Irregular array direction finding method based on spherical wave model

Abstract

The application discloses an irregular array direction-finding method based on a spherical wave model and belongs to the technical field of underwater acoustic direction finding. The application aims at the problem that the consistency of direction finding results under different array configurations is poor due to the plane wave approximation error of the existing direction finding method, and proposes a direction finding scheme based on a spherical wave model. The method comprises the following steps: constructing an acoustic coordinate system and determining the coordinates of each element; extracting a target signal to obtain a propagation time delay, calculating the distance from the target to each element and the distance to the origin; decomposing the irregular array into a plurality of base lines, combining the element coordinates and the origin distance, and establishing a direction finding equation of each base line based on the spherical wave model; and solving the direction finding equation set constructed by the plurality of base line equations to obtain the target direction. The spherical wave model is used to replace the plane wave approximation, the model error under the near-field condition is effectively reduced, and the consistency and precision of the direction estimation under different irregular arrays are improved. The application is suitable for underwater target measurement.

Description

Technical Field

[0001] This invention belongs to the field of underwater acoustic direction finding technology, and particularly relates to an irregular array direction finding method based on a spherical wave model. Background Technology

[0002] Ultra-short baseline (USBR) systems are widely used in underwater target orientation finding due to their advantages such as simple structure and convenient installation. A typical USBR system consists of a transponder mounted on an underwater platform and an acoustic array mounted on a surface ship. The surface ship obtains the underwater platform's azimuth information by measuring the propagation delay difference between the transponder signal and each array element.

[0003] In recent years, to meet the requirements of low cost, long endurance, and multi-user orientation finding, related research has proposed an anti-ultra-short baseline system. In this system, the acoustic array is no longer limited to being mounted on surface ships, but is integrated onto underwater platforms with different geometric configurations.

[0004] To accommodate different platform structures, acoustic arrays typically employ irregular array designs. Existing direction-finding methods for irregular arrays are usually derived based on a plane wave approximation model. Under near-field conditions, the plane wave approximation introduces a non-negligible direction-finding bias, and this bias varies across different array configurations, resulting in poor consistency in direction estimation results across different array configurations. Summary of the Invention

[0005] This application aims to address the problem of poor consistency in direction finding results under different array configurations caused by model approximation errors in existing direction finding methods. It provides an irregular array direction finding method based on a spherical wave model.

[0006] The first aspect of this application describes an irregular array direction finding method based on a spherical wave model, the method comprising:

[0007] An acoustic coordinate system is constructed based on an irregular array structure. Determine each element of the irregular array in the acoustic coordinate system. The coordinates below;

[0008] The target signal acquired by each primitive in the irregular array is extracted. The propagation delay information of the target signal is obtained using the target signal. The distance from the target to each primitive is calculated using the propagation delay information. Finally, the distance from the target to each primitive is used to calculate the distance from the target to the acoustic coordinate system. origin The distance between them;

[0009] The irregular array is decomposed into multiple baselines, and the coordinate information of the primitives and the target to the acoustic coordinate system are combined. origin Based on the spherical wave model, the direction-finding equations for all baselines are established, considering the distances between them and the distances from the target to each element.

[0010] By simultaneously establishing the direction-finding equations for multiple baselines, an irregular array of direction-finding equations is constructed. Solving this set of equations yields the target's azimuth.

[0011] This invention decomposes an irregular array into multiple baselines and establishes direction-finding equations for each baseline based on a spherical wave propagation model. By solving the set of direction-finding equations composed of each baseline, the target azimuth is obtained. Compared with existing direction-finding methods for irregular arrays, this invention can reduce the impact of plane wave approximation errors on the direction-finding results and improve the consistency of azimuth estimation results for different array configurations. Attached Figure Description

[0012] Figure 1 This is a schematic diagram of the orientation estimation process of the present invention;

[0013] Figure 2 A geometric relationship diagram between the three-dimensional baseline vector and the target's three-dimensional orientation vector;

[0014] Figure 3 This is a geometric diagram showing the relationship between the plane baseline vector and the target's three-dimensional orientation vector. Detailed Implementation

[0015] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application. It should be noted that, unless otherwise specified, the embodiments and features in the embodiments of this application can be combined with each other.

[0016] Specific implementation method one: Refer to Figures 1 to 3 This embodiment describes an irregular array direction finding method based on a spherical wave model, which includes:

[0017] An acoustic coordinate system is constructed based on an irregular array structure. Determine each element of the irregular array in the acoustic coordinate system. The coordinates below;

[0018] The target signal acquired by each primitive in the irregular array is extracted. The propagation delay information of the target signal is obtained using the target signal. The distance from the target to each primitive is calculated using the propagation delay information. Finally, the distance from the target to each primitive is used to calculate the distance from the target to the acoustic coordinate system. origin The distance between them;

[0019] The irregular array is decomposed into multiple baselines, and the coordinate information of the primitives and the target to the acoustic coordinate system are combined. origin Based on the spherical wave model, the direction-finding equations for all baselines are established, considering the distances between them and the distances from the target to each element.

[0020] By simultaneously establishing the direction-finding equations for multiple baselines, an irregular array of direction-finding equations is constructed. Solving this set of equations yields the target's azimuth.

[0021] Furthermore, the irregular array configuration constructs an acoustic coordinate system. The origin Located at the geometric center of the irregular formation, axis, shaft and The axes point to the front, right, and top of the center of the irregular formation facing the target.

[0022] Furthermore, in this invention, the distance from the target to each primitive is used to calculate the target to the acoustic coordinate system. origin The formula for the distance between them is:

[0023] ;

[0024] In the formula, N represents the number of primitives in the irregular array, where N is a positive integer. Represents the target to the acoustic coordinate system origin distance, This represents the distance from the target to the primitive k;

[0025] ;

[0026] In the formula, The propagation delay of the target signal to the primitive k; This represents the speed at which sound waves travel in water.

[0027] Furthermore, in this invention, the direction-finding equation is determined based on the irregular array structure. When the spatial configuration of the irregular array is a three-dimensional irregular array, it corresponds to a three-dimensional direction-finding equation; when the spatial configuration of the irregular array is a planar irregular array, it corresponds to a planar direction-finding equation.

[0028] Furthermore, in this invention, the stereo orientation equation is:

[0029] ;

[0030] In the formula, and These represent the distances from primitive i and primitive j to the origin of the acoustic coordinate system, respectively. distance, and Representing primitive i and primitive j in the acoustic coordinate system respectively The three-dimensional coordinate vector below; , , Representing three-dimensional coordinate vectors and acoustic coordinate systems respectively axis, shaft and The included angle of the axis; and These represent the distances from the target to primitive i and primitive j, respectively.

[0031] The distance and According to the corresponding primitives in the acoustic coordinate system The coordinates below are calculated to obtain:

[0032] .

[0033] Furthermore, in this invention, the plane direction finding equation is:

[0034] ;

[0035] In the formula, and represents the distance from the target to primitives i and j, respectively.

[0036] Furthermore, in this invention, when the spatial configuration of the irregular array is a three-dimensional irregular array, the direction-finding equations of the irregular array are:

[0037] ;

[0038] ;

[0039] In the formula, The matrix representing the position correlation of the primitives in a 3D array. Represents the distance correlation vector. Represents the vector related to the primitive length;

[0040] By solving the direction-finding equations corresponding to the three-dimensional irregular matrix, the three-dimensional azimuth vector of the target is obtained. Closed-form solution;

[0041] ;

[0042] In the formula, represent The generalized inverse.

[0043] Furthermore, in this invention, when the irregular array is a planar array, the direction-finding equations for the irregular array are:

[0044] ;

[0045] ;

[0046] In the formula, A two-dimensional orientation vector representing the target. This represents the matrix relating the positions of the primitive elements of a planar array.

[0047] By solving the direction-finding equations corresponding to the irregular planar matrix, the two-dimensional azimuth vector of the target is obtained. Closed-form solution;

[0048] ;

[0049] In the formula, represent The generalized inverse;

[0050] For the target's three-dimensional orientation vector The components can be determined based on the relationship between the square of the direction cosines;

[0051] .

[0052] Example 1: Combining Figure 1 , Figure 2 and Figure 3 This embodiment describes the azimuth estimation process of an irregular array orientation-finding method based on a spherical wave model as follows: Figure 1 As shown, it includes the following steps:

[0053] Step 1: Construct an acoustic coordinate system based on an irregular array And determine the coordinates of each element of the irregular array in this coordinate system;

[0054] Wherein, the acoustic coordinate system The origin Located at the geometric center of the irregular formation, axis, shaft and The axes point to the front, right, and top of the irregular formation, respectively.

[0055] Step 2: Process the target signals acquired by each element in the irregular array, extract the propagation delay information of the target signal to each element, and calculate the distance from the target to each element and the distance from the target to the acoustic coordinate system based on the propagation delay information. origin The distance;

[0056] The extraction process of the propagation delay information is common knowledge in the field of underwater acoustic positioning. Preferred methods include: cross-correlation: the most classic and widely used method, which calculates the cross-correlation function between the reference signal and the received signals of each primitive element, with the peak position corresponding to the delay; generalized cross-correlation (GCC-PHAT, etc.): improves robustness in noisy or reverberant environments; matched filtering: when the transmitted signal is known (such as a cooperative beacon), matched filtering can be used to achieve high-precision delay estimation; phase-based delay estimation: suitable for narrowband continuous wave signals.

[0057] The distance from the target to each element is obtained by calculating the propagation delay information and the speed of sound:

[0058] ;

[0059] In the formula, Let be the propagation delay of the target signal to the primitive k. This represents the speed at which sound waves travel in water. This represents the distance from the target to the primitive k.

[0060] The target to the acoustic coordinate system origin The distance is determined based on the average of the corresponding distances of each primitive.

[0061] ;

[0062] In the formula, This represents the number of primitives in an irregular array. Represents the target to the acoustic coordinate system origin The distance.

[0063] Step 3: Decompose the irregular array into multiple baselines, and establish the direction-finding equations for each baseline based on the coordinate information of the primitives in Step 1 and the distance information in Step 2, using the spherical wave model.

[0064] The direction finding equations are divided into direction finding equations corresponding to three-dimensional irregular arrays and direction finding equations corresponding to planar irregular arrays, based on the spatial configuration of the irregular array.

[0065] When the irregular array is a three-dimensional array, the direction-finding equations corresponding to the three-dimensional irregular array can be derived as follows:

[0066] Let primitives i and j be in the acoustic coordinate system The three-dimensional coordinate vector below is and The resulting three-dimensional baseline vector is ,like Figure 2 As shown.

[0067] Let the target be in the acoustic coordinate system The coordinates below are .in, The three-dimensional orientation vector representing the target. , , Representing the three-dimensional orientation vector and the acoustic coordinate system, respectively. axis, shaft and The included angle of the axis.

[0068] Let the angle between the target and the baseline ij be... Its geometric definition is as follows Figure 2 As shown. According to the vector projection theorem, the included angle It satisfies the following first geometric relation:

[0069] ;

[0070] In the formula, Represents Euclidean distance. represent transpose, This represents the baseline space vector pointing from primitive i to primitive j.

[0071] Furthermore, according to the law of cosines, the included angle It also satisfies the following second geometric relation:

[0072] ;

[0073] Combining the first and second geometric relations, we obtain the following third geometric relation:

[0074] ;

[0075] Expanding and simplifying the third geometric relation, we obtain the direction-finding equation corresponding to the three-dimensional irregular matrix as follows:

[0076] ;

[0077] In the formula, and These represent the distances from primitive i and primitive j to the origin of the acoustic coordinate system, respectively. The distance. The distance is determined based on the corresponding primitive in the acoustic coordinate system. The coordinates below are calculated to obtain:

[0078] ;

[0079] When the irregular array is a planar array, primitives i and j are in The coordinates of the direction are all 0 ( The resulting baseline vector is a planar baseline vector, such as... Figure 3 As shown. At this point, the direction-finding equation corresponding to the planar irregular matrix can be simplified from the direction-finding equation corresponding to the three-dimensional irregular matrix to:

[0080] ;

[0081] Step 4: Simultaneously establish the direction finding equations for multiple baselines to construct an irregular array of direction finding equations, and obtain the bearing of the underwater target by solving the direction finding equations.

[0082] The aforementioned irregular array direction-finding equations are divided into two categories based on the spatial configuration of the irregular array: the direction-finding equations corresponding to three-dimensional irregular arrays and the direction-finding equations corresponding to planar irregular arrays.

[0083] When the irregular array is a three-dimensional array, the direction-finding equations corresponding to the three-dimensional irregular array are:

[0084] ;

[0085] ;

[0086] In the formula, The matrix representing the position correlation of the primitives in a 3D array. Represents the distance correlation vector. This represents the vector related to the primitive length.

[0087] By solving the direction-finding equations corresponding to the three-dimensional irregular matrix, the three-dimensional azimuth vector of the target can be obtained. The closed-form solution.

[0088] ;

[0089] In the formula, represent The generalized inverse.

[0090] When the irregular array is a planar array, the direction-finding equations corresponding to the planar irregular array are:

[0091] ;

[0092] ;

[0093] In the formula, A two-dimensional orientation vector representing the target. This represents the matrix relating the positions of the primitive elements of a planar array.

[0094] By solving the direction-finding equations corresponding to the irregular planar matrix, the two-dimensional azimuth vector of the target can be obtained. The closed-form solution.

[0095] ;

[0096] In the formula, represent The generalized inverse.

[0097] For the target's three-dimensional orientation vector The components can be determined based on the relationship between the square of the direction cosine and the sum of squares.

[0098] ;

[0099] In summary, this invention discloses a direction-finding method for irregular array configurations based on a spherical wave model. This invention reduces the impact of plane wave approximation errors on direction-finding results and maintains consistency in azimuth estimation results under different array configurations.

[0100] While specific embodiments of this application have been described herein with reference to them, it should be understood that these embodiments are merely examples of the principles and applications of this application. Therefore, it should be understood that many modifications can be made to the exemplary embodiments, and other arrangements can be designed without departing from the spirit and scope of this application as defined by the appended claims. It should be understood that different dependent claims and features described herein can be combined in ways different from those described in the original claims. It is also understood that features described in conjunction with individual embodiments can be used in other described embodiments.

Claims

1. A direction-finding method for irregular arrays based on a spherical wave model, characterized in that, The method includes: An acoustic coordinate system is constructed based on an irregular array structure. Determine each element of the irregular array in the acoustic coordinate system. The coordinates below; The target signal acquired by each primitive in the irregular array is extracted. The propagation delay information of the target signal is obtained using the target signal. The distance from the target to each primitive is calculated using the propagation delay information. Finally, the distance from the target to each primitive is used to calculate the distance from the target to the acoustic coordinate system. origin The distance between them; The irregular array is decomposed into multiple baselines, and the coordinate information of the primitives and the target to the acoustic coordinate system are combined. origin Based on the spherical wave model, the direction-finding equations for all baselines are established, considering the distances between them and the distances from the target to each element. By simultaneously establishing the direction-finding equations for multiple baselines, an irregular array of direction-finding equations is constructed. Solving this set of equations yields the target's azimuth.

2. The irregular array direction finding method based on a spherical wave model according to claim 1, characterized in that, The irregular array formation constructs an acoustic coordinate system. The origin Located at the geometric center of the irregular formation, axis, shaft and The axes point to the front, right, and top of the center of the irregular formation facing the target.

3. The irregular array direction finding method based on a spherical wave model according to claim 1 or 2, characterized in that, The distance from the target to each primitive is used to calculate the target to the acoustic coordinate system. origin The formula for the distance between them is: ； In the formula, N represents the number of primitives in the irregular array, where N is a positive integer. Represents the target to the acoustic coordinate system origin distance, This represents the distance from the target to the primitive k; ； In the formula, The propagation delay of the target signal to the primitive k; This represents the speed at which sound waves travel in water.

4. The irregular array direction finding method based on a spherical wave model according to claim 3, characterized in that, The direction finding equations are determined based on the irregular array structure. When the spatial configuration of the irregular array is a three-dimensional irregular array, the corresponding three-dimensional direction finding equations are used. When the spatial configuration of the irregular array is a planar irregular array, the corresponding planar direction finding equations are used.

5. The irregular array direction finding method based on a spherical wave model according to claim 4, characterized in that, The equation for stereo orientation finding is: ； In the formula, and These represent the distances from primitive i and primitive j to the origin of the acoustic coordinate system, respectively. distance, and Representing primitive i and primitive j in the acoustic coordinate system respectively The three-dimensional coordinate vector below; , , Representing three-dimensional coordinate vectors and acoustic coordinate systems respectively axis, shaft and The included angle of the axis; and These represent the distances from the target to primitive i and primitive j, respectively. The distance and According to the corresponding primitives in the acoustic coordinate system The coordinates below are calculated to obtain: 。 6. The irregular array direction finding method based on a spherical wave model according to claim 5, characterized in that, The equation for plane orientation finding is: ； In the formula, and represents the distance from the target to primitives i and j, respectively.

7. The irregular array direction finding method based on a spherical wave model according to claim 5, characterized in that, When the spatial configuration of the irregular array is a three-dimensional irregular array, the direction-finding equations of the irregular array are: ； ； In the formula, The matrix representing the position correlation of the primitives in a 3D array. Represents the distance correlation vector. Represents the vector related to the primitive length; By solving the direction-finding equations corresponding to the three-dimensional irregular matrix, the three-dimensional azimuth vector of the target is obtained. Closed-form solution; ； In the formula, represent The generalized inverse.

8. The irregular array direction finding method based on a spherical wave model according to claim 5, characterized in that, When the irregular array is a planar array, the direction-finding equations for the irregular array are: ； ； In the formula, A two-dimensional orientation vector representing the target. This represents the matrix relating the positions of the primitive elements of a planar array. By solving the direction-finding equations corresponding to the irregular planar matrix, the two-dimensional azimuth vector of the target is obtained. Closed-form solution; ； In the formula, represent The generalized inverse; For the target's three-dimensional orientation vector The components can be determined based on the relationship between the square of the direction cosines; 。

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