CN103116162B - High-resolution sonar location method based on sparsity of objective space - Google Patents
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Abstract
The invention discloses a high-resolution sonar location method based on a sparsity of an objective space and mainly solves the problems that a limited array aperture causes insufficient spatial resolution and a signal source coherence causes an inaccurate estimation of an objective location and calculating work of subspace decomposition and data volume are considerable in the prior art. According to the method, a projection matrix which is from a spatial spectrum vector quantity to a ranks synthesis data vector is constructed. By taking advantage of the apriori information of the sparsity of the space target and obtaining data of large signal to noise ratio through a matched filtering, the spatial spectrum vector quantity is carried out with peak detection through an iterative computation to obtain the high-resolution spatial spectrum vector quantity. The objective location can be achieved by taking advantage of the received index value of a peak element through the calculation to gain an objective azimuth angle and an objective pitch angle. The location method has the advantages of being low in the needed data size and calculated amount in the iterative process, suitable for a hardware implementation, high in angular accuracy and improving markedly the spatial resolution.
Description
Technical Field
The invention belongs to the technical field of communication, and further relates to a high-resolution sonar positioning method based on target space sparsity in the field of array signal processing. The invention can effectively solve the problem of insufficient spatial resolution caused by limited aperture of the sonar transducer array and realize high-resolution sonar target positioning.
Background
The energy of the high-frequency electromagnetic wave in the water is rapidly attenuated along with the increase of the frequency, so that the low-frequency sound wave is an effective carrier for transmitting the underwater environment information, and the application and research of the sonar technology are widely concerned. Wherein, the target positioning by utilizing a sonar array is a main aspect of the application of the sonar technology.
At present, sonar target positioning technology mainly comprises a multi-beam forming method and a subspace method.
First, multi-beam forming. For example, an improved three-beam direction finding method is disclosed in "electroacoustic basis 2009, 33 (8): 42-44" article by huichiyuan, royal english, and lina, which is a three-beam direction finding method that performs multi-beam forming on data of all collected channels, obtains a quadratic curve by quadratic fitting using three larger beam forming output values, and locates a target by finding a peak value of the quadratic curve.
Second, the subspace approach. A high-resolution target direction finding method based on subspace decomposition is disclosed in a patent application of a direction finding method applicable to coherent information sources under a non-stationary noise background (application number: 200610113172.5, publication number: 101150345A) proposed by the institute of electronic countermeasure in radar domain of China's liberation military air force equipment. The method overcomes the coherence of a signal source through subarray smoothing, obtains a signal subspace and a noise subspace through characteristic decomposition of an obtained covariance matrix, then forms a spatial spectrum in the signal subspace, and orients a target through spectral peak search of the spatial spectrum, but the method still has the defects that the method reduces the aperture of an array, causes the reduction of spatial resolution, and simultaneously needs to acquire a large amount of data to estimate the covariance matrix, the required data amount is large, and the characteristic decomposition calculation amount in the method is large.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a high-resolution sonar positioning method based on target space sparsity. According to the method, the line-row synthesis is carried out on peak signal-to-noise ratio data of each channel of the sonar array according to the arrangement mode of array elements of the array, a projection matrix from a space spectrum vector to a line-row synthesis data vector is constructed, a high-resolution space spectrum vector is obtained by iteratively optimizing a cost function, peak detection is carried out on the space spectrum vector to obtain the azimuth pitch angle of a target, and therefore the target is positioned.
The method comprises the following specific implementation steps:
(1) collecting data received by each channel of the array and storing the data into a system memory;
(2) matched filtering
2a) Performing matched filtering on the acquired data of each channel by adopting a matched filtering formula;
2b) taking the maximum value of the data after each channel is matched and filtered;
(3) line and row synthesis
3a) Rearranging all the maximum values of the data obtained in the step 2b) on a two-dimensional plane according to the positions of the array elements corresponding to the channels of the data, and obtaining a data matrix as follows:
wherein 0 represents a zero matrix, M1、M2、M3、M4And M5Respectively represent five matrices;
3b) sequentially decimating the matrix M2、M3And M4Rearranging the extracted column vectors into a matrix, and adding all row vectors of the matrix to obtain a row synthesis data vector R;
3c) sequentially decimating the matrix M1、M3And M5Rearranging the extracted row vectors into a matrix, and arranging the matrixAdding all the column vectors to obtain a column synthesis data vector C;
(4) constructing a projection matrix
4a) Calculating projection matrix elements of the orientation dimensional spatial spectrum vector to the row synthesis data vector according to the following formula:
wherein A (r, c) represents the elements of the r-th row and c-th column in the projection matrix of the orientation-dimensional spatial spectrum vector to the row-synthesized data vector, 0 < r < L, L represents the dimension of the row-synthesized data vector in step 3b),n represents the dimension of the orientation dimension space spectrum vector, and j represents an imaginary number unit;
4b) arranging the elements obtained in the step 4a) according to the positions of rows and columns to form a projection matrix from an orientation dimensional space spectrum vector to a row synthesis data vector;
4c) calculating projection matrix elements of the pitch dimension spatial spectrum vector to the column synthesis data vector according to the following formula:
wherein B (h, l) represents the elements of the h row and l column in the projection matrix of the pitch-dimensional spatial spectrum vector to the column synthetic data vector, 0 < h < D, D represents the dimension of the column synthetic data vector in step 3c),k represents the dimension of the space spectrum vector of the pitch dimension, and j represents an imaginary number unit;
4d) arranging the elements obtained in the step 4c) according to the positions of rows and columns to form a projection matrix from the space spectrum vector of the pitch dimension to the column synthesis data vector;
(5) obtaining spatial spectral vectors
5a) Obtaining an orientation dimension spatial spectrum vector by solving the following formula:
wherein alpha represents an orientation-dimensional spatial spectral vector, | non-phosphorpRepresenting the p-norm of the solution vector, | represents the regularization parameter input by the user, | | represents the modulus of the solution vector, R represents the row-synthesized data vector obtained in step 3b), a represents the projection matrix of the orientation-dimensional spatial spectrum vector obtained in step 4a) to the row-synthesized data vector,an operation symbol indicating a minimum value;
5b) obtaining a pitch dimension spatial spectral vector by solving the following formula:
wherein beta represents a pitch-dimensional spatial spectral vector, | non-calculationpRepresenting the p-norm of the solution vector, | representing the regularization parameter input by the user, | | representing the modulus of the solution vector, C representing the column composite data vector obtained in step 3C), B representing the projection matrix of the pitch-dimensional spatial spectrum vector obtained in step 4B) to the column composite data vector,an operation symbol indicating a minimum value;
(6) peak detection
6a) Performing peak detection on the pitch dimensional space spectrum vector obtained in the step 5b) by adopting a threshold comparison method to obtain a peak value element index value of the pitch dimensional space spectrum vector;
6b) performing peak detection on the orientation dimension space spectrum vector obtained in the step 5a) by adopting a threshold comparison method to obtain an index value of a peak element of the orientation dimension space spectrum vector;
(7) target localization
7a) Substituting the index value of the peak value element of the space spectral vector of the pitch dimension obtained in the step 6a) into the following formula to calculate and obtain the pitch angle of the signal source:
wherein,the pitch angle of a signal source is shown, asin represents an arcsine function, lambda represents the wavelength of a system carrier wave, K represents the dimension of a pitch dimension space spectrum vector, d represents the space of system array elements, and u represents the index value of the peak value element of the pitch dimension space spectrum vector;
7b) substituting the index value of the peak value element of the orientation dimension space spectrum vector obtained in the step 6b) and the pitch angle of the signal source obtained in the step 7a) into the following formula to calculate and obtain the azimuth angle of the signal source:
wherein, theta is a signal source azimuth angle, asin represents an arcsine function, lambda represents a system carrier wave length, N represents the dimension of an orientation dimension space spectrum vector, d represents the system array element interval, v represents an index value of an orientation dimension space spectrum vector peak value element,representing the pitch angle of the signal source obtained in step 6 a).
Compared with the prior art, the invention has the following advantages:
first, the present invention can achieve simultaneous multi-target localization by performing peak detection on the high-resolution spatial spectral vectors to perform localization.
Secondly, by constructing a projection matrix from the space spectrum vector to the row-column synthetic data vector, the invention overcomes the correlation of the target signal source under the condition of not reducing the array aperture, and only needs single snapshot data, thereby reducing the required data volume.
Thirdly, the space spectral vector is obtained by adopting an iterative process, so that the method is suitable for hardware implementation and has small calculated amount.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a simulation diagram of the present invention.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
Referring to fig. 1, the specific implementation steps of the present invention are as follows:
step 1, collecting data received by each channel of the array and storing the data into a system memory.
And carrying out AD sampling on baseband receiving signals of channels corresponding to array elements of the sonar array, converting the baseband receiving signals into digital signals, and storing the digital signals obtained by conversion by using storage equipment.
And 2, matching and filtering.
2a) Performing matched filtering on the acquired data of each channel by adopting a matched filtering formula, respectively performing matched filtering on the acquired data of each channel in order to obtain peak signal-to-noise ratio data of each channel, and calculating the data after the matched filtering of the mth channel according to the following formula:
xm(t)＝FT-1[em·s*]
wherein x ism(t) denotes the data after the mth channel matching filtering, t denotes the time domain sampling point, FT-1Representing an inverse Fourier transform, emThe spectrum of the mth channel data is represented, s represents the known reference signal spectrum, represents the conjugate, and represents the vector multiplication.
2b) And taking the maximum value of the data after matched filtering of each channel.
And 3, synthesizing the array.
3a) Rearranging all the maximum values of the data obtained in the step 2b) on a two-dimensional plane according to the positions of the array elements corresponding to the channels of the data, and obtaining a data matrix as follows:
wherein 0 represents a zero matrix, M1、M2、M3、M4And M5Each representing five matrices.
3b) Sequentially decimating the matrix M2、M3And M4The extracted column vectors are rearranged to form a matrix, and all row vectors of the matrix are added to obtain a row synthesis data vector R.
3c) Sequentially decimating the matrix M1、M3And M5And rearranging the extracted row vectors into a matrix, and adding all column vectors of the matrix to obtain a column synthesis data vector C.
3a) Rearranging all the maximum values of the data obtained in the step 2 according to the positions of the channel array elements on the two-dimensional plane shown in the figure 3 to obtain a data matrix.
And 4, constructing a projection matrix.
According to the requirement of spatial resolution, N and K angle units are respectively divided in the azimuth angle range and the pitch angle range of the space where the signal source is located, and due to the fact that space domain sampling and time domain sampling are consistent, a projection matrix from a space spectrum vector to a row-column synthetic data vector is constructed according to a discrete Fourier kernel function.
4a) Calculating projection matrix elements of the orientation dimensional spatial spectrum vector to the row synthesis data vector according to the following formula:
wherein A (r, c) represents the elements of the r-th row and c-th column in the projection matrix of the orientation-dimensional spatial spectrum vector to the row-synthesized data vector, 0 < r < L, L represents the dimension of the row-synthesized data vector in step 3b),n denotes the dimension of the orientation-dimensional spatial spectral vector, and j denotes the imaginary unit.
4b) Arranging the elements obtained in the step 4a) according to the positions of rows and columns to form a projection matrix from the orientation-dimensional space spectrum vector to the row synthesis data vector.
4c) Calculating projection matrix elements of the pitch dimension spatial spectrum vector to the column synthesis data vector according to the following formula:
wherein B (h, l) represents the elements of the h row and l column in the projection matrix of the pitch-dimensional spatial spectrum vector to the column synthetic data vector, 0 < h < D, D represents the dimension of the column synthetic data vector in step 3c),k denotes the dimension of the spatial spectral vector in the pitch dimension, and j denotesImaginary unit.
4d) Arranging the elements obtained in the step 4c) according to the positions of rows and columns to form a projection matrix from the space spectrum vector of the pitch dimension to the column synthesis data vector.
And 5, obtaining a spatial spectrum vector.
The following two equations can be established by the projection matrix of the spatial spectrum vector to the row-column composite data matrix in step 4:
wherein α represents an orientation-dimensional spatial spectrum vector, R represents a row-synthesized data vector obtained in step 3B), a represents a projection matrix of the orientation-dimensional spatial spectrum vector obtained in step 4a) to the row-synthesized data vector, β represents a pitch-dimensional spatial spectrum vector, C represents a column-synthesized data vector obtained in step 3C), B represents a projection matrix of the pitch-dimensional spatial spectrum vector obtained in step 4B) to the column-synthesized data vector, and n represents a noise vector of the system.
The space spectrum vector can be obtained by solving the two equations, and the two equations can be solved by adopting the following method according to the maximum posterior probability estimation theory.
5a) Obtaining an orientation dimension spatial spectrum vector by solving the following formula:
wherein alpha represents an orientation-dimensional spatial spectral vector, | non-phosphorpRepresenting the p-norm of the solution vector, | represents the regularization parameter input by the user, | | represents the modulus of the solution vector, R represents the row-synthesized data vector obtained in step 3b), a represents the projection matrix of the orientation-dimensional spatial spectrum vector obtained in step 4a) to the row-synthesized data vector,the operation sign for obtaining the minimum value is shown.
5b) Obtaining a pitch dimension spatial spectral vector by solving the following formula:
wherein beta represents a pitch-dimensional spatial spectral vector, | non-calculationpRepresenting the p-norm of the solution vector, | representing the regularization parameter input by the user, | | representing the modulus of the solution vector, C representing the column composite data vector obtained in step 3C), B representing the projection matrix of the pitch-dimensional spatial spectrum vector obtained in step 4B) to the column composite data vector,the operation sign for obtaining the minimum value is shown.
The solving of both in step 5a) and step 5b) may be performed by an iterative process as shown in fig. 4.
And 6, peak value detection.
The process of detecting the peak value of the space spectrum vector by adopting a threshold value comparison method is simple, the accuracy of the peak value detection is higher, and the basic process of the threshold value comparison method is as follows:
solving a first-order difference of the space spectrum vector to obtain a difference vector; finding the zero crossing point of the differential vector and recording the zero crossing point index value; setting half of the maximum element value of the spatial spectrum vector as a threshold value; the element with the element median value larger than the threshold value at the zero crossing index value of the space spectrum vector is the peak element, and the index value corresponding to the peak element is the peak element index value of the space spectrum vector.
6a) And 5) performing peak detection on the pitch dimensional space spectrum vector obtained in the step 5b) by adopting a threshold comparison method to obtain a peak value element index value of the pitch dimensional space spectrum vector.
6b) And 5) performing peak detection on the orientation dimension space spectrum vector obtained in the step 5a) by adopting a threshold comparison method to obtain an index value of a peak element of the orientation dimension space spectrum vector.
And 7, positioning the target.
7a) Substituting the index value of the peak value element of the space spectral vector of the pitch dimension obtained in the step 6a) into the following formula to calculate and obtain the pitch angle of the signal source:
wherein,the pitch angle of a signal source is shown, asin represents an arcsine function, lambda represents the wavelength of a system carrier wave, K represents the dimension of a pitch dimension space spectrum vector, d represents the space of system array elements, and u represents the index value of the peak value element of the pitch dimension space spectrum vector;
7b) substituting the index value of the peak value element of the orientation dimension space spectrum vector obtained in the step 6b) and the pitch angle of the signal source obtained in the step 7a) into the following formula to calculate and obtain the azimuth angle of the signal source:
wherein, theta is a signal source azimuth angle, asin represents an arcsine function, lambda represents a system carrier wave length, N represents the dimension of an orientation dimension space spectrum vector, d represents the system array element interval, v represents an index value of an orientation dimension space spectrum vector peak value element,representing the pitch angle of the signal source obtained in step 6 a).
The effect of the present invention can be illustrated by the following simulation experiment:
1. simulation conditions
The operating system is an Intel (R) core (TM) i5CPU6503.20GHz 32-bit Windows operating system, the simulation software adopts MATLAB R (2011a), and the simulation parameter setting is shown in the following table.
| Parameter(s) | Parameter value |
| System carrier frequency | 25kHz |
| System array element spacing | 0.03m |
| Pulse repetition period | 2s |
| Duration of pulse | 85ms |
| Bandwidth of frequency modulation | 1kHz |
| Aperture of array | 0.36m |
| Signal to noise ratio | 25dB |
| Number of targets | 3 |
| Target azimuth | -3.5°，0°，3.5° |
| Target pitch angle | -3.5°，0°，3.5° |
2. Simulation result
Fig. 2(a) shows the spatial spectrum vector obtained by beamforming and the peak element obtained by peak detection, and "∘" in fig. 2(a) shows the peak element. Fig. 2(b) shows the spatial spectral vectors obtained by the subspace decomposition and the peak elements obtained by the peak detection, and "∘" in fig. 2(b) shows the peak elements. Fig. 2(c) shows the spatial spectrum vector obtained by the present invention and the peak element obtained by peak detection, and "∘" in fig. 2(c) shows the peak element. Fig. 2 shows that the beamforming method cannot resolve multiple targets with close spatial positions under the condition that the aperture of the array is limited, and the subspace decomposition method cannot resolve multiple targets with close spatial positions under the condition that the spatial signal source is coherent. The following table specifically illustrates that the azimuth and pitch angles of the three targets are all calculated with high precision.
| Space target | Azimuth angle | Pitch angle |
| Object 1 | -3.44° | -3.47° |
| Object 2 | 0.01° | 0.03° |
| Target 3 | 3.55° | 3.51° |
Claims (3)
1. A high-resolution sonar positioning method based on target space sparsity comprises the following steps:
(1) collecting data received by each channel of the array and storing the data into a system memory;
(2) matched filtering
2a) Performing matched filtering on the acquired data of each channel by adopting a matched filtering formula;
2b) taking the maximum value of the data after each channel is matched and filtered;
(3) line and row synthesis
3a) Rearranging all the maximum values of the data obtained in the step 2b) on a two-dimensional plane according to the positions of the array elements corresponding to the channels of the data, and obtaining a data matrix as follows:
wherein 0 represents a zero matrix, M1、M2、M3、M4And M5Respectively represent five matrices;
3b) sequentially decimating the matrix M2、M3And M4Rearranging the extracted column vectors into a matrix, and adding all row vectors of the matrix to obtain a row synthesis data vector R;
3c) sequentially decimating the matrix M1、M3And M5Rearranging the extracted row vectors into a matrix, and adding all column vectors of the matrix to obtain a column synthesis data vector C;
(4) constructing a projection matrix
4a) Calculating projection matrix elements of the orientation dimensional spatial spectrum vector to the row synthesis data vector according to the following formula:
wherein A (r, c) represents the elements of the r-th row and c-th column in the projection matrix of the orientation-dimensional spatial spectrum vector to the row-synthesized data vector, 0 < r < L, L represents the dimension of the row-synthesized data vector in step 3b),n represents the dimension of the orientation dimension space spectrum vector, and j represents an imaginary number unit;
4b) arranging the elements obtained in the step 4a) according to the positions of rows and columns to form a projection matrix from an orientation dimensional space spectrum vector to a row synthesis data vector;
4c) calculating projection matrix elements of the pitch dimension spatial spectrum vector to the column synthesis data vector according to the following formula:
wherein B (h, l) represents the elements of the h row and l column in the projection matrix of the pitch-dimensional spatial spectrum vector to the column synthetic data vector, 0 < h < D, D represents the dimension of the column synthetic data vector in step 3c),k represents the dimension of the space spectrum vector of the pitch dimension, and j represents an imaginary number unit;
4d) arranging the elements obtained in the step 4c) according to the positions of rows and columns to form a projection matrix from the space spectrum vector of the pitch dimension to the column synthesis data vector;
(5) obtaining spatial spectral vectors
5a) Obtaining an orientation dimension spatial spectrum vector by solving the following formula:
wherein alpha represents an orientation-dimensional spatial spectral vector, | non-phosphorpRepresenting the p-norm of the solution vector, | represents the regularization parameter input by the user, | | represents the modulus of the solution vector, R represents the row-synthesized data vector obtained in step 3b), a represents the projection matrix of the orientation-dimensional spatial spectrum vector obtained in step 4a) to the row-synthesized data vector,an operation symbol indicating a minimum value;
5b) obtaining a pitch dimension spatial spectral vector by solving the following formula:
wherein beta represents a pitch-dimensional spatial spectral vector, | non-calculationpRepresenting the p-norm of the solution vector, | representing the regularization parameter input by the user, | | representing the modulus of the solution vector, C representing the column composite data vector obtained in step 3C), B representing the projection matrix of the pitch-dimensional spatial spectrum vector obtained in step 4B) to the column composite data vector,an operation symbol indicating a minimum value;
(6) peak detection
6a) Performing peak detection on the pitch dimensional space spectrum vector obtained in the step 5b) by adopting a threshold comparison method to obtain a peak value element index value of the pitch dimensional space spectrum vector;
6b) performing peak detection on the orientation dimension space spectrum vector obtained in the step 5a) by adopting a threshold comparison method to obtain an index value of a peak element of the orientation dimension space spectrum vector;
(7) target localization
7a) Substituting the index value of the peak value element of the space spectral vector of the pitch dimension obtained in the step 6a) into the following formula to calculate and obtain the pitch angle of the signal source:
wherein,for the pitch angle of the signal source, asin represents the arcsine function, lambda tableShowing the wavelength of a carrier of the system, K showing the dimension of a pitch dimension space spectrum vector, d showing the space of array elements of the system, and u showing the index value of a peak value element of the pitch dimension space spectrum vector;
7b) substituting the index value of the peak value element of the orientation dimension space spectrum vector obtained in the step 6b) and the pitch angle of the signal source obtained in the step 7a) into the following formula to calculate and obtain the azimuth angle of the signal source:
wherein, theta is a signal source azimuth angle, asin represents an arcsine function, lambda represents a system carrier wave length, N represents the dimension of an orientation dimension space spectrum vector, d represents the system array element interval, v represents an index value of an orientation dimension space spectrum vector peak value element,representing the pitch angle of the signal source obtained in step 6 a).
2. The high-resolution sonar positioning method based on target space sparsity according to claim 1, comprising: the matched filtering formula in step 2a) is as follows:
xm(t)＝FT-1[em·s*]
wherein x ism(t) denotes the data after the mth channel matching filtering, t denotes the time domain sampling point, FT-1Representing an inverse Fourier transform, emThe spectrum of the mth channel data is represented, s represents the known reference signal spectrum, represents the conjugate, and represents the vector multiplication.
3. The high-resolution sonar positioning method based on target space sparsity according to claim 1, comprising: the threshold comparison method in the step (6) is as follows: solving a first-order difference of the space spectrum vector to obtain a difference vector; finding the zero crossing point of the differential vector and recording the zero crossing point index value; setting half of the maximum element value of the spatial spectrum vector as a threshold value; the element with the element median value larger than the threshold value at the zero crossing index value of the space spectrum vector is the peak element, and the index value corresponding to the peak element is the peak element index value of the space spectrum vector.
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| CN106885631B (en) * | 2017-02-17 | 2018-11-30 | 天津大学 | A kind of spectral method of detection based on digital projection |
| CN108931776A (en) * | 2017-05-23 | 2018-12-04 | 常熟海量声学设备科技有限公司 | A kind of high-precision Matched Field localization method |
| CN109541548B (en) * | 2018-11-22 | 2021-06-25 | 西安联丰迅声信息科技有限责任公司 | Air sonar positioning method based on matching field |
| CN109782216B (en) * | 2018-12-26 | 2022-08-23 | 中国电子科技集团公司第二十研究所 | Simple method for searching two-dimensional space spectrum peak |
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| CN111722185B (en) * | 2020-05-15 | 2023-10-13 | 深圳市微纳感知计算技术有限公司 | Characteristic sound positioning method, device and equipment |
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| US7542374B2 (en) * | 2006-09-28 | 2009-06-02 | Teledyne Rd Instruments, Inc. | System and method for acoustic Doppler velocity processing with a phased array transducer including applying correction factors to velocities orthogonal to the transducer face |
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| CN105488772A (en) * | 2016-01-26 | 2016-04-13 | 北京市环境保护监测中心 | Sensor signal peak value detection method |
| CN105488772B (en) * | 2016-01-26 | 2021-02-02 | 北京市环境保护监测中心 | Sensor signal peak value detection method |
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