A sum-and-difference beam direction finding method based on coordinate transformation

Abstract

The application relates to a sum-difference beam direction finding method based on coordinate conversion and belongs to the technical field of array signal processing. First, the sum-difference beam phase comparison method is used to calculate the angle discrimination value of the elevation angle under the normal coordinates, the angle discrimination value is corrected, the table is inquired to obtain the elevation deviation angle, and the elevation angle is calculated in combination with the initial elevation pointing angle of the array; then the coordinates are converted, the converted elevation angle under the converted coordinates is calculated by using the same method, and the direction of arrival can be uniquely determined through the elevation angle under the normal coordinates and the converted elevation angle under the converted coordinates, so that the DOA estimation of the signal is completed. The angle decoupling in the solving process is realized through the coordinate conversion, the data amount of the angle discrimination table stored locally can be obviously reduced, and the processing speed is greatly improved.

Description

Technical Field

[0001] This invention relates to the field of array signal processing technology, and in particular to a sum-difference beam direction finding method based on coordinate transformation. Background Technology

[0002] Array signal processing is a crucial branch of modern signal processing, and DOA (Direction of Arrival) estimation has always been considered an important research topic within this field. In traditional sum-difference direction finding methods, especially in two-dimensional direction finding, the angle values ​​for different azimuths under different initial array pointing directions are not the same. Furthermore, when solving for the signal azimuth in a conventional coordinate system, the azimuth and elevation angles are coupled, resulting in an extremely large amount of locally stored angle table data. For example, when the elevation angle range is 0°–90° with a step of 1°, the azimuth angle is 0°–180° with a step of 1°, and the deviation angle range of each angle line in the local angle table is -5°–5° with a step of 0.1°, the amount of angle value data required to solve for the azimuth using conventional methods is: 181 (dimensions of different array pointing angles) * 91 (dimensions of elevation angle introduced by angle coupling) * 101 (dimensions introduced by the deviation angle range of each angle line) = 1,663,571. It is evident that the multi-dimensional nature of data in the traditional sum-difference beamforming method imposes a burden on data storage and computational processing, thus limiting its applicability in engineering. Summary of the Invention

[0003] To reduce the amount of data required to solve the azimuth angle, this invention provides a sum-difference beam direction finding method based on coordinate transformation.

[0004] The technical problem to be solved by this invention is achieved by the following technical solution:

[0005] A sum-difference beam direction finding method based on coordinate transformation includes the following steps:

[0006] Step 1: Divide the uniform array into four identical 2x2 subarrays. The lower left and lower right subarrays are collectively called the lower subarray, the upper left and upper right subarrays are collectively called the upper subarray, the upper left and lower left subarrays are collectively called the left subarray, and the upper right and lower right subarrays are collectively called the right subarray. Calculate the sum of the received signals in the lower and upper subarrays of the uniform array, and output P. 12 P 34 :

[0007]

[0008]

[0009] In the above formula, [·] H W is the conjugate transpose of the matrix. 0_12 W 0_34A 12 A 34 They are respectively:

[0010] The weighted vector of the submatrix;

[0011] The weighted vector of the submatrix;

[0012] A 12 =e j·2πf·(X·cosФ·sinθ+Y·sin(Ф)) / c , is the signal receiving guide vector for the lower subarray;

[0013] A 34 =e j2πf·(X·cosФ·sinθ-Y·sin(Ф)) / c , is the signal receiving guide vector for the upper subarray;

[0014] In the above formula, j is the imaginary unit, f is the signal frequency, c is the speed of light, Ф and θ are the elevation and azimuth angles of the signal, Ф0 and θ0 are the initial pointing elevation and azimuth angles of the array, X and Y are the coordinate vectors of the two coordinate axes of the upper subarray, the lower subarray has the same X coordinate as the upper subarray, and the Y coordinates are opposites of each other.

[0015] Step 2: Calculate the angle value R of the elevation angle in conventional coordinates:

[0016]

[0017] In the above formula, imag(·) is the symbol for taking the complex part;

[0018] Step 3: Correct the angle detection value based on the initial pointing and pitch angle of the array:

[0019] R Refine =R·cos(Ф0)

[0020] Step 4: Transfer R Refine Substituting the angle detection table when Ф0=0, the pitch deviation angle ΔФ is obtained, and the signal pitch angle is calculated:

[0021] Ф=Ф0+ΔФ

[0022] Step 5: Perform coordinate transformation and calculate the initial pointing and pitch angle Ф of the array. 0_Switch And the initial pointing of the array, the conversion azimuth angle θ 0_Switch :

[0023] Ф 0_Switch =asin(cos(Ф0)sin(θ0))

[0024] θ 0_Switch =asin(sin(Ф0) / cos(Ф) 0_Switch ))

[0025] Step 6: Calculate the angle value R of the pitch angle in the transformed coordinate system. Switch :

[0026]

[0027] in:

[0028]

[0029]

[0030]

[0031]

[0032]

[0033]

[0034] In the above formula, Ф Switch and θ Switch These are the signal conversion elevation angle and the signal conversion azimuth angle, respectively. 13 and Y 13 These are the X and Y coordinate vectors of the array elements in the left subarray, respectively, and the Y coordinate of the right subarray is the same as that of the left subarray, while the X coordinate is the opposite of that of the left subarray.

[0035] Step 7: Correct the angle detection value based on the initial pointing conversion pitch angle of the array:

[0036] R Switch_Refine =R Switch ·cos(Ф 0_Switch )

[0037] Step 8: R Switch_Refine Substitute Ф 0_Switch The pitch deviation angle ΔФ is obtained by searching the angle table when ΔФ = 0. Switch The signal conversion pitch angle is calculated as follows:

[0038] Ф Switch =Ф 0_Switch +ΔФ Switch

[0039] Step 9: Output the calculated pitch angle and the converted pitch angle as the azimuth angle of the signal to complete the sum-difference beam direction finding.

[0040] Compared with the prior art, the present invention has the following advantages:

[0041] 1. The present invention can realize data dimensionality reduction and reduce the amount of local data storage. When the angle discrimination line correction and coordinate transformation angle decoupling technology proposed in the present invention is adopted, the required stored data dimension is only 101 (the dimension introduced only by the deviation angle range of a single angle discrimination line). Compared with the prior art, the data volume can be reduced by 16471 times!

[0042] 2. The present invention can simplify the retrieval process of angle discrimination values and improve the processing speed of the algorithm. Brief Description of the Drawings

[0043] Figure 1 is the overall flowchart of the present invention.

[0044] Figure 2 is a schematic diagram of the definition manner of subarrays in the present invention.

[0045] Figure 3 is a schematic diagram of coordinate transformation in the present invention.

[0046] Figure 4 is a comparison diagram of angle discrimination line correction results obtained by the angle discrimination value correction method proposed in the present invention. Wherein, Figure 4(a) is a data diagram before correction, and Figure 4(b) is a data diagram after correction.

[0047] Figure 5 shows the direction finding results of the direction finding method proposed in the present invention. Wherein, Figure 5(a) is an image of the pitch angle discrimination value, and Figure 5(b) is an image of the transformed pitch angle discrimination value. Detailed Description of the Embodiments

[0048] A sum-difference beam direction finding method based on coordinate transformation. According to the method, the sum outputs of the upper and lower subarrays are calculated first, the pitch angle discrimination value is obtained by using the difference-to-sum ratio between the sum outputs of the upper and lower subarrays, the deviation angle is retrieved from the angle discrimination table after correction, and then the actual pitch angle of the signal is calculated according to the initial pitch pointing angle of the array and the deviation angle; subsequently, the initial transformed pitch pointing angle of the array is calculated by using the initial pitch pointing angle and the initial azimuth pointing angle of the array, then the transformed pitch angle is calculated by using the difference-to-sum ratio of the left and right subarrays, and finally the DOA result of the signal is output.

[0049] With reference to Figure 1 , the method specifically includes the following steps:

[0050] Step 1: As shown in Figure 2 , the uniform planar array is equally divided into 4 identical subarrays in a "field" shape, the lower left subarray is defined as subarray 1, the lower right subarray as subarray 2, the upper left subarray as subarray 3, and the upper right subarray as subarray 4. Meanwhile, subarrays 1 and 2 are collectively referred to as the lower subarray, subarrays 3 and 4 are collectively referred to as the upper subarray, subarrays 1 and 3 are collectively referred to as the left subarray, and subarrays 2 and 4 are collectively referred to as the right subarray. The sum outputs P of the signals received by the lower subarray and the upper subarray in the uniform planar array are calculated respectively 12 , P 34 :

[0051]

[0052]

[0053] In the above formula, [·] H W is the conjugate transpose of the matrix. 0_12 W 0_34 A 12 A 34 They are respectively:

[0054] The weighted vector of the submatrix;

[0055] The weighted vector of the submatrix;

[0056] A 12 =e j·2πf·(X·cosФ · sinθ+Y·sin(Ф)) / c , is the signal receiving guide vector for the lower subarray;

[0057] A 34 =e j·2πf·(X·cosФ·sinθY·sin(Ф)) / c , is the signal receiving guide vector for the upper subarray;

[0058] In the above formula, j is a complex exponent and j 2 =-1, f is the signal frequency, c is the speed of light, Ф and θ are the elevation and azimuth angles of the signal, Ф0 and θ0 are the initial elevation and azimuth angles of the array, X and Y are the coordinate vectors of the two coordinate axes of the upper subarray (the X coordinates of the lower subarray and the upper subarray are the same, and the corresponding Y coordinates are opposites of each other).

[0059] Step 2: Calculate the angle value R of the elevation angle in conventional coordinates:

[0060]

[0061] In the above formula, imag(·) is the symbol for taking the complex part;

[0062] Step 3: Correct the angle detection value based on the initial pointing and pitch angle of the array:

[0063] R Refine =R·cos(Φ0)

[0064] In the above formula, R is simplified using trigonometric functions and Euler's formula as follows:

[0065] R = -imag(j·tan(πf·D) y ·(sinФ-sinФ0) / c))

[0066] In the above formula, D yLet be the aperture of the upper (or lower) subarray in the y-axis direction. Since sinФ and sinФ0 are not significantly different, we have:

[0067] R≈-imag(-j·(πf·D x ·(sinФ-sinФ0) / c))

[0068] In the above formula, sinФ-sinФ0 can be simplified to:

[0069] sinФ-sinФ0=sinФ0+ΔФsinФ0≈sinФ0-ΔФ·cosФ0-sinФ0=-ΔФ·cosФ0

[0070] From the above formula, we can obtain:

[0071] R = ΔФ·cosФ0·f·D y / c

[0072] When the array points to 0°, we have:

[0073] R = ΔФ·πf·D y / c

[0074] Therefore, only one angle detection line needs to be stored locally when Ф0=0. When the initial pitch pointing angle of the array is arbitrary, the angle detection value can be corrected by the cosine multiplier.

[0075] Step 4: Transfer R Refine Substituting the angle detection table when Ф0=0, the pitch deviation angle ΔФ is obtained, and the signal pitch angle is calculated:

[0076] Ф=Ф0+ΔФ

[0077] Step 5: As Figure 3 As shown, a coordinate transformation is performed to calculate the initial pointing and pitch angle Ф of the array. 0_Switch And the initial pointing of the array, the conversion azimuth angle θ 0_Switch :

[0078] Ф 0_Switch =asin(cos(Ф0)sin(θ0))

[0079] θ 0_Switch =asin(sin(Ф0) / cos(Ф) 0_Switch ))

[0080] In conventional coordinates, the elevation angle Ф is defined as the angle between the target direction and its projection onto the xOz plane. At 0 degrees, it is parallel to the xOz plane and perpendicular to the xOy plane where the array is located; therefore, only the azimuth angle exists. The azimuth angle θ is defined as the angle between the target direction's projection onto the xOz plane and the z-axis. At 0 degrees, it corresponds to the positive transverse direction of the xOy plane array. After coordinate transformation, the elevation angle Ф is transformed. Switch Defined as: the angle between the target direction and its projection onto the yOz plane; transformed azimuth angle θ Switch Defined as: the angle between the projection of the target direction onto the yOz plane and the z-axis.

[0081] Step 6: Calculate the angle value R of the pitch angle in the transformed coordinate system. Switch :

[0082]

[0083] in:

[0084]

[0085]

[0086]

[0087]

[0088]

[0089]

[0090] In the above formula, Ф Switch and θ Switch These are the signal conversion elevation angle and the signal conversion azimuth angle, respectively. 13 and Y 13 These are the X and Y coordinate vectors of the array elements in the left subarray, respectively, and the Y coordinate of the right subarray is the same as that of the left subarray, while the X coordinate is the opposite of that of the left subarray.

[0091] Before coordinate transformation, when solving for the azimuth using the left and right subarrays, the multiplier of the X-coordinate is X·cosФ·sinθ, which includes both the azimuth θ and the elevation Ф, meaning the azimuth and elevation angles are coupled. After coordinate transformation, the multiplier of the X-coordinate only includes the transformed elevation Ф. Switch This achieves angle decoupling;

[0092] Step 7: Correct the angle detection value based on the initial pointing conversion pitch angle of the array:

[0093] R Switch_Refine =R Switch cos(Ф 0_Switch )

[0094] The correction results are shown in Figure 4. As can be seen from Figure 4(a), the angle detection values ​​are not the same for the same azimuth incoming wave (i.e., the same deviation angle) when the array is at different initial elevation directions. Therefore, in the conventional sum-difference ratio phase direction finding method, it is necessary to save a set of angle detection values ​​locally for each initial elevation direction. However, in Figure 4(b), the angle detection value correction method of this invention can make the angle detection curves of different array initial elevation directions coincide within a certain deviation angle range. Therefore, only one angle detection line when Ф=0° needs to be saved.

[0095] Step 8: R Switch_Refine Substitute Ф 0_Switch The pitch deviation angle ΔФ is obtained by searching the angle table when ΔФ = 0. Switch The signal conversion pitch angle is calculated as follows:

[0096] Ф Switch =Ф 0_Switch +ΔФ Switch

[0097] When retrieving angle identification values, because the pitch angle value is calculated in a normal coordinate system, the stored local angle identification line is the angle identification line when Ф0=0 and θ0=0. At this time, Ф 0_Switch =0, therefore, since there is a certain symmetry between the upper and lower subarrays and the left and right subarrays, when calculating the pitch angle, the same angle detection line can be shared with the pitch angle calculation. Therefore, only one angle detection line needs to be stored locally.

[0098] Step 9: Output the calculated pitch angle and the converted pitch angle as the azimuth angle of the signal.

[0099] Simulation verification:

[0100] The simulation conditions in Figure 5 are as follows: with the initial array elevation pointing angle Ф0 = 5° and the initial array azimuth pointing angle θ0 = 30°, let the signal elevation angle Ф = 6.3° and the azimuth angle θ = 33°. After coordinate transformation, the initial array elevation pointing angle is Ф0°. 0_Switch =29.8742, therefore the initial pointing of the array is defined as (pitch angle, converted pitch angle) = (5°, 29.8742°); similarly, the signal azimuth to be estimated is (pitch angle, converted pitch angle) = (6.3°, 32.7756°).

[0101] First, the elevation angle in the standard coordinate system is calculated to be 0.1290°. From the angle line in Figure 5(a), the deviation angle is approximately 1.5 degrees. Therefore, the coarse measurement of the target elevation angle without secondary fitting (without difference fitting) is 5 + 1.5 = 6.5 degrees, with an error of 0.2 degrees. Next, the converted elevation angle of the signal is calculated, yielding a value of 0.2578°. From the angle line in Figure 5(b), the deviation angle is approximately 3.1 degrees. The resulting coarse measurement of the converted elevation angle (without difference fitting) is 29.8742 + 3.1 = 32.9742 degrees, with a direction finding error of 0.1986 degrees.

[0102] As shown in Figure 5, by correcting the angle value and transforming the coordinates, the direction of the incoming signal wave can be accurately estimated even when only one angle line data is stored.

[0103] In summary, this invention first calculates the pitch angle in conventional coordinates using the sum-difference beamforming method. After correcting the pitch angle, it looks up the pitch deviation angle in a table and calculates the pitch angle by combining it with the initial pitch pointing angle of the array. Then, the coordinates are transformed, and the transformed pitch angle in the transformed coordinates is calculated using the same method. The direction of arrival can be uniquely determined by the conventional coordinate pitch angle and the transformed coordinate pitch angle, thus completing the DOA estimation of the signal. This invention achieves angle decoupling in the solution process through coordinate transformation, which can significantly reduce the amount of locally stored pitch angle table data and greatly improve processing speed.

Claims

1. A sum-difference beam direction finding method based on coordinate transformation, characterized in that, Includes the following steps: Step 1: Divide the uniform array into four identical 2x2 subarrays. The lower left and lower right subarrays are collectively called the lower subarray, the upper left and upper right subarrays are collectively called the upper subarray, the upper left and lower left subarrays are collectively called the left subarray, and the upper right and lower right subarrays are collectively called the right subarray. Calculate the sum of the received signals in the lower and upper subarrays of the uniform array, and output P. 12 P 34 : In the above formula, [·] H W is the conjugate transpose of the matrix. 0_12 W 0_34 A 12 A 34 They are respectively: The weighted vector of the submatrix; The weighted vector of the submatrix; A 12 =e j·2πf·(X·cosФ·sinθ+Y·sin(Ф)) / c , is the signal receiving guide vector for the lower subarray; A 34 =e j·2πf·(X·cosФ·sinθ-Y·sin(Ф)) / c , is the signal receiving guide vector for the upper subarray; In the above formula, j is the imaginary unit, f is the signal frequency, c is the speed of light, Ф and θ are the elevation and azimuth angles of the signal, Ф0 and θ0 are the initial pointing elevation and azimuth angles of the array, X and Y are the coordinate vectors of the two coordinate axes of the upper subarray, the lower subarray has the same X coordinate as the upper subarray, and the Y coordinates are opposites of each other. Step 2: Calculate the angle value R of the elevation angle in conventional coordinates: In the above formula, imag(·) is the symbol for taking the complex part; Step 3: Correct the angle detection value based on the initial pointing and pitch angle of the array: R Refine =R·cos(Ф0) Step 4: Transfer R Refine Substituting the angle detection table when Ф0=0, the pitch deviation angle ΔФ is obtained, and the signal pitch angle is calculated: Ф=Ф0Ф Step 5: Perform coordinate transformation and calculate the initial pointing and pitch angle Ф of the array. 0_Switch And the initial pointing of the array, the conversion azimuth angle θ 0_Switch : F 0_Switch =and(cos(Ф0)sin(θ0)) θ 0_Switch =and(sin(Ф0) / cos(Ф 0_Switch )) Step 6: Calculate the angle value R of the pitch angle in the transformed coordinate system. Switch : in: In the above formula, Ф Switch and θ Switch These are the signal conversion elevation angle and the signal conversion azimuth angle, respectively. 13 and Y 13 These are the X and Y coordinate vectors of the array elements in the left subarray, respectively, and the Y coordinate of the right subarray is the same as that of the left subarray, while the X coordinate is the opposite of that of the left subarray. Step 7: Correct the angle detection value based on the initial pointing conversion pitch angle of the array: R Switch_Refine =R Switch cos(F 0_Switch ) Step 8: R Switch_Refine Substitute Ф 0_Switch The pitch deviation angle ΔФ is obtained by searching the angle table when ΔФ = 0. Switch The signal conversion pitch angle is calculated as follows: F Switch =F 0_Switch +ΔF Switch Step 9: Output the calculated pitch angle and the converted pitch angle as the azimuth angle of the signal to complete the sum-difference beam direction finding.

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