CN112748376B - Underwater three-dimensional space passive magnetic field positioning method based on MP-MUSIC method - Google Patents
Underwater three-dimensional space passive magnetic field positioning method based on MP-MUSIC method Download PDFInfo
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- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
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Abstract
The invention discloses an underwater three-dimensional space passive magnetic field positioning method based on an MP-MUSIC method, and belongs to the field of underwater passive magnetic field positioning. The underwater magnetic field source target positioning method mainly positions the underwater magnetic field source target, can overcome underwater interference, and ensures that accurate positioning can be realized in a complex marine environment. The positioning method adopts the magnetic sensor receiving array, has the advantages of small volume, portability and arrangement, reduces the calculation complexity by optimizing the MP-MUSIC algorithm, realizes the quick optimization approach of the positioning algorithm path, realizes the accurate positioning in the complex large-scene marine environment by two processes of fuzzy positioning and refined positioning, and has the positioning accuracy reaching the meter order of magnitude in a detection area of one hundred meters. The technology can be applied to positioning of the leakage position of the submarine power supply cable, detection and tracking of the moving position of an underwater vehicle, the position of a frogman and the like, and has a great application value.
Description
Technical Field
The invention relates to an underwater three-dimensional space passive magnetic field positioning method, in particular to an underwater three-dimensional space passive magnetic field positioning method based on an MP-MUSIC method, and belongs to the field of underwater magnetic field positioning.
Background
The traditional underwater detection positioning technology is mainly sonar detection, but the underwater sound propagation environment in a shallow sea water area is extremely deteriorated and is strongly interfered by echo reverberation of sonar, so that effective identification and tracking of a target cannot be realized. The underwater electromagnetic field is not easily influenced by environmental factors, and the target detection in shallow sea water areas is extremely advantageous. Underwater detection and communication based on electromagnetic field are used as an effective supplement of sound detection, and research surge is raised in scientific research institutions of various countries in recent years. The underwater target electromagnetic field positioning technology is a technology that a magnetic sensor equipped on a positioning device is used as an electromagnetic field signal receiving array, and an excitation magnetic field signal generated by a positioning target is measured and processed to estimate a target space position parameter.
In the last 70 th century, kuipers, raab proposed locating objects using electromagnetic tracking, and Kuipers et al used this magnetic field to locate objects by controlling the current in electrical coils to create a swinging magnetic field around the pointer vector. The northwest university of 2012 tenses, and li bin adopts an electromagnetic vector sensor to estimate DOA and polarization parameters of a plurality of signal sources in seawater, and based on a TLS-ESPRIT algorithm, successfully distinguishes 5 uncorrelated monochromatic underwater electromagnetic field sources. In 2014, the method for positioning the magnetic dipole by the Gong balance of the reworking group 710 of the Chinese ship by utilizing the magnetic field vector and the magnetic field tensor data improves the original single-point magnetic tensor, and the new magnetic tensor measurement system has higher underwater target positioning accuracy. In 2018, xulongfei, zheng Qusong and the like of the university of northwest industry research the problem of positioning underwater non-transparent objects by an electromagnetic field by adopting a total field-scattering field source adding technology in a time domain finite difference method of a shift operator, so that the calculation efficiency is improved, and the calculation time is shortened.
The underwater target electromagnetic field positioning technology utilizes measurement electromagnetic field signals to realize target positioning, and the equipment sensors only need a certain number of magnetic sensors, are easier to carry and set, and have lower cost compared with optical detection equipment and underwater acoustic detection equipment. The underwater electromagnetic field positioning technology has a good application scene in the detection and tracking of the shallow sea underwater target, so that the innovative exploration and the deep research on the related technical problems of the underwater electromagnetic field positioning still have important scientific research value and practical technical application significance.
Disclosure of Invention
The invention provides an underwater three-dimensional space passive magnetic field positioning method based on an MP-MUSIC optimization algorithm, which has strong magnetic resistance and interference resistance, can overcome underwater interference, and can accurately position a magnetic dipole source target in an underwater environment through algorithm inversion.
The purpose of the invention is realized by the following steps:
an underwater three-dimensional space passive magnetic field positioning method based on an MP-MUSIC method is characterized by comprising the following steps:
(1) In the length of L meterIn the underwater environment within the range of the positioning area with the width of W meters and the height of H meters, the positioning target is n magnetic dipole sources, and the magnetic dipole moment direction is
The magnetic dipole source is positioned
Arranging a circular magnetic sensor array underwater, wherein the number of the sensors is k, and the positions of sensor array elements are
I is more than or equal to 1 and less than or equal to k, the distance vector from the magnetic dipole source to the sensor array element is
(2) The magnetic induction intensity of the magnetic dipole source in the three-dimensional space measured by each magnetic sensor is as follows:
μ r for relative permeability, mu 0 Permeability of 4 pi x 10 in vacuum -7 H/m, N' is the number of turns of the coil in the closed current loop, I is the closed current for generating the magnetic dipole source, R is the radius of the coil, N i For underwater interference, T represents matrix transposition, and gain matrix is defined as a i (r i ) Let B i ＝a i (r i )m+n i The magnetic induction including three directions of intensity
Wherein
(3) Storing the magnetic induction intensity data measured by the k magnetic sensor array into an array
Where B is i Is the ith array element testThe magnetic induction of the quantity, D is a 3k × 1 matrix, and the array constituted by the gain matrix is A = [ a ] 1 T (r 1 ),a 2 T (r 2 ),…,a k T (r k )] T Where a is i (r i ) Is the gain matrix corresponding to the ith array element, A is 3k × 3 matrix, the corresponding matrix form operation relationship is D = Am + N,
is an underwater disturbance;
(4) Solving the covariance matrix R DD ＝E{DD H Where R is DD Is a 3k x 3k order matrix, H represents the conjugate transpose, E {. Cndot. } represents the desired operation, and R is obtained by matrix transformation DD ＝AE{mm H }A H +σ 2 I, where σ 2 I is a 3k multiplied by 3k order unit matrix for interference noise power;
(5) For covariance matrix R DD Decomposing the characteristic value to obtain R DD ＝U∑U H Where U is a 3k × 3k order eigenvector matrix and Σ is a diagonal matrix λ consisting of eigenvalues 1 ≥λ 2 ≥…λ 3k ≧ 0, defined by λ 1 ,λ 2 ,…λ n Form a one-dimensional matrix sigma S From λ n+1 ,λ n+2 ,…,λ 3k Form a one-dimensional matrix sigma N N magnetic dipole sources;
(6)∑ S the characteristic vector group corresponding to the medium characteristic value is defined as U S ，∑ N The feature vector group corresponding to the medium feature value is defined as U N Then U = [ U ] may be represented S ,U N ]Wherein U is S Is a signal subspace, U N Is a noise subspace, an orthogonal projection matrix P of the signal subspace is obtained 3k×3k ⊥ ＝I-U S U S H ；
(7) Calculating the target function of the MP-MUSIC algorithm as the minimum lambda of the generalized characteristic decomposition min (A H P 3k×3k ⊥ A,A H A)；
(8) The process of traversing and solving the minimum characteristic value by the optimized MP-MUSIC algorithm is divided into a fuzzy traversal process and a refining traversal process, the traversal process traverses all positions in a positioning area and searches for the globally minimum generalized characteristic value, and the method comprises the following steps:
(8-1) fuzzy traversal process: dividing the target location area into N × M × K volumes
The center point position of the region block
Representing the region, j is more than or equal to 1 and less than or equal to NxMxK, r tj Including position information of fuzzy traversal process, distance vector from magnetic dipole source to sensor array element
Traverse r t1 ,r t2 ,…,r tN×M×K Calculating a gain matrix A, substituting the gain matrix A into the generalized minimum eigenvalue lambda for solving different position points min (A H P 3k×3k ⊥ A,A H A) The central point corresponding to the minimum characteristic value is the target position obtained by fuzzy traversal, and the area block where the position is located is the area block where the target is likely to appear in the whole situation;
(8-2) refining the traversal process: the area block which is possibly generated by the target and is solved by the fuzzy traversal process is taken as a new positioning area of the target, and the area is subdivided into NN multiplied by MM multiplied by KK volumes
Traversing the position of the central point of the area block according to the step (8-1) to find the minimum characteristic value;
(8-3) when the refinement traversal process is finished, the minimum characteristic value is the global minimum generalized characteristic value;
(9) And the characteristic value corresponding point is the position of the target magnetic dipole source estimated by the MP-MUSIC algorithm, the algorithm is finished, and the positioning is completed.
The invention also includes such features:
in the step (1), k magnetic sensor arrays;
in step (7), the objective function is λ min (A H P 3k×3k ⊥ A,A H A) Therefore, the position of the target source can be located by finding the minimum characteristic value;
and (8) positioning through a fuzzy traversal process and a refining traversal process.
Compared with the prior art, the invention has the beneficial effects that:
the receiving array of the multi-polarization circular magnetic sensor is adopted, so that the sensitivity is high, the magnetic field signal is accurately received, the effective receiving and estimation of the magnetic field signal in any direction polarization mode of a radiation source are ensured, the volume of the magnetic sensor array is small, the power consumption is low, the chip packaging is basically realized, the carrying is convenient, and the setting is easy; the optimized MP-MUSIC algorithm has clear steps, stable performance, small calculation complexity and calculation amount, higher calculation speed than that of a common algorithm, can realize quick positioning, overcomes underwater interference and ensures high precision. The technology can be applied to positioning of the leakage position of the submarine cable, the moving position of an underwater vehicle, detection of the position of a frogman and the like, and has a great application value.
Drawings
FIG. 1 is a schematic view of a positioning device within a positioning area;
FIG. 2 is a schematic diagram of a receiving array arrangement for k magnetic induction sensors;
FIG. 3 is an overall flowchart of the method for positioning the passive magnetic field in the underwater three-dimensional space based on the MP-MUSIC algorithm;
FIG. 4 is a flow chart for fuzzy traversal;
FIG. 5 is a flow diagram for a refinement traversal.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and specific embodiments.
Example 1: an underwater detection region shown in the figure 1 is constructed by using simulation software, and a three-dimensional space coordinate axis is established, wherein the length unit is m. At coordinates (7, 0, 2) a magnetic dipole source is arranged, with the direction vector of the magnetic dipole moment set to (0, 1). The receiving magnetic sensors are arranged according to a k magnetic sensor receiving array in fig. 2, the radius of the receiving array is taken as 20m, and the height difference of each annular array is taken as 9m. And (3) acquiring the magnetic induction intensity data of the receiving sensor in a simulation manner, and adding Gaussian white noise to simulate underwater interference. Supposing that the position of a target magnetic dipole source is unknown, scrambling data is obtained through a magnetic sensor receiving array, the data is substituted into an optimized MP-MUSIC positioning algorithm program to obtain an optimal estimated position, the optimal estimated position is compared with a target source position (7, 0, 2) set by simulation, and finally whether the positioning algorithm can meet the index requirement is judged. The method comprises the following specific steps:
s100: in a relative magnetic permeability of
The seawater in which a magnetic dipole source to be positioned is arranged consists of a closed electrified coil, the number of turns of the coil is 1, the current of a closed circuit is 1A, and the radius of the coil is 1m.
S200:24 magnetic sensor array as shown in fig. 2, each of the magnetic sensor arrays has 8 magnetic sensors, the radius of the receiving array is 20m, the height difference of each of the annular arrays is 9m, and the coordinate positions of the receiving magnetic sensors 1,2, \ 8230;, 24 are set to (0, 20, 19), (14.1421, 19), (20, 0, 19), (14.1421, -14.1421, 19), (0, -20, 19), (-14.1421, -14.1421, 19), (0, 20, 19), (-14.1421, 19), (0, 20, 10), (14.1421, 10), (20, 0, 10), (14.1421, -14.1421, 10), (0, -20, 10), (-14.1421, 10), (-20, 0, 10), (-14.1421, 10), (0, 20, 1), (14.1421, 1), (20, 0, 1), (14.1421, -14.142, 1), (20, 0, 1), (-14.1421, 1), (-20, 0, 1), (-14.1421, 1). The magnetic sensor array measures magnetic induction intensity, so the array measurement data is written as D = [ B = 1 T ,B 2 T ,…,B k T ] T ，B i The magnetic induction measured for the magnetic sensor array element i. In order to simulate underwater interference, gaussian white noise n is added into the measured magnetic induction intensity data i ，B i And n i The signal-to-noise ratio of (A) is 20dB, so the measured data is B i ＝B i +n i The magnetic induction in the x direction in this example was measured to be [ -3.767 × 10 [ ] -5 ,3.328×10 -5 ,8.219×10 -5 ,3.032×10 -5 ,1.482×10 -5 ,-1.734×10 -5 ,-6.580×10 -5 ,-2.584×10 -5 ,1.366×10 -5 ,2.928×10 -5 ,1.147×10 -4 ,4.208×10 -5 ,2.009×10 -6 ,-2.928×10 -5 ,-9.329×10 -5 ,9.495×10 -6 ,1.185×10 -4 ,-3.741×10 -5 ,-7.039×10 -5 ,-5.529×10 -5 ,-3.327×10 -5 ,7.069×10 -5 ,-7.591×10 -6 ,-4.295×10 -6 ]。
S310: the positioning process is shown in FIG. 3, and the existing magnetic induction data D is measured w And substituting the data into an MP-MUSIC optimization algorithm. Setting the position of a magnetic dipole source to be positioned as r t ＝[x t ,y t ,z t ]Magnetic dipole moment direction of m = [0, 1 =] T 。
S320: for measured data D w To calculate the covariance matrix R DwDw Decomposition of eigenvalues to yield R DwDw ＝U∑U H Splitting the eigenvector component into signal subspaces U S Sum noise subspace U N Determining the signal subspace orthographic projection P k×k ⊥＝I-U S U S H And I is a k multiplied by k order identity matrix.
S330: solving for the minimum eigenvalue λ at the updated estimated position min (A w H P k×k ⊥ A w ,A w H A w ) In order to accurately position the target, the operation of updating the estimated position solution characteristic value is divided into a fuzzy traversal process and a detailed traversal process, and the specific operations are as follows:
s331: the fuzzy traversal process is as shown in fig. 4, the length, the width and the height of the underwater detection region as shown in fig. 1 are respectively divided into 20, 20 and 4 blocks to form 1600 5 × 5 × 5 cube region blocks, the central point position of each region block is used as the possible occurrence position of the target source, and the search of the global fuzzy minimum characteristic value is carried out. Calculating the vector r from each magnetic sensor array element to the central point position i Obtaining a gain matrix A, selecting the measurement data D from the x direction w Calculated P k×k ≥ And a gain matrix A corresponding to the direction w Calculating a generalized eigenvalue λ (A) w H P k×k ≥ A w ,A w H A w ) Traversing all central points, sequencing feature values from small to large to obtain the minimum feature value of 0.596, finding a position point corresponding to the minimum feature value, and finding the optimal estimation position r after the fuzzy traversal process t1 ＝[7.5,-2.5,2.5]。
S332: the thinning traversal process is as shown in fig. 5, the area block where the target source is located obtained in the fuzzy traversal process is used as the target positioning area in the thinning traversal process, and on the basis, the target source is accurately positioned. Dividing a 5 multiplied by 5 cubic region block into 255 cubic region blocks of 1 multiplied by 1, continuously taking the central point of each region block as a point which can appear in a target, traversing all points according to a fuzzy traversal process to solve a minimum characteristic value d to obtain a minimum characteristic value of 0.565, finding out an optimal estimation position r obtained in a thinning traversal process t2 ＝[6.5,-0.5,2.5]。
S400: after fuzzy traversal and refinement traversal, the position r of the final positioning target magnetic dipole source is obtained t ＝[6.5,-0.5,2.5]And the positioning precision reaches 1m.
S500: comparing the actual magnetic dipole source position (7, 0, 2) with the magnetic dipole source position r estimated by the positioning algorithm t ＝[6.5,-0.5,2.5]The positioning precision within the range of the positioning area in the figure 1 reaches 1m, and the high-precision positioning requirement is met; the minimum characteristic value is solved twice through fuzzy traversal and detailed traversal, the optimal position of the target source is searched, and the fast optimization approach of the positioning algorithm path is realized; and magnetic induction intensity data with the signal-to-noise ratio of 20dB is received, the positioning error can be controlled within 1%, and the advantage of overcoming underwater interference is met.
In conclusion: the invention discloses an underwater three-dimensional space passive magnetic field positioning method based on an MP-MUSIC optimization algorithm, and belongs to the field of underwater passive magnetic field positioning. The invention mainly positions the underwater magnetic field source target, can overcome underwater interference and ensure that accurate positioning can be realized in a complex marine environment. The positioning method adopts the magnetic sensor receiving array, has the advantages of small volume, portability and arrangement, reduces the calculation complexity by optimizing the MP-MUSIC algorithm, realizes the quick optimization approach of the positioning algorithm path, realizes the accurate positioning in the complex large-scene marine environment by two processes of fuzzy positioning and refined positioning, and has the positioning accuracy reaching the meter order of magnitude in a detection area of one hundred meters. The technology can be applied to positioning of the electric leakage position of the submarine power supply cable, detection and tracking of the moving position of an underwater vehicle, the position of a frogman and the like, and has a great application value.
Claims (3)
1. An underwater three-dimensional space passive magnetic field positioning method based on an MP-MUSIC method is characterized by comprising the following steps:
(1) In the underwater environment in the positioning area range with the length of L meters, the width of W meters and the height of meter, the positioning targets are n magnetic dipole sources, and the magnetic dipole moment direction is
The magnetic dipole source is positioned
Arranging a circular magnetic sensor array underwater, wherein the number of the sensors is k, and the positions of sensor array elements are
The distance vector from the magnetic dipole source to the sensor array element is
(2) The magnetic induction intensity of the magnetic dipole source in the three-dimensional space measured by each magnetic sensor is as follows:
μ r for relative permeability, mu 0 Permeability of 4 pi x 10 in vacuum -7 H/m, N' is the number of turns of the coil of the closed current loop, I 0 For generating a closed current for a magnetic dipole source, R is the coil radius, n i Is waterLower interference, T represents matrix transposition, and gain matrix is defined as a i (r i ) Let B i ＝a i (r i )m+n i The magnetic induction includes intensities in three directions, i.e.
Wherein
(3) Storing the magnetic induction intensity data measured by the k magnetic sensor arrays into an array D = [ B = 1 T ,B 2 T ,…,B k T ] T Where B is i Is the magnetic induction intensity measured by the ith array element, D is a 3k multiplied by 1 matrix, and the array formed by the gain matrix is A = [ a ] 1 T (r 1 ),a 2 T (r 2 ),…,a k T (r k )] T Where a is i (r i ) Is the gain matrix corresponding to the ith array element, A is 3k × 3 matrix, the corresponding matrix form operation relationship is D = Am + N,
is an underwater disturbance;
(4) Solving the covariance matrix R DD ＝E{DD H Here R DD Is a 3k x 3k order matrix, H represents the conjugate transpose, E {. Cndot. } represents the desired operation, and R is obtained by matrix transformation DD ＝AE{mm H }A H +σ 2 I, wherein σ 2 I is a 3k multiplied by 3k order identity matrix for interference noise power;
(5) For covariance matrix R DD Decomposing the characteristic value to obtain R DD ＝U∑U H Where U is a 3k × 3k order eigenvector matrix and Σ is a diagonal matrix λ consisting of eigenvalues 1 ≥λ 2 ≥…λ 3k Is ≥ 0, defined by λ 1 ,λ 2 ,…λ n Form a one-dimensional matrix sigma S From λ n+1 ,λ n+2 ,…,λ 3k Form a one-dimensional matrix∑ N N magnetic dipole sources;
(6)∑ S the feature vector group corresponding to the medium feature value is defined as U S ，∑ N The characteristic vector group corresponding to the medium characteristic value is defined as U N Then, it can represent U = [ ] S ,U N ]Wherein U is S Is a signal subspace, U N Is a noise subspace, an orthogonal projection matrix P of the signal subspace is obtained 3k×3k ⊥＝I-U S U S H ；
(7) Calculating the target function of the MP-MUSIC algorithm as the minimum lambda of the generalized characteristic decomposition min (A H P 3k×3k ⊥ A,A H A)；
(8) The process of traversing and solving the minimum characteristic value by the optimized MP-MUSIC algorithm is divided into a fuzzy traversal process and a refining traversal process, the traversal process traverses all positions in a positioning area and searches for the global minimum generalized characteristic value, and the steps are as follows:
(8-1) fuzzy traversal process: dividing the target location area into N × M × K volumes
The center point position of the region block
Representing the region, j is more than or equal to 1 and less than or equal to NxMxK, r tj Including position information of fuzzy traversal process, distance vector from magnetic dipole source to sensor array element
Traverse r t1 ,r t2 ,…,r tN×M×K Calculating a gain matrix A, substituting the gain matrix A into the generalized minimum eigenvalue lambda for solving different position points min (A H P 3k×3k ⊥ A,A H A) The central point corresponding to the minimum characteristic value is the target position obtained by fuzzy traversal, and the area block where the position is located is the area block where the target is likely to appear in the whole situation;
(8-2) refining the traversal process: will blurThe target possible area block solved by the traversal process is used as a new target positioning area, and the area is subdivided into NN multiplied by MM multiplied by KK volumes
Traversing the position of the central point of the area block according to the step (8-1) to find the minimum characteristic value;
(8-3) when the refinement traversal process is finished, the minimum characteristic value is the global minimum generalized characteristic value;
(9) And the characteristic value corresponding point is the position of the target magnetic dipole source estimated by the MP-MUSIC algorithm, the algorithm is finished, and the positioning is completed.
2. The method for underwater three-dimensional passive magnetic field positioning based on MP-MUSIC method as claimed in claim 1, wherein in step (7), the objective function is λ min (A H P 3k×3k ⊥ A,A H A) Therefore, the position of the target source can be located by finding the minimum feature value.
3. The MP-MUSIC method based underwater three-dimensional passive magnetic field positioning method of claim 1, wherein in step (8), the positioning is performed by fuzzy traversal process and refinement traversal process.
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