A Direct Localization Method for Non-Circular Sources Based on Dimensionality Reduction and Weighted Subspace Data Fusion

Abstract

The present invention discloses a non-circular source direct positioning method based on dimensionality reduction weighted subspace data fusion. First, the non-circular characteristics of the target signal are utilized to expand the spatial information to obtain an increased virtual array aperture. Secondly, a weight is assigned to balance the error caused by the difference in the signal-to-noise ratio at the receiving end to obtain higher positioning accuracy and better robustness. Then, a dimensionality reduction search method is adopted to eliminate the high computational complexity brought by the non-circular phase search. Finally, a spectral peak search is performed on the weighted fusion cost function after dimensionality reduction, and the K points with the minimum function values are the target positions. The present invention can effectively increase the array aperture, has higher spatial degrees of freedom and positioning accuracy, can estimate more targets, and has good robustness. In addition, while ensuring the estimation performance, the present invention significantly reduces the computational complexity through dimensionality reduction search.

Description

Technical Field

[0001] The present invention belongs to the technical field of wireless positioning, and in particular relates to a non-circular source direct positioning method based on dimensionality reduction weighted subspace data fusion. Background Art

[0002] Most of the traditional direct position determination (DPD) techniques are studied for unknown signals. From the perspective of information theory, the more original information that can be utilized, the better the performance of the algorithm 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, quadrature phase shift keying signals, etc. all belong to non-circular (NC) signal types. Therefore, the research on non-circular signal direct positioning algorithms has important practical application significance.

[0003] The existing non-circular signal direct positioning algorithms ignore the impact of path propagation loss on the algorithm performance. In practical applications, when the non-circular signals of the same radiation target impact different observation base stations, the signal-to-noise ratios of different observation stations are often different and unstable. In addition, while using the non-circular characteristics of the target signal to expand the array aperture, it also brings high-dimensional search, and the computational complexity increases greatly. To solve the above problems, the present invention proposes a non-circular source direct positioning method based on dimensionality reduction weighted subspace data fusion. Summary of the Invention

[0004] Object of the Invention: To solve the problems existing in the prior art, the present invention provides a non-circular source direct positioning method based on dimensionality reduction weighted subspace data fusion, which ensures the estimation performance and at the same time significantly reduces the computational complexity and is easy for real-time processing.

[0005] Technical Solution: A non-circular source direct positioning method based on dimensionality reduction weighted subspace data fusion according to the present invention includes the following steps:

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

[0007] (2) Utilize the non-circular characteristics to expand the received signal, calculate its covariance matrix, and perform eigen-decomposition on it;

[0008] (3) Estimate the projection weights of each observation station to obtain the weighted cost function f NC-WSDF ;

[0009] (4) Adopt a dimensionality reduction algorithm to eliminate the non-circular phase search dimension and obtain the simplified cost function f NRD-WSDF ;

[0010] (5) Perform a spectral peak search on the simplified cost function to obtain an accurate estimate of the target position.

[0011] Further, the received signal in step (1) is:

[0012]

[0013] where is the array manifold of the \(l\)-th base station, is the steering vector; according to the free space propagation loss model, assuming that the signal powers of \(K\) radiation sources are all \(P\) k , at the observation position \(u\) l = [x l , y l T The signal power received from the \(k\)-th radiation source (position vector \(p\) k = [x k , y k T ) is \(P\) l，k , then is the path propagation loss coefficient of the signal received from the \(k\)-th radiation source by the \(l\)-th base station, is the propagation loss matrix; considering non-circular signals with a non-circularity rate of 1, expressed as Assuming represents the non-circular phase, represents the amplitude of the signal, then the non-circular phase matrix is obtained:

[0014]

[0015]

[0016] where is a real-valued vector representing the signal amplitude; \(n\) l \((t)\) represents a Gaussian white noise vector, \(M\) is the number of array elements, \(K\) is the number of targets, \(t=(1,2,\cdots T)\) represents the number of snapshots, and \(l=(1,2,\cdots L)\) is the number of base stations.

[0017] Further, the implementation process of step (2) is as follows:

[0018] According to the non-circular characteristics, the received signals of each observation base station are extended to:

[0019]

[0020] Its covariance matrix is where \(T\) represents the number of snapshots; perform eigenvalue decomposition on this covariance matrix to obtain:

[0021]

[0022] Assume λ l，m (m = 1, 2, …, 2M) represents the eigenvalues sorted from largest to smallest, and the corresponding eigenvectors are represented by e l，m (m = 1, 2, …, 2M), then the signal subspace is represented as The noise subspace is represented as

[0023] Furthermore, the implementation process of step (3) is as follows:

[0024] Since:

[0025]

[0026] The received signals of each observation base station are rewritten as:

[0027]

[0028] Where:

[0029]

[0030] is the extended steering vector; rewrite the covariance matrix R l :

[0031]

[0032] Where I 2M×2M is a 2M×2M dimensional identity matrix. If the noise power remains unchanged during the entire observation process, the signal-to-noise ratio at different observation positions is proportional to the covariance matrix R l is decomposed into:

[0033]

[0034] The eigenvalues of the covariance matrix are represented as:

[0035]

[0036] Where are the K larger non-zero eigenvalues of R s , representing the received signal power, then the noise power estimate is represented as:

[0037]

[0038] The received signal power estimate of the l-th observation station is:

[0039]

[0040] Obtain the weighted cost function:

[0041]

[0042] Furthermore, the implementation process of step (4) is as follows:

[0043] Since is a real-valued vector, there is Rewrite the received signal:

[0044]

[0045] where

[0046]

[0047] is the extended steering vector, which contains the target position information and non-circular phase information. Separate the position information and non-circular phase information:

[0048]

[0049] where O N represents an N-dimensional zero matrix:

[0050]

[0051]

[0052] Obtain the cost function of the l-th observation station as:

[0053]

[0054] Apply the dimensionality reduction method to it and simplify the cost function to:

[0055]

[0056] where

[0057] Furthermore, the target positions in step (5) are the K points with the minimum cost function values.

[0058] Advantages: Compared with the prior art, the advantages of the present invention are as follows: the estimation accuracy and robustness of the algorithm proposed in the present invention are superior to those of the traditional two-step positioning technology, the subspace data fusion technology (Subspace Data Fusion, SDF), and the non-circular signal subspace data fusion technology (NC-SDF); compared with the traditional two-step positioning technology and the 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 the estimation performance. Brief Description of the Drawings

[0059] Figure 1 is a flowchart of the present invention;

[0060] Figure 2 is a scenario diagram of multi-array joint positioning;

[0061] Figure 3 is a schematic diagram showing the variation of the computational complexity of the present invention and the traditional positioning method with the number of search grid points;

[0062] Figure 4 is a schematic diagram of the RMSE performance of the present invention and the traditional positioning method under different signal-to-noise ratios;

[0063] Figure 5 is a schematic diagram of the RMSE performance of the present invention and the traditional positioning method under different numbers of snapshots. Detailed Embodiments

[0064] The present invention will be further described in detail below with reference to the accompanying drawings.

[0065] The present invention provides a non-circular source direct positioning method based on dimensionality reduction weighted subspace data fusion, as Figure 1 shown, which specifically includes the following steps:

[0066] Step 1: Construct a multi-array non-circular signal direct positioning model as Figure 2 shown; obtain the received signal information r l (t).

[0067] The received signal of the l-th observation base station is where is the array manifold of each base station, and is the steering vector. According to the free space propagation loss model, assuming that the radiation source signal powers are all P k , at the observation position u l = [x l , y l T the received signal from the k-th radiation source p k = [x k , y k ​​T The power of the signal is P l，k , then is the path propagation loss coefficient, is the propagation loss matrix. The present invention only considers non-circular signals with a non-circularity ratio of 1, which can be expressed as Assume represents the non-circular phase, represents the amplitude of the signal, then we can get:

[0068]

[0069]

[0070] where is a real-valued vector; n l (t) represents the Gaussian white noise vector.

[0071] Step 2: Use the non-circularity property to expand the received signal, calculate its covariance matrix, and perform eigenvalue decomposition on it.

[0072] According to the non-circularity property, the received signals at each observation base station can be expanded as:

[0073]

[0074] Its covariance matrix is where T represents the number of snapshots. Performing eigenvalue decomposition on this covariance matrix, we can get:

[0075]

[0076] Assume λ l，m (m = 1, 2,..., 2M) represents the eigenvalues sorted from largest to smallest, and the corresponding eigenvectors are represented by e l,m (m = 1, 2,..., 2M), then the signal subspace is represented as The noise subspace is represented as

[0077] Step 3: Estimate the projection weights of each observation station; obtain the weighted cost function f NC-WSDF .

[0078] Since:

[0079]

[0080]

[0081]

[0082] Φ -1 = Φ *

[0083]

[0084] The received signals of each observation base station can be rewritten as:

[0085]

[0086] Where:

[0087]

[0088] is the extended steering vector. Then the covariance matrix R can be rewritten as l :

[0089]

[0090] Where I 2M×2M is a 2M×2M dimensional identity matrix. Assuming that the noise power remains unchanged throughout the observation process, the signal-to-noise ratio at different observation positions is proportional to i.e., P l，k , this value is unknown in practical applications, but the covariance matrix R l can be decomposed into:

[0091]

[0092] Under the same assumption, the eigenvalues of the covariance matrix can be expressed as:

[0093]

[0094] Where, is the K larger non-zero eigenvalues of R s , representing the received signal power, then the noise power estimate is expressed as:

[0095]

[0096] The received signal power estimate of the l-th observation station is:

[0097]

[0098] Then the weighted cost function can be obtained:

[0099]

[0100] Step 4: According to the dimensionality reduction idea, eliminate the non-circular phase search dimension; obtain the simplified cost function f NRD-WSDF .

[0101] Since is a real-valued vector with Rewrite the received signal:

[0102]

[0103] where

[0104]

[0105] is the extended steering vector, which contains the target position information and non-circular phase information. Separate the position information and non-circular phase information:

[0106]

[0107] where O N represents an N-dimensional zero matrix.

[0108]

[0109]

[0110] Then, the cost function of the l-th observation station can be obtained as:

[0111]

[0112] Applying the dimensionality reduction method to it, this cost function can be simplified to:

[0113]

[0114] where

[0115] Step 5: Obtain the accurate estimation of the target position through spectral peak search.

[0116] Perform spectral peak search on the weighted fusion cost function f NRD-WSDF (p) after dimensionality reduction in Step 4. The K points with the minimum function values are the target positions.

[0117] The spatial degree of freedom obtained by the method of the present invention is DOF = 2M - 1, while for the traditional uniform linear array with the same number of array elements, the spatial degree of freedom is DOF = M - 1, increasing a certain degree of freedom. Figure 3 is a schematic diagram of the computational complexity of the method of the present invention and the traditional positioning method varying with the number of search grid points. The simulation conditions are: 3 targets, 5 observation base stations, each base station is equipped with a uniform linear array with 10 array elements, and the number of snapshots is 200. From Figure 3It can be seen that the method (NRD-WSDF) of the present invention eliminates the non-circular phase search dimension, and compared with the method before dimension reduction (NC-WSDF), the computational complexity is significantly reduced.

[0118] The performance estimation criterion of the present invention is defined as the root mean square error (RMSE):

[0119]

[0120] where Mont is the number of Monte Carlo experiments, K represents the number of targets, represents the estimated value of the mn-th experiment, and x k represents the actual value.

[0121] Figure 4 is the performance curve of the root mean square error (RMSE) of the method of the present invention and the traditional direct positioning method varying with the signal-to-noise ratio (SNR). The simulation conditions are as follows: there are 3 targets, their non-circular phases and positions are (10, 20, 30) and [(-300, -300), (100, 100), (900, 900)] respectively, 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 4 array elements, the number of snapshots is 100, and the simulation is carried out 500 times. From Figure 4 it can be seen that the present invention achieves higher positioning accuracy.

[0122] Figure 5 is the performance curve of the root mean square error (RMSE) of the method of the present invention and the traditional direct positioning method varying with the number of snapshots. The simulation conditions are as follows: there are 3 targets, their non-circular phases and positions are (10, 20, 30) and [(-300, -300), (100, 100), (900, 900)] respectively, 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 4 array elements, the signal-to-noise ratio (SNR) is 10 dB, and the simulation is carried out 500 times. From Figure 5 it can be seen that the method proposed by the present invention has better estimation performance and better robustness compared with the traditional two-step positioning and direct positioning methods.

[0123] In summary, from the analysis of the simulation effect diagram, it can be seen that a non-circular source direct positioning method based on dimensionality reduction weighted subspace data fusion proposed by the present invention can effectively increase the array aperture, has higher spatial degrees of freedom and positioning accuracy, can estimate more targets, and has good robustness. In addition, while ensuring the estimation performance, this method significantly reduces the computational complexity through dimensionality reduction search.

[0124] The embodiments of the present invention have been described in detail above in conjunction with the accompanying drawings. However, the present invention is not limited to the above embodiments, and various changes can be made without departing from the spirit of the present invention within the scope of knowledge possessed by those of ordinary skill in the art.

Claims

1. A non-circular source direct positioning method based on dimensionality reduction weighted subspace data fusion, characterized by comprising the following steps: (1) Construct a direct positioning model for multi-array non-circular signals to obtain the received signal information r l (t); (2) Utilize the non-circular property to expand the received signal, calculate its covariance matrix, and perform eigenvalue decomposition on it; (3) Estimate the projection weights of each observation station to obtain the weighted cost function f NC-WSDF ; (4) Use a dimensionality reduction algorithm to eliminate the non-circular phase search dimension and obtain the simplified cost function f NRD-WSDF ; (5) Conduct a spectral peak search on the simplified cost function to obtain an accurate estimate of the target position; The implementation process of step (3) is as follows: Since: The received signals of each observation base station are rewritten as: Where: is the extended steering vector; rewrite the covariance matrix R l : Among them, I 2M×2M is a 2M×2M dimensional identity matrix. If the noise power remains unchanged during the entire observation process, the signal-to-noise ratio at different observation positions is proportional to the covariance matrix R l is decomposed into: The eigenvalues of the covariance matrix are expressed as: Among them, are the K larger non-zero eigenvalues of R s and represent the received signal power. Then the noise power estimate is expressed as: The estimated value of the received signal power of the l-th observation station is: Obtain the weighted cost function:

2. The non-circular source direct localization method based on dimensionality reduction weighted subspace data fusion according to claim 1, characterized in that, The received signal in step (1) is: Among them, is the array manifold of the l-th base station, is the steering vector; according to the free space propagation loss model, assuming that the signal powers of K radiation sources are all P k , at the observation position u l = [x l , y l T the signal power received from the k-th radiation source, that is, the position vector p k = [x k , y k T is P l，k , then is the path propagation loss coefficient of the signal received from the k-th radiation source by the th base station, is the propagation loss matrix; considering a non-circular signal with a non-circularity rate of 1, expressed as Assume represents the non-circular phase, represents the amplitude of the signal, then the non-circular phase matrix is obtained:​​ Among them, is a real-valued vector representing the signal amplitude; n l (t) represents the Gaussian white noise vector, M is the number of array elements, K is the number of targets, t = (1, 2, … T) represents the number of snapshots, and l = (1, 2, … L) is the number of base stations.

3. The non-circular source direct localization method based on dimensionality reduction weighted subspace data fusion according to claim 1, characterized in that, The implementation process of step (2) is as follows: According to the non-circular property, the received signals of each observation base station are expanded as: Its covariance matrix is where T represents the number of snapshots; performing eigenvalue decomposition on this covariance matrix gives: Suppose λ l，m represents the eigenvalues sorted from largest to smallest, and the corresponding eigenvectors are represented by e l，m where m = 1, 2, …, 2M, then the signal subspace is represented as The noise subspace is represented as 4. The non-circular source direct positioning method based on dimensionality reduction weighted subspace data fusion according to claim 1, characterized in that The implementation process of step (4) is as follows: Since is a real-valued vector and has rewrite the received signal: Among them, For an extended steering vector that includes target location information and non-circular phase information, separate the location information and the non-circular phase information: Where, represents a zero matrix of dimension: Obtain the cost function of the i-th observation station as: Apply a dimensionality reduction method to it to simplify the cost function to: Among them, 5. The non-circular source direct positioning method based on dimensionality reduction weighted subspace data fusion according to claim 1, characterized in that The target position in step (5) is the k points with the minimum cost function values.

Images