Multi-array direct positioning method based on two-dimensional discrete fourier transform

Abstract

This invention discloses a multi-array direct positioning method based on two-dimensional discrete Fourier transform. First, the cross-covariance of the received signals from each observation station is calculated, and the automatically matched azimuth information of each observation station is obtained through two-dimensional discrete Fourier transform (2D-DFT). Then, a phase rotation matrix is ​​constructed to compensate for the azimuth information of each observation station, resulting in more accurate azimuth information. Finally, the target position is directly solved by combining the accurate information from all observation stations using the least squares approach. This multi-array direct positioning method based on two-dimensional discrete Fourier transform can effectively locate targets. Furthermore, this method eliminates the need for two-dimensional spectral peak search, significantly reducing computational complexity. At low signal-to-noise ratios, its positioning performance is close to that of the minimum variance distortionless response (MVDR) direct positioning algorithm and outperforms the traditional angle-of-arrival (AOA-K-Means) clustering two-step positioning method.

Description

Technical Field

[0001] This invention relates to the field of wireless positioning technology, and in particular to a multi-array direct positioning method based on two-dimensional discrete Fourier transform. Background Technology

[0002] Traditional passive localization techniques using multiple arrays are mostly two-step techniques. They require first estimating intermediate parameters from the original signal and then performing data association. The source location is then estimated using methods such as exhaustive search, least squares, and gradient descent. However, traditional two-step localization methods face challenges in data association. From an information theory perspective, the fewer signal processing steps, the better the algorithm's performance. Direct localization, on the other hand, eliminates the need for parameter association and can directly estimate the source location from the original signal. Compared to traditional two-step localization, direct localization avoids the propagation of parameter association errors, thus improving location estimation performance. Therefore, research on direct localization algorithms for multiple arrays has significant practical application value.

[0003] Existing multi-array direct localization algorithms all rely on exhaustive search of the cost function, which introduces a high-dimensional search problem and significantly increases computational complexity. In practical applications, real-time target localization is often required, which places demands on the computational complexity of the algorithms. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to address the deficiencies mentioned in the background technology by providing a multi-array direct positioning method based on two-dimensional discrete Fourier transform, which significantly reduces computational complexity while ensuring estimation performance and is easy to process in real time.

[0005] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0006] The multi-array direct localization method based on two-dimensional discrete Fourier transform includes the following steps:

[0007] Step 1) Construct a multi-array joint positioning model to obtain the received signal information r. l (t);

[0008] Step 1.1) Construct the array manifold for each observation station.

[0009] M is the number of large-scale uniform linear array elements equipped for each observation station, and K is the number of radiation sources;

[0010]

[0011] The guide vector is d, where d represents the element spacing and λ represents the signal wavelength; u l =[x l ,yl ] T Let x represent the position vector of the l-th observation station. l y l These are its x and y coordinates, respectively; the position vector of the k-th radiation source is p. k =[x k ,y k ] T x k y k These are its x and y coordinates; k = 1, 2, ..., K; the total position vector. θ l,k u represents the angle of arrival (°) of the k-th radiation source received by the l-th observation station. l (1) indicates taking vector u l The first element in, p k (1) indicates taking vector p k The first element in the array; ||·|| denotes the 2-norm;

[0012] Step 1.2): The received signal of the l-th observation station at sampling time t is obtained using a multi-array joint positioning model. s(t) is a K×1 dimensional transmitted signal vector, and its covariance matrix is ​​a diagonal matrix; n l (t) represents an M×1 dimensional Gaussian white noise vector;

[0013] Step 2) Calculate the cross-covariance matrix of the received signals at each observation station and perform a two-dimensional discrete Fourier transform on it;

[0014] Step 2.1): Calculate the cross-covariance R between the received signal from the first base station and the received signal from the (l+1)th base station according to the following formula. 1,l :

[0015]

[0016] In the formula, T represents the number of snapshots, t = 1, 2, ..., T, and L represents the number of observation stations;

[0017] Step 2.2) Construct the normalized DFT matrix

[0018]

[0019] In the formula, the (m1, n1)th element of matrix D is

[0020] The matrix obtained by performing 2D-DFT processing on the cross-covariance of the steering vectors of the 1st base station and the (l+1th base station) with respect to the kth source.

[0021] formation The (u,v)th element is:

[0022]

[0023] As the number of physical array elements M approaches infinity, i.e., M→∞, there must exist a pair of integers (u k ,v k ) makes at the same time All other elements are 0; at this time, The "ideal sparsity" has been achieved, with all power concentrated in the (u)th power of the 2D-DFT spectrum. k ,v k (Point) The location information automatically matched by each base station is provided by The position of the non-zero point is obtained, θ 1,k =arcsin(2u k / M), θ l+1,k =arcsin(2v k / M);

[0024] Step 2.3), according to Perform a 2D-DFT on the cross-covariance of the received signal and calculate the matrix. The index values ​​of the K largest elements in the array k = 1, 2, ..., K;

[0025] Step 2.4), according to For k = 1, 2, ..., K, make an initial estimate of the azimuth angle. This represents the initial estimate of the angle of arrival of the k radiation sources from the first observation station. This represents the initial estimate of the angle of arrival of the (l+1)th observation station for the k radiation sources;

[0026] Step 3), construct the phase rotation matrix and compensate for the orientation information;

[0027] Step 3.1), define the phase rotation matrix.

[0028] In the formula, the offset phase η∈(-π / M,π / M), ξ∈(-π / M,π / M);

[0029] Let the cross-covariance after phase rotation and 2D-DFT transformation be:

[0030]

[0031] matrix The (u1, v1)th element is:

[0032]

[0033] There must exist a phase offset η k ∈(-π / M,π / M), ξ k ∈(-π / M,π / M) makes At this time the matrix The lieutenant general has one and only one non-zero element, which means that "power leakage" is eliminated;

[0034] Step 3.2), search for η according to the following formula. 1,k and ξ l,k The estimated value:

[0035]

[0036]

[0037] in, Represents the first... OK, Represents the first... The column, ||·||, represents the 2-norm;

[0038] Step 3.3), according to and To accurately estimate the azimuth angle. This represents the precise estimate of the angle of arrival of the k radiation sources from the first observation station. Here is the precise estimate of the angle of arrival of the k radiation sources from the (l+1)th observation station, where k = 1, 2, ..., K;

[0039] Step 4), according to the formula Directly solve for the target position vector estimate In the formula,

[0040] Compared with the prior art, the present invention, employing the above technical solution, has the following technical effects:

[0041] The estimation accuracy of the algorithm proposed in this invention is better than that of the traditional AOA-K-Means clustering two-step localization method, and it is close to the estimation accuracy of the MVDR direct localization algorithm under low signal-to-noise ratio. Compared with AOA-K-Means clustering two-step localization technology and MVDR direct localization technology, this invention significantly reduces the computational complexity. Attached Figure Description

[0042] Figure 1 This is a flowchart of the present invention;

[0043] Figure 2 This is a diagram illustrating a multi-array joint positioning scenario.

[0044] Figure 3This diagram illustrates the computational complexity of the present invention and traditional positioning methods under different numbers of observation stations.

[0045] 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;

[0046] 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

[0047] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings:

[0048] This invention can be implemented in many different forms and should not be considered limited to the embodiments described herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully express the scope of the invention to those skilled in the art. In the drawings, components are enlarged for clarity.

[0049] This invention provides a multi-array direct positioning method based on two-dimensional discrete Fourier transform, such as... Figure 1 As shown, the specific steps include:

[0050] Step 1), construct as follows Figure 2 The multi-array joint positioning model shown obtains the received signal information r. l (t);

[0051] Step 1.1) Construct the array manifold for each observation station.

[0052] M is the number of large-scale uniform linear array elements equipped for each observation station, and K is the number of radiation sources;

[0053]

[0054] The guide vector is d, where d represents the element spacing and λ represents the signal wavelength; u l =[x l ,y l ] T Let x represent the position vector of the l-th observation station. l y l These are its x and y coordinates, respectively; the position vector of the k-th radiation source is p. k =[x k ,y k ] T x k y k These are its x and y coordinates; k = 1, 2, ..., K; the total position vector. θ l,ku represents the angle of arrival (°) of the k-th radiation source received by the l-th observation station. l (1) indicates taking vector u l The first element in, p k (1) indicates taking vector p k The first element in the array; ||·|| denotes the 2-norm;

[0055] Step 1.2): The received signal of the l-th observation station at sampling time t is obtained using a multi-array joint positioning model. s(t) is a K×1 dimensional transmitted signal vector, and its covariance matrix is ​​a diagonal matrix; n l (t) represents an M×1 dimensional Gaussian white noise vector;

[0056] Step 2) Calculate the cross-covariance matrix of the received signals at each observation station and perform a two-dimensional discrete Fourier transform on it;

[0057] Step 2.1): Calculate the cross-covariance R between the received signal from the first base station and the received signal from the (l+1)th base station according to the following formula. 1,l :

[0058]

[0059] In the formula, T represents the number of snapshots, t = 1, 2, ..., T, and L represents the number of observation stations;

[0060] Step 2.2) Construct the normalized DFT matrix

[0061]

[0062] In the formula, the (m1, n1)th element of matrix D is

[0063] The matrix obtained by performing 2D-DFT processing on the cross-covariance of the steering vectors of the 1st base station and the (l+1th base station) with respect to the kth source.

[0064] formation The (u,v)th element is:

[0065]

[0066] As the number of physical array elements M approaches infinity, i.e., M→∞, there must exist a pair of integers (u k ,v k ) makes at the same time All other elements are 0; at this time, The "ideal sparsity" has been achieved, with all power concentrated in the (u)th power of the 2D-DFT spectrum.k ,v k (Point) The location information automatically matched by each base station is provided by The position of the non-zero point is obtained, θ 1,k =arcsin(2u k / M), θ l+1,k =arcsin(2v k / M).

[0067] In applications where the target location information is unknown and the steering vector cannot be calculated, the orientation information for automatic matching can be obtained by performing a 2D-DFT on the cross-covariance of the received signals.

[0068] Step 2.3), according to Perform a 2D-DFT on the cross-covariance of the received signal and calculate the matrix. The index values ​​of the K largest elements in the array k = 1, 2, ..., K;

[0069] Step 2.4), according to For k = 1, 2, ..., K, make an initial estimate of the azimuth angle. This represents the initial estimate of the angle of arrival of the k radiation sources from the first observation station. This represents the initial estimate of the angle of arrival of the (l+1)th observation station for the k radiation sources;

[0070] Step 3), construct the phase rotation matrix and compensate for the orientation information;

[0071] In practice, even if a massive MIMO wireless communication system uses hundreds of antennas, the array aperture cannot be infinitely large. Therefore, Msin(θ) 1,k ) / 2 and Msin(θ) l+1,k In most cases, ) / 2 will not be exactly an integer, and accordingly, the power will be determined by the ()th power. <Msin(θ 1,k ) / 2>, <Msin(θ l+1,k The leakage from point M to surrounding points is represented by <·>, where <·> indicates rounding. Clearly, the degree of leakage is inversely proportional to M, but not to (Msin(θ)). 1,k ) / 2+Msin(θ l+1,k ) / 2- <Msin(θ 1,k ) / 2>- <Msin(θ l+1,k The value is proportional to 2; at this point, the estimation performance of the algorithm cannot be improved. In order to further improve the estimation accuracy, we introduce phase rotation to compensate for the error.

[0072] Step 3.1), define the phase rotation matrix.

[0073] In the formula, the offset phase η∈(-π / M,π / M), ξ∈(-π / M,π / M);

[0074] Let the cross-covariance after phase rotation and 2D-DFT transformation be:

[0075]

[0076] matrix The (u1, v1)th element is:

[0077]

[0078] There must exist a phase offset η k ∈(-π / M,π / M), ξ k ∈(-π / M,π / M) makes At this time the matrix The lieutenant general has one and only one non-zero element, which eliminates "power leakage" and thus enables more accurate estimation results;

[0079] Step 3.2), search for η according to the following formula. 1,k and ξ l,k The estimated value:

[0080]

[0081]

[0082] in, Represents the first... OK, Represents the first... The column, ||·||, represents the 2-norm;

[0083] Step 3.3), according to and To accurately estimate the azimuth angle. This represents the precise estimate of the angle of arrival of the k radiation sources from the first observation station. Here is the precise estimate of the angle of arrival of the k radiation sources from the (l+1)th observation station, where k = 1, 2, ..., K;

[0084] Step 4), when the distance between the observation station and the target is far enough, Established, p k (n) represents the vector p k The nth element, u l (n) represents the vector u l The nth element is transformed into matrix multiplication [1 - tan(θ)]. l,k )]p k=[1 -tan(θ)] l,k )]u l ;

[0085] Since the azimuth information obtained in step 3) is automatically matched, the information from all observation stations is combined to obtain J. 1,k p k =J 2,k b, According to the least squares principle, the estimated target position vector value is...

[0086]

[0087] Figure 3 This diagram illustrates the computational complexity (number of complex multiplications) of the method described in this invention compared to traditional positioning methods, as a function of the number of observation stations. Simulation conditions are: 3 targets, each observation station equipped with a uniform linear array of 8 elements, 100 snapshots, a global search range of 1000 meters, and a search step size of 0.5 meters. Figure 3 As can be seen, the method described in this invention does not require two-dimensional spectral peak search, and the computational complexity is significantly reduced.

[0088] The performance estimation standard of this invention is the root mean square error (RMSE), defined as follows:

[0089]

[0090] Where Mon represents the number of Monte Carlo experiments, and K represents the number of radiation sources. Let x represent the estimated position of the k-th target in the mn-th experiment, (x) k ,y k ) represents the actual value of the k-th target position.

[0091] Figure 4 This image shows the performance curves of the root mean square error (RMSE) as a function of signal-to-noise ratio (SNR) for the method described in this invention, compared to the traditional Angle of Arrival-K-Means (AOA-K-Means) clustering two-step localization method and the Minimum Variance Distortionless Response (MVDR) direct localization algorithm. The simulation conditions were as follows: four targets with positions [(-501 m, 701 m), (-102 m, 52 m), (803 m, 604 m), (1200 m, -100 m)], three observation base stations [(-900 m, -1200 m), (0 m, -1050 m), (900 m, -900 m)], each base station equipped with a uniform linear array of 40 elements, 200 snapshots, and 500 simulations. Figure 4It can be seen that the positioning accuracy of the present invention is close to that of the MVDR direct positioning algorithm, and is always better than the traditional AOA-K-Means clustering two-step positioning method. However, the computational complexity of the present invention is significantly reduced compared to the MVDR direct positioning algorithm.

[0092] Figure 5 This image shows the performance curves of the method described in this invention, the traditional Angle of Arrival-K-Means (AOA-K-Means) clustering two-step localization method, and the Minimum Variance Distortionless Response (MVDR) direct localization algorithm, comparing the root mean square error (RMSE) with the number of snapshots. Simulation conditions were as follows: four targets with positions [(-501 m, 701 m), (-102 m, 52 m), (803 m, 604 m), (1200 m, -100 m)], three observation base stations [(-900 m, -1200 m), (0 m, -1050 m), (900 m, -900 m)], each equipped with a uniform linear array of 40 elements, a signal-to-noise ratio of -5 dB, and 500 simulations. Figure 5 It can be seen that, under low signal-to-noise ratio, the location estimation performance of the method proposed in this invention is always better than the traditional AOA-K-Means clustering two-step localization method, and the localization accuracy is close to that of the MVDR direct localization algorithm.

[0093] In summary, the analysis of the simulation results shows that the multi-array direct localization method based on two-dimensional discrete Fourier transform proposed in this invention can effectively locate the target. Furthermore, this method eliminates the need for two-dimensional spectral peak search, significantly reducing computational complexity. At low signal-to-noise ratios, its localization performance is close to that of the MVDR direct localization algorithm and outperforms the traditional AOA-K-Means clustering two-step localization method.

[0094] It will be understood by those skilled in the art that, unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. It should also be understood that terms such as those defined in general dictionaries should be understood to have the same meaning as in the context of the prior art, and should not be interpreted in an idealized or overly formal sense unless defined as herein.

[0095] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A multi-array direct localization method based on two-dimensional discrete Fourier transform, characterized by the following steps: Step 1) Construct a multi-array joint positioning model to obtain the received signal information. ; Step 1.1), construct the array manifold for each observation station. ; M is the number of large-scale uniform linear array elements equipped for each observation station, and K is the number of radiation sources; The guide vector is d, where d represents the element spacing. Indicates the signal wavelength; This represents the position vector of the l-th observation station. , These are its x and y coordinates, respectively; the position vector of the k-th radiation source is... , , These are its horizontal and vertical coordinates, respectively; ; Total position vector , This represents the angle of arrival of the k-th radiation source received by the l-th observation station. Indicates taking a vector The first element in Indicates taking a vector The first element in; Represents the 2-norm; Step 1.2) uses a multi-array joint positioning model to obtain the received signal of the l-th observation station at sampling time t. , yes The transmitted signal vector is a dimensional vector, and its covariance matrix is ​​a diagonal matrix. express Gaussian white noise vector; Step 2), calculate the cross-covariance matrix of the received signals at each observation station, and perform a two-dimensional discrete Fourier transform on it; Step 2.1) Calculate the cross-covariance between the received signal of the first base station and the received signal of the (l+1)th base station according to the following formula. : In the formula, T represents the number of snapshots. L represents the number of observation stations; Step 2.2), construct the normalized DFT matrix. : 。 In the formula, The (m1, n1)th element of the matrix is ; The matrix obtained by performing 2D-DFT processing on the cross-covariance of the steering vectors of the 1st base station and the (l+1th base station) with respect to the kth source. l=1,2,…,L-1; formation The (u,v)th element is: When the number of physical array elements M approaches infinity, that is There must exist a pair of integers Make ,at the same time All other elements are 0; at this time, The "ideal sparsity" has been achieved, with all power concentrated in the first digit of the 2D-DFT spectrum. The location information automatically matched by each base station is provided by [the relevant authority / organization]. The position of the non-zero point is obtained. , ; Step 2.3), according to Perform a 2D-DFT on the cross-covariance of the received signal and calculate the matrix. The index values ​​of the K largest elements in the array , ; Step 2.4), according to , , Make an initial estimate of the azimuth angle. This represents the initial estimate of the angle of arrival of the k radiation sources from the first observation station. This represents the initial estimate of the angle of arrival of the (l+1)th observation station for the k radiation sources; Step 3), construct the phase rotation matrix and compensate for the orientation information; Step 3.1), define the phase rotation matrix. , ; In the formula, the offset phase , ; Let the cross-covariance after phase rotation and 2D-DFT transformation be: matrix The (u1, v1)th element is: There must be a phase offset. , Make , At this time, the matrix The lieutenant general has one and only one non-zero element, which eliminates "power leakage"; Step 3.2), obtained by searching according to the following formula and The estimated value: in, Representation matrix The OK, Representation matrix The List, Represents the 2-norm; Step 3.3), according to and To accurately estimate the azimuth angle. This represents the precise estimate of the angle of arrival of the k radiation sources from the first observation station. This represents the precise estimate of the angle of arrival of the k radiation sources from the (l+1)th observation station. ; Step 4), according to the formula Directly solve for the target position vector estimate In the formula, ; ; .

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