Multi-target azimuth lightweight high-precision estimation method and system based on uniform circular array

Abstract

The invention discloses a multi-target azimuth lightweight high-precision estimation method and system based on a uniform circular array, and belongs to the field of array antenna direction finding. The method comprises the following steps: firstly, constructing a uniform circular array model azimuth rough measurement model based on MUSIC, and obtaining a radiation source azimuth rough value; and then, constructing an azimuth accurate measurement model based on polynomial fitting, and obtaining a radiation source azimuth fine estimation value. The invention aims to solve the following problems in the MUSIC algorithm: (1) high-precision azimuth estimation is realized with an extremely small search step size, and the consumption of computing resources is relatively large; and (2) a plurality of radiation sources with relatively small difference values among orientations are relatively difficult to distinguish, and the like.

Description

Technical Field

[0001] This invention belongs to the field of array antenna direction finding, and specifically relates to a lightweight and high-precision estimation method and system for the azimuth of multiple targets based on a uniform circular array. Background Technology

[0002] A uniform circular array can achieve direction finding of electromagnetic radiation sources within a 360-degree range. The MUSIC algorithm can simultaneously estimate the azimuth of multiple radiation sources. Based on a uniform circular array, the MUSIC algorithm can achieve high-precision detection of multiple targets within a 360-degree range. However, the MUSIC algorithm's high-precision multi-target detection through high-resolution search has two problems: ① Achieving high-precision azimuth estimation with an extremely small search step size results in high computational resource consumption; ② It is difficult to distinguish multiple radiation sources with small azimuth differences. Summary of the Invention

[0003] To address the technical problems of the MUSIC algorithm mentioned in the background, such as "① achieving high-precision azimuth estimation with extremely small search step size, resulting in large computational resource consumption; ② difficulty in distinguishing multiple radiation sources with small differences between azimuths", this invention aims to design a lightweight and high-precision multi-target detection method, and proposes a lightweight and high-precision azimuth estimation method and system for multi-targets based on a uniform circular array.

[0004] To achieve the above objectives, a first aspect of the present invention adopts the following technical solution: a lightweight and high-precision multi-target azimuth estimation method based on a uniform circular array, comprising the following steps:

[0005] Step 1: Construct a rough azimuth measurement model based on a uniform circular array using MUSIC, and determine the search step size. Set the angle to 0.5-5 degrees (more preferably 2-3 degrees), extract the peak values ​​in the MUSIC spectrum, and obtain a rough estimate of the radiation source's orientation. ;

[0006] Step 2: Construct a precise orientation measurement model based on polynomial fitting:

[0007] For each search peak, an array manifold is constructed within a certain range around the peak, and polynomial fitting is performed on this array manifold. By solving for the unequal real stationary points of the polynomials, the azimuths of multiple radiation sources are accurately estimated using the locations of these stationary points, thus obtaining the fine-tuned azimuth values ​​of the radiation sources. Rough estimate based on the location of the radiation source and fine correction value of radiation source location A precise estimate of the radiation source's location was obtained. .

[0008] In a preferred embodiment, if other sensors, such as radar, have already detected a target in a certain direction, but the search peak cannot be obtained through step one of the method of the present invention, then a smaller step size (reducing by 0.4-0.6 degrees each time, and the search step size can be set to a minimum of about 0.5 degrees) is allowed to be used in step one to obtain the search peak.

[0009] In a preferred embodiment, the range near the search peak is determined by the beamwidth of the array antenna. If the beamwidth of the array antenna is N, the search range is set to ±N / 2.

[0010] In step two, the polynomial degree is not less than the number of radiation sources whose azimuth difference is less than or equal to the search step size.

[0011] In step two, the rough estimate of the radiation source's location is used. The corresponding array manifold of the circular array for:

[0012]

[0013] Let the array manifold response function be:

[0014]

[0015] In the formula, For fine-grained search variables of orientation, Determined based on the search scope. Represents the fine-grained search array manifold response;

[0016] Using a 4th degree polynomial Fit the curve to the equation, and let the coefficients of the fourth-order polynomial be...

[0017]

[0018] according to Design parameter matrix ,matrix row vectors for:

[0019]

[0020] according to Design response matrix ,matrix row vectors for:

[0021]

[0022] Traversal All possible values ​​are used to obtain the matrix. and ;

[0023] According to the least squares criterion, the coefficient matrix of the fourth-degree polynomial is:

[0024]

[0025] By solving for the stationary points of the polynomial, the fine-tuning value of the azimuth is obtained. for

[0026]

[0027] In the formula, Indicates by coefficient The stationary point solution function that constitutes a polynomial function;

[0028] Precise estimate of the location of the radiation source Represented as

[0029]

[0030] In the formula, This represents a rough estimate of the radiation source's location, obtained through step one; This is a fine-tuning value for the orientation of the radiation source.

[0031] In the preferred embodiment, in step one, the MUSIC spectrum is represented as:

[0032]

[0033] Search step size within the range of 0 to 360 degrees right Perform a traversal;

[0034] In a music spectrum, each peak represents a signal. Extract the peak values ​​from the music spectrum:

[0035]

[0036] In the formula, This represents the peak extraction function. This represents a rough estimate of the location of the radiation source.

[0037] The second aspect of the present invention also discloses a lightweight and high-precision multi-target azimuth estimation system based on a uniform circular array, including a coarse azimuth measurement model based on a uniform circular array model using MUSIC and a precise azimuth measurement model based on polynomial fitting.

[0038] In the MUSIC-based uniform circular array model for coarse azimuth measurement, the search step size... By setting the range to 0.5-5 degrees, the peak values ​​in the music spectrum are extracted to obtain a rough estimate of the radiation source's location. ;

[0039] In the polynomial fitting-based accurate azimuth measurement model, for each search peak, an array manifold is constructed within a certain range near the search peak, and a polynomial fit is performed on this array manifold. By solving for the unequal real stationary points of the polynomial, the azimuth of multiple radiation sources is accurately estimated using the positions of these stationary points, thus obtaining the fine-corrected azimuth values ​​of the radiation sources. Rough estimate based on the location of the radiation source and fine correction value of radiation source location A precise estimate of the radiation source's location was obtained. .

[0040] A third aspect of the present invention provides an array antenna that employs a lightweight and high-precision multi-target azimuth estimation method based on a uniform circular array or includes a lightweight and high-precision multi-target azimuth estimation system based on a uniform circular array.

[0041] A fourth aspect of the present invention discloses a processor for running a computer program, which executes the aforementioned lightweight and high-precision multi-target orientation estimation method based on a uniform circular array.

[0042] A fifth aspect of the present invention is to provide a terminal comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the program, implements the aforementioned lightweight and high-precision multi-target orientation estimation method based on a uniform circular array.

[0043] A sixth aspect of the present invention discloses a computer-readable medium having a computer program stored thereon, the computer program being executed by a processor to implement the aforementioned method for lightweight and high-precision estimation of the azimuth of multiple targets based on a uniform circular array.

[0044] The advantages of this invention are: it distinguishes multiple radiation sources with small azimuth differences with relatively small computational resources and accurately estimates the azimuths of these sources. The key steps are: first, a large step size is used to search the entire space; second, an array manifold is constructed within a certain range near the search peak, and a polynomial is fitted to this manifold. By solving for the unequal real stationary points of this polynomial, the azimuths of these targets are accurately estimated using the positions of these stationary points; this significantly reduces computational resource consumption while accurately distinguishing multiple radiation sources with small azimuth differences. Attached Figure Description

[0045] Figure 1 Schematic diagram of coordinate system definition;

[0046] Figure 2 The MUSIC spectrum with a step size of 1 degree;

[0047] Figure 3MUSIC spectrum with a step size of 5 degrees. Detailed Implementation

[0048] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0049] A lightweight and high-precision method for estimating the azimuth of multiple targets based on a uniform circular array includes the following steps:

[0050] Step 1: Construct a rough azimuth measurement model for a uniform circular array model based on MUSIC.

[0051] Step 2: Construct a precise orientation measurement model based on polynomial fitting.

[0052] Furthermore, step one includes:

[0053] With the center of the circular array as the origin of the coordinate system, The axis points to the first array element to construct a coordinate system, such as... Figure 1 As shown.

[0054] according to Figure 1 Construct a coordinate system, where the coordinates of any array element m are... for:

[0055] (1)

[0056] any signal unit vector in the coordinate system for:

[0057] (2)

[0058] Using the center of the circular array as a reference point, the signal Delay to reach the m-th array element It can be represented as:

[0059] (3)

[0060] In the formula, This represents the dot product operator. Represents the speed of light. Indicates the radius of the circular array. Indicates the total number of array elements. This represents the angle of arrival of the radiation source d.

[0061] The signal is relative to the center (reference point) of the circular array. The delay coefficient on array element m is shown in the following formula.

[0062] (4)

[0063] In the formula, Indicates signal The delay coefficient on array element m, It represents the imaginary unit. Indicates signal The frequency, obtained through signal reconnaissance, is used in azimuth estimation. It is considered a constant. When the total number of array elements is fixed, the signal... Delay coefficient on array element m Only the angle of arrival of the radiation source d Related. By signal In the array manifold formed by circular arrays for:

[0064] (5)

[0065] Assumption When multiple signals arrive at the circular array simultaneously, the output signal of the circular array is represented as...

[0066] (6)

[0067] In the formula, Indicates the number of signals. , This represents D mutually independent signals. This indicates the output signal of the circular array. Let D independent signals be represented by the array manifold formed by the circular array (represented by formula (5)).

[0068] The spatial covariance matrix of the output signal of the circular array is expressed as:

[0069] (7)

[0070] In the formula, The spatial covariance matrix of the output signal of the circular array is... Dimensional matrix; This represents the mean operator. According to the principles of the MUSIC algorithm, for... Eigenvalue decomposition is performed as shown in the following equation.

[0071] (8)

[0072] In the formula, A function that represents eigenvalue decomposition and sorts the features in descending order. Represents the eigenvector matrix, Represents the eigenvalue matrix. Eigenvalue sequence. Represented as:

[0073] (9)

[0074] In the formula, This function represents the extraction of diagonal elements from matrix U. ; They represent the eigenvalues ​​respectively. The corresponding eigenvectors, and are matrices. The column vector. The calculation process for the number of signals D is as follows:

[0075] (10)

[0076] In the formula, Represents statistical characteristic sequences The middle element is greater than Quantity, Based on experimental data (generally speaking, in engineering, the channels differ in each system; a signal source outputs data with known quantity and orientation, which is then injected into the system; the system calculates each characteristic value; and selects an appropriate method based on the actual number of targets), the system calculates the characteristic value for each target. From the above formula, we can see that:

[0077] Define noise space for

[0078] (11)

[0079] Define signal space for

[0080] (12)

[0081] In the formula, Represents eigenvalues The corresponding eigenvectors. According to the principles of the MUSIC algorithm, the MUSIC spectrum is represented as:

[0082] (13)

[0083] Search step size within the range of 0 to 360 degrees right Perform the traversal, and the traversal result is as follows Figure 2 and Figure 3 As shown.

[0084] Figure 2 and Figure 3 The results show that: ① When the search step size is 1 degree, the two real radiation sources at 115 degrees and 118 degrees only have one peak in the MUSIC algorithm, indicating that the MUSIC algorithm has difficulty distinguishing multiple radiation sources with small differences in azimuth. Simply reducing the search step size still cannot distinguish co-frequency signals with similar azimuths; ② The estimation error is larger when the search step size is 5 degrees than when it is 1 degree, indicating that the MUSIC algorithm can improve the azimuth estimation accuracy by using a smaller step size.

[0085] In a MUSIC spectrum, each peak represents a signal. The peak values ​​in the MUSIC spectrum are extracted as shown in the following formula.

[0086] (14)

[0087] In the formula, This represents the peak extraction function; you can refer to the `findpeaks` function in MATLAB. The rough estimate of the location of the radiation source is... dimensional vector, and The resolution is .

[0088] Furthermore, to address the problems of the MUSIC method, such as ① achieving high-precision azimuth estimation with an extremely small search step size, resulting in high computational resource consumption; and ② difficulty in distinguishing multiple radiation sources with small differences between azimuths, the search step size in step one is... Set a relatively large value (configurable based on the search range and computation time, e.g., 3 degrees) to obtain a rough estimate of the radiation source's location. .

[0089] Furthermore, in step two, an array manifold is constructed within a certain range near each search peak (determined by the array antenna beamwidth; if the array antenna beamwidth is N, the search range is usually set to ±N / 2; for example, the beamwidth of an L-band direction-finding array antenna is usually 30 degrees, so the array manifold within ±15 degrees near the search peak). Polynomial fitting is then performed on this manifold. By solving for the unequal real stationary points of this polynomial, the number of stationary points indicates the presence of several co-frequency targets with small azimuth differences. The azimuth of these targets is then accurately estimated through the location of the stationary points. This compensation method is particularly suitable for distinguishing multiple co-frequency radiation sources with small azimuth differences.

[0090] Step two includes:

[0091] Rough estimate of the radiation source's location The corresponding array manifold of the circular array for:

[0092] (15)

[0093] Compared with formula (5), this formula only changes the parameters. Change to .

[0094] Let the array manifold response function be as shown in the following equation.

[0095] (16)

[0096] In the formula, For fine-grained search variables of orientation, , This represents the response of the fine-grained search array manifold. For direction The corresponding array manifold of the circular array.

[0097] Based on the search range, since an array manifold is constructed within a ±15 degree range near the search peak, therefore... .

[0098] The polynomial degree should not be less than: the difference between azimuths should be less than or equal to the total number of radiation sources in the search step (to prevent the inability to distinguish multiple adjacent signals of the same frequency due to the degree being too small (e.g., 2nd degree), and the polynomial degree should not be too large (to prevent the stationary point from being indistinct due to the degree being too large). It should be determined based on simulation and practice.

[0099] For example, using a 4th degree polynomial to... Fit the curve to the equation, and let the coefficients of the fourth-order polynomial be...

[0100] (17)

[0101] according to Design parameter matrix ,matrix row vectors As shown below.

[0102] (18)

[0103] according to Design response matrix ,matrix row vectors As shown below.

[0104] (19)

[0105] Traversal All possible values ​​are used to obtain the matrix. and .

[0106] in ;

[0107] , , , , These represent the coefficients of the fourth-order binomial.

[0108] According to the least squares criterion, the coefficient matrix of the fourth-degree polynomial is:

[0109] (20)

[0110] By solving for the stationary points of the polynomial, the fine-tuning value of the azimuth is obtained. for

[0111] (twenty one)

[0112] In the formula, Indicates by coefficient The stationary point solution function constitutes a polynomial function. The solution function is relatively mature, such as the roots function in MATLAB. Given a matrix, the solution to this polynomial contains several unequal stationary points. This indicates the number of dimensions of the matrix.

[0113] Precise estimate of the location of the radiation source Represented as

[0114] (twenty two)

[0115] In the formula, This represents a rough estimate of the azimuth, obtained using the MUSIC method with a relatively large step size. This is the fine-tuning value for orientation.

[0116] Results: When the search step size is 3 degrees, the two actual radiation sources are 115 degrees and 118 degrees. Using the method of this invention, one peak value is obtained in step one, and then the two target azimuths can be accurately detected as 115 degrees and 118 degrees respectively through step two.

[0117] Typically, in the presence of a real radiation source, because the method of this invention uses a relatively long search step size (e.g., 2-3 degrees), it can usually only find one peak, rarely more than one or no search peak at all. If other sensors, such as radar, have already detected a target in a certain azimuth, but the search peak cannot be obtained through step one of the method of this invention, then a smaller step size (reducing by 0.4-0.6 degrees each time, and the search step size can be set to a minimum of about 0.5 degrees) is allowed for step one to obtain the search peak. For example, if the search step size is originally 3 degrees and the search peak cannot be obtained through step one of the method of this invention, then the step size is reduced by 0.5 degrees to 2.5 degrees, and the search peak is obtained through step one of the method of this invention again. If the search peak is still not obtained, then the step size is reduced by another 0.5 degrees to 2 degrees, and the search peak is obtained through step one of the method of this invention again, and so on, with the search step size set to a minimum of 0.5 degrees.

[0118] The method of this invention searches for possible target locations within the vicinity of a peak. If more than one peak is found in step one, each peak from step one will be traversed in step two. After traversing all peaks, a series of targets and their locations are obtained, and the final result is output. This series of target results is then merged, removing target values ​​with the same location and retaining the remaining target values.

[0119] Specifically, for each search peak (i.e., each peak value) obtained in step one, an array manifold is constructed within a certain range near each search peak (the beamwidth of the L-band direction-finding array antenna is 30 degrees, and an array manifold within ±15 degrees near the search peak is constructed), and step two is executed accordingly. For example, if there are two search peaks obtained in step one, for peak 1, a precise estimate of the azimuth of the radiation source is obtained, which is two target azimuths (angle 1 and angle 2, respectively); for peak 2, a precise estimate of the azimuth of the radiation source is obtained, which is two target azimuths (angle 3 and angle 4, respectively); if the difference between angle 2 and angle 3 is less than a threshold value (for example, if the difference between the calculated two angles is less than the threshold value, it is considered that the two calculated angles correspond to the same signal source, and the threshold value can be determined according to specific engineering practice), and the differences between other angles are not less than the threshold value, then the final output result is angle 1, angle 2, and angle 4, or the final output result is angle 1, angle 3, and angle 4.

[0120] This invention distinguishes multiple radiation sources with small azimuth differences and accurately estimates their azimuths with relatively small computational resources. The key steps are: first, a large step size is used to search the entire space; second, an array manifold is constructed within a certain range near the search peak, and a fourth-order polynomial is fitted to this manifold (assuming a maximum of four targets within this range; engineering applications show that the number of radiation sources with azimuth differences less than 3 degrees generally does not exceed four). By solving for the unequal real stationary points of this polynomial, the azimuths of these targets are accurately estimated using the locations of these stationary points.

[0121] If a polynomial is used to directly fit the music spectrum (full spectrum), the spectral values ​​are too large and the fitting effect is not obvious. This invention uses a coarse search for the array manifold near the peak and fits it with a fourth-order polynomial. The stationary points of the array manifold are analyzed to find multiple targets, thereby solving the problem of direction finding of multiple signals with the same frequency in the vicinity.

[0122] The above embodiments are only used to illustrate the technical solutions of the present invention. Those skilled in the art should understand that the above embodiments do not limit the present invention in any way. All technical solutions obtained by equivalent substitution or equivalent transformation fall within the protection scope of the present invention.

Claims

1. A lightweight and high-precision method for estimating the azimuth of multiple targets based on a uniform circular array, comprising the following steps: Step 1: Construct a rough azimuth measurement model based on a uniform circular array using MUSIC, and determine the search step size. By setting the range to 0.5-5 degrees, the peak values ​​in the music spectrum are extracted to obtain a rough estimate of the radiation source's location. ; Step 2: Construct a precise orientation measurement model based on polynomial fitting: For each search peak, an array manifold is constructed within a certain range around the peak, and polynomial fitting is performed on this array manifold. By solving for the unequal real stationary points of the polynomials, the azimuths of multiple radiation sources are accurately estimated using the locations of these stationary points, thus obtaining the fine-tuned azimuth values ​​of the radiation sources. ; Rough estimate based on the location of the radiation source and fine correction value of radiation source location A precise estimate of the radiation source's location was obtained. .

2. The lightweight and high-precision multi-target azimuth estimation method based on a uniform circular array according to claim 1, characterized in that, The search range near the search peak is determined by the beamwidth of the array antenna. If the beamwidth of the array antenna is N, the search range is set to ±N / 2.

3. The lightweight and high-precision multi-target azimuth estimation method based on a uniform circular array according to claim 1, characterized in that, In step two, the polynomial degree is not less than the number of radiation sources whose azimuth difference is less than or equal to the search step size.

4. The lightweight and high-precision multi-target azimuth estimation method based on a uniform circular array according to claim 1, characterized in that, In step two, the rough estimate of the radiation source's location is used. The corresponding array manifold of the circular array for: ； Let the array manifold response function be: ； In the formula, For fine-grained search variables of orientation, Determined based on the search scope. Represents the fine-grained search array manifold response; Using a 4th degree polynomial Fit the curve to the equation, and let the coefficients of the fourth-order polynomial be... ； according to Design parameter matrix ,matrix row vectors for: ； according to Design response matrix ,matrix row vectors for: ； Traversal All possible values ​​are used to obtain the matrix. and ; According to the least squares criterion, the coefficient matrix of the fourth-degree polynomial is: ； By solving for the stationary points of the polynomial, the fine-tuning value of the azimuth is obtained. for ； In the formula, Indicates by coefficient The stationary point solution function that constitutes a polynomial function; Precise estimate of the location of the radiation source Represented as ； In the formula, This represents a rough estimate of the radiation source's location, obtained through step one; This is a fine-tuning value for the orientation of the radiation source.

5. The lightweight and high-precision multi-target azimuth estimation method based on a uniform circular array according to claim 1, characterized in that, In step one, the MUSIC spectrum is represented as: ； Search step size within the range of 0 to 360 degrees right Perform a traversal; In a music spectrum, each peak represents a signal. Extract the peak values ​​from the music spectrum: ； In the formula, This represents the peak extraction function. This represents a rough estimate of the location of the radiation source.

6. A lightweight, high-precision multi-target azimuth estimation system based on a uniform circular array, characterized in that, This includes a coarse orientation measurement model based on a uniform circular array model using MUSIC and a precise orientation measurement model based on polynomial fitting. In the MUSIC-based uniform circular array model for coarse azimuth measurement, the search step size... By setting the range to 0.5-5 degrees, the peak values ​​in the music spectrum are extracted to obtain a rough estimate of the radiation source's location. ; In the polynomial fitting-based accurate azimuth measurement model, for each search peak, an array manifold is constructed within a certain range near the search peak, and a polynomial fit is performed on this array manifold. By solving for the unequal real stationary points of the polynomial, the azimuth of multiple radiation sources is accurately estimated using the positions of these stationary points, thus obtaining the fine-corrected azimuth values ​​of the radiation sources. ; Rough estimate based on the location of the radiation source and fine correction value of radiation source location A precise estimate of the radiation source's location was obtained. .

7. An array antenna, characterized in that, The method for lightweight and high-precision estimation of multi-target azimuth based on a uniform circular array as described in any one of claims 1-5, or the system for lightweight and high-precision estimation of multi-target azimuth based on a uniform circular array as described in claim 6, can be used.

8. A processor for running computer programs, characterized in that, When the computer program runs, it executes the lightweight and high-precision multi-target orientation estimation method based on a uniform circular array as described in any one of claims 1-5.

9. A terminal comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the lightweight and high-precision multi-target orientation estimation method based on a uniform circular array as described in any one of claims 1-5.

10. A computer-readable medium having a computer program stored thereon, characterized in that, The computer program, when executed by a processor, can implement the lightweight, high-precision multi-target azimuth estimation method based on a uniform circular array as described in any one of claims 1-5.

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