Two-dimensional direction finding method based on spot center fitting

Abstract

The present invention discloses a two-dimensional direction-finding method based on spot center fitting, the method comprising: performing front-end processing on the direction-finding signal of the target to be measured collected by the two-dimensional plane array; setting the scanning u value, converting the direction-finding signal after the front-end processing from the angle domain to the u domain, and obtaining a discrete azimuth spectrum matrix composed of beam output; normalizing the discrete azimuth spectrum matrix to obtain a grayscale spot diagram; merging the spots in the grayscale spot diagram according to the principle of symmetry; performing spot center fitting on the merged grayscale spot diagram to obtain the azimuth of the target to be measured, and realizing target direction-finding. The present invention innovatively transplants the spot center fitting method into the direction-finding of the two-dimensional plane array, and the method can be widely used in various sonar and radar platforms with high real-time requirements, and is not limited by the platform frequency and the number of array elements.

Description

Technical Field

[0001] The invention relates to the field of plane array orientation estimation, and in particular to a two-dimensional direction finding method based on light spot center fitting. Background Art

[0002] Beamforming azimuth spectrum and MUSIC are both classic azimuth estimation algorithms. They need to obtain the autocorrelation matrix based on the statistical information of the array data, perform dense scanning in the azimuth interval of interest, and confirm the target's azimuth by searching for spectrum peaks.

[0003] In radar and sonar systems, these high-precision direction estimation methods are difficult to apply in real time. Limited by the computing speed of the platform, the traditional beamforming azimuth spectrum is still widely used in practical applications. Within the azimuth range of interest, a series of beam outputs are obtained by scanning at a certain step size, and the target azimuth is obtained by spectrum peak search. For two-dimensional azimuth estimation, when the search step size decreases, the search amount of two-dimensional azimuth increases quadratically. Usually, due to the real-time requirements of the platform, the step size is generally set according to the half-beam width.

[0004] Note that the two-dimensional image of the sparsely discrete spatially sampled azimuth spectrum is similar to the spot diagram, both of which show a centrally blurred shape, such as Figure 1 As shown, they have a common goal: to search for the azimuth spectrum / spot center. Spot center positioning is one of the key technologies in optical measurement. It is usually used in aerospace, weapon systems, and laser detection. At present, the grayscale centroid method, ellipse center quadratic fitting, and Gaussian distribution fitting are usually used to calculate the spot center.

[0005] Similarly, in order to search for the true azimuth, the azimuth estimation method for the discrete azimuth spectrum will also calculate the target azimuth based on the amplitude or phase relationship of the output of multiple beams. The most common method is the amplitude ratio method. The traditional amplitude ratio method regards the beam pattern or azimuth spectrum as a function, such as a linear function or a Gaussian function, and calculates the target direction by interpolation. This method is similar to the Gaussian distribution fitting method at the center of the spot. It is simple and easy to use with low computational complexity, but the accuracy decreases when the signal-to-noise ratio decreases or the target deviates from the broadside direction. At present, all amplitude ratio methods and phase ratio methods are performed in the angle domain, and the target azimuth is confirmed by interpolation. For a planar array, the beam width of the azimuth spectrum increases as the azimuth or elevation angle deviates from the broadside, and the main lobe is no longer symmetrical about the central axis. Therefore, all kinds of fitting methods are bound to have deviations. Summary of the invention

[0006] The purpose of the present invention is to overcome the defects of the prior art and propose a two-dimensional direction finding method based on spot center fitting.

[0007] In order to achieve the above object, the present invention proposes a two-dimensional direction finding method based on spot center fitting, the method comprising:

[0008] Step 1) performing front-end processing on the direction-finding signal of the target to be measured collected by the two-dimensional plane array;

[0009] Step 2) setting the scanning u value, converting the direction finding signal processed by the front end from the angle domain to the u domain, and obtaining a discrete azimuth spectrum matrix composed of the beam output;

[0010] Step 3) normalizing the discrete azimuth spectrum matrix to obtain a grayscale spot diagram;

[0011] Step 4) merging the light spots in the grayscale light spot image by the principle of symmetry;

[0012] Step 5) Fit the center of the combined grayscale spot image to obtain the direction of the target to be measured and realize target direction finding.

[0013] As an improvement of the above method, the front-end processing of step 1) includes amplification, automatic gain control AGC and FFT.

[0014] As an improvement of the above method, the two-dimensional plane array in step 1) is a uniform rectangular array of N*M elements, the element spacing is d, and the wavelength is λ.

[0015] As an improvement of the above method, the step 2) specifically includes:

[0016] Set the u-axis scanning step length Δ u , v-axis scanning step length Δ v , not more than 0.891λ / (Nd) and 0.891λ / (Md) respectively;

[0017] By uniformly delaying and weighting the array element domain data x(t), we can obtain K u *K ν The beam outputs y(v, v, t), which are then squared to obtain a discrete normalized azimuth spectrum.

[0018] As an improvement of the above method, the step 4) specifically includes:

[0019] Step 4-1) merging edge lines;

[0020] Step 4-2) confirm the light spot position;

[0021] Step 4-3) Move the light spot to be excluded sideways to the side of the real light spot;

[0022] Step 4-4) Obtain the horizontal coordinate or vertical coordinate after the matrix is ​​translated by outward extension.

[0023] As an improvement of the above method, the step 4-2) specifically includes:

[0024] Write the normalized orientation spectrum in matrix form, Among them, K u , K v Respectively represent the number of rows and columns of the matrix;

[0025] When the target is at the edge, multiple light spots will appear. If the peak values ​​of multiple light spots are in the same row, the maximum value is the output P of the first column of the i-th row. i，1 and the Kth row of the i-th v Output of columns Compare the output of the second column with the second to last column, and take the spot with the larger value as the real spot; compare the output P of the second column of the i-th row i，2 and the Kth row of the i-th v -1 column output like If the light spot is on the right, it is considered that the light spot is on the left; otherwise, it is considered that the light spot is on the left.

[0026] As an improvement of the above method, the step 4-3) specifically includes:

[0027] If the spot is on the right, the combined multi-beam output matrix is ​​P(:, [3: K v , 2]); if the spot is on the left, the combined multi-beam output matrix is ​​P(:, [K v -1,1:K v -2]).

[0028] As an improvement of the above method, the step 4-4) specifically includes: the new horizontal coordinate after translation satisfies the following formula:

[0029]

[0030] The new vertical coordinate after translation satisfies the following formula:

[0031]

[0032] As an improvement of the above method, the step 5) adopts the centroid method, which specifically includes:

[0033] The center of gravity (u0, v0) of the light spot is calculated by using the pixel grayscale value of the fitting area near the light spot in the image as the weight:

[0034] according to The azimuth angle Φ and elevation angle θ of the target to be measured are calculated, thereby realizing two-dimensional direction finding.

[0035] As an improvement of the above method, the step 5) adopts the Gaussian center method, which specifically includes:

[0036] The intensity variation of the light spot is set to conform to the two-dimensional Gaussian distribution;

[0037] Take the logarithm of the two-dimensional Gaussian distribution function, transform the problem into a polynomial fit, and solve it through Q points, where Q ≥ 5. The solution of the center of gravity of the spot (u0, v0) is obtained by left division of the matrix;

[0038] according to The azimuth angle Φ and elevation angle θ of the target to be measured are calculated, thereby realizing two-dimensional direction finding.

[0039] Compared with the prior art, the advantages of the present invention are:

[0040] The present invention innovatively transplants the spot center fitting method into the direction finding of the two-dimensional planar array, and ensures the translation invariance of the azimuth spectrum by converting the direction finding from the angle domain to the u domain, thereby ensuring that the spot shape remains consistent; and proposes spot merging to improve the accuracy of edge direction finding, and fitting methods such as the centroid method and the Gaussian method can be applied to two-dimensional direction finding; this method can be widely used in various sonar and radar platforms with high real-time requirements, and is not limited by the platform frequency and the number of array elements. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 It is the laser spot diagram measured by the prior art experiment;

[0042] Figure 2 It is a flat formation;

[0043] Figure 3 is the u-domain azimuth spectrum, with a target signal-to-noise ratio of 40 dB, where Figure 3(a) is the azimuth (53°, 5°) and Figure 3(b) is the azimuth (0, 80°);

[0044] Figure 4 is the azimuth spectrum in the angle domain, with a target signal-to-noise ratio of 40 dB, where Figure 4(a) is the azimuth (53°, 5°) and Figure 4(b) is the azimuth (0, 80°);

[0045] Figure 5 is the Cartesian coordinate system of the plane array;

[0046] Figure 6 shows the azimuth spectrum and grayscale spot diagram obtained for the target (-40°, 25°), where Figure 6(a) is the azimuth spectrum with a step size of 0.2, Figure 6(b) is the grayscale spot diagram with a step size of 0.2, and Figure 6(c) is the grayscale spot diagram with a step size of 0.01;

[0047] Figure 7 is the u-domain spectrum after (-3°, 5°) is converted to the u-domain, where Figure 7(a) is the original output and Figure 7(b) is the output after merging at the center of the light spot;

[0048] Figure 8 shows the direction finding error (5 dB) obtained by the U-domain Gaussian center method and the angle domain interpolation method when the target is at different azimuths, where Figure 8 (a) is the U-domain Gaussian center method and Figure 8 (b) is the angle domain interpolation method. DETAILED DESCRIPTION

[0049] Compared with the processing in the angle domain, the U domain has translation invariance, which can keep the shape of the beam unchanged with the change of u value. If the processing is converted to the U domain, the azimuth spectrum can maintain axisymmetry and shape unchanged.

[0050] The purpose of the present invention is to perform two-dimensional direction finding for a planar array by using spot center fitting.

[0051] We propose to use the grayscale spot diagram and spot extraction method to perform two-dimensional direction finding in the U domain, achieving high-precision direction finding with low computational complexity.

[0052] The technical solution of the present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0053] Example 1

[0054] The embodiment of the present invention proposes a method for two-dimensional direction finding based on spot center fitting, which can be applied to radar, sonar and other systems with high real-time requirements, and obtains a high-accuracy azimuth estimation result with less calculation amount.

[0055] Taking a 6*6 element uniform linear array as an example, it is assumed that the array is arranged at a half-wavelength spacing of 20kHz. Figure 2 It is a flat formation.

[0056] In order to ensure the translation invariance of the azimuth spectrum, we first convert the two-dimensional direction finding from the angle domain to the U domain. Let the target signal-to-noise ratio be 40dB, the noise be Gaussian white noise, and the two-dimensional azimuth angles be set to (53°, 5°) and (0, 80°) respectively. Figure 3 is the U-domain azimuth spectrum, where Figure 3(a) is the azimuth (53°, 5°) and Figure 3(b) is the azimuth (0, 80°); and Figure 4 is the angle domain azimuth spectrum, where Figure 4(a) is the azimuth (53°, 5°) and Figure 4(b) is the azimuth (0, 80°). It can be seen that the U-domain azimuth spectrum is translation invariant, and the main lobe shape of the azimuth spectrum at any two-dimensional angle is the same; while the main lobe of the azimuth spectrum in the angle domain becomes wider as the two-dimensional angle deviates from the broadside.

[0057] The specific steps include:

[0058] 1. Front-end processing

[0059] Consistent with the front-end processing of other existing sonar / radar platforms, we first perform amplification, automatic gain control AGC, and FFT.

[0060] 2. Beamforming

[0061] 1. Scan u value setting

[0062] For a rectangular array of N*M elements, the element spacing = d, and the wavelength is λ. u = cosθcosφ, v = cosθsinφ, and the observation range of u and v is between -1 and 1. For a uniform array, the scanning step lengths of the u and v axes are set to be fixed, Δ u and Δ v The step size should not be larger than the 3dB beam width in the u domain, i.e. 0.891λ / (Nd) and 0.891λ / (Md). The scanning beam u and v values ​​include and

[0063] Beamforming

[0064] The existing sonar and radar real-time processing platforms basically use traditional beamforming CBF, which obtains K by uniformly delaying and weighting the data x(t) received by the array element domain at time t. u *K v The beam outputs y(u, v, t), which are then squared to obtain a discrete azimuth spectrum P(u, v).

[0065] y(v, v, t) = ω H (u, v)x(t), P(u, v) = E{y(v, v, t) 2}. E{} is the expected value. For a uniform linear array, the weight vector is For Figure 5 Plane matrix, weight vector w(u, v) = e -jpk ,in p is the matrix composed of the three-dimensional coordinates of each array element. Assume that array element No. 1 is point 0, and the coordinates of the i+1th array element are [p xi , p yi , p zi ], the coordinates of the N*Mth array element are [p x(N*M-1) , p y(N*M-1) , p z(N*M-1) ]. Since the array is a planar array, it can be simplified to:

[0066]

[0067] 3. Grayscale spot diagram

[0068] K u *K v The discrete azimuth spectrum matrix composed of beam outputs is normalized to P. The minimum value is 0 and the maximum value is 1. The grayscale spot diagram is shown in Figure 6, where Figure 6(a) is the azimuth spectrum with a step size of 0.2, Figure 6(b) is the grayscale spot diagram with a step size of 0.2, and Figure 6(c) is the grayscale spot diagram with a step size of 0.01. i , v j ) is the i-th row and j-th column of the matrix P, which can be abbreviated as P i，j .

[0069] 4. Spot Merging

[0070] When the maximum value is at the edge, that is, in the first or last column, or in the first or last row, more than one spot will appear in the output. This may lead to misjudgment. For example, in Figure 7(a), the actual target is located at the right spot, but the output has two maximum values ​​(at the left and right + signs, with horizontal coordinates of -1 and 1, respectively). If the spot center is directly fitted, more than one center may appear. In addition, since the number of points involved in the fitting of each spot decreases, the center estimation error increases. We propose to merge the spots into one by the principle of symmetry, as shown in Figure 7(b).

[0071] 1. Edge line merging

[0072] The edge lines are considered as the same line, as shown in FIG7 , the first column and the last column are merged; if the light spot is at the upper and lower edges, the first row and the last row are merged.

[0073] 2. Confirm the spot position

[0074] In the same row as the peak value, compare the output of the second column of P with the second to last column. The light spot with the larger output should be the real light spot.

[0075] If multiple spot peaks are in the same row, the maximum value is P i，1 and Compare the output of the second column with the second to last column. The light spot with the larger output is the real light spot. If the light spot is on the right, it is considered that the light spot is on the left; otherwise, it is considered that the light spot is on the left.

[0076] 3. Shift the light spot

[0077] If the spot is on the right, the combined multi-beam output matrix is ​​P(:, [3: K v , 2]); if the spot is on the left, the combined multi-beam output matrix is ​​P(:, [K v -1,1:K v -2]). The new matrix has one less column than the original one.

[0078] 4. Confirm the horizontal (vertical) coordinates after translation

[0079] Since the orientation estimation is performed in the u domain, and u and v should be in the interval [-1, 1], we propose to obtain the horizontal coordinate of the translated column vector of the matrix by outward extension (if the translated row vector needs to confirm its vertical coordinate).

[0080]

[0081] The vertical coordinate after translation satisfies the following formula:

[0082]

[0083] 5. Spot center fitting

[0084] 1. Center of gravity method

[0085] The centroid method calculates the centroid of the light spot by using the grayscale value of the pixels near the light spot in the image as the weight. The grayscale image pixel obtained by the azimuth spectrum is K u *K v , the gray value of the pixel in the i-th row and j-th column is P i，j .

[0086] Spot segmentation: Set the area involved in fitting according to a certain threshold Alternatively, the image segmentation method is used to perform spot segmentation.

[0087] The calculated center of gravity (u0, v0) is the orientation of the target.

[0088]

[0089] 2. Gaussian Center Method

[0090] The Gaussian center method assumes that the intensity variation of the spot follows a Gaussian distribution. In fact, this is very close to the analytical expression of the beam pattern and is consistent with the characteristics of a bell-shaped distribution. Assuming that the two-dimensional Gaussian distribution is satisfied as shown in (4), k u and k v is an unknown quantity that affects the shape of the distribution surface.

[0091] P(u,v)=Aexp(-k u (u-u0) 2 -k v (v-v0) 2 )) (5)

[0092] Taking the logarithm of it, we get

[0093]

[0094] The problem is then transformed into a polynomial fit, XK = Y, and is solved through Q points, Q ≥ 5.

[0095]

[0096]

[0097] Y=[lnP1,...,lnP Q ] T (9)

[0098] K=X\Y (10)

[0099] Left dividing the matrix yields the polynomial coefficients.

[0100]

[0101] 6. Angle restoration

[0102] u0 and v0 calculated in (11) are The azimuth and elevation angles are restored.

[0103] Simulation test

[0104] Set a 6*6 uniform plane square array, and the target signal-to-noise ratio = 20dB. Set the u-domain scanning step size to 0.2, then a total of 121 beams need to be scanned between the two-dimensional interval of -1 to 1. Through 200 Monte Carlo simulations, the average estimation results are statistically obtained. For targets in non-edge orientations, the performance of the centroid method and the Gaussian method is similar; for targets in edge orientations, the performance of the Gaussian method is better than the centroid method. Compared with the currently commonly used angle domain linear interpolation method, the orientations obtained by U-domain processing are closer to the set true values, as shown in the following table.

[0105] Table 1 Experimental data

[0106]

[0107] By setting different azimuths of the target and performing interpolation processing in the U domain and angle domain, the result is shown in Figure 8, where Figure 8(a) is the U domain Gaussian center method and Figure 8(b) is the angle domain interpolation method. The error of the angle domain method increases as the target deviates from 0 degrees. When the target azimuth just falls on the observation sampling, the error is small. Therefore, at different azimuths, the mean square error shows an oscillation similar to the SINC function. Compared with the angle domain processing, the U domain processing greatly reduces the estimation error. When θ is close to 0 degrees, it is close to the end-fire direction, and the calculation error has a greater impact on θ. The estimation in the U domain may also have some large errors.

[0108] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit the present invention. Although the present invention is described in detail with reference to the embodiments, it should be understood by those skilled in the art that any modification or equivalent replacement of the technical solutions of the present invention does not depart from the spirit and scope of the technical solutions of the present invention and should be included in the scope of the claims of the present invention.

Claims

1. A two-dimensional direction finding method based on spot center fitting, the method comprising: Step 1) performing front-end processing on the direction-finding signal of the target to be measured collected by the two-dimensional plane array; Step 2) setting the scanning u value, converting the direction finding signal processed by the front end from the angle domain to the u domain, and obtaining a discrete azimuth spectrum matrix composed of the beam output; Step 3) normalizing the discrete azimuth spectrum matrix to obtain a grayscale spot diagram; Step 4) merging the light spots in the grayscale light spot image by the principle of symmetry; Step 5) performing spot center fitting on the combined grayscale spot image to obtain the orientation of the target to be measured and realize target direction finding; The step 4) specifically includes: Step 4-1) merging edge lines; Step 4-2) confirm the light spot position; Step 4-3) Move the light spot to be excluded sideways to the side of the real light spot; Step 4-4) obtaining the horizontal coordinate or vertical coordinate after the matrix is ​​translated by outward extension; The step 4-2) specifically includes: Write the normalized orientation spectrum in matrix form, Among them, K u , K v Respectively represent the number of rows and columns of the matrix; When the target is at the edge, multiple light spots will appear. If the peak values ​​of multiple light spots are in the same row, the maximum value is the output P of the first column of the i-th row. i，1 and the Kth row of the i-th v Output of columns Compare the output of the second column with the second to last column, and take the spot with the larger value as the real spot; compare the output P of the second column of the i-th row i,2 and the Kth row of the i-th v -1 column output like If the light spot is on the right, it is considered that the light spot is on the right; otherwise, it is considered that the light spot is on the left. The step 4-3) specifically includes: If the light spot is on the right, the combined multi-beam output matrix is ​​P(:,[3:K v ,2]); if the spot is on the left, the combined multi-beam output matrix is ​​P(:,[K v -1,1:K v -2]); The step 4-4) specifically includes: the new horizontal coordinate after translation satisfies the following formula: The new vertical coordinate after translation satisfies the following formula:

2. The two-dimensional direction finding method based on spot center fitting according to claim 1 is characterized in that: The front-end processing of step 1) includes amplification, automatic gain control AGC and FFT.

3. The two-dimensional direction finding method based on spot center fitting according to claim 1, characterized in that: The two-dimensional plane array in step 1) is a uniform rectangular array of N*M elements, the element spacing is d, and the wavelength is λ.

4. The two-dimensional direction finding method based on spot center fitting according to claim 3 is characterized in that: The step 2) specifically includes: Set the u-axis scanning step length Δ u , v-axis scanning step length Δ v , not more than 0.891λ / (Nd) and 0.891λ / (Md) respectively; By uniformly delaying and weighting the array element domain data x(t), we can obtain K u *K v The beam outputs y(u, v, t), which are then squared to obtain a discrete normalized azimuth spectrum.

5. The two-dimensional direction finding method based on spot center fitting according to claim 1, characterized in that: The step 5) adopts the centroid method, which specifically includes: The center of gravity (u0, v0) of the light spot is calculated by using the pixel grayscale value of the fitting area near the light spot in the image as the weight: according to The azimuth angle Φ and elevation angle θ of the target to be measured are calculated, thereby realizing two-dimensional direction finding.

6. The two-dimensional direction finding method based on spot center fitting according to claim 1, characterized in that: The step 5) adopts the Gaussian center method, which specifically includes: The intensity variation of the light spot is set to conform to the two-dimensional Gaussian distribution; Take the logarithm of the two-dimensional Gaussian distribution function, transform the problem into a polynomial fit, and solve it through Q points, where Q ≥ 5. The solution of the center of gravity of the spot (u0, v0) is obtained by left division of the matrix; according to The azimuth angle Φ and pitch angle θ of the target to be measured are calculated, thereby realizing two-dimensional direction finding.

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