Direct positioning method and device for non-gaussian signal of multipath using orthogonal subspace compensation

Abstract

The application discloses a kind of direct positioning method and device of multipath non-gaussian signal using orthogonal subspace compensation, first, construct non-gaussian signal multi-array positioning model under multipath environment;Second, the fourth order cumulant matrix of the signal received by each observation station is calculated;Then, the fourth order cumulant matrix is virtually processed, and is sorted according to phase, and is de-redundant, to obtain virtual signal;Then, the virtual signal of all observation stations is combined to construct cost function to directly search emitter position, to obtain initial estimate;Finally, the initial estimate of position is compensated according to orthogonal subspace compensation method, to obtain fine estimate.The application makes full use of the characteristics of non-gaussian signal, can inhibit Gaussian noise, significantly expand array aperture and available degree of freedom;Positioning performance is obviously superior to the traditional angle of arrival clustering two-step positioning method and subspace data fusion direct positioning method.

Description

Technical Field

[0001] This invention belongs to the field of wireless positioning technology, and particularly relates to a method and apparatus for direct positioning of multipath non-Gaussian signals using orthogonal subspace compensation. 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, followed by estimating the radiation source location 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 radiation source location from the original signal. Compared to traditional two-step localization techniques, 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] Traditional Direct Position Determination (DPD) techniques are mostly designed for unknown signals. From an information theory perspective, the more raw information available, the better the algorithm's performance. Research shows 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 exponentially distributed signals, normally distributed signals, and quadrature amplitude modulation signals are all non-Gaussian (NG) signal types. Therefore, research on direct positioning algorithms for non-Gaussian signals has significant practical application value.

[0004] Existing multi-array localization algorithms in multipath environments require first clustering the multipath signals and then decohering the coherent signals in each cluster. This leads to a loss of array aperture and a reduction in available degrees of freedom, undoubtedly decreasing localization performance. To address these issues, this invention proposes a direct localization method using orthogonal subspace compensation for multipath non-Gaussian signals. Summary of the Invention

[0005] Purpose of the invention: This invention provides a method and apparatus for direct positioning of multipath non-Gaussian signals using orthogonal subspace compensation. It can fully utilize the characteristics of non-Gaussian signals to expand the array aperture, suppress Gaussian noise, suppress multipath effects, increase available degrees of freedom, and improve positioning accuracy, without requiring additional parameter matching processes and multipath signal clustering.

[0006] Technical solution: The present invention provides a method for direct localization of multipath non-Gaussian signals using orthogonal subspace compensation, comprising the following steps:

[0007] (1) Construct a multi-array localization model for non-Gaussian signals under multipath environment to obtain received signal information;

[0008] (2) Calculate the fourth-order cumulant matrix of the received signals at each observation station;

[0009] (3) The fourth-order cumulant matrix is ​​virtualized, and its order and redundancy removal are performed according to the phase to obtain the virtual signal.

[0010] (4) Construct a cost function by combining the virtual signals from each observation station to obtain an initial estimate of the radiation source location;

[0011] (5) The initial estimation results are compensated according to the orthogonal subspace compensation method to obtain a precise estimate of the radiation source location.

[0012] Furthermore, the implementation process of step (1) is as follows:

[0013] In a two-dimensional planar positioning scenario, L observation stations with known locations, K radiation sources with unknown locations, and V reflectors with unknown locations are constructed. The l-th observation station is located at o. l =[o l,x ,o l,y ] T (l=1,2,…,L), where, (·) T Indicates transpose, o l,x The x-coordinate of the location of the l-th observation station, o l,y The ordinate represents the position of the l-th observation station;

[0014] Each observatory is equipped with a uniform linear array of M elements parallel to the x-axis; the k-th radiation source is located at p. k =[p k,x ,p k,y ] T (k = 1, 2, ..., K), where p k,x p represents the x-coordinate of the location of the k-th radiation source. k,y The ordinate represents the location of the k-th radiation source; the received signal at time t from the l-th observation station is:

[0015]

[0016] Among them, s k (t) represents the emitted signal of the k-th radiation source at time t, n l (t) is the additive white Gaussian noise vector of the l-th observation station, K represents the number of radiation sources, and α l,k β represents the fading coefficient of the direct path from the k-th radiation source to the l-th observation station. l,k,v Let represent the fading coefficient of the k-th radiation source reaching the l-th observation station via the v-th reflection path, and assume |αl,k |>|β l,k,v |; and Let V represent the direct path of the k-th radiation source and the steering vector of the v-th reflection path of that radiation source, respectively. They satisfy the following:

[0017]

[0018] Where d represents the element spacing and λ represents the signal carrier wavelength. The AOA represents the direct path from the k-th radiation source to the l-th observation station, satisfying... This represents the AOA of the k-th radiation source reaching the l-th observation station via the v-th reflection path.

[0019] Furthermore, the implementation process of step (2) is as follows:

[0020] Define the source vector s(t) = [s1(t), s2(t), ..., s K (t)] T Assuming they are independent, their fourth-order cumulant matrix is ​​expressed as:

[0021]

[0022] Where 1≤k1,k2,k3,k4≤K, s k1 Let represent the k1-th element in s(t). Indicates a diagonal matrix. Represents the mathematical expectation, (·) H This indicates the conjugate transpose, (·) * Indicates conjugate; the generalized direction vector from the k-th radiation source to the l-th observation station is defined as... The generalized array manifold of the l-th observation station is: B l =[b l,1 ,b l,2 ,…,b l,K ], then the received signal at time t of the l-th observation station is rewritten as: r l (t)=B l s(t)+n l (t), whose fourth-order cumulant matrix is ​​expressed as:

[0023]

[0024] in, For virtual generalized array manifolds, ⊙ represents the Khatri-Rao product. For the Kronecker product, 1 ≤ k1, k2, k3, k4 ≤ M; since the number of snapshots T is finite, the second-order cumulant... and fourth-order cumulants The estimated values ​​are as follows:

[0025]

[0026]

[0027] This allows us to estimate the fourth-order cumulant matrix of the signal received by the l-th observation station.

[0028] Furthermore, the implementation process of step (3) is as follows:

[0029] For the fourth-order cumulant matrix R in step (2) 4x,l After virtualization, the following is obtained:

[0030]

[0031] Where, vector It includes the Kronecker product of the direct path and the reflection path steering vectors; z l Based on the phase, sorting and redundancy removal are performed to obtain a 4M-3 dimensional virtual signal vector z. l .

[0032] Furthermore, the implementation process of step (4) is as follows:

[0033] The cost function is constructed as follows:

[0034]

[0035] Where, p = [p x ,p y ] T Represents the position variable, θ l (p) represents the AOA of the direct path from p to the l-th observation station, the virtual steering vector. Based on |α l,k |>|β l,k,v |, when θ l (p)=θ l (p k When f(p) reaches an extreme value, a spectral peak search is performed on f(p), and the coordinates corresponding to the first K peaks are the initial estimate of the radiation source location.

[0036] Furthermore, the implementation process of step (5) is as follows:

[0037] Define the covariance matrix:

[0038]

[0039] Due to the multipath effect, the virtual signal is first... Decoherence processing is performed, and enhanced spatial smoothing techniques are used to smooth the z-axis. l Perform decoherence; define the smoothed submatrix length as W, and obtain the smoothed covariance matrix:

[0040]

[0041] Among them, M w =4M-W-2,Γ i,j Represented by matrix R l The submatrix formed by the elements from row i to row i+W-1 and column j to column j+W-1 J is a commutation matrix where all elements on the opposite diagonal are 1 and all other elements are 0;

[0042] Then to Eigenvalue decomposition yields the noise subspace.

[0043]

[0044] Among them, VK+K are the larger eigenvalues ​​and the remaining M w -VK-K eigenvalues ​​form a diagonal matrix and The corresponding eigenvectors constitute the signal subspace. and noise subspace

[0045] Stacking the steering vectors of the L observation stations together, we get:

[0046]

[0047] in, Stacking the noise subspaces of the L observation stations together, we get:

[0048]

[0049] Then the following relationship holds:

[0050]

[0051] Will Performing a first-order Taylor expansion at the initial estimate of the radiation source location, and neglecting second-order and higher-order error terms, then... Approximately:

[0052]

[0053] Define offset but Rewritten as:

[0054]

[0055] The least squares solution for the offset is:

[0056]

[0057] The precise estimate of the location of the k-th radiation source is expressed as:

[0058]

[0059] Based on the same inventive concept, the present invention provides an apparatus comprising a memory and a processor, wherein:

[0060] Memory is used to store computer programs that can run on a processor;

[0061] A processor, configured to, while running the computer program, perform the steps of the direct localization method for multipath non-Gaussian signals using orthogonal subspace compensation as described above.

[0062] Based on the same inventive concept, the present invention provides a storage medium storing a computer program, which, when executed by at least one processor, implements the steps of the direct localization method for multipath non-Gaussian signals using orthogonal subspace compensation as described above.

[0063] Beneficial effects: Compared with the prior art, the beneficial effects of the present invention are as follows: The present invention can make full use of the characteristics of non-Gaussian signals to expand the array aperture, suppress Gaussian noise, suppress multipath effects, increase available degrees of freedom, improve positioning accuracy, and does not require additional parameter pairing process and multipath signal clustering processing; the position estimation accuracy of the present invention is better than the traditional Angle of Arrival Clustering (AOA-Clustering) two-step positioning method and the Subspace Data Fusion (SDF) direct positioning method. Attached Figure Description

[0064] Figure 1 This is a flowchart of the present invention;

[0065] Figure 2 This is a scenario diagram for joint localization of non-Gaussian signals using multiple arrays in a multipath environment.

[0066] Figure 3 This diagram illustrates the computational complexity of the present invention and traditional positioning methods under different numbers of observation stations.

[0067] 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;

[0068] Figure 5This is a schematic diagram illustrating the root mean square error performance of the present invention and the traditional positioning method under different snapshot numbers. Detailed Implementation

[0069] The invention will now be further described with reference to the accompanying drawings.

[0070] This invention provides a direct localization method for multipath non-Gaussian signals using orthogonal subspace compensation, such as... Figure 1 As shown, the specific steps include:

[0071] Step 1: Construct as follows Figure 2 The multi-array joint localization model for non-Gaussian signals in a multipath environment is shown; the received signal information r is obtained. l (t).

[0072] exist Figure 2 In the two-dimensional planar positioning scenario shown, which includes L observation stations at known locations, K radiation sources at unknown locations, and V reflectors at unknown locations, the l-th observation station is located at o l =[o l,x ,o l,y ] T (l=1,2,…,L), where, (·) T Indicates transpose, o l,x The x-coordinate of the location of the l-th observation station, o l,y The ordinate represents the location of the l-th observation station. Each observation station is equipped with a uniform linear array of M elements parallel to the x-axis. The k-th radiation source is located at p. k =[p k,x ,p k,y ] T (k = 1, 2, ..., K), where p k,x p represents the x-coordinate of the location of the k-th radiation source. k,y The ordinate represents the location of the k-th radiation source. The received signal at time t from the l-th observation station is:

[0073]

[0074] Among them, s k (t) represents the emitted signal of the k-th radiation source at time t, n l (t) is the additive white Gaussian noise vector of the l-th observation station, K represents the number of radiation sources, V reflectors form V reflection paths, α l,k β represents the fading coefficient of the direct path from the k-th radiation source to the l-th observation station. l,k,v Let represent the fading coefficient of the k-th radiation source reaching the l-th observation station via the v-th reflection path, and assume that... and Let V represent the direct path of the k-th radiation source and the steering vector of the v-th reflection path of that radiation source, respectively. They satisfy the following conditions: Where d represents the element spacing and λ represents the signal carrier wavelength. The AOA represents the direct path from the k-th radiation source to the l-th observation station, satisfying... This represents the AOA of the k-th radiation source reaching the l-th observation station via the v-th reflection path.

[0075] Step 2: Calculate the fourth-order cumulant matrix of the received signals at each observation station.

[0076] Define the source vector s(t) = [s1(t), s2(t), ..., s K (t)] T Assuming they are independent, their fourth-order cumulant matrix can be expressed as:

[0077]

[0078] Where 1≤k1,k2,k3,k4≤K, Let represent the k1-th element in s(t). Indicates a diagonal matrix. Represents the mathematical expectation, (·) H This indicates the conjugate transpose, (·) * This indicates conjugate. The generalized direction vector from the k-th radiation source to the l-th observation station is defined as... The generalized array manifold of the l-th observation station is:

[0079] B l =[b l,1 ,b l,2 ,…,b l,K ]

[0080] Then the received signal at time t of the l-th observation station can be rewritten as r l (t)=B l s(t)+n l (t), whose fourth-order cumulant matrix can be expressed as:

[0081]

[0082] in, For virtual generalized array manifolds, ⊙ represents the Khatri-Rao product. For the Kronecker product, 1 ≤ k1, k2, k3, k4 ≤ M. In practical applications, since the number of snapshots T is finite, the second-order cumulant... and fourth-order cumulants The estimated values ​​can be expressed as follows:

[0083]

[0084]

[0085] Therefore, the fourth-order cumulant matrix of the signal received by the l-th observation station can be easily estimated.

[0086] Step 3: Virtualize the fourth-order cumulant matrix, sort it, remove redundancy, and obtain the virtual signal z. l .

[0087] For R in step 2 4x,l Virtualization processing yields:

[0088]

[0089] Where, vector It includes the Kronecker product of the direct path and the reflection path steering vectors. (The last part, "z," appears to be incomplete and lacks context.) l By sorting and removing redundancy based on phase, a 4M-3 dimensional virtual signal vector can be obtained.

[0090] Step 4: Construct a cost function by combining the virtual signals from each observation station to obtain an initial estimate of the radiation source location.

[0091] Construct the following cost function:

[0092]

[0093] Where, p = [p x ,p y ] T Represents the position variable, θ l (p) represents the AOA of the direct path from p to the l-th observation station, the virtual steering vector. Based on the assumption in step 1 |α l,k |>|β l,k,v | Similar to the derivation in step 3, when θ l (p)=θ l (p k When f(p) reaches an extreme value, a spectral peak search is performed on f(p), and the coordinates corresponding to the first K peaks are the initial estimate of the radiation source location.

[0094] Step 5: Compensate the initial estimation result using the orthogonal subspace compensation method to obtain a precise estimate of the radiation source location.

[0095] Define the covariance matrix:

[0096]

[0097] Due to the multipath effect, it is necessary to first process the virtual signal. Decoherence processing is performed, and enhanced spatial smoothing techniques are then used to smooth the z-axis. l Perform decoherence. Define the length of the smoothed submatrix as W, and we can obtain the smoothed covariance matrix:

[0098]

[0099] Among them, M w =4M-W-2,Γ i,j Represented by matrix R l The submatrix formed by the elements from row i to row i+W-1 and column j to column j+W-1 J is a commutation matrix where all elements on the opposite diagonal are 1 and all other elements are 0. Then, for... Eigenvalue decomposition yields the noise subspace.

[0100]

[0101] Among them, VK+K are the larger eigenvalues ​​and the remaining M w -VK-K eigenvalues ​​form a diagonal matrix and The corresponding eigenvectors constitute the signal subspace. and noise subspace

[0102] Stacking the steering vectors of the L observation stations together, we get:

[0103]

[0104] in, Stacking the noise subspaces of the L observation stations together, we get:

[0105]

[0106] Then the following relationship holds:

[0107]

[0108] Where 0 represents a vector consisting entirely of zeros; Performing a first-order Taylor expansion at the initial estimate of the radiation source location, and neglecting second-order and higher-order error terms, then... It can be approximated as:

[0109]

[0110] Define offset but It can be rewritten as

[0111]

[0112] The least squares solution for the offset is:

[0113]

[0114] The precise estimate of the location of the k-th radiation source can be expressed as:

[0115]

[0116] Based on the same inventive concept, the present invention also provides an apparatus comprising a memory and a processor, wherein:

[0117] Memory is used to store computer programs that can run on a processor;

[0118] A processor, configured to, while running the computer program, perform the steps of the direct localization method for multipath non-Gaussian signals using orthogonal subspace compensation as described above.

[0119] Based on the same inventive concept, the present invention also provides a storage medium storing a computer program, which, when executed by at least one processor, implements the steps of the direct localization method for multipath non-Gaussian signals using orthogonal subspace compensation as described above.

[0120] The spatial degrees of freedom obtained by the method of this invention is 4M-4, while the spatial degrees of freedom of a traditional uniform linear array with the same number of array elements is M-1, thus increasing the degree of freedom. Figure 3 This diagram illustrates the computational complexity (number of complex multiplications) of the present invention and traditional positioning methods as a function of the number of observation stations. The simulation conditions are: two radiation sources, each containing two reflector paths; each observation station equipped with a uniform linear array of 10 elements; 200 snapshots; a global search range of 1000 meters; a search step size of 5 meters; and a spatial smoothing subarray length of 5. From... Figure 3 It can be seen that the computational complexity of this invention lies between that of the traditional AOA-Clustering method and the SDF direct localization method.

[0121] The performance estimation standard of this invention is the root mean square error (RMSE), defined as follows:

[0122]

[0123] Where Mon represents the number of Monte Carlo trials, and K represents the number of targets. Let x represent the estimated position of the k-th target in the mm-th experiment, (x) k y k ) represents the actual value of the k-th target position.

[0124] Figure 4 The graph shows the performance of the root mean square error as a function of signal-to-noise ratio (SNR) compared to the two-step localization method of Angle of Arrival Clustering (AOA-Clustering) and the direct localization method of Subspace Data Fusion (SDF). The simulation conditions are as follows: there are 4 targets with positions [(-592.5 m, 623.5 m), (-200.5 m, -174.5 m), (720.5 m, 452.5 m), (941.5 m, -296.5 m)], 4 observation base stations [(-900 m, -1200 m), (-300 m, -1100 m), (300 m, -1000 m), (900 m, -900 m)], each base station is equipped with a uniform linear array with 10 elements, each target has one reflection path and one direct path to reach the observation base station, the number of snapshots is 500, and the simulation is run 500 times. Figure 4 It can be seen that the positioning accuracy of the present invention is consistently superior to that of the traditional AOA-Clustering two-step positioning method and the SDF direct positioning method.

[0125] Figure 5 The graph shows the performance of the root mean square error of the two-step localization method (Angle of Arrival Clustering, AOA-Clustering) and the direct localization method (Subspace Data Fusion, SDF) as a function of the number of snapshots. The simulation conditions are as follows: there are 4 targets with positions [(-592.5 m, 623.5 m), (-200.5 m, -174.5 m), (720.5 m, 452.5 m), (941.5 m, -296.5 m)], 4 observation base stations [(-900 m, -1200 m), (-300 m, -1100 m), (300 m, -1000 m), (900 m, -900 m)], each base station is equipped with a uniform linear array with 10 elements, each target has one reflection path and one direct path to reach the observation base station, the signal-to-noise ratio is 5 dB, and the simulation is run 500 times. Figure 5 It can be seen that when the number of snapshots is greater than 5, the position estimation performance of this invention is always better than the traditional AOA-Clustering two-step localization method and the SDF direct localization method.

[0126] In summary, the analysis of the simulation results shows that the present invention can effectively locate the target. In addition, it can make full use of the characteristics of non-Gaussian signals to expand the array aperture, suppress Gaussian noise, suppress multipath effects, increase the available degrees of freedom, and does not require additional parameter matching process and multipath signal clustering processing. Its positioning accuracy is better than the traditional AOA-Clustering two-step positioning method and SDF direct positioning method.

[0127] The embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention.

Claims

1. A method for direct localization of multipath non-Gaussian signals using orthogonal subspace compensation, characterized in that, Includes the following steps: (1) Construct a multi-array localization model for non-Gaussian signals under multipath environment to obtain the received signal information; (2) Calculate the fourth-order cumulant matrix of the received signals at each observation station; (3) The fourth-order cumulant matrix is ​​virtualized, and its order and redundancy removal are performed according to the phase to obtain the virtual signal. ; (4) By combining the virtual signals from each observation station, a cost function is constructed to obtain an initial estimate of the radiation source location; (5) The initial estimation results are compensated using the orthogonal subspace compensation method to obtain a precise estimate of the radiation source location; The implementation process of step (1) is as follows: In a two-dimensional planar positioning scenario, L observation stations with known locations, K radiation sources with unknown locations, and V reflectors with unknown locations are constructed. The l-th observation station is located at... ,in, Indicates transpose. The x-coordinate of the location of the l-th observation station. The ordinate represents the position of the l-th observation station; Each observation station is equipped with a uniform linear array of M elements parallel to the x-axis; the k-th radiation source is located at... ,in, The x-coordinate represents the location of the k-th radiation source. The ordinate represents the location of the k-th radiation source; the received signal at time t from the l-th observation station is: ； in, This represents the emitted signal of the k-th radiation source at time t. Let K be the additive white Gaussian noise vector of the l-th observation station, and let K represent the number of radiation sources. This represents the fading coefficient of the direct path from the k-th radiation source to the l-th observation station. Let represent the fading coefficient of the k-th radiation source reaching the l-th observation station via the v-th reflection path, and assume that... ; and Let V represent the direct path of the k-th radiation source and the steering vector of the v-th reflection path of that radiation source, respectively. They satisfy the following: ； Where d represents the element spacing. Indicates the signal carrier wavelength. The AOA represents the direct path from the k-th radiation source to the l-th observation station, satisfying... , This represents the AOA (Aspect-Oriented Area) of the k-th radiation source reaching the l-th observation station via the v-th reflection path; The implementation process of step (2) is as follows: Define source vector Assuming they are independent, their fourth-order cumulant matrix is ​​expressed as: ； in, , express The Middle One element, Indicates a diagonal matrix. Represents the mathematical expectation. This indicates the conjugate transpose. Indicates conjugate; the generalized direction vector from the k-th radiation source to the l-th observation station is defined as... The generalized array manifold of the l-th observation station is: Then the received signal at time t of the l-th observation station is rewritten as: Its fourth-order cumulant matrix is ​​expressed as: ； in, For virtual generalized array manifolds, For Khatri-Rao product, For Kronecker product, Due to the limited number of snapshots T, the second-order cumulative quantity and fourth-order cumulants The estimated values ​​are as follows: ； ； This allows us to estimate the fourth-order cumulant matrix of the signal received by the l-th observation station. .

2. The method for direct localization of multipath non-Gaussian signals using orthogonal subspace compensation according to claim 1, characterized in that, The implementation process of step (3) is as follows: For the fourth-order cumulant matrix in step (2) After virtualization, the following is obtained: ； Where, vector It includes the Kronecker product of the direct path and the reflection path steering vectors; Based on the phase, sorting and redundancy removal are performed to obtain a 4M-3 dimensional virtual signal vector. .

3. The method for direct localization of multipath non-Gaussian signals using orthogonal subspace compensation according to claim 2, characterized in that, The implementation process of step (4) is as follows: The cost function is constructed as follows: ； in, Represents a position variable. express The AOA of the direct path to the l-th observation station, and the virtual steering vector. ,based on ,when hour, If an extreme value is obtained, then for Performing a spectral peak search yields the coordinates corresponding to the first K peaks, which constitute the initial estimate of the radiation source's location. , .

4. The method for direct localization of multipath non-Gaussian signals using orthogonal subspace compensation according to claim 3, characterized in that, The implementation process of step (5) is as follows: Define the covariance matrix: ； Due to the multipath effect, the virtual signal is first... Decoherence processing is performed, and enhanced spatial smoothing techniques are used to... Perform decoherence; define the length of the smooth subarray as... The smoothed covariance matrix is ​​obtained as follows: ； in, , Represented by matrix The Arrive line, number Listed to number A submatrix composed of column elements. , A cross-commutation matrix in which all elements on the opposite diagonal are 1 and all other elements are 0; Then to Eigenvalue decomposition yields the noise subspace. : ； in, eigenvalues ​​and the remainder The eigenvalues ​​form a diagonal matrix. and The corresponding feature vectors respectively constitute the signal subspace and noise subspace ; Stacking the steering vectors of the L observation stations together, we get: ； in, By stacking the noise subspaces of the L observation stations together, we obtain: ； Then the following relationship holds: ； Will Performing a first-order Taylor expansion at the initial estimate of the radiation source location, and neglecting second-order and higher-order error terms, then... Approximately: ； Define offset , ,but Rewritten as: ； The least squares solution for the offset is: ； The precise estimate of the location of the k-th radiation source is expressed as: 。 5. A device, characterized in that, Includes memory and processor, wherein: Memory is used to store computer programs that can run on a processor; A processor, configured to, while running the computer program, perform the steps of the direct localization method for multipath non-Gaussian signals using orthogonal subspace compensation as described in any one of claims 1 to 4.

6. A storage medium, characterized in that, The storage medium stores a computer program that, when executed by at least one processor, implements the steps of the direct localization method for multipath non-Gaussian signals using orthogonal subspace compensation as described in any one of claims 1 to 4.

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