the de-blurred phase.

[0067] Step 4) Perform phase correction on the covariance matrix of the preprocessed received signal based on the deblurred phase;

[0068] Step 5) Perform Toeplitz correction on the phase-corrected covariance matrix;

[0069] Step 6) Estimate the incident angle using the DOA algorithm on the covariance matrix after phase correction and Toeplitz correction.

[0070] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and embodiments.

[0071] Example 1

[0072] like Figure 1 As shown, Embodiment 1 of the present invention proposes an improved DOA (Directed Aspect of Origin) method for underwater acoustic positioning. The overall implementation process is divided into seven steps completed sequentially. The input signal is orthogonally demodulated and converted into a baseband signal. During initial positioning, the baseband signal undergoes DFT beamforming to obtain an initial estimate of the azimuth of arrival. If a positioning result has already been obtained, pre-beamforming is used to obtain an initial estimate of the azimuth of arrival. Phase-shift beamforming is performed based on the initial estimated azimuth to obtain linear array data. Pulse compression is applied to the linear array to acquire data near the peak value. LS-ESPRIT spectrum estimation is performed using the data near the peak value to obtain the precise azimuth of arrival.

[0073] Specifically, the steps of this invention are as follows: Step 1) A linear basis matrix is ​​formed by n adjacent primitives with a distance of d, such as... Figure 2 As shown, the received signal x(t) of the array is preprocessed;

[0074] Step 2) Calculate the covariance matrix of the preprocessed received signal obtained in Step 1);

[0075] Step 3) For the covariance matrix of the received signal obtained in Step 2), calculate the phase difference θ between the first and nth primitives. 1n Defuzzing is performed to obtain θ 1n ";

[0076] Step 4) Apply the defuzzified θ obtained in step 3) 1n "Perform phase correction on the covariance matrix of the received signal;"

[0077] Step 5) Perform Toeplitz correction on the phase-corrected covariance matrix obtained in Step 4);

[0078] Step 6) The incident angle is estimated using the DOA algorithm on the covariance matrices obtained in Step 5) after phase correction and Toeplitz correction.

[0079] Preferably, step 1) of the present invention includes:

[0080] Step 1-1) First, determine whether the received signal is a beacon transmission signal. If yes, proceed to step 1-2); if no, re-receive the signal.

[0081] Step 1-2) Perform matched filtering on the received signal x(t) to obtain X(t).

[0082] Steps 1-3) Perform signal correlation on the X(t) obtained by matched filtering to obtain the received signal delay difference TimeDelay of n primitives.

[0083]

[0084] Among them, timedelay ab Let be the time delay difference of the received signal between primitive a and primitive b.

[0085] Preferably, step 2) of the present invention includes:

[0086]

[0087] Where E(·) represents the expectation, (·) H r represents the conjugate transpose of a matrix. ab Let R be the covariance of the received signals between primitive a and primitive b. XX Let be the covariance matrix of the received signal.

[0088] Preferably, step 3) of the present invention includes:

[0089] Step 3-1) First, determine the phase difference between primitive 1 and primitive n before defuzzification.

[0090]

[0091] Where r 1n Let θ be the covariance between primitive 1 and primitive n obtained in step 2). 1n The phase difference between the first and nth primitives before the fuzzy problem is solved.

[0092] Step 3-2) Use the time delay difference (timedelay) obtained in Step 1-3) 1n Convert to the corresponding phase difference.

[0093]

[0094] Where c is the speed of sound and λ is the wavelength.

[0095] Step 3-3) Determine the range of the actual phase difference. The distance between primitive 1 and primitive n is (n-1)×d, therefore the absolute value of the phase difference |θ| max The maximum is as shown in formula (5).

[0096]

[0097] Steps 3-4) at (θ) 1n +2kπ)∈[-|θ| max ,|θ| max Explore abs(θ) within the range of (k = ±1, ±2, ...). 1n +2kπ-θ 1n The minimum value of θ') gives the corresponding value of k. 1n "=θ 1n +2kπ is the phase after deblurring.

[0098] Preferably, step 4) of the present invention includes:

[0099]

[0100] Where γ is a phase correction coefficient between 0 and 1, R XX ′ is the covariance matrix obtained after phase correction.

[0101] Preferably, step 5) of the present invention includes:

[0102]

[0103]

[0104]

[0105] Among them, T(R) XX ′) is the R after Toeplitz correction. XX ′, It is r i Complex conjugate.

[0106] Preferably, step 6) of the present invention includes:

[0107] Step 6-1) Apply the covariance matrix T(R) obtained in step 5) XX Find the eigenvalues; the eigenvalues ​​of the covariance matrix are obtained by power-law eigendecomposition to obtain the largest eigenvalue.

[0108] Step 6-2) Take the eigenvector U corresponding to the maximum eigenvalue. x The incident angle of the signal is solved by constructing a sub-signal space; the constructed sub-signal space is as follows:

[0109]

[0110]

[0111] Where n is the number of elements in the linear array, U x (1:n-1) represents taking the eigenvector U x The first n-1 elements, U x (2:n) represents taking the eigenvector U x U y The last n-1 elements; the angle between the ultra-short baseline received signal and the coordinate axis normal:

[0112]

[0113] The "+" in the upper right corner indicates finding the pseudo-inverse of a matrix, angle(·) indicates finding the phase of a complex number, c represents the speed of sound, and f c Here, d represents the center frequency of the received signal, d represents the element spacing of the ultra-short baseline, and θ represents the angle between the received signal and the coordinate axis.

[0114] Example 2

[0115] Embodiment 2 of the present invention proposes an improved DOA system for underwater acoustic localization, implemented based on the method of Embodiment 1. The system includes:

[0116] A preprocessing module is used to preprocess the received signal of the linear array; the linear array includes n primitives with an adjacent distance of d.

[0117] The covariance matrix calculation module is used to calculate the covariance matrix of the preprocessed received signal.

[0118] The deblurring module is used to deblur the phase difference between the first and nth primitives based on the covariance matrix of the received signal, and obtain the deblurred phase.

[0119] The phase correction module is used to perform phase correction on the covariance matrix of the preprocessed received signal based on the deblurred phase.

[0120] The Toeplitz correction module is used to perform Toeplitz correction on the phase-corrected covariance matrix.

[0121] The DOA module is used to estimate the incident angle using the DOA algorithm on the covariance matrix after phase correction and Toeplitz correction.

[0122] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to the embodiments, those skilled in the art should understand that modifications or equivalent substitutions to the technical solutions of the present invention do not depart from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. An improved DOA method for underwater acoustic positioning, the method comprising: Step 1) pre-processing the received signal of a linear array; the linear array comprising n adjacent elements with a distance of d; Step 2) calculating the covariance matrix of the pre-processed received signal; Step 3) de-ambiguating the phase difference between the 1st element and the nth element according to the covariance matrix of the received signal to obtain a de-ambiguited phase; Step 4) phase correcting the covariance matrix of the pre-processed received signal according to the de-ambiguited phase; Step 5) Toeplitz correcting the phase-corrected covariance matrix; Step 6) estimating the incident angle using DOA algorithm on the covariance matrix after phase correction and Toeplitz correction.

2. The improved DOA method for underwater acoustic positioning according to claim 1, characterized in that, The Step 1) specifically comprises: Step 1-1) judging whether the received signal is a beacon transmitted signal, if yes, go to Step 1-2); if no, re-receive the signal; Step 1-2) performing matched filtering on the received signal x(t) to obtain a signal X(t); Step 1-3) performing signal correlation on X(t) to obtain the time delay difference TimeDelay of the received signal of n elements: where timedelay ab timedelay is the time delay between the a-th and b-th elements, a e [1, n], b e [1, n].

3. The improved DOA method for underwater acoustic positioning according to claim 2, characterized in that, The Step 2) specifically comprises: calculating the covariance matrix of the signal X(t) according to the following formula: where E(·) denotes expectation, (·) H denotes the conjugate transpose of a matrix, r ab Rab is the covariance of the received signal between the a-th and b-th elements.

4. The improved DOA method for underwater acoustic positioning according to claim 3, characterized in that, The Step 3) specifically comprises: Step 3-1) The covariance r between the No. 1 element and the No. n element is calculated according to the No. 1 element and the No. n element 1n The phase difference θ between the No. 1 element and the No. n element is calculated from the following equation 1n : wherein j represents the imaginary part; abs(·) represents taking the absolute value; Step 3-2) The time delay difference timedelay is obtained according to the result of Step 1-3) 1n converted into the corresponding phase difference θ 1n ′: wherein c is the sound speed and λ is the wavelength; Step 3-3) The absolute value maximum |θ| of the phase difference is obtained according to the following formula max : Steps 3-4) at (θ) 1n +2kπ)∈[-|θ| max ,|θ| max Within the range of θ, k = ±1, ±2, ..., find abs(θ) 1n +2kπ-θ 1n The minimum value of θ') corresponds to the value of k, then θ'') 1n "=θ 1n +2kπ represents the phase after deblurring.

5. The improved DOA method for underwater acoustic positioning according to claim 4, characterized in that, The Step 4) comprises: According to the deobfuscated phase θ 1n "the covariance matrix R of the preprocessed received signal XX Phase correction is performed, and the covariance matrix R obtained after phase correction is obtained from the following equation XX ′: wherein γ is a phase correction coefficient between 0 and 1.

6. The improved DOA method for underwater acoustic positioning according to claim 5, characterized in that, The Step 5) specifically comprises: The covariance matrix R obtained after phase correction XX Toeplitz correction is performed on the covariance matrix R to obtain a Toeplitz corrected covariance matrix T(R XX ′): where T(R XX the ith element of T(R m denotes the mth basis element, is the complex conjugate of r i .

7. The improved DOA method for underwater acoustic positioning according to claim 6, characterized in that, The Step 6) specifically comprises: Step 6-1) Perform eigen decomposition of the Toeplitz corrected covariance matrix T(R XX ) using power method to obtain the largest eigenvalue; Step 6-2) Take the eigenvector U corresponding to the largest eigenvalue x Constructing the first subsignal space U x1 and the second subsignal space U x2 : U x1 = U x (1:n-1) U x2 = U x (2:n) where U x (1 :n - 1) denotes the first n - 1 elements of the eigenvector U x (2 :n) denotes the last n - 1 elements of the eigenvector U x (2 :n) denotes the last n - 1 elements of the eigenvector U x (2 :n) denotes the last n - 1 elements of the eigenvector U y (2 :n) denotes the last n - 1 elements of the eigenvector U obtaining the angle θ between the super-short baseline received signal and the normal of the coordinate axis to realize the estimation of the incident angle according to the following formula: where the upper right "+" denotes the pseudo-inverse of a matrix, angle(·) denotes the phase of a complex number, c denotes the sound speed, f c is the center frequency of the received signal, and d denotes the inter-element spacing of the USBL.

8. An improved DOA system for underwater acoustic positioning, characterized by The system comprises: a pre-processing module for pre-processing the received signal of a linear array; the linear array comprising n adjacent elements with a distance of d; a covariance matrix calculation module for calculating the covariance matrix of the pre-processed received signal; a de-ambiguity processing module for de-ambiguating the phase difference between the 1st element and the nth element according to the covariance matrix of the received signal to obtain a de-ambiguited phase; a phase correction module for phase correcting the covariance matrix of the pre-processed received signal according to the de-ambiguited phase; a Toeplitz correction module for Toeplitz correcting the phase-corrected covariance matrix; and a DOA module for estimating the incident angle using DOA algorithm on the covariance matrix after phase correction and Toeplitz correction.

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