Taylor compensation based multi-array non-circular signal positioning method

Abstract

The application discloses a multi-array non-circular signal positioning method based on Taylor compensation, which comprises the following steps: first, the spatial information is extended by using the elliptical covariance information of a target signal to obtain an increased virtual array aperture; second, the bearing information of each observation station is obtained by using the rotation invariant technology (ESPRIT) and Taylor compensation is performed on the bearing information; third, the bearing information of each observation station is associated with a signal source by using a non-circular phase; fourth, the initial estimation of the target position is directly solved according to the least square idea by combining the information of all base stations; and finally, Taylor compensation is performed on the initial estimation to improve the estimation accuracy. Compared with the traditional two-step positioning algorithm, the subspace data fusion algorithm (SDF) and the Capon direct positioning algorithm, the application has higher spatial degrees of freedom and positioning accuracy and can estimate more targets. In addition, the method can ensure the estimation performance while significantly reducing the calculation complexity.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of wireless positioning, and particularly relates to a multi-array non-circular signal positioning method based on Taylor compensation. BACKGROUND

[0002] Most of the traditional multi-array passive positioning technologies are researched for unknown signals. From the perspective of information theory, the more original information that can be utilized, the better the performance of the algorithm is in theory. Research shows that considering the signal characteristics of the target source when establishing the algorithm model can further improve the positioning accuracy. In modern communication systems, amplitude modulation signals, binary phase shift keying, pulse amplitude modulation signals, and quadrature phase shift keying signals are all non-circular (NC) signal types. Therefore, the research on multi-array passive positioning algorithms for non-circular signals has important practical application significance.

[0003] The existing multi-array passive positioning algorithms for non-circular signals utilize the elliptical covariance information of the target signal to expand the array aperture, which also brings a high-dimensional search problem, greatly increasing the computational complexity. In addition, the traditional two-step positioning method also has problems in data association. In order to solve the above problems, the application provides a multi-array non-circular signal positioning method based on Taylor compensation. SUMMARY

[0004] The application aims to solve the problems existing in the prior art, and provides a multi-array non-circular signal positioning method based on Taylor compensation, which significantly reduces the computational complexity while ensuring the estimation performance, and is easy to process in real time.

[0005] TECHNICAL SOLUTION: The multi-array non-circular signal positioning method based on Taylor compensation provided by the application comprises the following steps:

[0006] (1) Construct a multi-array non-circular signal positioning model to obtain received signal information;

[0007] (2) Utilize the elliptical covariance information of the target signal to expand the received signal, calculate the covariance matrix thereof, and perform eigenvalue decomposition on the covariance matrix;

[0008] (3) Obtain bearing information by direction finding at each observation station, estimate the non-circular phase, and perform Taylor compensation on the bearing information;

[0009] (4) Associate the bearing information of all observation stations to solve the initial estimate of the target position;

[0010] (5) Perform Taylor compensation on the initial estimate to obtain the accurate estimate of the target position.

[0011] Preferably, the ESPRIT technology is applied to obtain the bearing information by direction finding at each observation station.

[0012] Preferably, the initial estimate of the target position is directly obtained by associating all observation station data using the least squares method.

[0013] Beneficial effects: Compared with the prior art, the beneficial effects of the present invention are as follows: The estimation accuracy of the algorithm proposed in this invention is better than that of traditional two-step localization technology, subspace data fusion technology, and Capon direct localization technology; Compared with traditional two-step localization technology, subspace data fusion algorithm and Capon direct localization algorithm, the proposed method has more degrees of freedom and can identify more targets; The present invention can significantly reduce computational complexity while ensuring estimation performance. Attached Figure Description

[0014] Figure 1 This is a flowchart of the present invention;

[0015] Figure 2 This is a diagram illustrating a multi-array joint positioning scenario.

[0016] Figure 3 This diagram illustrates the computational complexity of the present invention and traditional positioning methods under different numbers of observation stations.

[0017] Figure 4 This is a schematic diagram illustrating the root mean square error performance of the present invention and traditional positioning methods under different signal-to-noise ratios;

[0018] Figure 5 This diagram illustrates the root mean square error performance of the present invention and traditional positioning methods under different snapshot numbers. Detailed Implementation

[0019] The present invention will now be described in further detail with reference to the accompanying drawings.

[0020] This invention provides a method for locating non-circular signals from multiple arrays based on Taylor compensation, such as... Figure 1 As shown, the specific steps include:

[0021] Step 1: Construct as follows Figure 2 The multi-array non-circular signal positioning model is shown; the received signal information r is obtained. l (t).

[0022] The received signal of the l-th observation base station is in, For each observation station, the array manifold The guide vector is denoted by d, where d represents the element spacing, M represents the number of antenna elements at each observation base station, K represents the number of radiation sources, and λ represents the signal wavelength. l =[x l ,y l ] T Let p represent the location of the l-th observation station and the location of the k-th radiation source.k = [x k , y k ] T , u l (1), p k (1) represent the first element in the orientation vector u l and p k , respectively, and θ l,k represents the direction of arrival (DOA) of the kth source received at the ith observation station. The present invention only considers the strictly second-order non-circular signals with the non-circular rate of 1, which can be expressed as Assuming represents the non-circular phase, represents the amplitude of the non-circular signal, we can obtain:

[0023]

[0024]

[0025] wherein is a real value vector; n l (t) represents a Gaussian white noise vector.

[0026] Step 2: Using the elliptical covariance information of the target signal, the received signal at each observation base station is expanded as:

[0027]

[0028] wherein the row exchange matrix J is defined as

[0029]

[0030] which can be regarded as the expanded direction matrix, and

[0031]

[0032] wherein the expanded steering vector is

[0033]

[0034]

[0035] The covariance matrix of the ith observation station can then be calculated as wherein T represents the number of snapshots, (·) H represents the conjugate transpose, (·) * represents the conjugate; the eigen-decomposition of the covariance matrix is performed to obtain:

[0036]

[0037] Assume λ l,m (m = 1, 2, …, 2M) represent the eigenvalues sorted in descending order, and the corresponding eigenvectors are denoted as e l,m (m = 1, 2, …, 2M), then the signal subspace is denoted as The noise subspace is denoted as Σ l is a diagonal matrix composed of eigenvalues.

[0038] Step 3: Apply ESPRIT technique to the direction finding information obtained by each observation station to estimate the non-circular phase and perform Taylor compensation on the direction finding information.

[0039] Define row exchange matrices J1, J2

[0040]

[0041]

[0042] where,

[0043]

[0044]

[0045] denotes a zero matrix. According to the orthogonality of the signal subspace and the noise subspace, we can get That is, there exists an invertible matrix T l such that Then we can get

[0046]

[0047]

[0048] where, (·) + denotes the generalized inverse, Γ l is a diagonal matrix

[0049]

[0050] Performing eigenvalue decomposition on can easily obtain Γ l , which contains the direction information of the target in its diagonal elements. Denote the kth diagonal element of Γ l as μ l,k , then the estimated steering vector can be written as

[0051]

[0052] The extended steering vector can be denoted as

[0053]

[0054] Matrix transformation is performed to separate the azimuth information and the non-circular phase information

[0055]

[0056] where, is a block diagonal matrix composed of steering vectors, is a vector containing non-circular phase

[0057]

[0058]

[0059] Here, the non-circular phase is unknown, but when the estimated value of the non-circular phase approaches the true value , the following equation is established

[0060]

[0061] Definition then the following equation is established

[0062]

[0063] Definition then can be simplified as

[0064]

[0065] Let e = [1, 0] T , then According to the Lagrange multiplier method, the following function can be constructed

[0066]

[0067] where, is a multiplier. Let The derivative of is zero, that is,

[0068]

[0069] then

[0070]

[0071] And because can be obtained

[0072]

[0073] Substitute it back into We can get

[0074]

[0075] So the initial estimate of non-circular phase can be obtained according to the above formula Since the non-circular phase from the same radiation source target is unique, according to the estimated non-circular phase And the eigenvalue μ l,k The angle of arrival estimate of the lth observation station about the kth target can be easily obtained Where angle(·) represents taking the phase.

[0076] In order to reduce the influence of intermediate parameter estimation error on positioning performance and improve estimation accuracy, consider the obtained angle of arrival initial estimate And the non-circular phase initial estimate Carry out Taylor compensation. Assuming an unbiased steering vector Where First-order Taylor expansion is performed on And the second and higher order error terms are ignored, then Can be approximated as

[0077]

[0078] Define the offset Then Can be rewritten as

[0079]

[0080] According to the orthogonal relationship between the steering vector and the noise subspace, we have Where 0 represents a zero vector, then

[0081]

[0082] The least squares solution of the offset is

[0083]

[0084] Where, (·) + Indicates the generalized inverse, then the refined estimate of the angle of arrival And the refined estimate of the non-circular phase Can be expressed as

[0085]

[0086]

[0087] Step 4: Directly solve the initial estimate of target position according to the least square idea.

[0088] When the observation station is far enough from the target, the following formula is established

[0089]

[0090] Where, p k (n) represents the nth element of the vector p k , u l (n) represents the nth element of the vector u l , and the above formula is converted into matrix multiplication

[0091] [1-tan(θ l,k )]p k = [1-tan(θ l,k )]u l

[0092] Then, by combining the information of all observation stations, the following formula is obtained

[0093] F 1,k p k = F 2,k G

[0094] Where,

[0095]

[0096]

[0097]

[0098] Then, the initial estimate of the kth target position can be calculated by the following formula

[0099]

[0100] Step 5: Taylor compensation is performed on the initial estimate of target position to obtain the accurate estimate of target position.

[0101] By fusing the information of all observation stations, the total steering vector of L observation stations can be obtained as

[0102]

[0103] Then, is orthogonal to it, i.e. In order to further improve the accuracy of target position estimation, Taylor compensation is considered for the initial estimate of target position , the first-order Taylor expansion is performed on , and the second-order and higher-order error terms are ignored, then can be approximated as

[0104]

[0105] wherein, denotes the n-th element of the vector , defines the offset then can be rewritten as

[0106]

[0107] According to can be obtained

[0108]

[0109] The least square solution of the offset is

[0110]

[0111] The refined estimate of the k-th target position can be expressed as

[0112]

[0113] The spatial degrees of freedom obtained by the method of the present application is DOF=2(M-1), while the spatial degrees of freedom of the conventional uniform linear array is DOF=M-1 under the same number of array elements, thus the freedom is increased. Figure 3 The figure shows the calculation complexity (complex multiplication times) of the method of the present application and the conventional positioning method varying with the number of observation stations. The simulation conditions are: 3 targets, each base station is equipped with a uniform linear array with 4 array elements, the number of snapshots is 200, the global search range is 2000 meters, and the search step is 1 meter. From Figure 3 It can be seen that the method of the present application does not need spectrum peak search, and the calculation complexity is significantly reduced.

[0114] The performance estimation standard of the present application is the root mean square error (root mean square error, RMSE) defined as:

[0115]

[0116] wherein, Mon is the number of Monte Carlo experiments, K represents the number of targets, (x k , y k ) represents the actual value of the k-th target position.

[0117] Figure 4The root mean square error of the method of the application and the traditional two-step positioning method, subspace data fusion algorithm and Capon direct positioning algorithm is plotted as a function of signal-to-noise ratio. The simulation conditions are: there are 3 targets, their non-circular phases and positions are (10 rad, 30 rad, 50 rad) and [(-510 m, 100 m), (410 m, 320 m), (920 m, 220 m)], 3 observation base stations [(-900 m, -900 m), (0 m, -700 m), (900 m, -1200 m)], each base station is equipped with a uniform linear array with 5 array elements, the number of snapshots is 150, and the simulation is performed 500 times. Figure 4 It can be seen that the application achieves higher positioning accuracy.

[0118] Figure 5 The root mean square error of the method of the application and the traditional two-step positioning method, subspace data fusion algorithm and Capon direct positioning algorithm is plotted as a function of the number of snapshots. The simulation conditions are: there are 3 targets, their non-circular phases and positions are (10 rad, 30 rad, 50 rad) and [(-510 m, 100 m), (410 m, 320 m), (920 m, 220 m)], 3 observation base stations [(-900 m, -900 m), (0 m, -700 m), (900 m, -1200 m)], each base station is equipped with a uniform linear array with 7 array elements, the signal-to-noise ratio is 15 decibels, and the simulation is performed 500 times. Figure 5 It can be seen that the method of the application has better estimation performance than the traditional two-step positioning method, subspace data fusion algorithm and Capon direct positioning algorithm.

[0119] In summary, from the analysis of the simulation results, the method of the application can effectively increase the array aperture, has higher spatial degrees of freedom and positioning accuracy, and can estimate more targets. In addition, the method does not require spectrum peak search, and significantly reduces the computational complexity.

[0120] The embodiments of the application are described in detail above in combination with the drawings, but the application is not limited to the above-described embodiments, and various changes can be made within the knowledge of those skilled in the art without departing from the purpose of the application.

Claims

1. A Taylor compensation based multi-array non-circular signal positioning method, characterized in that it comprises the following steps: (1) constructing a multi-array non-circular signal positioning model to obtain received signal information; (2) using the elliptical covariance information of the target signal to extend the received signal, calculating its covariance matrix, and performing eigenvalue decomposition thereon; (3) obtaining azimuth information by direction finding at each observation base station, estimating non-circular phase, and performing Taylor compensation on the azimuth information; (4) correlating the azimuth information of all observation base stations to solve the initial estimate of the target position; (5) performing Taylor compensation on the initial estimate to obtain the accurate estimate of the target position; wherein the received signal of the lth observation base station is is the array flow pattern of each observation station, is the steering vector, d represents the inter-element distance, M represents the number of antenna elements of each observation base station, K represents the number of radiation sources, and λ represents the signal wavelength; u l = [x l , y l ] T represents the position of the lth observation base station, and the position of the kth radiation source is p k = [x k , y k ] T , u l (1), p k (1) respectively represent the first element in the orientation vector u l and p k , and θ l,k represents the angle of arrival of the kth radiation source received by the lth observation base station, represents a real-valued vector, n l (t) represents a Gaussian white noise vector; for a strictly second-order non-circular signal with a non-circularity of 1, wherein, denotes a non-circular phase, denotes the amplitude of the non-circular signal; The azimuth information obtained by direction finding at each observation base station is applied to ESPRIT technology, which comprises the following steps: To perform eigen decomposition to obtain a diagonal matrix Γ l , the kth diagonal element of Γ l is the eigenvalue μl ,k , and the estimated steering vector is extended and transformed by a matrix to obtain a block diagonal matrix composed of steering vectors and a vector containing non-circular phase represents non-circular phase; represents a signal subspace, e l,K represents an eigenvector; and row exchange matrices J1 and J2 are represented as: wherein, denotes a zero matrix; The estimated value of the non-circular phase is obtained by using matrix decomposition method and Lagrange multiplier method According to the estimated non-circular phase With the eigenvalue μl ,k , the angle of arrival estimation value of the lth observation station about the kth target is obtained The total steering vector of the L observation base stations is obtained by fusing the initial estimate of the target position of all observation base stations, and the least squares solution of the offset is then is orthogonal to it, i.e. initial estimate of the target position performing Taylor compensation, for performing first-order Taylor expansion and ignoring second-order and higher-order error terms, then is approximated as wherein denotes the n-th element of the vector defines the offset then is rewritten as According to obtained The accurate estimate of the kth target position is represented as 2. The Taylor compensation based multi-array non-circular signal positioning method according to claim 1, characterized in that the received signal of each observation base station is extended using the elliptical covariance information of the target signal as follows: The row exchange matrix J is defined as wherein, 3. The Taylor compensation based multi-array non-circular signal positioning method according to claim 1, characterized in that the initial estimate of the target position is calculated by correlating the angle of arrival estimates from the same radiation source of all observation base stations using the least squares method according to the uniqueness of the non-circular phase. is the extended direction matrix, and where the extended steering vector is The covariance matrix of the lth observation station is calculated as where T represents the number of snapshots, (·) H denotes the conjugate transpose, (·) * denotes taking the conjugate; performing eigen decomposition on the covariance matrix, we have: λ l,m denotes the eigenvalues ordered from large to small, and the corresponding eigenvectors are denoted by e l,m denotes, m = 1, 2, …, 2M, then the signal subspace is denoted by The noise subspace is denoted by Σ l is a diagonal matrix consisting of the eigenvalues. ​

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