High-resolution azimuth estimation algorithm for multiple targets in small aperture array based on phase difference

Abstract

A phase-difference-based high-resolution azimuth estimation algorithm for a small-aperture array with multiple targets comprises the following steps: 1) according to various array structures, the coordinate vectors of the array elements are subtracted and then combined accordingly to obtain new vectors along each coordinate axis; 2) the phase of each array element is obtained by performing a fast Fourier transform on the array element sampling data, the phase difference between the array elements is obtained by subtracting the phase of each array element, and the phase differences are combined according to the combination of the array element coordinate vector differences to extract the component k of the incident direction along each coordinate axis. x , k y and k z 3) After obtaining the various components of the incident direction, the unambiguous incident angle across the entire spatial range is calculated using inverse trigonometric functions. This invention utilizes a combination of array element sampling data to achieve more accurate target direction estimation, enhances resistance to noise and other interference, and broadens the applicable frequency band, enabling flexible application to various arrays, as well as direction estimation using multi-line spectrum signals and broadband signals.

Description

Technical Field

[0001] The present invention belongs to the field of direction of arrival estimation algorithms in signal processing, and in particular relates to a multi-target high-resolution direction of arrival estimation algorithm suitable for a small aperture array. Background Art

[0002] Direction of Arrival (DOA) estimation is a key research area in array signal processing, particularly in military radar, sonar, and civilian communication systems. Accurate DOA estimates play a crucial role in subsequent signal selection and identification. In modern warfare, electromagnetic interference is becoming increasingly severe, necessitating a continuous effort to research new methods to enhance equipment's anti-interference capabilities, meet the demands of wider bandwidth applications, achieve greater coverage and enhanced concealment, and gain an advantage in complex electromagnetic environments. Therefore, advanced DOA estimation algorithms are a current research hotspot and focus. Key breakthroughs lie in achieving higher estimation accuracy, reducing the computational complexity of algorithms to achieve faster estimation, and reducing the number of array elements or the array aperture.

[0003] Classical DOA estimation algorithms are often used with large antenna arrays, requiring a large array aperture, a large number of elements, and strong computing power. However, small, mobile devices, due to their compact size and low operating power, cannot accommodate large antenna arrays, requiring only small-aperture arrays. Continuing to use classical algorithms will result in unreliable DOA estimation results due to the small array aperture, small number of elements, and weak computing power. Summary of the Invention

[0004] Aiming at the deficiencies of the prior art, the present invention proposes a small aperture array multi-target high-resolution azimuth estimation algorithm based on phase difference.

[0005] This invention targets small-aperture arrays capable of being carried by small, mobile devices, and leverages the phase differences and geometric relationships between array elements for rapid DOA estimation. This method utilizes a combination of array element sampling data to achieve more accurate DOA estimates, broadening the frequency band applicability and enabling flexible application to various array configurations, as well as DOA estimation for multi-line spectrum and broadband signals. The invention offers advantages such as low computational complexity, small array aperture requirements, and a reduced number of array elements, making it suitable for small-aperture array, multi-target, and real-time positioning systems.

[0006] The present invention provides a small aperture array multi-target high-resolution azimuth estimation algorithm based on phase difference, comprising the following steps:

[0007] Step 1: Establish a rectangular coordinate system and obtain the coordinate vector difference of each array element by subtracting the coordinate vector of each array element. etc., among which represents the coordinate vector of array element n minus the coordinate vector of array element m; the differences of the coordinate vectors of each array element are combined accordingly to obtain new vectors along each coordinate axis;

[0008] Step 2: Perform a fast Fourier transform on the sampled data of each array element, converting it from the time domain to the frequency domain, so that the phase of each array element can be obtained; the phase difference between the array elements is obtained by subtracting the phase of each array element; according to the combination method of the array element coordinate vector difference in step 1, the phase difference between the array elements is combined according to this combination method to obtain the component k of the incident direction along each coordinate axis x , k y and k z ;

[0009] Step 3: The component k of the incident direction along each coordinate axis obtained in step 2 x , k y and k z , the incident direction can be obtained using inverse trigonometric functions.

[0010] Furthermore, step 1 specifically includes:

[0011] 1.1 Establishing the coordinate system:

[0012] According to the array of various structures selected, a rectangular coordinate system is established. Taking the origin of the rectangular coordinate system as the reference point, the corresponding coordinate vector of each array element can be obtained. Subtract the coordinate vectors of each array element, that is, Get the difference between the coordinate vector of array element n and the coordinate vector of array element m

[0013] 1.2 Find the combination of components of each coordinate axis:

[0014] Get the coordinate vector difference of each array element After that, we can combine and scale them accordingly to get the unit vector along the coordinate axis, that is,

[0015]

[0016] Furthermore, step 2 specifically includes:

[0017] 2.1 Obtaining the phase difference between array elements:

[0018] The sampling data of each array element is fast Fourier transformed from the time domain to the frequency domain, so the phase of each array element can be obtained. The phase difference between the array elements is obtained by subtracting the phase of each array element. The signal at the origin is set to s(t), and the signal received by each array element has a delay τ relative to the signal at the origin. n, then the signal at each array element can be expressed as s(t-τ n ), n=1,2,…,M. The distance the signal travels from the origin to array element n is Then the delay information of the signal at array element n relative to the origin is Where c is the signal propagation speed, such as Figure 2 The time delay in the time domain corresponds to the phase shift in the frequency domain, as shown in the following formula:

[0019]

[0020] From formula (2), we can see that the phase information contains the incident direction information we are interested in. The goal of the algorithm is to extract the incident direction from the phase information. The phase difference can be expressed as follows using formula (2):

[0021]

[0022] From the left and right sides of equation (3), we can see that the difference between the phases is equivalent to the difference between the coordinate vectors of the array elements.

[0023] 2.2 Extract the component of the incident direction using phase difference:

[0024] After finding the combination of the array element coordinate vector differences in step 1, the phase differences between the array elements can be combined according to this combination to obtain the component k of the incident direction along each coordinate axis. x , k y and k z ,Right now

[0025]

[0026] Furthermore, step 3 specifically includes:

[0027] The component k of the incident direction along each coordinate axis obtained in step 2 x , k y and k z , the four-quadrant inverse tangent function is used to realize the azimuth angle estimation without ambiguity in the range of 360°, and the conventional inverse tangent function is used to realize the pitch angle estimation without ambiguity in the range of 180°, thereby realizing the unambiguous estimation of the incident angle in the full space range, that is,

[0028]

[0029] In summary, the mathematical model of the present invention obtains new vectors along each coordinate axis by combining the differences in array element coordinate vectors, and uses the dot product of the new vectors and the incident signal wave vector to extract the components of the incident wave vector along each coordinate axis, and then uses inverse trigonometric functions to obtain the DOA estimate.

[0030] Compared with the prior art, the present invention has the following beneficial effects:

[0031] (1) The present invention can use array element sampling data in combination to obtain a more accurate DOA estimation value and enhance the ability to resist interference such as noise.

[0032] (2) The present invention can make the applicable range of the frequency band wider and the applicable size of the aperture larger without the problem of phase winding.

[0033] (3) The present invention can be flexibly applied to various types of formations, as well as azimuth estimation of multi-line spectrum signals, broadband signals, etc.

[0034] The advantage of the present invention is that it can make composite use of array element sampling data to make target azimuth estimation more accurate, have stronger ability to resist interference such as noise, make the applicable range of the frequency band wider, and can be flexibly applied to various formations, as well as azimuth estimation of multi-line spectrum signals, broadband signals, etc., and is suitable for small aperture arrays, multi-target, and real-time positioning systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 It is a schematic diagram of the algorithm flow;

[0036] Figure 2 It is a schematic diagram of the signal incident model;

[0037] Figure 3 It is a schematic diagram of the planar cross array structure;

[0038] Figure 4 a~ Figure 4 g is a schematic diagram of the combination of the array element coordinate vector difference along the positive direction of the x-axis. Figure 4 a~ Figure 4 g corresponds to These 7 combinations:

[0039] Figure 5 a~ Figure 5 g is a schematic diagram of the combination of the array element coordinate vector difference along the positive direction of the y-axis. Figure 5 a~ Figure 5 g corresponds to These 7 combinations:

[0040] Figure 6 This is a schematic diagram of the structure of a small movable platform;

[0041] Figure 7 It is a schematic diagram of the combination of array element coordinate vector differences along the positive direction of the x-axis;

[0042] Figure 8 It is a schematic diagram of the combination of array element coordinate vector differences along the positive direction of the y-axis;

[0043] Figure 9 It is a schematic diagram of the combination of array element coordinate vector differences along the positive direction of the z-axis;

[0044] Figure 10 a~ Figure 10 b is a schematic diagram comparing the calculation spacing of the present invention and the existing algorithm, Figure 10 a is a schematic diagram of the existing algorithm for calculating spacing, right Figure 10 b is a schematic diagram of the calculated spacing of the present invention. DETAILED DESCRIPTION

[0045] The present invention will be further described below with reference to the accompanying drawings.

[0046] Example 1

[0047] This embodiment describes how the present invention is applied to a planar cross array.

[0048] Planar cross array structure such as Figure 3 As shown, array element 1 and array element 2 are located at the positive and negative half axes of the x-axis, respectively, and array element 3 and array element 4 are located at the positive and negative half axes of the y-axis, respectively.

[0049] The algorithm first combines the unit vector along the positive x-axis according to the array element coordinate vector difference. According to the structure of the plane cross array, it is easy to know that The combination of these 7 array element coordinate vector differences can obtain a new vector along the positive x-axis, such as Figure 4 As shown by the arrows in the small and medium figures a to g. Then, by dividing by the length of the new vector, that is, the distance between array element 1 and array element 2, we can get the unit vector along the positive x-axis. Therefore, corresponding to the frequency domain, the algorithm can use 7 combinations of phase differences. The incident wave vector component k x Estimates.

[0050] Similarly, the unit vector along the positive direction of the y-axis is combined according to the difference of the array element coordinate vectors. The combination of these 7 array element coordinate vector differences can obtain a new vector along the positive y-axis, such as Figure 5 As shown by the arrows in the small and medium figures a to g. Dividing by the length of the new vector, that is, the distance between array element 3 and array element 4, we can get the unit vector along the positive y-axis. Corresponding to the frequency domain, the algorithm can use 7 combinations of phase differences The incident wave vector component k y Estimates.

[0051] In estimating k x and k yThe sampling data of 4 array elements and all phase difference combinations have been used to obtain k x and k y After the estimated value of , the four-quadrant inverse tangent function can be used to obtain the azimuth angle θ = atan2 (ky, kx) in the 360° range.

[0052] Example 2

[0053] This embodiment describes how the present invention is applied to a small movable platform.

[0054] The three-dimensional structure of a small movable platform is as follows Figure 6 As shown in the figure, the three-dimensional structure and its corresponding coordinates show that it is a four-element array with an approximately linear shape, rather than a regular tetrahedron array. Therefore, the existing phase difference algorithm cannot be applied to this structure. The present invention can use a new idea to integrate phase information to solve the incident angle.

[0055] According to the algorithm principle of the present invention, the positive component of the incident direction along the x-axis is first solved according to the structural characteristics of the formation. It is not difficult to find from the three-dimensional structure diagram that The coordinate vector combination method can obtain a new vector along the positive x-axis, such as Figure 7 As shown by the arrow in the middle, dividing by the corresponding length can get the unit vector along the positive direction of the x-axis. Therefore, the phase difference can be used The incident wave vector component k x Estimates.

[0056] Secondly, the positive component of the incident direction along the y-axis is solved according to the structural characteristics. It is easy to see from the three-dimensional structure diagram that and The coordinate vector difference combination method can obtain a new vector along the positive direction of the y-axis, such as Figure 8 As shown by the arrow in the middle, dividing by the corresponding length can get the unit vector along the positive direction of the y-axis. Therefore, the phase difference can be used and The incident wave vector component k y Estimates.

[0057] As for the component along the z-axis, it is not difficult to find that its structure is not regularly symmetrical, so it is not possible to directly obtain the component along the z-axis simply by combining the differences in the coordinate vectors of the array elements, as is done with a regular tetrahedron array. The new vector obtained by the combination of is (-1.3, 0, 0.3). This is not a new vector along the positive z-axis. Multiplying it with the incident direction cannot extract k. z However, although it is not possible to directly extract k z Component, but it can be found that the result is -1.3k x +0.3k z, and then the previously extracted k x Component to further extract k z Component, that is, add 1.3 times k on this basis x The estimated value is 0.3 times k z Therefore, the present invention can finally be used and Four phase differences for the incident wave vector component k z Estimation of . Figure 9 As shown, k can be obtained by multiplying the phase difference by the corresponding coefficient according to the actual shape and size of the device. z For example, Figure 6 The equipment dimensions shown are That is, 4.5 times k is extracted at this time x , multiply it by 1.3 / 4.5 to get 1.3 times k x , and then with Received -1.3k x +0.3k z Add them together to get 0.3 times k z , then we get a simple k z Quantity.

[0058] At this point, the components k of the incident wave vector x , k y , k z All of them have been obtained, and the incident angle can be obtained by using inverse trigonometric functions.

[0059] Example 3

[0060] This embodiment explains how the present invention makes the applicable range of the frequency band wider and the applicable range of the aperture larger.

[0061] The present invention can obtain a smaller calculation spacing than the existing algorithms at the algorithm level under the condition that the array parameters are the same (the same number of array elements, the same array element spacing, the same array aperture, etc.). The calculation spacing refers to the wave path difference between the two points where the phase difference is directly calculated, that is, the distance between the two points where the phase difference is calculated that the incident wave passes through. Taking a planar cross array as an example, Figure 10 As shown, Figure a on the left shows the calculation spacing (bold line) of the existing algorithm, while Figure b on the right shows the calculation spacing (bold line) of the present invention. When the calculation spacing is smaller, the upper limit of the applicable frequency is higher. Therefore, given the same array parameters, the present invention can use a wider frequency band than the existing algorithm. In other words, the algorithm of the present invention is less likely to suffer from phase wrapping problems.

[0062] From another perspective, when the applied frequency band range is the same, the present invention can use a larger aperture than existing algorithms. For phase-difference-based azimuth estimation algorithms, while a larger aperture is not necessary to achieve greater angular resolution, pursuing a larger aperture can improve their resistance to noise and other interference. This is because a larger distance between two points results in a larger path difference, which corresponds to a larger phase difference. When the phase difference between two points is larger, the disturbance caused by noise and other interference on the phase values ​​of the two points is smaller relative to the phase difference, resulting in a stronger algorithm resistance to noise and other interference. Therefore, using an array with a larger aperture is advantageous. However, it is well known that when the calculation spacing is greater than half the signal's wavelength, phase wrapping can occur, leading to erroneous estimation results. Being able to use a larger aperture without being plagued by phase wrapping is highly beneficial for improving azimuth estimation performance. The present invention has a smaller calculation spacing than existing algorithms for the same aperture. In other words, when the calculation spacing is the same, the present invention can use a larger aperture than existing algorithms, thereby enhancing resistance to noise and other interference and obtaining more accurate azimuth estimates.

[0063] In summary, when the present invention and the existing algorithm are applied to the same planar cross array, the present invention can be applied to a wider frequency band; when the applied frequency band is the same, the present invention can use a larger aperture than the existing algorithm and has a stronger ability to resist interference such as noise.

Claims

1. A phase difference-based small aperture array multi-target high-resolution azimuth estimation algorithm, characterized by comprising the following steps: Step 1: Establish a rectangular coordinate system and obtain the coordinate vector difference of each array element by subtracting the coordinate vector of each array element. represents the coordinate vector of array element n minus the coordinate vector of array element m; the differences of the coordinate vectors of each array element are combined accordingly to obtain new vectors along each coordinate axis; Step 2: Perform a fast Fourier transform on the sampled data of each array element, converting it from the time domain to the frequency domain, so that the phase of each array element can be obtained; the phase difference between the array elements is obtained by subtracting the phase of each array element; according to the combination method of the array element coordinate vector difference in step 1, the phase difference between the array elements is combined according to this combination method to obtain the component k of the incident direction along each coordinate axis x , k y and k z ; Step 3: The component k of the incident direction along each coordinate axis obtained in step 2 x , k y and k z , the incident direction can be obtained using inverse trigonometric functions; Step 1 includes the following steps: 1.1 Establishing the coordinate system: According to the array of various structures selected, a rectangular coordinate system is established. Taking the origin of the rectangular coordinate system as the reference point, the corresponding coordinate vector of each array element can be obtained. Subtract the coordinate vectors of each array element, that is, Get the difference between the coordinate vector of array element n and the coordinate vector of array element m 1.2 Find the combination of components of each coordinate axis: Get the coordinate vector difference of each array element After that, we can combine and scale them accordingly to get the unit vector along the coordinate axis, that is, Step 2 includes: 2.1 Obtaining the phase difference between array elements: The sampling data of each array element is fast Fourier transformed from the time domain to the frequency domain, so the phase of each array element can be obtained. The phase difference between the array elements is obtained by subtracting the phase of each array element. The signal at the origin is set to s(t), and the signal received by each array element has a delay τ relative to the signal at the origin. n , then the signal at each array element can be expressed as s(t-τ n ), n=1,2,…,M; the distance the signal travels from the origin to the array element n is Then the delay information of the signal at array element n relative to the origin is Where c is the signal propagation speed; the time delay in the time domain corresponds to the phase shift in the frequency domain, as shown in the following formula: From formula (2), we can see that the phase information includes the incident direction information. The goal of the algorithm is to extract the incident direction from the phase information; from equation (2), the phase difference can be expressed as follows: From the left and right sides of equation (3), we can see that the difference between phases is equivalent to the difference between array element coordinate vectors; 2.2 Extract the component of the incident direction using phase difference: After finding the combination of the array element coordinate vector differences in step 1, the phase differences between the array elements can be combined according to this combination to obtain the component k of the incident direction along each coordinate axis. x , k y and k z ,Right now:

2. The phase difference-based small aperture array multi-target high-resolution azimuth estimation algorithm according to claim 1, characterized in that: Step 3: The component k of the incident direction along each coordinate axis obtained in step 2 x , k y and k z , the four-quadrant inverse tangent function is used to realize the azimuth angle estimation without ambiguity in the range of 360°, and the conventional inverse tangent function is used to realize the pitch angle estimation without ambiguity in the range of 180°, thereby realizing the unambiguous estimation of the incident angle in the full space range, that is,

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