CN111027166A - Method for rapidly analyzing ocean elements in sea area around boat position - Google Patents
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Abstract
The invention discloses a method for rapidly analyzing ocean elements in the sea area around a boat position, which comprises the following steps: (1) carrying out interpolation processing on temperature and salt flow data acquired by a naval vessel track, and further processing to obtain an ocean temperature and salt flow distance matrix; (2) performing empirical orthogonal function decomposition on the ocean temperature and salinity flow distance flat matrix to obtain a modal result; (3) carrying out significance test on the modal result, and judging whether the modal result has physical significance or not to obtain an effective modal result; (4) establishing a target functional by using the effective modal result, solving a minimum value of the target functional, and constructing a real-time analysis model; (5) and (3) substituting the modal result obtained by the decomposition in the step (2) into the real-time analysis model to obtain a real-time analysis result of the ocean temperature and salt flow elements of the sea area around the ship position, so that the real-time prediction of the ocean temperature and salt flow elements of the sea area around the ship position is realized when the naval ship sails in the unknown sea area. The invention carries out decomposition analysis on the four-dimensional temperature and salt flow field by an empirical orthogonal function method, thereby realizing real-time analysis on ocean temperature and salt flow factors in the sea area around the boat position.
Description
Technical Field
The invention relates to real-time analysis of ocean elements, in particular to a method for rapidly analyzing ocean elements in the sea area around a boat position.
Background
In all parts of the world, abnormal climates can be seen, wherein the influence of oceans on the climate is particularly important, and particularly the real-time change trend and the characteristics of ocean temperature salt flow are extremely important for military decisions, exercises and the like. However, in the past ocean thermal salt current analysis, because continuous, large-range and real-time ocean survey data are lacked, observation data or non-real-time data of sporadic regions and sites are often analyzed, the method is poor in representativeness, and the reliability of the obtained analysis result is low, so that military and civil requirements of the current society are difficult to meet, few real-time analysis and research on the ocean thermal salt current are needed, further sufficient knowledge on the real-time distribution rule and the flow characteristic of the ocean thermal salt current is lacked, and if the real-time distribution rule and the flow characteristic of the ocean thermal salt current can be known and mastered, the real-time analysis on the ocean thermal salt current has important significance.
In recent years, satellite observation remote sensing technology and naval vessel observation technology develop rapidly, and continuous and real-time ocean temperature observation data can be obtained, so that the ocean temperature and salt flow can be reasonably analyzed by adopting a new analysis method, namely an Empirical Orthogonal Function (EOF) method, and an ocean temperature and salt flow element space-time four-dimensional orthogonal mode is obtained, and the mode not only effectively considers the correlation between the same element and different space-time points, but also effectively considers the thermodynamic correlation between different elements. By using the method, the precision and the level of analysis can be effectively improved, and certain help is provided for the development of marine military.
Disclosure of Invention
The invention aims to overcome the defects in the prior art and provides a method for rapidly analyzing ocean elements in the sea area around a ship position. The invention carries out decomposition analysis on the four-dimensional temperature salt flow field by an Empirical Orthogonal Function (EOF) method, thereby realizing real-time analysis on ocean temperature salt flow elements in the sea area around the boat position.
The technical scheme adopted by the invention is as follows: a method for rapidly analyzing ocean elements in the sea area around a boat position comprises the following steps:
step 1, carrying out interpolation processing on temperature and salt flow data acquired by a naval vessel track, and further processing to obtain an ocean temperature and salt flow range matrix;
step 2, performing empirical orthogonal function decomposition on the ocean temperature and salinity flow distance matrix obtained by processing in the step 1 to obtain a modal result;
step 3, carrying out significance test on the modal result obtained by decomposition in the step 2, and judging whether the modal result obtained in the step 2 has physical significance to obtain an effective modal result;
step 4, establishing a target functional by using the effective modal result obtained in the step 3, solving a minimum value of the target functional, and constructing a real-time analysis model;
and 5, substituting the modal result obtained by decomposing in the step 2 into the real-time analysis model obtained by constructing in the step 4 to obtain a real-time analysis result of the ocean temperature and salinity flow elements of the sea area around the ship position, so as to realize the real-time prediction of the ocean temperature and salinity flow elements of the sea area around the ship when the ship navigates in the unknown sea area.
Further, in step 1, the interpolation processing of the temperature and salt flow data acquired by the ship track to obtain the range-flat result of the temperature and salt flow data includes:
forming an ocean temperature saline flow matrix X from temperature saline flow data acquired by ocean satellites and track observation, performing interpolation processing on the ocean temperature saline flow matrix X, and performing pitch processing on interpolation results to obtain an ocean temperature saline flow pitch matrix X';
ocean temperature salt flow matrix X adopts XabNote that the ocean temperature salt flow matrix X 'is X'abAnd then:
in the formula, xab(a 1.. m; b 1.. n) represents the warm saline flow element of the original data at the time point of the a-th spatial position b, yab(a 1.. multidot.m; b 1.. multidot.n) represents the temperature salt flow at the time point b from the level data at the spatial position aAnd (4) element.
Further, in step 2, performing empirical orthogonal function decomposition on the ocean temperature and salt flow distance flat matrix obtained by processing in step 1 to obtain a modal result includes:
step 2-1, in the empirical orthogonal function decomposition, regarding the ocean temperature and salinity gradient matrix X 'obtained in step 1 as a two-dimensional random process X' (P ', T') depending on the spatial position P 'and the time T', and regarding the values X '(P', T ') of the two-dimensional random process X' (P ', T') at m spatial positions and n time pointsi',Tj') (i ═ 1,. ·, m; j 1.. n) are all random variables;
x '(P', T ') is represented by X'ijThen the random variable X' (P)i,Tj) (i 1.., m; j 1.. n) is represented by a matrix as:
in formula (II), X'ijRepresenting a range-flat matrix represented by a two-dimensional random process in time space, cij(i 1.. m; j 1.. n) represents the warm saline flow element at the j time point of the ith spatial position, wherein m elements in each column represent the warm saline flow elements at different spatial positions at the same time point, and n elements in each row represent the warm saline flow elements at different time points at the same spatial position;
step 2-2, representing each distance matrix X 'in a time-space two-dimensional random process'ijExpressed as the sum of the products of m "values" dependent only on spatial position and n "values" dependent only on time, i.e.
Wherein P represents a spatial mode matrix, T represents a time coefficient matrix, PikValue of the temperature salt flow element, t, representing different spatial positions at the same timekjRepresenting the temperature and salt flow element values at different moments at the same position;
then, the ocean temperature salt flow range matrix X' is expressed as the product of the matrices:
X'＝PT (4)
obtaining an irrelevant space modal matrix P and a time coefficient matrix T between each row of vectors, and arranging each row of vectors in the time coefficient matrix T from large to small according to the corresponding eigenvalue to form a principal component vector;
step 2-3, solving the spatial modal matrix P by adopting a Jacobi method, and calculating a sea temperature salt flow distance-flat matrix X ' and a transposed matrix X ' of the sea temperature salt flow distance-flat matrix 'TThe product of (c), constitutes the Jacobi matrix S:
step 2-4, calculating the eigenvalue and the eigenvector of the Jacobi matrix S, wherein the space modal matrix P is obtained after the eigenvector of the Jacobi matrix S is arranged from large to small according to the magnitude of the eigenvalue; the spatial mode matrix P, the Jacobi matrix S and a diagonal matrix Lambda formed by eigenvalues of the Jacobi matrix S satisfy the relationship:
S×P＝P×Λ (6)
multiplying both sides of formula (6) by P simultaneouslyTObtaining:
PTX'＝PTPT (7)
the obtained space mode matrix P is an orthogonal matrix and satisfies PPTIf I, then equation (7) is modified as:
T＝PTX' (8)
calculating according to a formula (8) to obtain a time coefficient matrix T, wherein each row of values in the time coefficient matrix T represents a time coefficient of a corresponding mode;
and 2-5, multiplying the spatial mode matrix P obtained by calculation in the step 2-4 by the time coefficient matrix T to form a new ocean temperature salt flow range matrix X ', and comparing the new ocean temperature salt flow range matrix X ' with a decomposed ocean temperature salt flow range matrix X ' shown in a formula (4), and verifying that the empirical orthogonal function decomposition method has feasibility.
Further, in step 3, the significance test is performed on the modal result obtained by decomposing in step 2, and whether the modal result obtained in step 2 has a physical significance is determined, and obtaining an effective modal result includes: and (3) checking whether the spatial modal matrix P obtained by decomposing in the step (2) has physical significance by adopting the error range of the calculated characteristic value, specifically:
the error range of the characteristic value is as follows:
wherein n is a time point, ezIs an intermediate variable, λzCharacteristic values of the Jacobi matrix S;
if λz-λz-1>ezThe spatial modes corresponding to the two characteristic values are considered to be valuable;
after verification, the first r spatial modes pass significance verification, and then the first r spatial modes are considered as effective spatial modes.
Further, in step 4, the establishing of the target functional by using the effective modal result obtained in step 4, and the minimum value of the target functional, and the establishing of the real-time analysis model includes:
constructing a characteristic vector matrix A by using the effective space mode obtained in the step 3, and assuming that an analysis result obtained by a real-time analysis model is AaAnd then:
in the formula (I), the compound is shown in the specification,
represents the mean value of each row element of the feature vector matrix a,
is the deviation of the analysis value from the mean value, where σ is the standard deviation matrix;
let H be the projection operator, construct the cost functionJ(Aa):
In the formula, AbRepresenting the initial field, derived from equation (11):
the real-time analysis model obtained from equation (12) is:
Aa＝(HTH)-1HTAb(13)
in the formula, AaThe analysis result obtained for the real-time analysis model.
The invention has the beneficial effects that: (1) the ocean temperature salt flow element space-time four-dimensional orthogonal mode obtained by the method not only effectively considers the correlation between different space-time points of the same element, but also effectively considers the dynamic thermal correlation between different elements. (2) The satellite observation is combined with the track observation, and a comprehensive temperature and salt flow initial field of the system can be obtained. (3) The invention adopts a correlation coefficient matrix instead of a background field error covariance matrix, and the correlation coefficient matrix not only uses a distance sample, but also uses the standard deviation of each element for normalization and standardization, thereby being beneficial to decomposing the orthogonal mode of each element dynamic matching. (4) The data processing in the early stage is possibly complicated, but the calculated amount is greatly reduced after the real-time analysis model is obtained, so that the labor cost is reduced, and the operation requirement of a computer is lowered. And fifthly, the prediction and analysis level of China to the unknown deep sea field can be improved, so that a safe marine environment is constructed.
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FIG. 1: the invention discloses a flow schematic diagram of a method for rapidly analyzing marine factors in the sea area around a boat position.
Detailed Description
In order to further understand the contents, features and effects of the present invention, the following embodiments are illustrated and described in detail with reference to the accompanying drawings:
the invention relates to an innovation of the original ocean temperature and salt flow element analysis, in particular to a method for analyzing temperature and salt flow data acquired by a ship position track at a current time period by using an Empirical Orthogonal Function (EOF), and interpolating the temperature and salt flow data to a peripheral sea area profile by a data assimilation means to construct an ocean temperature, salinity and flow rate statistical real-time analysis model.
As shown in the attached figure 1, a method for rapidly analyzing marine elements in the sea area around a boat position comprises the following steps:
(1) carrying out interpolation processing on temperature and salt flow data acquired by a naval vessel track, and further processing to obtain a distance and level result of the temperature and salt flow data
Firstly, temperature and salinity flow data acquired from high-resolution marine satellites and track observation form a marine temperature and salinity flow matrix X, the marine temperature and salinity flow matrix X is subjected to interpolation processing, and then the interpolation result is subjected to range flattening processing to obtain a marine temperature and salinity flow range flattening matrix X'.
Ocean temperature salt flow matrix X adopts XabNote that the ocean temperature salt flow matrix X 'is X'abAnd (4) showing. Each data in the ocean temperature and salinity flow range matrix X' is the average value of the original data of the point minus different moments of the position, namely:
in the formula, xab(a 1.. m; b 1.. n) represents the warm saline flow element of the original data at the time point of the a-th spatial position b, yab(a 1.. m; b 1.. n) represents the warm saline flow element at the b-th time point from the plateau data at the a-th spatial position.
(2) Performing empirical orthogonal function decomposition on the ocean temperature and salt flow distance flat matrix to obtain a modal result
Next, a specific procedure of the empirical orthogonal function decomposition will be described.
① in the empirical orthogonal function decomposition, the ocean temperature salt flow distance flat matrix X ' obtained in (1) is regarded as a two-dimensional random process X ' (P ', T ') depending on the space position P ' and the time T ', and the two-dimensional random process X ' (P ', T ') is at m space positions and n space positionsValue X' at point in time (P)i',Tj') (i ═ 1,. ·, m; j 1.. n) are all random variables.
X '(P', T ') is represented by X'ijThen the random variable X' (P)i,Tj) (i 1.., m; j 1.. n) is represented by a matrix as:
in formula (II), X'ijRepresenting a range-flat matrix represented by a two-dimensional random process in time space, cij(i 1.. m; j 1.. n) represents the warm saline flow element at the j time point of the ith spatial position, wherein m elements in each column represent the warm saline flow elements at different spatial positions at the same time point, and n elements in each row represent the warm saline flow elements at different time points at the same spatial position;
② further represent each of the pitch matrices X 'in a time-space two-dimensional random process'ijExpressed as the sum of the products of m "values" dependent only on spatial position and n "values" dependent only on time, i.e.
Wherein P represents a spatial mode matrix, T represents a time coefficient matrix, PikValue of the temperature salt flow element, t, representing different spatial positions at the same timekjIndicating the values of the warm saline flow element at different times at the same location.
Then, the ocean temperature salt flow range matrix X' is expressed as the product of the matrices:
X'＝PT (4)
thus, a spatial mode matrix P and a time coefficient matrix T which are not related (orthogonal) between each row vector are obtained, and each row vector in the time coefficient matrix T is arranged from large to small according to the corresponding eigenvalue to form a principal component vector.
③, solving the spatial modal matrix P by adopting a Jacobi method, and calculating a sea temperature salt flow distance flat matrix X ' and a transposed matrix X ' of the sea temperature salt flow distance flat matrix 'TThe product of (c), constitutes the Jacobi matrix S:
④ calculating the eigenvalue and eigenvector of the Jacobi matrix S, wherein the eigenvector of the Jacobi matrix S is arranged from large to small according to the magnitude of the eigenvalue to obtain a spatial mode matrix P, and the diagonal matrix Λ formed by the spatial mode matrix P, the Jacobi matrix S and the eigenvalue of the Jacobi matrix S satisfies the relationship:
S×P＝P×Λ (6)
multiplying both sides of formula (6) by P simultaneouslyTObtaining:
PTX'＝PTPT (7)
the obtained space mode matrix P is an orthogonal matrix and satisfies PPTIf I, then equation (7) is modified as:
T＝PTX' (8)
thus, a time coefficient matrix T is obtained by calculation according to the formula (8), and each row of values in the time coefficient matrix T represents a time coefficient of a corresponding mode.
Through the steps, the characteristic vector matrix P and the time coefficient matrix T can be obtained. And (3) multiplying the obtained spatial mode matrix P and the time coefficient matrix T to form a new ocean temperature salt flow range-flat matrix X ', comparing the new ocean temperature salt flow range-flat matrix X ' with the decomposed ocean temperature salt flow range-flat matrix X ' shown in the formula (4), and verifying that the result error of the empirical orthogonal function decomposition is small, thereby showing that the empirical orthogonal function decomposition method has feasibility.
(3) The significance of the decomposed modal result is checked to judge whether the modal result has physical significance, and therefore an effective modal result can be obtained
In order to check whether the spatial mode matrix P obtained by decomposition has practical physical significance, a significance check is performed, especially when the number of spatial points is much larger than the number of collected samples, a check is performed by calculating an eigenvalue error range, where the eigenvalue error range is:
wherein n is a time point, ezIs an intermediate variable, λzCharacteristic values of the Jacobi matrix S;
if λz-λz-1>ezThe spatial mode vector corresponding to these two eigenvalues is considered a valuable quantity.
Through the verification, the first r spatial modes pass the significance verification, the cumulative variance contribution rate of the first spatial modes is large, the representativeness is strong, the spatial modes are valuable, and the first r spatial modes are considered to be effective spatial modes.
(4) Constructing a real-time analysis model by using the effective modal result, namely establishing a target functional, solving a minimum value of the target functional, and constructing the real-time analysis model
And then constructing a real-time analysis model, wherein in an actual situation, the number n of samples is often far less than the number m of position points, even if n feature vectors are obtained, the number of effective modes is the first r in consideration of inevitable errors such as manual processing calculation and the like, so that a feature vector matrix is constructed by using the first r effective modes and is represented by A.
Assuming that the analysis result obtained by the real-time analysis model is AaAnd then:
in the formula (I), the compound is shown in the specification,
represents the mean value of each row element of the feature vector matrix a,
for analysis of value distanceThe deviation of the values, where σ is the standard deviation matrix.
Let H be the projection operator, construct the cost function J (A)a):
In the formula, AbRepresenting the initial field, derived from equation (11):
the real-time analysis model obtained from equation (12) is:
Aa＝(HTH)-1HTAb(13)
in the formula, AaThe analysis result obtained for the real-time analysis model.
(5) Practical application
And (3) substituting the modal result (namely, the spatial modal matrix P) obtained by the empirical orthogonal function decomposition in the step (2) into the real-time analysis model obtained by the step (4) to obtain the final real-time analysis result of the ocean temperature and salt flow elements of the sea area around the ship position, so that the real-time prediction of the ocean temperature and salt flow of the sea area around the ship is realized when the ship sails in the unknown sea area, and the guarantee is provided for the marine sailing.
Although the preferred embodiments of the present invention have been described above with reference to the accompanying drawings, the present invention is not limited to the above-described embodiments, which are merely illustrative and not restrictive, and those skilled in the art can make many modifications without departing from the spirit and scope of the present invention as defined in the appended claims.
Claims (5)
1. A method for rapidly analyzing ocean elements in the sea area around a boat position is characterized by comprising the following steps:
step 1, carrying out interpolation processing on temperature and salt flow data acquired by a naval vessel track, and further processing to obtain an ocean temperature and salt flow range matrix;
step 2, performing empirical orthogonal function decomposition on the ocean temperature and salinity flow distance matrix obtained by processing in the step 1 to obtain a modal result;
step 3, carrying out significance test on the modal result obtained by decomposition in the step 2, and judging whether the modal result obtained in the step 2 has physical significance to obtain an effective modal result;
step 4, establishing a target functional by using the effective modal result obtained in the step 3, solving a minimum value of the target functional, and constructing a real-time analysis model;
and 5, substituting the modal result obtained by decomposing in the step 2 into the real-time analysis model obtained by constructing in the step 4 to obtain a real-time analysis result of the ocean temperature and salinity flow elements of the sea area around the ship position, so as to realize the real-time prediction of the ocean temperature and salinity flow elements of the sea area around the ship when the ship navigates in the unknown sea area.
2. The method for rapidly analyzing the ocean elements in the sea area around the ship position according to claim 1, wherein in the step 1, the step of interpolating the temperature and salt flow data acquired by the ship track to obtain the leveling result of the temperature and salt flow data comprises the following steps:
forming an ocean temperature saline flow matrix X from temperature saline flow data acquired by ocean satellites and track observation, performing interpolation processing on the ocean temperature saline flow matrix X, and performing pitch processing on interpolation results to obtain an ocean temperature saline flow pitch matrix X';
ocean temperature salt flow matrix X adopts XabNote that the ocean temperature salt flow matrix X 'is X'abAnd then:
in the formula, xab(a 1.. m; b 1.. n) represents the warm saline flow element of the original data at the time point of the a-th spatial position b, yab(a 1.. m; b 1.. n) represents the warm saline flow element at the b-th time point from the plateau data at the a-th spatial position.
3. The method for rapidly analyzing sea elements in the sea area around the boat position according to claim 1, wherein in the step 2, the empirical orthogonal function decomposition is performed on the sea temperature and salt flow distance flat matrix obtained by the processing in the step 1, and the obtaining of the modal result comprises:
step 2-1, in the empirical orthogonal function decomposition, regarding the ocean temperature and salinity gradient matrix X 'obtained in step 1 as a two-dimensional random process X' (P ', T') depending on the spatial position P 'and the time T', and regarding the values X '(P', T ') of the two-dimensional random process X' (P ', T') at m spatial positions and n time pointsi',Tj') (i ═ 1,. ·, m; j 1.. n) are all random variables;
x '(P', T ') is represented by X'ijThen the random variable X' (P)i,Tj) (i 1.., m; j 1.. n) is represented by a matrix as:
in formula (II), X'ijRepresenting a range-flat matrix represented by a two-dimensional random process in time space, cij(i 1.. m; j 1.. n) represents the warm saline flow element at the j time point of the ith spatial position, wherein m elements in each column represent the warm saline flow elements at different spatial positions at the same time point, and n elements in each row represent the warm saline flow elements at different time points at the same spatial position;
step 2-2, representing each distance matrix X 'in a time-space two-dimensional random process'ijExpressed as the sum of the products of m "values" dependent only on spatial position and n "values" dependent only on time, i.e.
Wherein P represents a spatial mode matrix, T represents a time coefficient matrix, PikValue of the temperature salt flow element, t, representing different spatial positions at the same timekjRepresenting the temperature and salt flow element values at different moments at the same position;
then, the ocean temperature salt flow range matrix X' is expressed as the product of the matrices:
X'＝PT (4)
obtaining an irrelevant space modal matrix P and a time coefficient matrix T between each row of vectors, and arranging each row of vectors in the time coefficient matrix T from large to small according to the corresponding eigenvalue to form a principal component vector;
step 2-3, solving the spatial modal matrix P by adopting a Jacobi method, and calculating a sea temperature salt flow distance-flat matrix X ' and a transposed matrix X ' of the sea temperature salt flow distance-flat matrix 'TThe product of (c), constitutes the Jacobi matrix S:
step 2-4, calculating the eigenvalue and the eigenvector of the Jacobi matrix S, wherein the space modal matrix P is obtained after the eigenvector of the Jacobi matrix S is arranged from large to small according to the magnitude of the eigenvalue; the spatial mode matrix P, the Jacobi matrix S and a diagonal matrix Lambda formed by eigenvalues of the Jacobi matrix S satisfy the relationship:
S×P＝P×Λ (6)
multiplying both sides of formula (6) by P simultaneouslyTObtaining:
PTX'＝PTPT (7)
the obtained space mode matrix P is an orthogonal matrix and satisfies PPTIf I, then equation (7) is modified as:
T＝PTX' (8)
calculating according to a formula (8) to obtain a time coefficient matrix T, wherein each row of values in the time coefficient matrix T represents a time coefficient of a corresponding mode;
and 2-5, multiplying the spatial mode matrix P obtained by calculation in the step 2-4 by the time coefficient matrix T to form a new ocean temperature salt flow range matrix X ', and comparing the new ocean temperature salt flow range matrix X ' with a decomposed ocean temperature salt flow range matrix X ' shown in a formula (4), and verifying that the empirical orthogonal function decomposition method has feasibility.
4. The method for rapidly analyzing sea elements in the sea area around the boat position according to claim 1, wherein in step 3, the significance of the modal result obtained by decomposing in step 2 is checked, whether the modal result obtained in step 2 has physical significance is judged, and obtaining the effective modal result comprises: and (3) checking whether the spatial modal matrix P obtained by decomposing in the step (2) has physical significance by adopting the error range of the calculated characteristic value, specifically:
the error range of the characteristic value is as follows:
wherein n is a time point, ezIs an intermediate variable, λzCharacteristic values of the Jacobi matrix S;
if λz-λz-1>ezThe spatial modes corresponding to the two characteristic values are considered to be valuable;
after verification, the first r spatial modes pass significance verification, and then the first r spatial modes are considered as effective spatial modes.
5. The method for rapidly analyzing sea elements in the sea area around the boat position according to claim 1, wherein in step 4, the step of establishing a target functional by using the effective modal result obtained in step 4, and the step of minimizing the target functional to construct a real-time analysis model comprises the steps of:
constructing a characteristic vector matrix A by using the effective space mode obtained in the step 3, and assuming that an analysis result obtained by a real-time analysis model is AaAnd then:
in the formula (I), the compound is shown in the specification,
representing feature vector momentsThe mean value of each row of elements of array a,
is the deviation of the analysis value from the mean value, where σ is the standard deviation matrix;
let H be the projection operator, construct the cost function J (A)a):
In the formula, AbRepresenting the initial field, derived from equation (11):
the real-time analysis model obtained from equation (12) is:
Aa＝(HTH)-1HTAb(13)
in the formula, AaThe analysis result obtained for the real-time analysis model.
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| CN111815041A (en) * | 2020-06-28 | 2020-10-23 | 青岛哈船海智科技有限公司 | Seawater temperature field prediction method based on improved EOF |
| CN114036975A (en) * | 2021-10-19 | 2022-02-11 | 中国科学院声学研究所 | Target signal extraction method based on frequency domain-wavenumber domain deconvolution |
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