A method for underwater DOA estimation based on high degree of freedom

Abstract

This application proposes an underwater DOA estimation method based on high degrees of freedom, which specifically includes the following steps: obtaining multiple source signals at different angles received by a mutually prime array transducer; using a mutually prime array RECA to increase the number of continuous virtual array elements; analyzing the signal received on the virtual ULA and performing an inverse discrete Fourier transform; obtaining the predicted angle of the signal source through the peak of the discrete inverse Fourier transform IDFT spectrum; and finally evaluating the performance of the DOA estimation method through the root mean square error. This application uses the characteristics of a large number of continuous virtual array elements under high degrees of freedom to receive more signals from signal sources at different angles using a small number of actual array elements, thereby saving costs; by controlling a certain signal-to-noise ratio and number of snapshots of the transmitted signal, the signals transmitted by the signal source in a complex ocean environment can be received, and the accuracy of this method is better than that of the efficient discrete inverse Fourier transform, thereby building an integrated positioning system to improve the accuracy of underwater positioning.

Description

Technical Field

[0001] The present application belongs to the technical field of target positioning, and specifically relates to an underwater DOA estimation method based on high degree of freedom. Background Art

[0002] Direction of arrival (DOA) estimation in array signal processing has become an important direction in military and civilian fields, including radar, sonar, wireless communication and underwater positioning. However, in the marine environment with severe multipath effects, the complex ocean channel poses a great challenge to the estimation of underwater signals. Therefore, it is necessary to study an effective algorithm to improve the accuracy of DOA estimation of signals in complex underwater environments.

[0003] In the early stage, the main research on DOA estimation was in uniform linear arrays, including multiple signal classification (MUSIC) and rotation invariant subspace (ESPRIT) algorithms. Afterwards, many scholars made improvements on these two methods, proposing SS-MUSIC algorithm, ROOT-MUSIC algorithm, matrix-constrained ESPRIT algorithm and real-valued space ESPRIT algorithm. In recent years, PPval and PPVaidyanathan proposed a nested array, whose array structure is composed of two uniform linear arrays nested. M physical array elements can be used to increase the degree of freedom to O(M 2 ). Since the nested array spacing is small, mutual coupling effect will occur, which reduces the estimation performance. On this basis, PPval and PPVaidyanathan proposed a coprime array, which is composed of two uniform subarrays, and the two subarrays M and N are prime numbers to each other. M+N physical array elements obtain O(MN) degrees of freedom.

[0004] Sparse arrays are different from traditional uniform arrays. Sparse arrays can estimate more signal sources with fewer array elements. Then, the construction method of extending continuous degrees of freedom was studied, and it was found that the underwater DOA estimation method with high degrees of freedom has higher accuracy.

[0005] The invention proposes an underwater DOA estimation method based on RECA with high degrees of freedom. First, through the characteristics of RECA with a large number of continuous virtual array elements, the performance of discrete inverse Fourier transform in underwater DOA estimation under high degrees of freedom is studied and analyzed. A more accurate DOA estimation method is designed to accurately locate different signal sources in complex marine environments.

[0006] Application Contents

[0007] The technical problem solved by the present invention is to provide an underwater DOA estimation method based on high degree of freedom to solve the shortcomings of the above-mentioned background technology.

[0008] This application proposes an underwater DOA estimation method based on high degree of freedom, which specifically includes the following steps:

[0009] Step 1: Obtain multiple signal sources at different angles received by the mutual prime array transducer;

[0010] Step 2: Use the coprime array RECA to increase the number of continuous virtual array elements;

[0011] Step 3: Analyze the signal received on the virtual ULA and perform an inverse discrete Fourier transform;

[0012] Step 4: Obtain the predicted angle of the signal source by calculating the peak value of the discrete inverse Fourier transform IDFT spectrum; and

[0013] Step 5: Evaluate the performance of the DOA estimation method by the root mean square error.

[0014] The predicted angle of the signal source is obtained by the above method, and the mean square error of the signal is analyzed to ensure the accurate positioning of the signal source; according to the characteristics of a large number of continuous virtual array elements under high degrees of freedom, a small number of actual array elements can receive more signals from signal sources at different angles, thereby saving costs; using the signals emitted by signal sources at different angles, a reliable underwater DOA estimation method based on RECA inverse Fourier transform is designed to achieve the purpose of accurate positioning; by controlling a certain signal-to-noise ratio and number of snapshots of the transmitted signal, the signals emitted by the signal source in a complex marine environment can be received, and the accuracy of this method is better than that of the efficient discrete inverse Fourier transform, thereby building an integrated positioning system to improve the accuracy of underwater positioning.

[0015] Preferably, in the second step, it includes redefining the extended coprime array RECA:

[0016] where S in the coprime array consists of three subarrays (S1, S2, S3) with N, 2M-1-J and J sensors, where N and M are coprime integers, N>M and the total number of sensors is T=N+2M-1; J is the number of repositioned sensors; in addition, the element spacing of subarray S1 is d r1 =Md0, and the element spacing of subarray S2 is d r2 =Nd0; the displacement between S1 and S2 is L=M+N; S1, S2, S3 are respectively expressed as

[0017]

[0018] Where M≥3.

[0019] Further preferably, when the holes in the central differential common matrix generated by the shifted subarray can be filled,

[0020] More preferably, when When , the intermediate continuous common array is <-D,D>, where D = 2MN + 2M-JN-1 and cDOF = 2D+1.

[0021] Further preferably, about The coprime array RECA:

[0022] For odd numbers M,

[0023] ω(l)=1,l∈<1,M-1>

[0024] For even M,

[0025]

[0026] Where ω(l) represents the number of hole groups.

[0027] Further preferably, for a fixed total number of sensors T, the following model is constructed to achieve the maximum number of sensors in the RECA continuous array,

[0028]

[0029] in N=T-2M+1.

[0030] Preferably, in the fourth step, it includes defining Fourier transform DFT:

[0031] S1. Define a periodic signal, then its main value interval is a finite length signal;

[0032] S2, applying Fourier series DFS to the periodic signal;

[0033] S3, define a new change called Fourier transform DFT, which is the main value period of the Fourier series DFS;

[0034] S4. The DFT is the final numerically computable Fourier transform DFT of any finite length sequence.

[0035] Further preferably, define a finite length sequence x n , which has N samples on 0≤n≤N-1, as an N-point sequence; let is the n-point sequence x n Create a periodic signal with a period of N, that is:

[0036]

[0037] and

[0038]

[0039] in:

[0040]

[0041] The discrete inverse Fourier transform of an N-point DFTX(k) is given by:

[0042]

[0043] or

[0044]

[0045] In complex ocean environments, underwater acoustic signals are affected by other signals and it is difficult to accurately locate the signal source. RECA has the characteristics of high degree of freedom, and uses discrete inverse Fourier transform to establish a mathematical model to predict signal sources at different angles to obtain accurate positioning.

[0046] Compared with the prior art, the beneficial results of this application are:

[0047] (1) The predicted angle of the signal source is obtained by the above method, and the mean square error of the signal is analyzed to ensure the accurate positioning of the signal source;

[0048] (2) Based on the characteristics of a large number of continuous virtual array elements under high degrees of freedom, a small number of actual array elements can be used to receive signals from more signal sources at different angles, thereby saving costs;

[0049] (3) Using the signals from signal sources at different angles, a reliable underwater DOA estimation method based on RECA inverse Fourier transform is designed to achieve accurate positioning.

[0050] (4) By controlling the signal-to-noise ratio and snapshot number of the transmitted signal to a certain extent, the signals transmitted by the signal source can be received in a complex ocean environment, and the accuracy of this method is better than that of the efficient discrete inverse Fourier transform, thereby building an integrated positioning system to improve the accuracy of underwater positioning. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] The accompanying drawings are included to provide a further understanding of the embodiments and are incorporated into and constitute a part of this specification. The accompanying drawings illustrate the embodiments and are used together with the description to explain the principles of the present application. It will be easy to recognize other embodiments and many expected advantages of the embodiments because they become better understood by reference to the following detailed description. The elements of the drawings are not necessarily to scale with each other. The same reference numerals refer to corresponding similar parts.

[0052] Figure 1 This is a flow chart of an underwater DOA estimation method based on high degree of freedom according to an embodiment of the present application;

[0053] Figure 2 It is the spatial spectrum of the MVDR method in the embodiment of this application;

[0054] Figure 3 It is a highly efficient inverse Fourier transform spatial spectrum in the embodiment of the present application;

[0055] Figure 4 It is a spatial spectrum diagram of the inverse Fourier transform based on RECA high degree of freedom in the embodiment of the present application;

[0056] Figure 5 A mean square error diagram of the inverse Fourier transform signal-to-noise ratio of the MVDR method, the efficient inverse Fourier transform method, and RECA in the embodiments of the present application;

[0057] Figure 6 It is a mean square error diagram of the inverse Fourier transform snapshot number of the MVDR method, the efficient inverse Fourier transform method and RECA in the embodiments of the present application. DETAILED DESCRIPTION

[0058] In the following detailed description, reference is made to the accompanying drawings, which form a part of the detailed description and are shown by illustrative specific embodiments in which the present application can be practiced. To this end, directional terms, such as "top", "bottom", "left", "right", "up", "down", etc., are used with reference to the orientation of the figures described. Because the components of the embodiments can be positioned in several different orientations, directional terms are used for the purpose of illustration and are by no means limiting. It should be understood that other embodiments may be utilized or logical changes may be made without departing from the scope of the present application. Therefore, the following detailed description should not be adopted in a limiting sense, and the scope of the present application is defined by the appended claims.

[0059] Figure 1 Flowchart of the underwater DOA estimation method based on high degree of freedom according to an embodiment of the present application, as shown in FIG. Figure 1 As shown, the present application discloses an underwater DOA estimation method based on high degree of freedom, which specifically includes the following steps:

[0060] Step 1: Obtain multiple signal sources at different angles received by the mutual prime array transducer;

[0061] Step 2: Use the coprime array RECA to increase the number of continuous virtual array elements;

[0062] According to the characteristic of a large number of continuous virtual array elements under high degrees of freedom, a small number of actual array elements can be used to receive signals from more signal sources at different angles, thereby saving costs.

[0063] Specifically, it includes redefining the extended coprime array RECA:

[0064] where S in the coprime array consists of three subarrays (S1, S2, S3) with N, 2M-1-J and J sensors, where N and M are coprime integers, N>M and the total number of sensors is T=N+2M-1; J is the number of repositioned sensors; in addition, the element spacing of subarray S1 is d r1 =Md0, and the element spacing of subarray S2 is d r2 =Nd0; the displacement between S1 and S2 is L=M+N; S1, S2, S3 are respectively expressed as

[0065]

[0066] Where M≥3.

[0067] (1) When the holes in the central differential matrix generated by the shifted subarray can be filled, That is, after the array element moves, the position of the shifted array element is subtracted from the original array element position.

[0068] (2) When When , the intermediate continuous common array is <-D,D>, where D = 2MN + 2M-JN-1 and cDOF = 2D+1.

[0069] In this embodiment cDOF refers to continuous degree of freedom.

[0070] (3) About The coprime array RECA:

[0071] For odd numbers M,

[0072] ω(l)=1,l∈<1,M-1>

[0073] For even M,

[0074]

[0075] Where ω(l) represents the number of hole groups.

[0076] In addition, for a fixed total number of sensors T, the following model is constructed to achieve the maximum number of sensors in the RECA continuous array,

[0077]

[0078] in N=T-2M+1.

[0079] Step 3: Analyze the signal received on the virtual ULA and perform an inverse discrete Fourier transform;

[0080] By controlling the signal-to-noise ratio and snapshot number of the transmitted signal to a certain extent, the signals transmitted by the signal source can be received in complex ocean environments, and the accuracy of this method is better than that of the efficient discrete inverse Fourier transform, thereby building an integrated positioning system to improve the accuracy of underwater positioning.

[0081] Figure 2 The spatial spectrum of the MVDR method is shown as Figure 2 This method first estimates the autocorrelation matrix R through the received snapshot signal x(n), and calculates the inverse matrix R of the autocorrelation matrix R -1 Then, according to the array geometry, the corresponding guiding vector a(θ) is constructed so that θ follows a certain step and P is calculated. θ , for P θ Perform peak selection of the spatial spectrum, find out the θ corresponding to the peak point and obtain the angle prediction of the signal source.

[0082] Step 4: Obtain the predicted angle of the signal source by calculating the peak value of the discrete inverse Fourier transform IDFT spectrum;

[0083] Specifically, it includes defining the Fourier transform DFT:

[0084] S1. Define a periodic signal, then its main value interval is a finite length signal;

[0085] S2, applying Fourier series DFS to periodic signals;

[0086] S3. Define a new variation called Fourier transform DFT, which is the main value period of Fourier series DFS;

[0087] S4, then DFT is the final numerically computable Fourier transform DFT of any finite length sequence.

[0088] Furthermore, we define a finite length sequence x n , which has N samples on 0≤n≤N-1, as an N-point sequence; let is the n-point sequence x n Create a periodic signal with a period of N, that is:

[0089]

[0090] and

[0091]

[0092] in:

[0093]

[0094] The discrete inverse Fourier transform of an N-point DFTX(k) is given by:

[0095]

[0096] or

[0097]

[0098] Step 5: Evaluate the performance of the DOA estimation method by the root mean square error.

[0099] Figure 3 Shown is a high-efficiency inverse Fourier transform spatial spectrum in an embodiment of the present application, Figure 4 The spatial spectrum diagram of the inverse Fourier transform based on the high degree of freedom of RECA in the embodiment of the present application is shown as follows: Figure 3 and Figure 4 As shown, by performing discrete inverse Fourier transform on the signals received at different angles and taking advantage of the large number of continuous RECA array elements, the predicted angle of the signal source can be obtained.

[0100] Furthermore, Figure 5-6 The figure shows the mean square error of the inverse Fourier transform signal-to-noise ratio and the number of snapshots of the MVDR method, the efficient inverse Fourier transform method, and RECA. The estimation accuracy of the three methods is evaluated by calculating the mean square error between the predicted angle and the actual angle.

[0101] In a complex ocean environment, underwater acoustic signals are affected by other signals and it is difficult to accurately locate the signal source; RECA has the characteristics of high degrees of freedom, and uses discrete inverse Fourier transform to establish a mathematical model to predict signal sources at different angles to obtain accurate positioning.

[0102] The present invention proposes an underwater DOA estimation method based on RECA high degree of freedom and applies it to an underwater positioning system. The predicted angle of a signal source is obtained by the above method, and the mean square error of the signal is analyzed to ensure the accurate positioning of the signal source. By utilizing the signals emitted by signal sources at different angles, a reliable underwater DOA estimation method based on RECA inverse Fourier transform is designed to achieve the purpose of accurate positioning, thereby building an integrated positioning system and improving the accuracy of underwater positioning.

[0103] The above description is only a preferred embodiment of the present application and an explanation of the technical principles used. Those skilled in the art should understand that the scope of the invention involved in the present application is not limited to the technical solution formed by a specific combination of the above technical features, but should also cover other technical solutions formed by any combination of the above technical features or their equivalent features without departing from the above invention concept. For example, the above features are replaced with the technical features with similar functions disclosed in this application (but not limited to) by each other to form a technical solution.

Claims

1. A method for estimating underwater DOA based on high degree of freedom, characterized in that: The method specifically comprises the following steps: Step 1: Obtain multiple signal sources at different angles received by the mutual prime array transducer; Step 2: Using the coprime array RECA to increase the number of continuous virtual array elements; including redefining the extended coprime array RECA: where S in the coprime array consists of three subarrays (S1, S2, S3) with N, 2M-1-J and J sensors, where N and M are coprime integers, N>M and the total number of sensors is T=N+2M-1; J is the number of repositioned sensors; in addition, the element spacing of subarray S1 is dr1=Md o , and the element spacing of subarray S2 is d r2 =Nd o ; The displacement between S1 and S2 is L = M + N; S1, S2, S3 are respectively expressed as Where M≥3; Step 3: Analyze the signal received on the virtual ULA and perform an inverse discrete Fourier transform; Step 4: Obtain the predicted angle of the signal source by the peak value of the discrete inverse Fourier transform IDFT spectrum; including defining the Fourier transform DFT: S1, defining a periodic signal, then its main value interval is a finite length signal; S2, applying the Fourier series DFS to the periodic signal; S3, defining a new change called Fourier transform DFT, which is the main value period of the Fourier series DFS; S4, then the DFT is the final numerically computable Fourier transform DFT of any finite length sequence; and Step 5: Evaluate the performance of the DOA estimation method by the root mean square error.

2. The underwater DOA estimation method based on high degree of freedom according to claim 1, characterized in that: When the holes in the central differential matrix generated by the shifted subarray can be filled, 3. The underwater DOA estimation method based on high degree of freedom according to claim 1, characterized in that: when When , the intermediate continuous common array is <-D, D>, where D = 2MN + 2M-JN-1 and cDOF = 2D+1.

4. The underwater DOA estimation method based on high degree of freedom according to claim 1, characterized in that: about The coprime array RECA: For odd numbers M, ω(l)=1,l∈<1,M-1> For even M, Where ω(l) represents the number of hole groups.

5. The underwater DOA estimation method based on high degree of freedom according to claim 1, characterized in that: For a fixed total number of sensors T, the following model is constructed to achieve the maximum number of sensors in the RECA continuous array, in N=T-2M+1.

6. The underwater DOA estimation method based on high degree of freedom according to claim 1, characterized in that: Define a finite length sequence x n , which has N samples on 0≤n≤N-1, as an N-point sequence; let is the n-point sequence x n Create a periodic signal with a period of N, that is: and in: The discrete inverse Fourier transform of an N-point DFTX(k) is given by: or

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