Direct positioning and polarization parameter estimation method based on multi-station subspace data fusion

Abstract

The direct positioning and polarization parameter estimation method based on multi-station subspace data fusion relates to a direct positioning and polarization parameter estimation method based on multi-station subspace data fusion.The purpose of the present application is to solve the problem that the traditional two-step single-station passive positioning algorithm cannot avoid multi-item positioning parameter estimation, resulting in poor convergence and positioning accuracy. The specific process is as follows: step one: generating a multi-station subspace data matrix; step two: constructing a cost extremum function about the position of the radiation source target; step three: performing spectral peak search on the cost extremum function in a two-dimensional plane, determining the target position based on the spectral peak, and determining the spatial DOA estimation result based on the target position; step four: based on the spatial DOA estimation result determined in step three, the DOA parameter in the polarization domain is recovered. The present application is used in the field of radiation source positioning.

Description

Technical Field

[0001] This invention relates to a direct positioning and polarization parameter estimation method based on multi-station subspace data fusion. Background Technology

[0002] With the continuous development of integrated electronic warfare and reconnaissance in modern electronic warfare, passive positioning and tracking systems, as a supplement and improvement to active detection systems, are evolving towards higher precision, lower payload, and faster speed. In modern complex radar electronic warfare, the ability to efficiently detect and identify enemy and friendly targets at long range has become a crucial aspect of warfare evolution. Furthermore, due to the dominant role of airborne operations, passive positioning systems for moving platforms have seen the most widespread and rapid development. However, traditional two-step single-station passive positioning algorithms cannot avoid estimating multiple positioning parameters, and the accuracy of parameter extraction directly determines the convergence and positioning accuracy of the solution method. Summary of the Invention

[0003] The purpose of this invention is to solve the problem that traditional two-step single-station passive positioning algorithms cannot avoid the estimation of multiple positioning parameters, resulting in poor positioning convergence and positioning accuracy.

[0004] The specific process of the direct localization and polarization parameter estimation method based on multi-station subspace data fusion is as follows:

[0005] Step 1: Generate a subspace data matrix for multiple stations;

[0006] Step 2: Construct the cost extremum function for the location of the radiation source target;

[0007] Step 3: Perform spectral peak search on the cost extremum function in the two-dimensional plane, determine the target location based on the spectral peak, and determine the spatial domain DOA estimation result based on the target location;

[0008] Step 4: Based on the spatial DOA estimation results determined in Step 3, recover the DOA parameters of the polarization domain.

[0009] The beneficial effects of this invention are as follows:

[0010] The purpose of this invention is to achieve high-precision direct localization of multiple signal sources while obtaining the polarization (DOA) information of these sources. The direct localization algorithm involved in this invention directly utilizes angle information data received by an array from multiple joint observation stations within multiple observation time slots to achieve localization.

[0011] Meanwhile, this invention obtains the polarization DOA information of the information source, with the aim of applying the polarization sensitive array to passive positioning. The polarization sensitive array has strong anti-interference ability, robust detection ability and high resolution, and has better positioning accuracy than the scalar array used in traditional algorithms.

[0012] Meanwhile, the application uses a cost extreme value function for two-dimensional coordinates to estimate the target position.

[0013] The application realizes direct positioning and polarization parameter estimation of subspace data fusion of multiple stations, position maps of multiple observation stations and target position maps, and search region maps as shown in Figure 1 The application significantly improves the precision of direct positioning of multiple radiation sources and can obtain DOA information of the polarization domain of the signal source.

[0014] The target is a radar, an airplane, a missile, a ground radiation radar, etc. BRIEF DESCRIPTION OF DRAWINGS

[0015] Figure 1 It is a position map of multiple observation stations and a target position map and a search region map used by the application;

[0016] Figure 2 It is a placement map of the orthogonal dipole circular array used on each observation station;

[0017] Figure 3 It is a spectral peak map of spatial positioning;

[0018] Figure 4 It is an estimation result map of the polarization auxiliary angle and the polarization phase angle;

[0019] Figure 5 It is a map of the positioning root mean square error changing with the signal noise ratio under different algorithms;

[0020] Figure 6 It is a map of the positioning root mean square error changing with the number of snapshots under different algorithms;

[0021] Figure 7 It is a spatial spectrum map obtained by using a single station to observe two signal sources with a distance of 40m;

[0022] Figure 8 It is a spatial spectrum map obtained by using a joint multiple station to observe two signal sources with a distance of 40m. DETAILED DESCRIPTION

[0023] Specific implementation one: the specific process of the direct positioning and polarization parameter estimation method based on the subspace data fusion of multiple stations is as follows:

[0024] Step one: generate the subspace data matrix of multiple stations (formula 3);

[0025] Step two: construct a cost extreme value function about the target position of the radiation source;

[0026] Step three: searching the cost extremum function in two-dimensional plane for spectral peak, determining target position based on the spectral peak, and determining the spatial DOA estimation result based on the target position;

[0027] Step four: restoring the DOA parameter in polarization domain based on the spatial DOA estimation result determined in step three

[0028] The target is a radar, an airplane, a missile, a ground radiation radar, etc.

[0029] Specific implementation method two: different from the specific implementation method one, the step one generates the subspace data matrix (formula 3) of multiple stations; the specific process is as follows:

[0030] The observation receiving array is composed of M orthogonal dipole elements, and there is an observation receiving array on each observation station, and the receiving array is placed as shown in Figure 2

[0031] The radiation source signal is a far-field incident narrowband signal, that is, the radiation source signal reaching the receiving array position can be assumed as a parallel plane wave signal;

[0032] There are Q stationary radiation source targets emitting electromagnetic wave signals in the far-field region of the observation receiving array, and the signals are transmitted to the receiving array through a straight line, and the coordinate of the position of the qth stationary radiation source target is denoted as p q ∈R D×1 , where q = 1, 2,..., Q, D is the spatial coordinate dimension, and R is a real number, and the output response of the receiving array of the kth observation station at t time is represented as formula (1):

[0033]

[0034] In the formula, the orthogonal dipole element includes a subarray with a dipole polarization direction of the x-axis positive direction and a subarray with a dipole polarization direction of the y-axis positive direction;

[0035] The signal received by the subarray with the dipole polarization direction of the x-axis positive direction (the first M orthogonal dipole elements form an array, and one array is divided into two subarrays) is denoted as x h,k (t), and the signal received by the subarray with the dipole polarization direction of the y-axis positive direction is denoted as x v,k (t); A h,k and A v,k are the spatial-polarization joint steering vectors, s q (t) represents the value of the signal of the qth radiation source target at t time, n h (t) and n v (t) are Gaussian white noises; ​s(t) is the value of the signal at time t, a u,k (φ q ) is the spatial steering vector of the kth observation station; a p,1 (φ q ,γ q ,η q ) and a p,2 (φ q ,γ q ,η q ) are the polarization steering vectors of the two sub-arrays, respectively, φ q is the spatial elevation angle, γ q is the polarization auxiliary angle, and η q is the polarization phase angle, and T is the transpose;

[0036] Since the dipole polarization direction is a single direction of the sub-array receiving signal and cannot include all the polarization direction information of the source, in order to construct a joint observation model, x h,k (t) and x v,k (t) are summed to obtain x(t) containing all the polarization information, and x(t) is processed to ensure the DOA estimation performance of different polarization direction signals, as shown in the following formula (3):

[0037]

[0038] In the formula, A is the steering vector matrix, N(t) is the Gaussian white noise, M is the number of orthogonal dipole array elements in the observation array, and t is the time t;

[0039] wherein DOA is the direction of arrival estimation.

[0040] The other steps and parameters are the same as those in the first embodiment.

[0041] In the third embodiment, the polarization steering vectors a p,1 (φ q ,γ q ,η q ) and a p,2 (φ q ,γ q ,η q ) are represented as shown in the formula (2):

[0042]

[0043] In the formula, j is the imaginary unit, and j 2 =-1.

[0044] The other steps and parameters are the same as those in the first or second embodiment.

[0045] Specific implementation four: the difference between this implementation and one of the specific implementations one to three is that the spatial orientation vector a u,k (φ q ) = [u q,1 ,...,u q,m ,...,u q,M ] T , the first array element u q,1 is set as the reference array element, and the mth array element is in the form of u q,m = exp(-jπ(m-1)sin(φ q )).

[0046] The other steps and parameters are the same as one of the specific implementations one to three.

[0047] Specific implementation five: the difference between this implementation and one of the specific implementations one to four is that the cost extremum function about the target position of the radiation source is constructed in step two; the specific process is as follows:

[0048] The covariance matrix of the observation signal r k (n) of the kth observation station is defined as formula (4):

[0049]

[0050] In the formula, R k is the covariance matrix of the observation signal r k (n) of the kth observation station, E[] is the expectation, the upper index H represents the conjugate, a k,n (x k ) is the spatial-polarization domain orientation vector of the kth observation station containing the target source position information, s k (n) is the signal received by the kth observation station, n k (n) is the Gaussian white noise received by the kth observation station, x k is the information received by the kth observation station, and the information is the two-dimensional position information of the radiation source; n is the nth sampling;

[0051] The covariance matrix of the observation signal r k (n) of the kth observation station can be obtained as formula (5):

[0052]

[0053] In the formula, is the covariance matrix of the radiation source signal at the kth observation station (the upper index s represents s k (n)); σ 2 is the noise power, wherein the information contained in x k is the two-dimensional position information of the radiation source, and I MM is an M-dimensional identity matrix; N is the number of snapshots;

[0054] According to the array signal processing theory, it can be proved that R k is non-singular, and R k = R k H ;

[0055] The covariance matrix R k of the observation signal r k of the kth observation station is decomposed, and the decomposition result can be expressed in the following form (6):

[0056]

[0057] In the formula, Σ s is a diagonal matrix composed of Q large eigenvalues (the eigenvalues of R k ), U s is a signal subspace composed of Q large eigenvectors corresponding to the Q large eigenvalues; Σ N is a diagonal matrix composed of M-Q small eigenvalues (the eigenvalues of R k ), and U N is a noise subspace composed of M-Q small eigenvectors corresponding to the M-Q small eigenvalues.

[0058] According to the above derivation, when the noise is Gaussian white noise, Σ N = σ 2 I (M-Q)(M-Q) ;

[0059] In the formula, I (M-Q)(M-Q) is an (M-Q)(M-Q)-dimensional identity matrix.

[0060] U N and U N are brought into the following formula to obtain a cost extremum function.

[0061] According to the orthogonal relationship between the noise subspace U N and the signal subspace U s , a cost extremum function P k (x k ) about the radiation source position (x k ) can be obtained.

[0062] The other steps and parameters are the same as those in one of the first to fourth embodiments.

[0063] The sixth embodiment is different from the first to fifth embodiments in that the expression of the cost extremum function P k (x k ) is as follows:

[0064]

[0065] In the formula, a k (x k P is the airspace steering vector of the k-th observation station. k (x k ) is the cost extremum function.

[0066] x k It can be viewed as a point in a two-dimensional plane;

[0067] The above formula can be used as the objective function to search for the location of the radiation source target in a two-dimensional plane. The peak value of the objective function corresponds to the estimated location of the target radiation source.

[0068] The other steps and parameters are the same as those in one of the specific implementation methods one to five.

[0069] Specific Implementation Method Seven: This implementation method differs from Specific Implementation Methods One to Six in that, a k,n (x k The representation of ) is:

[0070]

[0071] Where φ q γ is the airspace elevation angle, representing the ratio of the distance difference between the radiation source and the observation station; q For the auxiliary angle of the polarization domain, η q This represents the phase angle of the polarization domain.

[0072] The other steps and parameters are the same as those in one of the specific implementation methods one to six.

[0073] Specific Implementation Method Eight: This implementation method differs from Specific Implementation Methods One through Seven in that, in step three, a spectral peak search is performed on the cost extremum function in a two-dimensional plane, the target location is determined based on the spectral peak, and the spatial domain DOA estimation result is determined based on the target location; the specific process is as follows:

[0074] like Figure 1 As shown, a two-dimensional spectral peak search is performed on the cost extremum function with respect to the radiation source location near the desired location of the target signal;

[0075] Finally, the logarithm of the cost extremum function of all observation stations is taken and then summed to obtain the horizontal and vertical coordinates of the spectral peak, which are the target coordinates.

[0076] Finally, the spatial DOA estimation result can be calculated based on the difference between the obtained target location and the location of a certain observation station. Based on this, the DOA parameters of the polarization domain are recovered;

[0077] The ratio of (the difference between the target's x-axis position and the x-axis position of a certain observation station) to (the difference between the target's y-axis position and the y-axis position of a certain observation station) is the spatial DOA estimation result.

[0078] The other steps and parameters are the same as those in any of the specific implementation methods one to seven.

[0079] Specific Implementation Method Nine: This implementation method differs from Specific Implementation Methods One through Eight in that, in step four, the DOA parameters of the polarization domain are recovered based on the spatial DOA estimation results determined in step three. The specific process is as follows:

[0080] The following method uses matrix vectorization to recover the polarization parameters, retrieving the signal x received from the k-th observation station. h,k The autocorrelation matrix of (t) is denoted as R. 11 Signal x v,k The autocorrelation matrix of (t) is denoted as R. 22 The signal x received by the kth observation station h,k The cross-correlation moment of (t) is denoted as R. 12 Signal x v,k The cross-correlation moment of (t) is denoted as R. 21 ;

[0081] R 11 R 22 R 12 Or R 21 The expression form is Equation (8):

[0082]

[0083] In the formula, R zt′ Represents R 11 R 22 R 12 Or R 21 ;

[0084] x z (t) represents x h,k (t) or x v,k (t), when z takes 1, x z (t) is x h,k (t), when z takes 2, x z (t) is x v,k (t);

[0085] x t′ (t) represents x h,k (t) or x v,k (t), when z takes 1, x t′ (t) is x h,k (t), when z takes 2, xt′ (t) is x v,k (t);

[0086] A p,t′ The polarization domain steering vector matrix represents different subarrays (the array is composed of M orthogonal dipole subarray elements, and one array is divided into 2 subarrays);

[0087] z and t′ are constants, 1≤z, t′≤2;

[0088] A u =[a u (φ1),a u (φ2),...,a u (φ Q [)] is the spatial guiding vector matrix, a u (φ Q ) is the guide vector;

[0089] A p,z The polarization domain steering vector matrix represents different subarrays (the array is composed of M orthogonal dipole subarray elements, and one array is divided into 2 subarrays);

[0090] R ss I represents the target signal covariance matrix; Q χ is a Q-dimensional identity matrix; z,t′ It consists of ideal Gaussian white noise received by two subarrays, and is a function representing the noise energy;

[0091] Among them, the target signal covariance matrix Signal power;

[0092] For R zt′ The vectorization process is performed as shown in equation (9):

[0093]

[0094] In the formula, r zt′ For R zt′ After vectorization, vec(·) represents the vector of diagonal elements. For I Q Perform vector processing. b z′t Diagonal elements; For A u The conjugate transpose of , ⊙ is the inner product, A u This is the spatial guiding vector matrix;

[0095] remember achievable Based on the above vectorization result r zt′, combined with the least square method, the following equation can be derived The polarization parameter can be derived according to recovery, in the following equation represent The qth element in the matrix is shown in the following equation (10) and equation (11):

[0096]

[0097]

[0098] In the equation, is an intermediate variable, is a Kronecker product, is a guiding vector of is a conjugate transpose of is a guiding vector of is a conjugate transpose of is an intermediate variable, is a polarization domain auxiliary angle estimate value, is a spatial domain elevation angle estimate value, is a polarization domain phase angle estimate value, is an intermediate variable, imag is an imaginary part, and mod is a modulus value.

[0099] The other steps and parameters are the same as one of the first to eighth embodiments.

[0100] Embodiment:

[0101] The present application will be further described in detail below in combination with the accompanying drawings and embodiments.

[0102] As shown in Figure 2 , the antenna array used in the present example is a 7-element one-dimensional orthogonal dipole uniform array, and the element spacing is set to half the wavelength of the signal. The search step size of the present algorithm for the x and y axes is 10m when searching for the peak of the two-dimensional coordinate spectrum. The search interval of the two-step cross positioning MUSIC algorithm, which is used for comparison, is set to 1°. The performance indicators used for comparison mainly include: Root Mean Square Error (RMSE): N represents the number of Monte Carlo experiments, x q (n) represents the position of the qth radiation source, represents the estimated positioning of the qth radiation source in the nth experiment, and the noise tolerance is set to 0.25. The polarization angles of the two radiation sources set in the simulation experiment are set to fixed polarization: γ q = 50°, η q= 60°; the other is set to random polarization: γ q ∈ [0°, 90°], η q ∈ [0°, 360°). The distribution trajectory of the joint multi-station is a circle with a radius of 3.2 KM, and 30 observation stations are uniformly distributed.

[0103] The target is a radar, an airplane, a missile, a ground radiation radar, etc.

[0104] Step (1): Generate the subspace data matrix of the multi-station

[0105] Suppose there are multiple airborne platforms carrying single arrays, and the received signals come from a ground far-field narrowband stationary radiation source, and the target position vector is x q To achieve direct positioning of the radiation source target by multiple joint observation platforms, K observation platforms intercept signals of the target radiation source at different positions.

[0106] The signal model received by the array antenna at the kth observation station is formula (13):

[0107]

[0108] In the formula, k = 1, 2, …, K; r k (t) is the array output signal of the radiation source received by the antenna element at the kth observation station at time t; a k (x q ) is the array stream vector of the qth radiation source signal received by the kth observation station to the antenna element; n k (t) is the corresponding complex noise; s q (t) is the signal transmitted by the qth radiation source; a k (x q , γ q , η q ) is a polarization domain steering vector containing the position information of the target radiation source, x q represents the position of the qth radiation source;

[0109] Therefore, the unified received N-shot data signal model can be further written as formula (15):

[0110] r = A(x q )s + n (15)

[0111] In the formula, r is the signal received by the observation station from the radiation source, is the signal received by the kth observation station from the radiation source; s is the radiation source signal, s = [s1, s2, …, s Q ] T , s KLet n be the signal from the k-th radiation source; n is Gaussian white noise. A is the joint steering vector of the spatial domain and polarization domain, as shown in equation (16):

[0112]

[0113] In the formula, The joint spatial-polarization domain steering vector of the first radiation source. The spatial-polarization domain joint steering vector of the q-th radiation source;

[0114] Step (2): Construct the cost extremum function with respect to the location of the radiation source.

[0115] The received signal r is based on the number of N samples taken by the antenna array at the k-th observation station. k (n), matrix R is obtained by calculating the time-averaged autocorrelation using finite signal sampling data. k As shown in equation (17):

[0116]

[0117] The obtained average autocorrelation matrix R k Eigenvalue decomposition is performed to obtain the radiation source signal subspace U. s and noise subspace U N During the continuous interception and reception of radiation source signals by the observation platform, steps (1) and (2) are repeated to fuse all K observation data from the platform and construct the objective function P(x). n To achieve accurate target location by accumulating observation time, the expression is shown in equation (18) below:

[0118]

[0119] Perform a two-dimensional coordinate peak search on the objective function to obtain the coordinate position of the objective.

[0120] Step (3): Perform spectral peak search on the objective function in the two-dimensional plane.

[0121] like Figure 1 As shown, a two-dimensional spectral peak search is performed on the target function with respect to the radiation source location near the desired location of the target signal. Finally, the logarithms of the spectral functions from all observation stations are taken and summed; the horizontal and vertical coordinates of the resulting spectral peaks are the target coordinates. The spatial DOA estimation result can then be calculated based on the difference between the obtained target location and the location of a certain observation point.

[0122] Step (4): Recover the DOA parameters of the polarization domain

[0123] The covariance matrix of the received signal is vectorized, and a least square method is combined to restore the polarization domain DOA parameter of the signal source.

[0124] Referring to Figure 3 The polarization angle estimation result is shown in the figure. When the signal-to-noise ratio is 10 dB and the snapshot number is 1000, the target position is as shown in the figure. Figure 1 The peak values of the spectrum function proposed in the application are relatively obvious, verifying the feasibility of the algorithm of the application.

[0125] Referring to Figure 4 The root mean square error under different algorithms is shown in the figure. The simulation settings are the same as those in Figure 3 It can be seen that the algorithm of the application can accurately position while obtaining the polarization angle information of the radiation source, and has good estimation accuracy.

[0126] Referring to Figure 5 The root mean square error under different algorithms is shown in the figure. When the snapshot number is fixed at 2000, a single target is positioned, and the target is 10 km away from the observation station. 200 Monte Carlo experiments are performed under each signal-to-noise ratio, and it can be seen that the RMSE of the algorithm of the application is smaller than that of the two cross-positioning algorithms, and the estimation performance is better.

[0127] Referring to Figure 6 The root mean square error under different algorithms is shown in the figure. When the signal-to-noise ratio is fixed at 20 dB, a single target is positioned, and the target is 10 km away from the observation station. 200 Monte Carlo experiments are performed under each snapshot number, and it can be seen that the RMSE of the algorithm of the application is smaller than that of the two cross-positioning algorithms, and the estimation performance is better.

[0128] Referring to Figure 7 and Figure 8 The resolution under single station and multiple stations is shown in the figure. The signal-to-noise ratio is fixed at 20 dB, the snapshot number is 2000, a single observation station and 30 joint observation stations are used to position two targets, the distance between the two targets is 40 m, and the position of the single observation station is at the joint observation station closest to the source. It can be seen that the joint multiple stations proposed in the application can estimate the position of the spectrum peak, but the single station cannot distinguish the two spectrum peaks. The superiority of the joint multiple stations proposed in the application is verified.

[0129] The above is an embodiment of the application, and is not intended to limit the application. The meshless DOA estimation method provided by the application is also applicable to other non-uniform and different element arrays. Without departing from the essence and scope of the application, some adjustments and optimizations can be made, and the protection scope of the application is subject to the claims.

[0130] In summary, the application proposes a direct positioning and polarization parameter estimation method based on multi-station subspace data fusion for orthogonal dipole antenna array, which takes joint multi-station direct positioning as the basis, combines the polarization sensitive array, first sums the multi-shot matrices received by two sub-arrays of different polarization directions, obtains the noise subspace and signal subspace by processing the matrix, constructs the spectral function, obtains the positioning of the target radiation source through the spectral peak search of two-dimensional coordinates, and combines the vectorization of the covariance matrix and the least square method to restore the polarization domain parameters of the target radiation source. And the two-step positioning MUSIC algorithm is compared, and the advantage of the algorithm in the estimation accuracy is verified.

[0131] The application also has other various embodiments, and those skilled in the art can make various corresponding changes and modifications according to the application without departing from the spirit and essence of the application, but these corresponding changes and modifications should all belong to the protection scope of the claims attached to the application.

Claims

1. A direct positioning and polarization parameter estimation method based on multi-station subspace data fusion, characterized in that: The specific process of the method is as follows: Step 1: Generate a subspace data matrix for multiple stations; Step 2: Construct the cost extremum function for the location of the radiation source target; Step 3: Perform spectral peak search on the cost extremum function in the two-dimensional plane, determine the target location based on the spectral peak, and determine the spatial domain DOA estimation result based on the target location; Step 4: Based on the spatial DOA estimation results determined in Step 3, recover the DOA parameters of the polarimetric domain; The process of generating a multi-station subspace data matrix in step one is as follows: The observation and receiving array consists of M orthogonal dipole array elements, and each observation station has one observation and receiving array. The radiation source signal is a far-field incident narrowband signal, meaning that the radiation source signal arriving at the receiving array position can be assumed to be a parallel plane wave signal. There are Q stationary radiation source targets emitting electromagnetic wave signals in the far-field region of the observation and receiving array. The signals travel in a straight line to reach the receiving array. The coordinates of the position of the qth stationary radiation source target are marked as p. q ∈R D×1 Where q = 1, 2, ..., Q, D is the spatial coordinate dimension, and R is a real number, then the output response of the receiving array of the k-th observation station at time t is expressed as in equation (1): In the formula, the signal received by the subarray whose dipole polarization direction is in the positive x-axis direction is defined as x. h,k (t), let the signal received by the subarray with the dipole polarization direction in the positive y-axis be x. v,k (t); A h,k and A v,k The spatial-polarization domain joint steering vector, s q (t) represents the signal value of the q-th radiation source target at time t, n h (t) and n v (t) represents Gaussian white noise; Let s(t) be the Kronecker product, and a be the value of the signal at time t. u,k (φ q ) represents the airspace steering vector of the k-th observation station; a p,1 (φ q ,γ q ,η q ) and a p,2 (φ q ,γ q ,η q ) is the polarization domain steering vector, φ q For the airspace pitch angle, γ q For the auxiliary angle of the polarization domain, η q The polarization phase angle is T, and T is the transpose. For x h,k (t) and x v,k (t) is summed to obtain x(t) containing all polarization information. x(t) is then processed to ensure the DOA estimation performance for signals with different polarization directions, as shown in equation (3) below: In the formula, A is the steering vector matrix, N(t) is Gaussian white noise, M is the number of orthogonal dipole elements in the observation array, and t is time t. Where DOA is the direction of arrival estimate; In step two, a cost extremum function is constructed regarding the location of the radiation source target; the specific process is as follows: Define the observation signal r of the k-th observation station k The covariance matrix of (n) is given by equation (4): R k =E[r k (n)r k H (n)] =E{[a k,n (x k )s k (n)+n k (n)][a k,n (x k )s k (n)+n k (n)] H } (4) In the formula, R k The observation signal r of the k-th observation station k The covariance matrix of (n), E[] is the expectation, and the superscript H indicates finding the conjugate. k,n (x k ) is the spatial-polarization domain steering vector of the k-th observation station containing target source location information, s k (n) represents the signal received by the k-th observation station, n k (n) represents the Gaussian white noise received at the k-th observation station, x k The information received by the k-th observation station is the two-dimensional location information of the radiation source; n represents the nth sampling. The observation signal r of the kth observation station can be obtained. k The covariance matrix of (n) is given by equation (5): In the formula, Let σ be the covariance matrix of the radiation source signal at the k-th observation station; 2 Let x be the noise power, where x is the noise power. k The information contained therein is the two-dimensional location information of the radiation source, I M Let R be an M-dimensional identity matrix; N be the number of snapshots; R be the number of snapshots. k It is non-singular, and R k =R k H ; The observation signal r of the kth observation station k The covariance matrix R of (n) k The eigenvalue decomposition is performed, and the decomposition result can be expressed in the following form (6): In the formula, Σ s It is a diagonal matrix composed of Q large eigenvalue decompositions, U s The signal subspace is formed by the Q larger eigenvectors corresponding to the Q larger eigenvalues; Σ N It is a diagonal matrix consisting of MQ smaller eigenvalues, U N The noise subspace is formed by the MQ smaller eigenvectors corresponding to the MQ smaller eigenvalues; From the above derivation, it can be seen that, assuming the noise is Gaussian white noise, we have Σ N =σ 2 I (M-Q)(M-Q) ; In the formula, I (M-Q)(M-Q) It is a (MQ)(MQ) dimensional identity matrix; From the noise subspace U N With signal subspace U s The orthogonality between them allows us to obtain the cost extremum function P for the location of the radiation source. k (x k ); The cost extremum function P k (x k The expression for ) is: In the formula, a k (x k P is the airspace steering vector of the k-th observation station. k (x k ) is the cost extremum function; The a k,n (x k The representation of ) is: Where φ q γ is the pitch angle in the airspace; q For the auxiliary angle of the polarization domain, η q The phase angle of the polarization domain; In step three, a spectral peak search is performed on the cost extremum function in a two-dimensional plane. The target location is determined based on the spectral peak, and the spatial DOA estimation result is determined based on the target location. The specific process is as follows: A two-dimensional spectral peak search is performed on the cost extremum function with respect to the radiation source location near the desired location of the target signal; Finally, the logarithm of the cost extremum function of all observation stations is taken and then summed to obtain the horizontal and vertical coordinates of the spectral peak, which are the target coordinates. Finally, the spatial DOA estimation result can be calculated based on the difference between the obtained target location and the location of a certain observation station. In step four, based on the spatial DOA estimation results determined in step three, the DOA parameters of the polarization domain are recovered; the specific process is as follows: The signal x received by the k-th observation station h,k The autocorrelation matrix of (t) is denoted as R. 11 Signal x v,k The autocorrelation matrix of (t) is denoted as R. 22 The signal x received by the kth observation station h,k The cross-correlation moment of (t) is denoted as R. 12 Signal x v,k The cross-correlation moment of (t) is denoted as R. 21 ; R 11 R 22 R 12 or R 21 The expression form is Equation (8): In the formula, R zt′ Represents R 11 R 22 R 12 or R 21 ; x z (t) represents x h,k (t) or x v,k (t), when z takes 1, x z (t) is x h,k (t), when z takes 2, x z (t) is x v,k (t); x t′ (t) represents x h,k (t) or x v,k (t), when z takes 1, x t′ (t) is x h,k (t), when z takes 2, x t′ (t) is x v,k (t); A p,t′ Represents the polarization domain steering vector matrix of different subarrays; z and t′ are constants, 1≤z, t′≤2; A u =[a u (φ1),a u (φ2),...,a u (φ Q [)] is the spatial guiding vector matrix, a u (φ Q ) is the guide vector; A p,z Represents the polarization domain steering vector matrix of different subarrays; R ss I represents the target signal covariance matrix; Q χ is a Q-dimensional identity matrix; z,t′ It consists of ideal Gaussian white noise received by two subarrays respectively; Among them, the target signal covariance matrix Signal power; For R zt′ The vectorization process is performed as shown in equation (9): In the formula, r zt′ For R zt′ After vectorization, vec(·) represents the vector of diagonal elements. For I Q Perform vector processing. b z′t Diagonal elements; For A u The conjugate transpose of , ⊙ is the inner product, A u This is the spatial guiding vector matrix; remember achievable Based on the above vectorization result r zt′ Combining the least squares method, we can deduce that Polarization parameters can be based on Restore, in the following formula represent The q-th element in the equation is shown in equations (10) and (11): In the formula, As an intermediate variable, For Kronecker product, for The guide vector, for The conjugate transpose of . for The guide vector, for The conjugate transpose of . As an intermediate variable, This is the estimate of the auxiliary angle in the polarization domain. This is an estimate of the airspace pitch angle. This is the estimated phase angle value in the polarization domain. Here, 'imag' is the imaginary part, and 'mod' is the modulo value.

2. The direct positioning and polarization parameter estimation method based on multi-station subspace data fusion according to claim 1, characterized in that: The polarization domain steering vector a p,1 (φ q ,γ q ,η q ) and a p,2 (φ q ,γ q ,η q The representation is shown in equation (2): In the formula, j is the imaginary unit, j 2 =-1.

3. The direct positioning and polarization parameter estimation method based on multi-station subspace data fusion according to claim 2, characterized in that: The spatial steering vector a of the k-th observation station u,k (φ q )=[u q,1 ,...,u q,m ,...,u q,M ] T The first array element u q,1 Set as the reference element, the m-th element is of the form u q,m =exp(-jπ(m-1)sin(φ) q )).

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