A fast method for locating non-circular sources using multiple arrays based on ESPRIT and weighted dimensionality reduction search

Abstract

The present invention discloses a multi-array non-circular source rapid positioning method based on ESPRIT and weighted dimensionality reduction search, comprising the following steps: first, using the elliptical covariance information of the target signal to expand the spatial information to obtain an increased virtual array aperture; second, obtaining the azimuth information of each observation station through the rotational invariance technique (ESPRIT); then, using the non-circular phase to associate the azimuth information of each observation station with the signal source; and then, combining the information of all base stations and using the least squares method to directly solve the target position as an initial estimate. Finally, a weighted dimensionality reduction search is performed within a small range near the initial estimate to improve the estimation accuracy. Compared with traditional two-step positioning algorithms, subspace data fusion algorithms (SDF), and Capon direct positioning algorithms, the present invention has higher spatial degrees of freedom and positioning accuracy, and can estimate more targets. In addition, the method significantly reduces the computational complexity while ensuring estimation performance.

Description

Technical Field

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

[0002] Traditional multi-array passive location 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 location 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 multi-array passive location algorithms for non-circular signals has important practical applications.

[0003] Existing multi-array passive location algorithms for non-circular signals ignore signal losses during propagation. In practical applications, when signals from the same radiating target impact different observation stations, the received signal-to-noise ratio (SNR) at each station often varies and is unstable. Furthermore, while leveraging the elliptical covariance information of the target signal to expand the array aperture, it also introduces high-dimensional search issues, significantly increasing computational complexity. To address these issues, the present invention proposes a multi-array method for rapid non-circular source location: combining ESPRIT with weighted dimensionality reduction search. Summary of the Invention

[0004] Purpose of the invention: In order to solve the problems existing in the prior art, the present invention provides a multi-array non-circular source rapid positioning method: combining ESPRIT with weighted dimensionality reduction search, while ensuring estimation performance, significantly reducing the computational complexity and facilitating real-time processing.

[0005] Technical solution: A multi-array non-circular source rapid location method based on ESPRIT and weighted dimensionality reduction search, including the following steps:

[0006] 6) Construct a multi-array non-circular signal direct positioning model, which includes l observation base stations and k radiation sources, and obtain the received signal r of the lth observation base station l (t);

[0007] 7) The received signal r l (t) is expanded to receive signal z l (t), calculate the received signal z l The covariance matrix R of (t) l , and the covariance matrix R l Feature decomposition;

[0008] 8) Based on the ESPRIT rotation-invariant subspace algorithm, the direction of the l-th observation base station is obtained, and the projection weight of the non-circular phase and the l-th observation base station is estimated.

[0009] 9) Correlating all observation station data based on the non-circular phase and least squares method in step 3) to obtain a rough estimate of the target position;

[0010] 10) Perform a weighted dimensionality reduction search within the range near the rough estimate to obtain an accurate estimate of the target position.

[0011] Preferably, the received signal r of the lth observation base station in step 1) l (t) is:

[0012]

[0013] in, is the array flow pattern of the lth observation base station, is the guidance vector, d represents the array element spacing, M is the number of array elements, K is the number of targets, and 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 signal power is P l，k , [] T Represents the transpose of the matrix, and the propagation loss matrix is:

[0014]

[0015] Path propagation loss coefficient:

[0016]

[0017] Non-circular signal:

[0018] Noncircular phase matrix:

[0019]

[0020] Amplitude of non-circular signal:

[0021]

[0022] represents the amplitude of the non-circular signal, where M is the number of array elements, K is the number of targets, t = (1, 2, ..., T) represents the number of snapshots, l = (1, 2, ..., L) is the number of base stations, is the amplitude of the non-circular signal; n l (t) represents the Gaussian white noise vector, Indicates non-circular phase.

[0023] Preferably, in step 2), the signal z is received l (t) is expressed as:

[0024]

[0025] The row exchange matrix J is expressed as:

[0026]

[0027] The expanded direction matrix is ​​expressed as:

[0028]

[0029] Steering vector Expressed as:

[0030]

[0031]

[0032] in(·) * represents conjugation, u l (1) represents the vector u l The first element, p k (1) represents the vector p k The first element of γ l，k Represents variables to facilitate subsequent derivation;

[0033] Then the covariance matrix is:

[0034]

[0035] Where T represents the number of snapshots, (·) H represents the conjugate transpose;

[0036] Perform eigendecomposition on the covariance matrix and get:

[0037]

[0038] 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), the signal subspace is expressed as:

[0039]

[0040] The noise subspace is expressed as,

[0041]

[0042] ∑ l is a diagonal matrix of eigenvalues.

[0043] Preferably, the implementation process of step 3) is:

[0044] Define the row exchange matrix J1, J2:

[0045]

[0046]

[0047] matrix:

[0048]

[0049]

[0050] represents the zero matrix;

[0051] According to the orthogonality of the signal subspace and the noise subspace,

[0052]

[0053]

[0054] T l represents a reversible matrix,

[0055] Diagonal matrix Γ l Expressed as:

[0056]

[0057] Let the diagonal matrix Γ be l The kth diagonal element of is μ l，k , then the estimated steering vector is expressed as:

[0058]

[0059] The expanded steering vector is expressed as:

[0060]

[0061] Perform matrix transformation to separate the orientation information and non-circular phase information:

[0062]

[0063] The orientation information is a block diagonal matrix composed of steering vectors Expressed as:

[0064]

[0065] Vector containing non-circular phase information Expressed as:

[0066]

[0067] Constructor

[0068]

[0069] definition:

[0070] is the multiplier, vector e=[1,0] T ,make Vector The derivative of is zero, that is:

[0071]

[0072] get:

[0073]

[0074] Also because

[0075]

[0076] get:

[0077]

[0078] Substitute it back into You can get:

[0079]

[0080] Vector The second element of takes the phase and divides it by 2 to get the non-circular phase estimate

[0081] The weight of the received data at the lth observation station is expressed as:

[0082]

[0083] represents the estimated value of the received signal power at the lth observation station; represents the noise power estimate of the lth observation station.

[0084] Preferably, in step 4), the rough estimate of the k-th target position is expressed as:

[0085]

[0086] Among them, the matrix:

[0087]

[0088]

[0089]

[0090] u L Represents the position vector of the lth observation station and the estimated angle of arrival of the lth observation station with respect to the kth target

[0091] Preferably, the implementation process of step 5) is: according to the function constructed by the Lagrange multiplier method in step 4) and the weight of the data received by each observation station,

[0092] Substitution Get the cost function after weighted dimensionality reduction:

[0093]

[0094] in,

[0095]

[0096]

[0097] and Represents vectors and The nth element in

[0098] The cost function is used to search for peaks, and the K peak positions obtained are the precise values ​​of the estimated values. Δx represents the possible deviation of the x-coordinate during the peak search, and Δy represents the possible deviation of the y-coordinate during the peak search.

[0099] Beneficial effects: Compared with the existing technology, the beneficial effects of the present invention are: the estimation accuracy of the algorithm proposed in the present invention is better than the traditional two-step positioning technology, subspace data fusion technology, and Capon direct positioning technology; compared with the traditional two-step positioning technology, subspace data fusion algorithm and Capon direct positioning algorithm, the proposed method has more degrees of freedom and can identify more targets; the present invention can significantly reduce the computational complexity while ensuring the estimation performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0100] Figure 1 is a flow chart of the present invention;

[0101] Figure 2 The multi-array joint positioning scene graph of the present invention;

[0102] Figure 3 Schematic diagram showing how the algorithm running time of the present invention and the traditional positioning method changes with the search step size;

[0103] Figure 4 Schematic diagram of the root mean square error performance of the present invention and the traditional positioning method under different signal-to-noise ratios;

[0104] Figure 5 Schematic diagram of the root mean square error performance of the present invention and the traditional positioning method under different snapshot numbers. DETAILED DESCRIPTION

[0105] The present invention will be further explained below with reference to the accompanying drawings.

[0106] The present invention provides a multi-array non-circular source fast positioning method: combining ESPRIT with weighted dimensionality reduction search, such as Figure 1 As shown, the specific steps include:

[0107] Step 1: Construct Figure 2 The multi-array non-circular signal positioning model shown in FIG; the received signal information r is obtained l (t).

[0108] The received signal of the lth observation base station is in, For the array flow pattern at each observation station, is the steering vector, and d represents the array element spacing. Since the signal will be lost when propagating in the air, 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 signal power is P l，k ,definition is the path propagation loss coefficient, is the propagation loss matrix. The present invention only considers non-circular signals with a non-circularity of 1, which can be expressed as Assumptions represents a non-circular phase, represents the amplitude of the non-circular signal, we can get:

[0109]

[0110]

[0111] in, is a real-valued vector; n l (t) represents the Gaussian white noise vector.

[0112] Step 2: Using the elliptical covariance information of the target signal, the received signal of each observation base station is expanded to:

[0113]

[0114] The row exchange matrix J is defined as

[0115]

[0116] can be viewed as an extended direction matrix, and

[0117]

[0118] Among them, the extended steering vector for

[0119]

[0120]

[0121] Then the covariance matrix of the lth observation station can be calculated as Where T represents the number of snapshots, (·) H represents the conjugate transpose, (·) * Indicates taking conjugate; perform eigendecomposition on the covariance matrix and obtain:

[0122]

[0123] 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 ∑ l is a diagonal matrix composed of eigenvalues.

[0124] Step 3: Apply ESPRIT technology to obtain the azimuth information of each observation station and estimate the non-circular phase and the weight of the received data of each observation station.

[0125] Define row switching matrix J1, J2

[0126]

[0127]

[0128] in,

[0129]

[0130]

[0131] Represents the zero matrix. According to the orthogonality of the signal subspace and the noise subspace, we can get That is, there exists a reversible matrix T l , making Then you can get

[0132]

[0133]

[0134] in,(·) + represents the generalized inverse, Γ l is a diagonal matrix

[0135]

[0136] right By performing eigendecomposition, we can easily obtain Γ l , whose diagonal elements contain the target's orientation information, denoted by Γ l The kth diagonal element of is μ l，k , then the estimated steering vector can be written as

[0137]

[0138] The expanded steering vector can be recorded as

[0139]

[0140] Perform matrix transformation to separate the azimuth information and non-circular phase information

[0141]

[0142] in, is a block diagonal matrix composed of steering vectors, is a vector containing a noncircular phase

[0143]

[0144]

[0145] Here, the non-circular phase is unknown, but when the estimated value of the non-circular phase Approximating the true value When , the following formula is established

[0146]

[0147] definition Then the following formula holds

[0148]

[0149] definition but Can be simplified to

[0150]

[0151] Let e ​​= [1, 0] T , then According to the Lagrange multiplier method, the following function can be constructed

[0152]

[0153] in, Let right The derivative of is zero, that is

[0154]

[0155] but

[0156]

[0157] Also because Can get

[0158]

[0159] Substitute it back into Can get

[0160]

[0161] Therefore, the non-circular phase can be estimated according to the above formula

[0162] Rewrite the covariance matrix R l :

[0163]

[0164] Among them, I 2M×2MIt is a 2M×2M dimensional unit matrix. Assuming that the noise power remains unchanged during the entire observation process, the signal-to-noise ratio of different observation positions is proportional to Covariance matrix R l can be broken down into:

[0165]

[0166] Where diag{·} represents a diagonal matrix, Represents the noise power of the lth observation station. The eigenvalue of the covariance matrix is ​​expressed as:

[0167]

[0168] 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:

[0169]

[0170] The estimated power of the received signal at the lth observation station is:

[0171]

[0172] Then the received data weight of the lth observation station can be obtained

[0173] Step 4: Based on the non-circular phase and the least squares method, the data of all observation stations are correlated to directly solve the rough estimate of the target position.

[0174] According to the non-circular phase estimated in step 3 and eigenvalue μ l，k , we can easily obtain the estimated value of the arrival angle of the lth observation station with respect to the kth target Because the non-circular phase of the target from the same radiation source is unique. When the distance between the base station and the target is far enough, the following formula is established

[0175]

[0176] Among them, p k (n) represents the vector p k The nth element, u l (n) represents vector u l The nth element of , converting the above formula into matrix multiplication

[0177] [1-tan(θ l，k )]p k =[1 -tan(θ l，k )]u l

[0178] Then, combining the information from all observation stations, we can get

[0179] F 1，k p k =F 2，k G

[0180] in,

[0181]

[0182]

[0183]

[0184] Then, the rough estimate of the kth target position can be calculated as follows:

[0185]

[0186] Step 5: Perform a weighted dimensionality reduction search in a small range around the rough estimate to obtain a precise estimate of the target location.

[0187] According to the function constructed by the Lagrange multiplier method in step 4 and the weight of the data received by each observation station, Substitution The cost function after weighted dimensionality reduction can be obtained

[0188] in,

[0189]

[0190]

[0191] The values ​​of Δx and Δy can be adjusted according to the weight of the received data. When the weight is relatively small, the value can be appropriately increased. When the weight is relatively large, the value can be appropriately reduced. and Represents vectors and The nth element in .

[0192] The spatial degree of freedom obtained by the method of the present invention is DOF=2(M-1), while the spatial degree of freedom of the traditional uniform linear array is DOF=M-1 under the condition of the same number of array elements, which increases the degree of freedom to a certain extent. Figure 3 This is a schematic diagram showing how the running time of the method of the present invention and the traditional positioning method changes with the search step size. The simulation conditions are: 2 targets, 5 observation base stations, each base station is equipped with a uniform linear array with 3 elements, the number of snapshots is 200, the global search range is 2000 meters, and the local search range is 10 meters. Figure 3It can be seen that the method of the present invention transforms the high-dimensional global spectral function search of each observation station into a local search, and the computational complexity is significantly reduced.

[0193] The performance estimation standard of the present invention is the root mean square error (RMSE) which is defined as:

[0194]

[0195] Among them, Mon is the number of Monte Carlo experiments, K is the number of targets, represents the estimated value of the kth target position in the mnth experiment, (x k ,y k ) represents the actual value of the kth target position.

[0196] Figure 4 The performance curve of the root mean square error of the method of the present invention and the traditional two-step positioning method, subspace data fusion algorithm and Capon direct positioning algorithm as the signal-to-noise ratio changes. The simulation conditions are: there are 3 targets, their non-circular phases and positions are (10 radians, 30 radians, 70 radians) and [(100 meters, 900 meters), (-500 meters, 500 meters), (900 meters, 200 meters)], 5 observation base stations [(-900 meters, -900 meters), (-450 meters, -700 meters), (0 meters, -1000 meters), (450 meters, -800 meters), (900 meters, -1100 meters), each base station is equipped with a uniform linear array with 5 elements, the number of snapshots is 200, the local search range is 10 meters, the search step is 1 meter, and the simulation is performed 500 times. From Figure 4 It can be seen that the present invention achieves higher positioning accuracy.

[0197] Figure 5 The performance curve of the root mean square error of the method of the present invention and the traditional two-step positioning method, subspace data fusion algorithm and Capon direct positioning algorithm as the number of snapshots changes. The simulation conditions are: there are 3 targets, their non-circular phases and positions are (10 radians, 30 radians, 70 radians) and [(100 meters, 900 meters), (-500 meters, 500 meters), (900 meters, 200 meters)], 5 observation base stations [(-900 meters, -900 meters), (-450 meters, -700 meters), (0 meters, -1000 meters), (450 meters, -800 meters), (900 meters, -1100 meters), each base station is equipped with a uniform linear array with 5 elements, a signal-to-noise ratio of 20 decibels, a local search range of 10 meters, a search step of 1 meter, and 500 simulations. From Figure 5 It can be seen that the method proposed in the present invention has better estimation performance than the traditional two-step positioning method, the subspace data fusion algorithm and the Capon direct positioning algorithm.

[0198] In summary, analysis of the simulation results demonstrates that the proposed multi-array non-circular source rapid localization method, combining ESPRIT with weighted dimensionality reduction search, effectively increases the array aperture, achieving higher spatial degrees of freedom and positioning accuracy, and enabling the estimation of more targets. Furthermore, this method significantly reduces computational complexity by transforming the high-dimensional global spectral function search at each observation station into a local search while maintaining estimation performance.

[0199] The embodiments of the present invention are described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Various changes can be made within the scope of knowledge possessed by ordinary technicians in this field without departing from the spirit of the present invention.

Claims

1. A multi-array non-circular source fast location method based on ESPRIT and weighted dimensionality reduction search, characterized by: The following steps are involved: 1) Construct a multi-array non-circular signal direct positioning model, which includes l observation base stations and k radiation sources, and obtain the received signal r of the lth observation base station l (t); 2) The received signal r l (t) is expanded to receive signal z l (t), calculate the received signal z l The covariance matrix R of (t) l , and the covariance matrix R l Feature decomposition; 3) Based on the ESPRIT rotation-invariant subspace algorithm, the direction of the l-th observation base station is obtained, and the projection weight of the non-circular phase and the l-th observation base station is estimated. in, represents the estimated value of the received signal power at the lth observation station; represents the noise power estimate of the lth observation station; 4) Correlating the data of all observation stations based on the non-circular phase and least squares method in step 3) to obtain a rough estimate of the target position; 5) Perform a weighted dimensionality reduction search within the range near the rough estimate to obtain an accurate estimate of the target position.

2. The multi-array non-circular source rapid location method based on ESPRIT and weighted dimensionality reduction search according to claim 1, characterized in that: The received signal r of the lth observation base station in step 1) l (t) is: in, is the array flow pattern of the lth observation base station, is the guidance vector, d represents the array element spacing, M is the number of array elements, K is the number of targets, and 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 signal power is P l，k , [] T Represents the transpose of the matrix, and the propagation loss matrix is: Path propagation loss coefficient: Non-circular signal: Noncircular phase matrix: Amplitude of non-circular signal: in, represents the amplitude of the non-circular signal, M is the number of array elements, K is the number of targets, t is the number of snapshots, t = 1, 2, ..., T, l is the number of base stations, l = 1, 2, ..., L, is the amplitude of the non-circular signal; n l (t) represents the Gaussian white noise vector, Indicates non-circular phase.

3. The multi-array non-circular source rapid location method based on ESPRIT and weighted dimensionality reduction search according to claim 2, characterized in that: Step 2) Receive signal z l (t) is expressed as: The row exchange matrix J is expressed as: The expanded direction matrix is ​​expressed as: Steering vector Expressed as: in,(·) * represents conjugation, u l (1) represents the vector u l The first element, p k (1) represents the vector p k The first element of γ l，k Represents variables to facilitate subsequent derivation; Then the covariance matrix is: Where T represents the number of snapshots, (·) H represents conjugate transpose; Perform eigendecomposition on the covariance matrix and get: Assume λ l，m Represents the eigenvalues ​​sorted from large to small, m = 1, 2, ..., 2M, and the corresponding eigenvector is e l，m Indicates that m = 1, 2, ..., 2M; The signal subspace is expressed as: The noise subspace is expressed as: Among them, ∑ l is a diagonal matrix of eigenvalues.

4. The multi-array non-circular source rapid location method based on ESPRIT and weighted dimensionality reduction search according to claim 3, characterized in that: The implementation process of step 3) is: Define the row exchange matrix J1, J2: matrix: in, represents the zero matrix; According to the orthogonality of the signal subspace and the noise subspace: Among them, T l represents a reversible matrix; Diagonal matrix Γ l Expressed as: Let the diagonal matrix Γ be l The kth diagonal element of is μ l，k , then the estimated steering vector is expressed as: The expanded steering vector is expressed as: Perform matrix transformation to separate the orientation information and non-circular phase information: The orientation information is a block diagonal matrix composed of steering vectors Expressed as: Vector containing non-circular phase information Expressed as: Constructor definition: is the multiplier, vector e=[1,0] T ,make Vector The derivative of is zero, that is: get: And because: get: Substitute it back into get: Vector The second element of takes the phase and divides it by 2 to get the non-circular phase estimate The weight of the received data at the lth observation station is expressed as:

5. The multi-array non-circular source rapid location method based on ESPRIT and weighted dimensionality reduction search according to claim 4, characterized in that: In step 4): the rough estimate of the kth target position is expressed as: Among them, the matrix: u L Represents the position vector of the lth observation station and the estimated angle of arrival of the lth observation station with respect to the kth target 6. The multi-array non-circular source rapid location method based on ESPRIT and weighted dimensionality reduction search according to claim 5, characterized in that: The implementation process of step 5) is as follows: Based on the function constructed by the Lagrange multiplier method in step 4) and the weight of the data received by each observation station, Substitution Get the cost function after weighted dimensionality reduction: in, in, and Represents vectors and The nth element in The cost function is used to search for peaks, and the K peak positions obtained are the precise values ​​of the estimated values. Δx represents the possible deviation of the x-coordinate during the peak search, and Δy represents the possible deviation of the y-coordinate during the peak search.

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