CN117471397A - Circular array two-dimensional DOA estimation method based on graph signal processing - Google Patents
Circular array two-dimensional DOA estimation method based on graph signal processing Download PDFInfo
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- CN117471397A CN117471397A CN202311511773.1A CN202311511773A CN117471397A CN 117471397 A CN117471397 A CN 117471397A CN 202311511773 A CN202311511773 A CN 202311511773A CN 117471397 A CN117471397 A CN 117471397A
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- 238000000034 method Methods 0.000 title claims abstract description 20
- 239000011159 matrix material Substances 0.000 claims abstract description 16
- 230000003595 spectral effect Effects 0.000 claims description 3
- 238000007476 Maximum Likelihood Methods 0.000 claims description 2
- 239000000654 additive Substances 0.000 claims description 2
- 230000000996 additive effect Effects 0.000 claims description 2
- 230000000694 effects Effects 0.000 abstract description 3
- 238000005259 measurement Methods 0.000 abstract 1
- 238000004422 calculation algorithm Methods 0.000 description 11
- 230000005855 radiation Effects 0.000 description 3
- 238000004364 calculation method Methods 0.000 description 2
- 238000001228 spectrum Methods 0.000 description 2
- 230000009286 beneficial effect Effects 0.000 description 1
- 230000005540 biological transmission Effects 0.000 description 1
- 238000010586 diagram Methods 0.000 description 1
- 238000005070 sampling Methods 0.000 description 1
- 238000004088 simulation Methods 0.000 description 1
Classifications
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
- G01S5/02—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using radio waves
- G01S5/04—Position of source determined by a plurality of spaced direction-finders
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S3/00—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received
- G01S3/02—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received using radio waves
- G01S3/14—Systems for determining direction or deviation from predetermined direction
- G01S3/46—Systems for determining direction or deviation from predetermined direction using antennas spaced apart and measuring phase or time difference between signals therefrom, i.e. path-difference systems
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- Physics & Mathematics (AREA)
- Engineering & Computer Science (AREA)
- General Physics & Mathematics (AREA)
- Radar, Positioning & Navigation (AREA)
- Remote Sensing (AREA)
- Measurement Of Velocity Or Position Using Acoustic Or Ultrasonic Waves (AREA)
- Radar Systems Or Details Thereof (AREA)
Abstract
The invention belongs to the technical field of array direction finding, and particularly relates to a circular array two-dimensional DOA estimation method based on graph signal processing. According to the method, a directed graph among array elements is constructed, a measurement signal is projected by utilizing an adjacent matrix of the directed graph, and finally a residual matrix is constructed, so that the azimuth angle and the pitch angle of a target signal are obtained. The method has good effect in various signal-to-noise ratio environments, can accurately estimate the azimuth of the target, and is simple and practical.
Description
Technical Field
The invention belongs to the technical field of array direction finding, and particularly relates to a circular array two-dimensional DOA estimation method based on graph signal processing.
Background
Array direction finding is to set multiple sensors at different positions in space to form a sensor array, to receive (multipoint parallel sampling) and process the space signal field by using the array, to extract the signals received by the array and their characteristic information (parameters), to suppress interference and noise or uninteresting information, and to calculate the position of the radiation source by using the time difference or phase difference of the signal arrival measured by the multiple array element positions.
Disclosure of Invention
The invention provides a novel circular array DOA estimation method, which is based on a circular array, and is characterized in that a receiving signal is projected to a map domain for processing by constructing an adjacent matrix, a residual matrix is constructed, and finally, a spectrum peak is obtained by minimizing the residual, wherein the angle corresponding to the peak is the required azimuth angle of a radiation source. Compared with a Fourier transform method of a graph, the method avoids carrying out characteristic value calculation on the matrix for multiple times, obviously improves the calculation speed in two-dimensional search, improves the resolution, and improves the accuracy compared with the traditional music algorithm
The technical scheme adopted by the invention is as follows:
a circular array two-dimensional DOA estimation method based on graph signal processing, a single source signal is incident to a uniform circular array from an unknown angle, wherein an array antenna is composed of M array elements, the number of the array elements is equal to the number of channels, each array element receives the signal and then sends the signal to a processor through a respective transmission channel, and the algorithm provided by the method comprises the following steps:
s1, obtaining a receiving signal matrix X= [ X [1 ]],x[2],…,x[L]]The total snapshot number is L, and the received data at the first snapshot is x [ L ]]＝A(θ)s[l]+n[l]In s [ l ]]And n [ l ]]The received signal and the noise are respectively received,is in the shape of M multiplied by 1 dimension uniform circular array manifold, and the expression is as follows:
in which θ andthe azimuth angle of incidence and the pitch angle, respectively, and the array radius r is set to 1/2 of the incident wavelength λ.
S2, constructing a graph adjacent matrix B of the array so thatAnd assuming that each element is only adjacent elementsThe adjacency matrix B is set to the following form:
wherein the method comprises the steps ofAnd constructs an array airspace map according to the adjacent matrix form, and as shown in fig. 1, sets the array according to the airspace map.
S3, constructing residual quantity epsilon=BX-X= (B-I) n, and obtaining a covariance matrix of epsilon according to the property of Gaussian random vector under the background of additive Gaussian white noiseFinally, the probability density function of epsilon is obtained as follows: />
S4, carrying out maximum likelihood estimation on the residual quantity epsilon to obtain an estimated quantity x H (B-I)Q -1 (B-I)x。
S5, converting the estimation amount into trace (x H (B-I)Q -1 (B-I) x) and performing two-dimensional spectral peak search to obtain incidence parameter with minimum residual error, namely
Obtaining DOA estimation results
The method has the beneficial effects that the incidence parameters of the radiation source, namely the azimuth angle and the pitch angle, can be accurately estimated. Compared with the graph Fourier transform method, the method has the advantages that characteristic values are not required to be calculated for multiple times in two-dimensional search, the operation time is obviously reduced, the accuracy is improved compared with the traditional music algorithm, and the method is simple and good in effect.
Drawings
FIG. 1 is a spatial map of an array constructed from an adjacency matrix;
FIG. 2 is a graph of DOA estimated spectral peaks for a uniform circular array at a fixed signal-to-noise ratio and snapshot count;
FIG. 3 is a graph showing DOA estimation performance comparison of a uniform circular array under different signal-to-noise ratios;
FIG. 4 is a graph showing DOA estimation performance comparison of a 10dB signal-to-noise ratio environment uniform circular array under different snapshot numbers;
FIG. 5 is a graph showing DOA estimation performance comparison of a 5dB signal-to-noise ratio environment uniform circular array under different snapshot numbers;
FIG. 6 is a graph showing DOA estimation performance comparison of a 0dB signal-to-noise ratio environment uniform circular array under different snapshot numbers;
FIG. 7 is a graph showing the comparison of DOA estimation performance of a uniform circular array with a-10 dB signal-to-noise ratio under different snapshot numbers.
Detailed Description
The present invention will be described in detail with reference to the following examples:
assuming that the array element number of the uniform circular array is 8, the snapshot number is 10, the signal to noise ratio is 10dB, and the method utilizesAnd carrying out two-dimensional search on the azimuth angle and the pitch angle, and obtaining a spectrum peak diagram shown in figure 2. Next, some scenes were simulated using 100 monte carlo. Firstly, DOA estimation is carried out under different signal-to-noise ratio environments when the fixed array element number is 8 and the snapshot number is 10, and the DOA estimation accuracy is measured by adopting root mean square error, namely:
wherein θ is i Andmeasuring azimuth and pitch angle, θ and +.>The azimuth angle and the pitch angle of the wave are respectively. The simulation results are shown in fig. 3. Then, the fixed array element number is 8, the fixed signal to noise ratio is 10dB, DOA estimation is carried out under the condition of different snapshot numbers, and the algorithm performance is verified, as shown in figure 4. The array element number is kept unchanged, the fixed signal to noise ratio is 5dB, DOA estimation is carried out under the condition of different snapshot numbers, and the algorithm performance is verified, as shown in figure 5. The array element number is kept unchanged, the fixed signal to noise ratio is 0dB, DOA estimation is carried out under the condition of different snapshot numbers, and the algorithm performance is verified, as shown in figure 6. Keeping the array element number unchanged, fixing the signal-to-noise ratio to-10 dB, and carrying out DOA estimation under the condition of different snapshot numbers to verify the algorithm performance, as shown in figure 7.
Direction finding effect:
to verify the effectiveness of the DOA estimation algorithm, the algorithm performance is observed by varying the signal-to-noise ratio, the number of snapshots. 1-6, along with the change of signal-to-noise ratio, snapshot number and the like, the estimated error is almost lower than or equal to that of the traditional music algorithm, and the effectiveness of the novel uniform circular array DOA estimation algorithm is proved.
Claims (1)
1. A circular array two-dimensional DOA estimation method based on graph signal processing adopts a circular array formed by M array elements to receive signals transmitted from unknown angles by single-source signals, defines the number of the array elements to be equal to the number of channels, and carries out DOA estimation after each array element receives the signals, and is characterized by comprising the following steps:
s1, defining the obtained receiving signal matrix as X= [ X [1 ]],x[2],…,x[L]]The total snapshot number is L, and the received data at the first snapshot is x [ L ]]＝A(θ)s[l]+n[l]In s [ l ]]And n [ l ]]The received signal and the noise are respectively received,is in the shape of M multiplied by 1 dimension uniform circular array manifold, and the expression is:
in which θ andthe incidence azimuth angle and the pitch angle are respectively set, and the array radius r is set to be 1/2 of the incidence wavelength lambda;
s2, constructing a graph adjacent matrix B of the array so thatAnd each array element is only connected with the adjacent array element, and the adjacent matrix B is set as follows:
wherein the method comprises the steps ofConstructing an array airspace map according to the adjacent matrix form;
s3, constructing residual quantity epsilon=BX-X= (B-I) n, and obtaining a covariance matrix of epsilon according to the property of the complex Gaussian random vector under the background of additive Gaussian white noiseFinally, the probability density function of epsilon is obtained as follows: />
S4, carrying out maximum likelihood estimation on the residual quantity epsilon to obtain an estimated quantity x H (B-I)Q -1 (B-I)x；
S5, converting the estimation amount into trace (x H (B-I)Q -1 (B-I) x) and performing two-dimensional spectral peak search to obtain incidence parameter with minimum residual error, namely
Obtaining DOA estimation results
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Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN117970228A (en) * | 2024-03-28 | 2024-05-03 | 中国人民解放军火箭军工程大学 | Multi-target DOA estimation method based on uniform circular array |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN117970228A (en) * | 2024-03-28 | 2024-05-03 | 中国人民解放军火箭军工程大学 | Multi-target DOA estimation method based on uniform circular array |
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