A direct location method for non-circular sources using multi-arrays based on weighted Euler ESPRIT

Abstract

The present invention discloses a multi-array non-circular source direct positioning method based on weighted Euler ESPRIT, comprising: first, utilizing the non-circular characteristics of the target signal and the Euler transform to expand spatial information to obtain an increased virtual array aperture; second, assigning a weight to balance the error caused by the difference in signal-to-noise ratio at the receiving end to obtain higher positioning accuracy; finally, performing a spectral peak search on the weighted fusion cost function, and the K points with the largest function values ​​are the target positions. The multi-array non-circular source direct positioning method based on weighted Euler ESPRIT designed by the present invention can effectively increase the array aperture, has higher spatial degrees of freedom and positioning accuracy, and can estimate more targets. In addition, this method significantly reduces the computational complexity through Euler transform while ensuring estimation performance.

Description

Technical Field

[0001] The present invention relates to the technical field of multi-array non-circular source positioning, and in particular to a multi-array non-circular source direct positioning method based on weighted Euler ESPRIT. Background Art

[0002] Traditional direct position determination (DPD) techniques mostly focus on unknown signals. From an information theory perspective, the more raw information available, the better the algorithm's performance. Research has shown that considering the signal characteristics of the target source when building the algorithm model can further improve positioning accuracy. In modern communication systems, signals such as amplitude modulation, binary phase-shift keying, pulse amplitude modulation, and quadrature phase-shift keying are all non-circular (NC) signals. Therefore, research on direct positioning algorithms for non-circular signals has important practical applications.

[0003] Existing direct localization algorithms for non-circular signals ignore the impact of path propagation losses on algorithm performance. In practical applications, when non-circular signals from the same radiating target impact different observation base stations, the signal-to-noise ratio (SNR) at each station often varies and becomes unstable. Furthermore, while exploiting the non-circular characteristics of the target signal expands the array aperture, it also introduces a high-dimensional search, significantly increasing computational complexity. To address these issues, the present invention proposes a multi-array direct localization method for non-circular sources based on weighted Euler ESPRIT. Summary of the Invention

[0004] In view of this, the purpose of the present invention is to provide a multi-array non-circular source direct positioning method based on weighted Euler ESPRIT, which significantly reduces the computational complexity while ensuring the estimation performance and is easy to process in real time.

[0005] In order to achieve the above object, the present invention adopts the following technical solutions:

[0006] A multi-array non-circular source direct positioning method based on weighted Euler ESPRIT, the positioning method comprising the following steps:

[0007] Step S1: construct a multi-array non-circular signal direct positioning model to obtain the receiving signal of each observation base station;

[0008] Step S2: Expand the received signal obtained in step S1 according to the non-circular characteristic and the Euler transform to obtain an expanded received signal, and then calculate the covariance matrix of the expanded received signal;

[0009] Step S3: Estimate the projection weight of each observation base station based on the covariance matrix obtained in step S2;

[0010] Step S4: Construct weighted fusion cost function f NC-Euler-WESPRIT ;

[0011] Step S5: Perform spectrum peak search on the weighted fusion cost function constructed in step S4 to obtain an accurate estimate of the target position.

[0012] Furthermore, in step S1, for the lth observation base station, the received signal is:

[0013]

[0014] In formula (1), For each base station array flow type, is the steering vector, where d is the array element spacing and λ is the wavelength. According to the free space propagation loss model, it is assumed that the radiation source signal power is P k , at the observation position u l =[x l ,y l ] T The radiation received from the kth source p k =[x k ,y k ] T The power of the signal is P l，k ,

[0015] but is the path propagation loss coefficient, is the propagation loss matrix, represents a real-valued vector; n l (t) represents the Gaussian white noise vector.

[0016] Furthermore, in step S1, only non-circular signals with a non-circularity rate of 1 are considered. Assumptions represents a non-circular phase, represents the amplitude of the signal, we get:

[0017]

[0018]

[0019] Furthermore, the step S2 specifically includes:

[0020] Step S201: Expand the received signal obtained in step S1 to:

[0021]

[0022] In formula (4), H l is represented as an expanded array flow pattern, and in(·) * , Re(·), Im(·) represent conjugate, real part and imaginary part respectively;

[0023] Step S202: Definition: Then the direction matrix H l Expressed as:

[0024]

[0025] In formula (5),

[0026] Step S203: First calculate the covariance matrix of the received signal, which is expressed as Where T represents the number of snapshots, (·) H represents the conjugate transpose; then perform eigendecomposition on the covariance matrix to obtain: in, Expressed as the signal subspace, is represented as the noise subspace.

[0027] Furthermore, the step S3 specifically includes:

[0028] Step S301: Rewrite the covariance matrix R l :

[0029]

[0030] In formula (6), I 2M×2M is a 2M×2M dimensional identity matrix;

[0031] Step S302: Assume that the noise power remains constant during the entire observation process and the signal-to-noise ratio at different observation positions is proportional to Covariance matrix R l is broken down into: Then the eigenvalues ​​of the covariance matrix are expressed as:

[0032]

[0033] In formula (7), It is R s The K non-zero eigenvalues ​​of represent the received signal power, and the noise power estimate is expressed as:

[0034] Step S303: According to the eigenvalue of the covariance matrix and the noise power estimate obtained in step S302, the received signal power estimate of the observed base station is obtained, and the expression is: Then the projection weight of l observation stations is:

[0035] Furthermore, the step S4 specifically includes:

[0036] Step S401: According to the orthogonality of the signal subspace and the noise subspace, we obtain: Among them, there exists a reversible matrix T such that

[0037] Step S402: define a reversible matrix, the expression is:

[0038]

[0039]

[0040] In formula (8) and formula (9),

[0041] Step S403: Define is a zero matrix, then we get:

[0042]

[0043] In formula (10), T1H l The k-th column element of

[0044]

[0045] Step S404: Accordingly, the following is obtained:

[0046] Step S405: According to the sum-difference-product formula, we obtain:

[0047] T1H l =T2H l Ξ l (11)

[0048] In formula (8),

[0049] Step S406: According to the least square method, we obtain:

[0050]

[0051] In formula (12), (·) + represents Moore-Penrose pseudoinverse;

[0052] Step S407: By calculating the Perform eigendecomposition and obtain γ l，k(k=1, 2, ...K), and then combine the data of L observation stations to construct a weighted fusion spectrum function, which is expressed as:

[0053]

[0054] In formula (13), v l，k (k=1, 2, ...K) represents the diagonal matrix Ξ l The kth diagonal element of .

[0055] Furthermore, in step S5, when performing spectrum peak search on the weighted fusion cost function, K points with the largest function values ​​are used as accurate estimates of the target position.

[0056] The beneficial effects of the present invention are:

[0057] The estimation accuracy of the algorithm proposed in the present invention is better than that of traditional two-step positioning technology and subspace data fusion technology (SDF); compared with traditional two-step positioning technology and subspace data fusion algorithm, the proposed method has more degrees of freedom and can identify more targets; the present invention can significantly reduce the computational complexity without sacrificing estimation performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 Schematic diagram of the process of a multi-array non-circular source direct positioning method based on weighted Euler ESPRIT provided in Example 1;

[0059] Figure 2 Schematic diagram of the multi-array non-circular signal direct positioning model provided in Example 1;

[0060] Figure 3 A schematic diagram showing how the algorithm running time varies with the number of search grid points for the positioning method provided in Example 1 and the traditional positioning method;

[0061] Figure 4 Schematic diagram of RMSE performance of the positioning method provided in Example 1 and the traditional positioning method under different signal-to-noise ratios;

[0062] Figure 5 This is a schematic diagram of the RMSE performance of the positioning method provided in Example 1 and the traditional positioning method under different snapshot numbers. DETAILED DESCRIPTION

[0063] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts shall fall within the scope of protection of the present invention.

[0064] Example 1

[0065] See also Figure 1-Figure 5 This embodiment provides a multi-array non-circular source direct positioning method based on weighted Euler ESPRIT. The specific steps of the method are as follows: Figure 1 As shown, the method specifically includes the following steps:

[0066] Step 1: Construct Figure 2 The multi-array non-circular signal direct positioning model shown in the figure is used to obtain the received signal information r l (t).

[0067] Specifically, in this embodiment, step 1 specifically includes:

[0068] The received signal of the lth observation base station is in, For each base station array flow type, is the steering vector, where d is the array element spacing and λ is the wavelength.

[0069] According to the free space propagation loss model, it is assumed that the radiation source signal power is P k , at the observation position u l =[x l ,y l ] T The radiation received from the kth source p k =[x k ,y k ] T The power of the signal is P l，k ,but is the path propagation loss coefficient, is the propagation loss matrix.

[0070] Specifically, in this embodiment, only non-circular signals with a non-circularity rate of 1 are considered, which can be expressed as Assumptions represents a non-circular phase, represents the amplitude of the signal, we can get:

[0071]

[0072]

[0073] In the formula, is a real-valued vector; n l (t) represents the Gaussian white noise vector.

[0074] Step 2: Based on the non-circular characteristics and Euler transform, the received signal of each observation base station is expanded to:

[0075]

[0076] Among them H l can be seen as an expanded array flow pattern, and

[0077]

[0078]

[0079] in(·) * , Re(·), and Im(·) represent conjugate, real part, and imaginary part, respectively.

[0080] definition Then the direction matrix H l It can be expressed as

[0081]

[0082] In the formula,

[0083] The covariance matrix can then be calculated as Where T represents the number of snapshots, (·) H represents conjugate transpose;

[0084] Perform eigendecomposition on the covariance matrix and get:

[0085]

[0086] Assume λ l，m (m=1, 2, ..., 2M) represents the eigenvalues ​​sorted from large to small, and the corresponding eigenvectors are represented by e l，m (m=1,2,…,2M) represents, then the signal subspace is expressed as The noise subspace is expressed as

[0087] Step 3: Estimate the projection weight of each observation station.

[0088] Specifically, in this embodiment, step 3 specifically includes:

[0089] Rewrite the covariance matrix R l :

[0090]

[0091] Among them, I 2M×2M is a 2M×2M dimensional identity matrix;

[0092] Assuming that the noise power remains constant during the entire observation process, the signal-to-noise ratio at different observation locations is proportional to Covariance matrix R l can be broken down into:

[0093]

[0094] The eigenvalues ​​of the covariance matrix are expressed as:

[0095]

[0096] in, It is R s The K larger non-zero eigenvalues ​​of represent the received signal power, and the noise power estimate is expressed as:

[0097]

[0098] The estimated power of the received signal at the lth observation station is:

[0099]

[0100] Then the projection weight of the lth observation station can be obtained

[0101] Step 4: Construct weighted fusion cost function f NC-Euler-WESPRIT .

[0102] Specifically, in this embodiment, step 4 specifically includes:

[0103] According to the orthogonality of the signal subspace and the noise subspace, we can get

[0104]

[0105] That is to say, there exists a reversible matrix T such that

[0106]

[0107] Define an invertible matrix

[0108]

[0109]

[0110] In the formula,

[0111] is a zero matrix. Then we can get

[0112]

[0113] Among them, T1H l The k-th column element of

[0114]

[0115] Similarly,

[0116]

[0117] Among them, T2H l The k-th column element of

[0118]

[0119] Then according to the sum-difference-product formula, we can get

[0120] T1H l =T2H l Ξ l

[0121] In the formula,

[0122] According to the least squares method, we can get

[0123]

[0124] in,(·) + represents the Moore-Penrose pseudo-inverse. Then, by By performing eigendecomposition, we can easily get γ l，k (k=1, 2, ...K).

[0125] Finally, by combining the data from L observation stations, a weighted fusion spectrum function can be constructed:

[0126]

[0127] Among them, v l，k (k=1, 2, ...K) represents the diagonal matrix Ξ l The kth diagonal element of .

[0128] Step 5: Get an accurate estimate of the target position by searching for the spectrum peak.

[0129] Specifically, the weighted fusion cost function f in step 4 NC-Euler-WESPRIT Perform spectrum peak search, and the K points with the largest function value are the target positions.

[0130] The spatial degree of freedom obtained by the method provided in this embodiment is DOF=2M-1, while the spatial degree of freedom of a traditional uniform linear array with the same number of array elements is DOF=M-1, which increases the degree of freedom to a certain extent. Figure 3 The following is a schematic diagram showing how the running time of the method described in this embodiment and the traditional positioning method changes with the number of search grid points. The simulation conditions are: 3 targets, 6 observation base stations, each base station is equipped with a uniform linear array with 5 elements, the number of snapshots is 200, and the signal-to-noise ratio is 15dB. Figure 3 It can be seen that the method (NC-Euler-WESPRIT) described in the present invention converts a complex matrix into a real matrix, and the computational complexity is significantly reduced compared to the method before conversion (NC-ESPRIT).

[0131] The performance estimation standard of the method provided in this embodiment is the root mean square error (RMSE), which is defined as:

[0132]

[0133] Among them, Mon is the number of Monte Carlo experiments, K is the number of targets, represents the estimated value of the mnth experiment, x k Indicates actual value.

[0134] Figure 4 The performance curve of the root mean square error (RMSE) of the method described in this embodiment and the traditional direct positioning method as the signal-to-noise ratio (SNR) changes. The simulation conditions are: there are 3 targets, their non-circular phases and positions are (10, 20, 30) and [(-3000, -3000), (0, 0), (3000, 3000)], 6 observation base stations [(-6000, -9000), (-3600, -7000), (-1200, -10000), (1200, -8000), (3600, -11000), (6000, -12000)], each base station is equipped with a uniform linear array with 6 elements, the number of snapshots is 100, and the simulation is repeated 1000 times. Figure 4 It can be seen that this embodiment achieves higher positioning accuracy.

[0135] Figure 5The performance curve of the root mean square error (RMSE) of the method described in this embodiment and the traditional direct positioning method varies with the number of snapshots. The simulation conditions are: there are 3 targets, their non-circular phases and positions are (10, 20, 30) and [(-3000, -3000), (0, 0), (3000, 3000)], 6 observation base stations [(-6000, -9000), (-3600, -7000), (-1200, -10000), (1200, -8000), (3600, -11000), (6000, -12000)], each base station is equipped with a uniform linear array with 6 elements, a signal-to-noise ratio (SNR) of 15dB, and 1000 simulations. From Figure 5 It can be seen that the direct positioning method proposed in this embodiment has better estimation performance than the traditional two-step positioning method.

[0136] In summary, analysis of the simulation results demonstrates that the proposed multi-array non-circular source direct localization method based on weighted Euler ESPRIT can effectively increase array aperture, achieve higher spatial degrees of freedom and positioning accuracy, and estimate more targets. Furthermore, this method significantly reduces computational complexity through Euler transformation while maintaining estimation performance. Any details not described in detail herein are generally known to those skilled in the art.

[0137] The above describes in detail the preferred embodiments of the present invention. It should be understood that those skilled in the art can make numerous modifications and variations based on the concepts of the present invention without inventive effort. Therefore, any technical solutions that can be derived by those skilled in the art through logical analysis, reasoning, or limited experimentation based on the concepts of the present invention and the prior art should be within the scope of protection defined by the claims.

Claims

1. A multi-array non-circular source direct positioning method based on weighted Euler ESPRIT, characterized by: The positioning method comprises the following steps: Step S1: construct a multi-array non-circular signal direct positioning model to obtain the receiving signal of each observation base station; Step S2: Expand the received signal obtained in step S1 according to the non-circular characteristic and the Euler transform to obtain an expanded received signal, and then calculate the covariance matrix of the expanded received signal; Step S3: Estimate the projection weight of each observation base station based on the covariance matrix obtained in step S2; Step S4: Construct weighted fusion cost function f NC-Euler-WESPRIT , including the following steps: Step S401, subspace orthogonality: According to the orthogonality of the signal subspace and the noise subspace, there exists a reversible matrix T such that the subspace relationship is satisfied after transformation; Step S402: Construct a reversible matrix: define two matrices T1 and T2 to transform the original data structure and extract the real and imaginary part information; Step S403, combination operation: construct matrix T1H l and T2H l , the differential relationship is derived based on the matrix differential expression; Step S404, eigendecomposition: extracting the angle information matrix contained in the matrix difference expression; Step S405, least squares solution: using the least squares method to solve the matrix expression containing the parameters to be estimated; Step S406: Construct a cost function: construct a weighted fusion cost function using data from multiple observation stations and the obtained angle estimates for target positioning; Step S5: Perform spectrum peak search on the weighted fusion cost function constructed in step S4 to obtain an accurate estimate of the target position.

2. The multi-array non-circular source direct positioning method based on weighted Euler ESPRIT according to claim 1, characterized in that: In step S1, for the lth observation base station, the received signal is: In formula (1), For each base station array flow type, is the steering vector, where d is the array element spacing and λ is the wavelength. According to the free space propagation loss model, it is assumed that the radiation source signal power is P k , at the observation position u l =[x l ,y l ] T The radiation received from the kth source p k =[x k ,y k ] T The power of the signal is P l,k , but is the path propagation loss coefficient, is the propagation loss matrix, represents a real-valued vector; n l (t) represents the Gaussian white noise vector.

3. The multi-array non-circular source direct positioning method based on weighted Euler ESPRIT according to claim 2, characterized in that: In step S1, only the non-circular signal with a non-circularity rate of 1 is considered. Assumptions represents a non-circular phase, represents the amplitude of the signal, we get:

4. The multi-array non-circular source direct positioning method based on weighted Euler ESPRIT according to claim 3, characterized in that: The step S2 specifically includes: Step S201: Expand the received signal obtained in step S1 to: In formula (4), H l is represented as an expanded array flow pattern, and Where (·)*, Re(·), and Im(·) represent conjugate, real part, and imaginary part, respectively; Step S202: Definition: Then the direction matrix H l Expressed as: In formula (5), Step S203: First calculate the covariance matrix of the received signal, which is expressed as Where T represents the number of snapshots, (·) H represents the conjugate transpose; then perform eigendecomposition on the covariance matrix to obtain: in, Expressed as the signal subspace, is represented as the noise subspace.

5. The multi-array non-circular source direct positioning method based on weighted Euler ESPRIT according to claim 4, characterized in that: The step S3 specifically includes: Step S301: Rewrite the covariance matrix R l : In formula (6), I 2M×2M is a 2M×2M dimensional identity matrix; Step S302: Assume that the noise power remains constant during the entire observation process and the signal-to-noise ratio at different observation positions is proportional to Covariance matrix R l is broken down into: Then the eigenvalues ​​of the covariance matrix are expressed as: In formula (7), It is R s The K non-zero eigenvalues ​​of represent the received signal power, 1≤m≤K, then the noise power estimate is expressed as: Step S303: According to the eigenvalue of the covariance matrix and the noise power estimate obtained in step S302, the received signal power estimate of the observed base station is obtained, and the expression is: Then the projection weight of l observation stations is:

6. The multi-array non-circular source direct positioning method based on weighted Euler ESPRIT according to claim 5, characterized in that: The step S4 specifically includes: Step S401: According to the orthogonality of the signal subspace and the noise subspace, we obtain: Among them, there exists a reversible matrix T such that Step S402: define a reversible matrix, the expression is: In formula (8) and formula (9), Step S403: Define is a zero matrix, then we get: In formula (10), T1H l The k-th column element of Accordingly, we get: Step S404: According to the sum-difference-product formula, we obtain: T1H l =T2H l The l (11) Formula (11) Step S405: According to the least square method, we obtain: In formula (12), (·) + represents Moore-Penrose pseudoinverse; Step S406: By calculating the Perform eigendecomposition and obtain γ l，k , k = 1, 2, ..., K and then combine the data of L observation stations to construct a weighted fusion spectrum function, which is expressed as: In formula (13), v l，k represents the diagonal matrix Ξ l The k-th diagonal element of , k = 1, 2,…, K.

7. The multi-array non-circular source direct positioning method based on weighted Euler ESPRIT according to claim 6, characterized in that: In step S5, when performing spectrum peak search on the weighted fusion cost function, K points with the largest function values ​​are used as accurate estimates of the target position.

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