A non-uniform translation method for extended array continuous difference arrays

Abstract

The application discloses a non-uniform moving method of an extended array continuous difference array, which comprises the following steps: determining the physical array element position of an array for DOA estimation; determining the position of each virtual array element in the difference array of the physical array, and obtaining the maximum interval of all adjacent virtual array elements; obtaining a corresponding synthetic array by non-uniformly moving the physical array; the difference array of the obtained synthetic array is completely continuous, and a DOA estimation method is applied to the synthetic array, so that a corresponding DOA estimation value is obtained. The application can fill the holes in the difference array of the original physical array by moving the array in a specific form, and obtain a completely continuous and aperture-extended difference array. The method of the application can obtain an extended array aperture and enhanced DOA estimation precision without adding additional physical array elements in the original array, so that the construction cost of the array is reduced, and the method is easy to implement in engineering.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of azimuth estimation of sparse arrays, and particularly to a non-uniform moving method of extended array continuous difference array. BACKGROUND

[0002] Azimuth estimation using sparse arrays has attracted great attention because, compared with uniform arrays, sparse arrays can obtain greater degrees of freedom and greater array aperture; at the same time, the number of array elements of sparse arrays with small element spacing (less than or equal to half a wavelength) is less than that of uniform linear arrays, so the mutual coupling effect between array elements can be effectively reduced. However, the difference array of a coprime array or other sparse array is not completely continuous, that is, there are holes in the difference array, which greatly affects the continuous degrees of freedom of the sparse array, thereby reducing the performance of subspace-based algorithms. Therefore, this problem needs to be solved. SUMMARY

[0003] In view of this, the purpose of the present application is to provide a non-uniform moving method of extended array continuous difference array to solve the technical problems mentioned in the background. The present application utilizes the mobility of the array to synthesize the array outputs at different positions of the array, which can effectively fill the holes in the difference array without increasing the number of physical array elements, thereby obtaining greater degrees of freedom and greater array aperture, and ultimately achieving better angle estimation effect.

[0004] In order to achieve the above-mentioned purpose, the present application adopts the following technical solutions:

[0005] A non-uniform moving method of extended array continuous difference array, the moving method comprising:

[0006] Step S1, for a physical array Calculate the difference array to obtain the maximum spacing between adjacent virtual array elements in the difference array

[0007] Step S2, at the current position of the physical array The original position of the array

[0008] Step S3, move the physical array From the original position To the following positions respectively: Where d is the unit spacing between array elements, and its value is equal to half the wavelength of the incident signal.

[0009] Step S4, phase compensation is performed on the array at each position.

[0010] Step S5, the array outputs after phase compensation in step S4 are synthesized to obtain a synthesized array.

[0011] Step S6, using the virtualization method on the synthetic array obtained in step S5, to obtain the difference array of the synthetic array

[0012] Step S7, using the difference array obtained in step S6 using the DOA estimation method to obtain the final angle estimation value.

[0013] Further, in the step S1, the physical array whose element position set is

[0014] Further, in the step S1, the difference array, whose element set is

[0015] Further, in the step S2, when the physical array is in the original position , its array output is:

[0016]

[0017] In formula (1), K represents the number of sources, d is the unit distance between elements, which is equal to half the wavelength of the incident signal, λ is the wavelength of the incident signal, v represents the array moving speed, a(θ k ) is the array direction vector, and s k (t) is the signal amplitude, A=[a(θ1), a(θ2),..., a(θ K )] is the array direction matrix, is the signal vector, and w(t) is the noise vector.

[0018] Further, in the step S3, the displacement of the physical array is set to wherein is represented as:

[0019]

[0020] In formula (2), represents the floor function, represents the ceiling function, and q represents the displacement number.

[0021] Further, in the step S3, after each movement of the physical array, the array output vector is:

[0022]

[0023] In formula (3), wherein

[0024] Further, in the step S4, the array output at each position is phase compensated by multiplying a phase correction factor The expression is:

[0025]

[0026] In the formula (4),

[0027] Further, in the step S5, the array outputs are synthesized, and the expression is:

[0028]

[0029] In the formula (5), A is the transpose of the direction matrix, B1 and are the direction matrices after phase compensation of the array outputs, wherein the set of element positions of the synthesized array corresponding to y(t) is

[0030] Further, in the step S6, the synthesized array The expression of the corresponding difference array is:

[0031]

[0032] The beneficial effects of the present application are:

[0033] The method provided by the present application can obtain a synthesized array with a completely continuous difference array under the condition of non-uniform movement of the array, thereby greatly improving the resolution and estimation accuracy of the array under the condition of unchanged physical element number. The method provided by the present application can improve the degree of freedom, array aperture, identifiable source number and array estimation accuracy of the array by using the movement characteristics of the array under the condition of limited array physical aperture. The method can reduce the hardware manufacturing cost of the array and is suitable for ship-borne, satellite-borne and other platforms. BRIEF DESCRIPTION OF DRAWINGS

[0034] Figure 1 FIG. 1 is a flowchart of an extended array continuous difference array non-uniform movement method provided in Embodiment 1;

[0035] Figure 2 FIG. 2 is a diagram of array movement provided in Embodiment 1;

[0036] Figure 3 FIG. 3 is an angle estimation performance diagram of the non-uniform movement method provided in Embodiment 1 under different signal-to-noise ratios.

[0037] Figure 4 Figure for angle estimation performance of the non-uniform moving method provided in Embodiment 1 with fast snap changes;

[0038] Figure 5 Figure for resolution of the non-uniform moving method provided in Embodiment 1. DETAILED DESCRIPTION

[0039] In order to make the objects, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are some but not all of the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by a person of ordinary skill in the art without creative work fall within the protection scope of the present application.

[0040] Embodiment 1

[0041] Referring to Figures 1-5 , the embodiment provides a non-uniform moving method of an extended array continuous difference array, which specifically comprises the following steps:

[0042] For a physical array , a difference array thereof is calculated to obtain the maximum distance between adjacent virtual elements in the difference array

[0043] The physical array is moved from the original position to the following positions respectively: , wherein d is the unit length of the physical array, and the value thereof is equal to half of the wavelength of the incident signal.

[0044] The array at each position is subjected to phase compensation. The output of each array subjected to phase compensation is synthesized to obtain a synthesized array.

[0045] The difference array of the synthesized array is obtained by using a virtualization method.

[0046] The difference array obtained is subjected to DOA estimation to obtain the final angle estimation value.

[0047]

[0048] The difference array obtained is subjected to DOA estimation to obtain the final angle estimation value.

[0049] ​​In order to make the method more clear, a specific example is provided for illustration, which specifically includes:

[0050] Step 1: Assuming that the initial array element position of the array is as shown in the first row of Figure 2 , the element position set is {0, 12, 13, 24, 26}d.

[0051] Step 2: The difference array of the initial array is as shown in the second last row of the figure, and the maximum continuous hole length in the difference array is

[0052] Step 3: In order to fill the hole in the difference array of the original array, the array is moved to the position of in turn.

[0053] Specifically, at different positions, the output of the array is:

[0054]

[0055]

[0056] In the formula, K represents the number of sources, d is the unit distance of the elements, λ is the wavelength of the incident signal, v represents the array moving speed, a(θ k ) is the array direction vector, s k (t) is the signal amplitude, A = [a(θ1), a(θ2),..., a(θ K )] is the direction matrix of the array, is the signal vector, w(t) and w(t+md / v)(m q d / v)(m q ∈[1, 2, 5]) are noise vectors.

[0057] Among them,

[0058]

[0059] Step 4: Multiply the output of the array after the above movement by the phase correction factor for phase compensation, and the expression is:

[0060]

[0061] In the formula,

[0062] Step 5: Synthesize the outputs of the array at different positions, and the expression is:

[0063]

[0064] Among them

[0065] Step 6: Apply virtualization to the output of the above synthesized array to obtain the corresponding difference matrix, expressed as:

[0066]

[0067] The obtained difference matrix is ​​as follows Figure 2 As shown in the last row, the holes in the difference matrix are completely eliminated, and the aperture is correspondingly increased.

[0068] Step 7: Apply the appropriate DOA estimation method to the synthetic array to obtain the corresponding DOA estimate.

[0069] To verify the correctness and advancement of the method in this embodiment, a simulation experiment was conducted. The specific simulation results are as follows: Figures 3-5 As shown, specifically, Figure 3 The graph shows the angle estimation performance of the method in this example as the signal-to-noise ratio (SNR) changes. It can be seen that this method can significantly improve the DOA estimation accuracy, and the higher the SNR, the higher the estimation accuracy. Figure 4 This diagram shows the angle estimation performance of the method in this embodiment as the snapshot ratio changes. It can be seen that regardless of the number of snapshots, this method can effectively improve the DOA estimation accuracy. Furthermore, the higher the number of snapshots, the higher the estimation accuracy. Figure 5 This is a resolution performance graph of the method in this embodiment. It can be seen that the method proposed in this embodiment can effectively improve the array resolution.

[0070] In summary, this invention proposes a non-uniform movement method for extended array continuous difference matrices. In scenarios where the array moves, it utilizes the array's movement characteristics to synthesize the array outputs at specific locations, thereby filling the holes in the original array and obtaining a synthesized array with higher degrees of freedom, larger aperture, and better estimation results. The method proposed in this invention can obtain a synthesized array with a completely continuous difference matrix even in scenarios with non-uniform array movement, thus significantly improving the array's resolution and estimation accuracy without changing the physical array element count. This method can improve the array's degrees of freedom, array aperture, number of identifiable sources, and array estimation accuracy by utilizing its movement characteristics, even when the array's physical aperture is limited. Using this method, the hardware manufacturing cost of the array can be reduced, making it suitable for shipborne, spaceborne, and other platforms.

[0071] Any aspects of this invention not described in detail are well-known to those skilled in the art.

[0072] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A method for non-uniform movement of an extended array of continuous difference matrices, characterized in that, The movement method includes: Step S1, for the physical array Calculate its difference matrix to obtain the maximum spacing between adjacent virtual matrix elements in the difference matrix. Step S2, using the physical array The current position is the original position of the array. Step S3: The physical array From the original position Move to the following positions respectively: Where d is the unit spacing between array elements, and its value is equal to half the wavelength of the incident signal; the displacement of the physical array each time it moves is set to... in, Represented as: In formula (2), Indicates rounding down. This indicates rounding up, and q represents the number of shifts. Step S4: Perform phase compensation on the array at each location; Step S5: Combine the outputs of each array after phase compensation in step S4 to obtain a composite array; Step S6: Using a virtualization method, obtain the difference matrix of the synthesized array obtained in step S5. Step S7: Perform a step S6 on the difference matrix obtained in step S6. The final angle estimate is obtained by using the DOA estimation method.

2. The non-uniform movement method of an extended array continuous difference matrix according to claim 1, characterized in that, In step S1, the physical array Its array element position set is 3. The non-uniform movement method of an extended array continuous difference matrix according to claim 2, characterized in that, In step S1, the difference matrix has a set of elements.

4. The non-uniform movement method of an extended array continuous difference matrix according to claim 3, characterized in that, In step S2, when the physical array is in its original position At that time, its array output is: In formula (1), K represents the number of signal sources, d is the unit spacing between array elements, which is equal to half the wavelength of the incident signal, λ is the wavelength of the incident signal, v represents the array moving speed, and a(θ) k ) is the array direction vector, and s k (t) represents the signal amplitude, A = [a(θ1), a(θ2), ..., a(θ)] K [)] is the direction matrix of the array. Let w(t) be the signal vector and w(t) be the noise vector.

5. The non-uniform movement method of an extended array continuous difference matrix according to claim 4, characterized in that, In step S3, after each movement, the output vector of the physical array is: In formula (3), in, 6. The non-uniform movement method of an extended array continuous difference matrix according to claim 5, characterized in that, In step S4, the array output at each location is multiplied by a phase correction factor. Phase compensation is performed using the following method, expressed as: Formula (4) 7. The non-uniform movement method of an extended array continuous difference matrix according to claim 6, characterized in that, In step S5, the array outputs at each position obtained from formula (4) are synthesized, and the specific expression is as follows: In formula (5), A T This is the transpose of the direction matrix. and This is the direction matrix after phase compensation of the array output. Wherein, the set of array element positions corresponding to the composite array of y(t) is:

8. The non-uniform movement method of an extended array continuous difference matrix according to claim 7, characterized in that, In step S6, the synthesized array The specific expression for its corresponding difference matrix is:

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