A non-line-of-sight target single station positioning method based on angle constraint back projection

Abstract

This invention proposes a single-station localization method for non-line-of-sight targets based on angle-constrained back projection, aiming to solve the problems of low localization accuracy and low noise tolerance for non-line-of-sight targets in complex environments. Applied to the field of non-line-of-sight target detection technology, this method addresses the limitations of traditional back projection imaging algorithms. These algorithms are constrained by underlying time delay compensation and coherent accumulation mechanisms, requiring large-span physical spatial view diversity to overcome the azimuth resolution bottleneck. Furthermore, in complex environments, they are highly susceptible to background clutter and multipath sidelobe interference, and face the challenge of blind correlation due to the unknown mapping relationship between multipath signals and physical reflective surfaces. This method first introduces an angle-of-arrival constraint to limit the spatial imaging range of the back projection algorithm, obtaining a grid energy spectrum for multipath energy focusing. Subsequently, by executing a local extremum optimization strategy in the image domain, clutter and multipath sidelobe interference in the energy spectrum are accurately removed, and spatial discrete imaging feature points with strong multipath interference are extracted with high confidence. Finally, the system introduces a building layout map as a spatial topological constraint prior. Based on the aforementioned feature points, it constructs and traverses the association assumptions between multipaths and physical walls to perform a mirror-inverse mapping of the propagation link, and optimizes global coherence energy within the solution space, thereby accurately resolving the final physical location coordinates of non-line-of-sight targets. This effectively overcomes the challenges of blind association and limited physical aperture.

Description

Technical Field

[0001] This invention belongs to the field of non-line-of-sight target detection technology, and specifically relates to a non-line-of-sight target localization technology. Background Technology

[0002] Sixth-generation mobile networks (6G) are entrusted with the important mission of realizing integrated sensing and communication (ISAC). Leveraging ultra-high bandwidth and ultra-large-scale antenna arrays, they enable wireless signals to possess extremely high resolution in the time and angle domains, which is of great significance for promoting the evolution of traditional communication infrastructure into a high-precision sensing and positioning platform. Especially in the field of vehicle-to-everything (V2X), high-precision ISAC positioning services can provide advanced autonomous driving with beyond-line-of-sight (NLOS) vehicle-road cooperative sensing capabilities that overcome physical obstructions, and also have broad application prospects in cross-disciplinary fields such as intelligent navigation, emergency rescue, and low-altitude economy. However, due to the inherent characteristics of the complex urban traffic environment, severe non-line-of-sight (NLOS) obstructions can lead to a lack of direct paths, significantly reducing the sensing capabilities of individual vehicle sensors and the system's positioning performance. Furthermore, to reduce the hardware costs of network deployment and on-board units (OBUs), building an uplink communication collaborative sensing architecture of "end-side transmission and network-side computation" based on a single base station receiving uplink sensing signals from vehicles has become an important development direction. In single-base station non-line-of-sight (NLS) positioning systems, the network side must deduce the target's physical location solely from the target's uplink signal. However, the NLS multipath propagation mechanism is extremely complex, and signal blind correlation is significant, leading to a sharp increase in the difficulty of high-precision positioning under single-base station constraints. Currently, traditional positioning algorithms still have limitations in single-base station NLS scenarios. Geometrically constrained single-base station positioning algorithms utilize antenna array processing to estimate the angle of arrival (AoA) and time of arrival (ToA) of multipath signals to establish spatial geometric equations. In uplink Single-Input Multiple-Output (SIMO) scenarios, user terminals lack array antennas, and key information such as the transmission angle is unobservable. This results in a much larger number of unknowns in the geometric equations than the number of available equations, forming a typical algebraically underdetermined problem that is difficult to apply directly. Fingerprint localization algorithms use features such as Channel State Information (CSI) or Received Signal Strength (RSS) for database similarity matching, thus avoiding the difficulties of geometric solutions. However, in complex urban environments with strong multipath propagation and highly symmetrical scene layouts, this algorithm is prone to the "multi-point co-image" phenomenon where multiple physical locations have similar fingerprints, leading to severe localization ambiguity and coordinate drift, severely limiting the system's robustness.

[0003] In recent years, to overcome the limitations of geometric calculation and feature matching to obtain stable and physically interpretable positioning results, positioning algorithms based on spatial imaging mechanisms have received widespread attention. Traditional backprojection (BP) imaging algorithms achieve target focusing of multipath energy in the image domain through underlying time delay compensation and coherent accumulation mechanisms. However, limited by the spatial inversion mapping principle based on equal-time-delay trajectories, the high azimuth resolution of traditional BP algorithms heavily relies on large-span physical spatial view diversity (such as aperture synthesis based on a mobile platform). Under the stringent constraints of single-base stationary reception, the system lacks physical aperture expansion capabilities, making it difficult for the algorithm to break through the azimuth resolution bottleneck; furthermore, in complex occlusion environments, multipath sidelobes and background clutter interference are severe, leading to failure in accurate target focusing and positioning. Therefore, achieving high-precision positioning under single-base non-line-of-sight conditions remains a significant challenge, regardless of whether relying solely on instantaneous geometric observation, feature fingerprint matching, or traditional backprojection spatial imaging mechanisms. Summary of the Invention

[0004] In view of this, the purpose of this invention is to propose a single-station localization method for non-line-of-sight targets based on angle-constrained back projection. This method first introduces an angle-of-arrival constraint to limit the spatial imaging range of the back projection algorithm, obtaining a grid energy spectrum for multipath energy focusing. Subsequently, by executing a local extremum optimization strategy in the image domain, clutter and multipath sidelobe interference in the energy spectrum are accurately removed, and spatial discrete imaging feature points with strong multipath interference are extracted with high confidence. Finally, the system introduces a building layout map as a spatial topological constraint prior. Based on the aforementioned feature points, the system constructs and traverses the association assumptions between multipath paths and physical walls to perform a mirror-inverse mapping of the propagation links, and performs global coherent energy optimization in the solution space, thereby accurately resolving the final physical location coordinates of the non-line-of-sight target.

[0005] To achieve the above objectives, the technical solution adopted by this invention is: a non-line-of-sight target single-station localization method based on angle-constrained back projection, comprising the following steps:

[0006] S101: Uplink signal acquisition. The BS receives the linear frequency modulated signal and filters ambient noise using an adaptive threshold method to obtain the receiver matrix. ;

[0007] S102: Multipath angle of arrival estimation, and establishment of adaptive spatial angle confidence intervals for each multipath component. ;

[0008] S103: Multipath imaging, based on angle-constrained back-projection radar imaging, to obtain the scene energy distribution matrix. ;

[0009] S104: Hard truncation of side lobes, which achieves hard truncation of spatial side lobes through local peak detection mechanism in the image domain;

[0010] S105: Strong multipath extraction, which achieves deterministic extraction of the coordinates of strong multipath scattering centers by performing pixel energy saliency sorting on the radar imaging matrix;

[0011] S106: Topological association hypothesis. A set of association hypotheses between multipath and physical reflector is constructed based on enumeration. The optimal multipath combination is determined by the candidate physical propagation paths within the known scene. Match physical propagation path labels to generate multipath correlation mapping vectors. ;

[0012] S107: Virtual source inverse calculation: Perform mirror inverse calculation on the strong multipath coordinates based on the multipath correlation mapping vector to solve for the virtual source spatial coordinates under each assumption. ;

[0013] S108: Global coherence optimization calculates the coherence energy spectrum of the virtual source under all association assumption combinations, and uses the spatial coordinates corresponding to the global maximum coherence energy as the final localization result for non-line-of-sight targets. .

[0014] Based on the above technical solution, the receiving matrix in step S101 The representation method is as follows:

[0015] ;

[0016] in, Represents the number of array elements. This represents the length of the discrete time delay sequence. The background clutter suppression method for the received signal is as follows:

[0017] ;

[0018] ;

[0019] ;

[0020] in, The raw signal received by the radar; Indicates the clutter suppression power threshold; Indicates the effective dynamic tolerance in decibels (dB);

[0021] Based on the above technical solution, the spatial angle of arrival estimation method for the multipath components in step S102 is as follows:

[0022] ;

[0023] ;

[0024] in, The spatial angular energy spectrum reconstructed based on Angle-FFT; The phase coherence index term is used to compensate for the spatial path difference between antenna array elements; The wavelength of the signal; The element spacing is used; the method for determining the spatial angle confidence interval of the multipath components is as follows:

[0025] ;

[0026] ;

[0027] in, For the array in the estimated angle Physical Rayleigh resolution limit in direction (unit: degrees). Adjust the expansion coefficient for the preset confidence level (typically ranging from 100 to 100%). This coefficient is adaptively configured based on the system's empirical tolerance for the angle of arrival estimation error; This is the boundary of the angle confidence domain corresponding to the finally established multipath component.

[0028] Based on the above technical solution, the rear projection radar imaging steps based on angle constraints in step S103 are as follows:

[0029] First, considering the actual detection coverage of the radar system, the physical boundary of the continuous three-dimensional observation scene is defined as follows: , as well as The discrete search grid is constructed based on the spatial step size as follows:

[0030] ;

[0031] ;

[0032] ;

[0033] ;

[0034] in, , as well as The coordinates of the initial geometric boundary of the observed scene; , as well as This refers to the resolution size of the three-dimensional spatial grid. The preset spatial grid scaling factor; Indicates the speed of signal propagation; The sampling frequency of the receiving system;

[0035] Next, the energy of each imaging grid is calculated using angular constraints, as follows:

[0036] ;

[0037] ;

[0038] ;

[0039] ;

[0040] ;

[0041] in, This represents the angle constraint factor for each grid cell; For the position index of the grid; Indicates the time delay index of the grid; as well as Let represent the theoretical angle of arrival and theoretical time delay of the grid, respectively. The calculation steps are as follows:

[0042] ;

[0043] ;

[0044] in, The coordinates of the receiving base station are known quantities. The normal installation angle of the receiving base station, such as when the array normal is parallel to the x-axis, then ;

[0045] Based on the above technical solution, step S104 is as follows:

[0046] By introducing the spatial sliding window neighborhood The energy spectrum is traversed pixel by pixel, and only the center pixel whose energy equals the maximum energy within the sliding window is retained; otherwise, its energy is set to zero. The specific steps are as follows:

[0047] ;

[0048] ;

[0049] in, This represents the energy matrix after detection; This is the set of discrete candidate scattering centers after removing side lobes.

[0050] Based on the above technical solution, in step S105, after obtaining the discrete candidate feature point set... Subsequently, to further remove background noise and high-order weak clutter from the image, this method introduces a preset multipath constraint factor. Energy optimization processing is performed on the candidate feature point set to obtain the energy-optimal multipath combination. The steps are as follows:

[0051] ;

[0052] in, Let be the energy constraint threshold of the imaging matrix, and be... The Middle High power values. This allows for the extraction of several strong multipath streams from complex received signals.

[0053] Based on the above technical solution, in step S106, the set of candidate physical propagation topology states contained in the known observation scene is first defined:

[0054] ;

[0055] in, Representative physical wall surface First-order reflection;

[0056] To construct the set of assumptions relating multipath and physical reflector, the system employs a full permutation traversal strategy to construct the associated mapping state vector:

[0057] ;

[0058] in, Representative at the Under this combination of assumptions, forcibly assigning the first Multipath features The specific physical propagation topology; The total number of combinations in the entire hypothesis space; if each multipath has Given the possible wall association states, under a full permutation traversal without pruning, assuming the total dimension of the space is... ;

[0059] Based on the above scheme, in step S107, for any candidate combination The system employs a multipath inverse solution module; if this hypothesis combination determines a certain multipath feature point... For physical wall surface For the first reflection path, the system will retrieve the three-dimensional geometric feature parameters of the wall surface and perform a mirror-symmetric inverse transformation on the multipath coordinates; based on the principle of mirror projection, the multipath feature points will be... Back-derived to the virtual source isomorphic coordinates under the corresponding assumption Its algebraic mapping operator satisfies:

[0060] ;

[0061] in, This indicates the physical wall surface Spatial normal eigenvectors; represents the spatial intercept constant of the geometric equation of the wall; represents the absolute physical distance of the wall relative to the observation origin. The square of the Euclidean norm of the normal vector;

[0062] Based on the above scheme, in step S108, the virtual source mapping coordinates of all multipaths under any combination are obtained. Subsequently, the system performs coherent superposition within a continuous three-dimensional physical computation domain to generate the scene energy spectrum for this specific combination:

[0063] ;

[0064] in, The square of the Euclidean norm represents spatial distance; A Gaussian kernel smoothing factor to control the energy focusing range; express The corresponding power;

[0065] The system iterates through and calculates all The system calculates the spatial energy spectrum corresponding to various combinations of assumptions and constructs an optimization objective function. Since a correct physical scattering topology causes the coordinates of each virtual source to overlap, resulting in a large energy peak, the system selects the optimal combination of topological assumptions by solving for the global maximum. Its decision formula satisfies:

[0066] ;

[0067] Based on the above global optimization results, the system extracts the optimal combination of hypotheses. The system uses the spatial coordinates at the peak of the spatial energy as the target's position estimate in the current non-line-of-sight occlusion environment. The steps are as follows:

[0068] .

[0069] The present invention has the following beneficial effects:

[0070] (1) Compared with the traditional feature fingerprint matching and positioning method, the present invention replaces the simple data similarity comparison by constructing the underlying physical geometry propagation link and the spatial coherent energy focusing mechanism, which fundamentally eliminates the positioning ambiguity and coordinate drift caused by "multiple points in the same image" in complex urban highly symmetrical scenarios, and greatly improves the environmental robustness and physical interpretability of the non-line-of-sight positioning system.

[0071] (2) Compared with the traditional back projection (BP) imaging algorithm, this invention reconstructs the solution domain through the angle of arrival (AOA) prior constraint and performs propagation link mirror inversion by using the physical wall as a reflecting mirror, thus transforming the environmental multipath into a multidimensional distributed virtual observation perspective. This mechanism breaks the rigid dependence of the underlying time delay compensation mechanism on the diversity of perspectives in a large span of physical space. The system can break through the azimuth resolution bottleneck without the need for a moving platform to synthesize the physical aperture, and achieve precise target focusing under static receiving conditions.

[0072] (3) Compared with the traditional single-base station positioning method based on geometric constraints, this invention introduces building layout map as a spatial topology constraint prior and combines multipath virtual source mirroring inverse calculation mechanism to fill the lack of observable key information such as user terminal transmit angle (AOD) in uplink communication, effectively overcome the bottleneck of algebraic underdetermined solution in non-line-of-sight scenarios, and realizes high-precision positioning of target absolute position under single-base station constraints. Attached Figure Description

[0073] Figure 1 This is a flowchart of a non-line-of-sight target single-station localization method based on angle-constrained back projection proposed in this invention;

[0074] Figure 2 This is a flowchart of the angle-constrained back projection imaging steps of a non-line-of-sight target single-station localization method based on angle-constrained back projection proposed in this invention.

[0075] Figure 3 This is a flowchart of the strong multipath extraction steps of a non-line-of-sight target single-station localization method based on angle-constrained back projection proposed in this invention.

[0076] Figure 4 This is a flowchart of the spatial topology assumptions and coherent energy optimization steps for a non-line-of-sight target monostation localization method based on angle-constrained back projection proposed in this invention. Detailed Implementation

[0077] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0078] like Figure 1 As shown, the design concept of this invention is to provide a non-line-of-sight target single-station localization method based on angle-constrained back projection, including:

[0079] S101: Uplink signal acquisition. The BS receives the linear frequency modulated signal and filters ambient noise using an adaptive threshold method to obtain the receiver matrix. ;

[0080] S102: Multipath angle of arrival estimation, and establishment of adaptive spatial angle confidence intervals for each multipath component. ;

[0081] S103: Multipath imaging, based on angle-constrained back-projection radar imaging, to obtain the scene energy distribution matrix. ;

[0082] S104: Hard truncation of side lobes, which achieves hard truncation of spatial side lobes through local peak detection mechanism in the image domain;

[0083] S105: Strong multipath extraction, which achieves deterministic extraction of the coordinates of strong multipath scattering centers by performing pixel energy saliency sorting on the radar imaging matrix;

[0084] S106: Topological association hypothesis. A set of association hypotheses between multipath and physical reflector is constructed based on enumeration. The optimal multipath combination is determined by the candidate physical propagation paths within the known scene. Match physical propagation path labels to generate multipath correlation mapping vectors. ;

[0085] S107: Virtual source inverse calculation: Perform mirror inverse calculation on the strong multipath coordinates based on the multipath correlation mapping vector to solve for the virtual source spatial coordinates under each assumption. ;

[0086] S108: Global coherence optimization calculates the coherence energy spectrum of the virtual source under all association assumption combinations, and uses the spatial coordinates corresponding to the global maximum coherence energy as the final localization result for non-line-of-sight targets. .

[0087] like Figure 2 This is a flowchart of the angle-constrained back projection imaging steps of a non-line-of-sight target single-station localization method based on angle-constrained back projection proposed in this invention.

[0088] The steps for estimating the angle of arrival in multipath space are as follows: S202:

[0089] ;

[0090] ;

[0091] in, The spatial angular energy spectrum reconstructed based on Angle-FFT; The phase coherence index term is used to compensate for the spatial path difference between antenna array elements; The wavelength of the signal; The element spacing is used. The method for determining the spatial angular confidence interval of the multipath components is as follows: S203:

[0092] ;

[0093] ;

[0094] in, For the array in the estimated angle Physical Rayleigh resolution limit in direction (unit: degrees). Adjust the expansion coefficient for the preset confidence level (typically ranging from 100 to 100%). This coefficient is adaptively configured based on the system's empirical tolerance for the angle of arrival estimation error; This is the final established boundary of the angle confidence domain corresponding to this multipath component;

[0095] The physical space meshing steps are as follows: S204:

[0096] Based on the actual detection coverage of the radar system, the physical boundary of the continuous three-dimensional observation scene is set as follows: , as well as The discrete search grid is constructed based on the spatial step size as follows:

[0097] ;

[0098] ;

[0099] ;

[0100] ;

[0101] in, , as well as The coordinates of the initial geometric boundary of the observed scene; , as well as This refers to the resolution size of the three-dimensional spatial grid. The preset spatial grid scaling factor; Indicates the speed of signal propagation; The sampling frequency of the receiving system;

[0102] The time-delay spatial power mapping based on angle constraints is as follows: S205:

[0103] ;

[0104] ;

[0105] ;

[0106] ;

[0107] ;

[0108] in, This represents the angle constraint factor for each grid cell; For the position index of the grid; Indicates the time delay index of the grid; as well as Let represent the theoretical angle of arrival and theoretical time delay of the grid, respectively. The calculation steps are as follows:

[0109] ;

[0110] ;

[0111] in, The coordinates of the receiving base station are known quantities. The normal installation angle of the receiving base station, such as when the array normal is parallel to the x-axis, then .

[0112] like Figure 3 This is a flowchart of the strong multipath extraction steps of a non-line-of-sight target single-station localization method based on angle-constrained back projection proposed in this invention.

[0113] First, by introducing spatial sliding window neighborhoods The energy spectrum is traversed pixel by pixel, and only the energy of the center pixel is retained if it is equal to the maximum energy within the sliding window; otherwise, its energy is set to zero. The specific steps are as follows: S302:

[0114] ;

[0115] ;

[0116] in, This represents the energy matrix after detection; This is the set of discrete candidate scattering centers after removing side lobes;

[0117] Based on the above technical solution, in step S105, after obtaining the discrete candidate feature point set... Subsequently, to further remove background noise and high-order weak clutter from the image, this method introduces a preset multipath constraint factor. Energy optimization processing is performed on the candidate feature point set to obtain the energy-optimal multipath combination. The steps are as follows (S303):

[0118] ;

[0119] in, Let be the energy constraint threshold of the imaging matrix, and be... The Middle High power values. This allows for the extraction of several strong multipath streams from complex received signals.

[0120] like Figure 4 This is a flowchart of the spatial topology assumptions and coherent energy optimization steps for a non-line-of-sight target monostation localization method based on angle-constrained back projection proposed in this invention.

[0121] First, define the set of candidate physical propagation topology states S402 contained within the known observation scenario:

[0122] ;

[0123] in, Representative physical wall surface First-order reflection;

[0124] To construct the set of assumptions relating multipath and physical reflector, the system employs a full permutation traversal strategy to construct the associated mapping state vector:

[0125] ;

[0126] in, Representative at the Under this combination of assumptions, forcibly assigning the first Multipath features The specific physical propagation topology; The total number of combinations in the entire hypothesis space; if each multipath has Given the possible wall association states, under a full permutation traversal without pruning, assuming the total dimension of the space is... ;

[0127] For any candidate combination The system employs a multipath inverse calculation module S403. If this hypothesis combination determines a multipath feature point... For physical wall surface For the first reflection path, the system will retrieve the three-dimensional geometric feature parameters of the wall surface and perform a mirror-symmetric inverse transformation on the multipath coordinates; based on the principle of mirror projection, the multipath feature points will be... Back-derived to the virtual source isomorphic coordinates under the corresponding assumption Its algebraic mapping operator satisfies:

[0128] ;

[0129] in, This indicates the physical wall surface Spatial normal eigenvectors; represents the spatial intercept constant of the geometric equation of the wall; represents the absolute physical distance of the wall relative to the observation origin. The square of the Euclidean norm of the normal vector;

[0130] Obtain the virtual source mapping coordinates of all multipaths under any combination. Then, the system coherently superimposes data in a continuous three-dimensional grid space to generate the scene energy spectrum S404 for this specific combination:

[0131] ;

[0132] in, The square of the Euclidean norm represents spatial distance; A Gaussian kernel smoothing factor to control the energy focusing range; express The corresponding power;

[0133] The system iterates through and calculates all The system calculates the spatial energy spectrum corresponding to various combinations of topological assumptions and constructs an optimization objective function. Since a correct physical scattering topology causes the coordinates of all virtual sources to overlap, resulting in a large energy peak, the system selects the optimal combination of topological assumptions by solving for the global maximum. Its decision formula satisfies S405:

[0134] ;

[0135] Based on the above global optimization results, the system extracts the optimal combination of hypotheses. The system uses the spatial coordinates at the peak of the spatial energy as the target's position estimate in the current non-line-of-sight occlusion environment. The steps are as follows (S406):

[0136] ;

[0137] The above embodiments should be understood as illustrative only and not as limiting the scope of protection of the present invention. After reading the description of the present invention, those skilled in the art can make various alterations or modifications to the present invention, and these equivalent changes and modifications also fall within the scope defined by the claims of the present invention.

Claims

1. A non-line-of-sight target single-station localization method based on angle-constrained back projection, characterized in that, Includes the following steps: S101: Uplink signal acquisition. The BS receives the linear frequency modulated signal and filters ambient noise using an adaptive threshold method to obtain the receiver matrix. ; S102: Multipath angle of arrival estimation, and establishment of adaptive spatial angle confidence intervals for each multipath component. ; S103: Multipath imaging, based on angle-constrained back-projection radar imaging, to obtain the scene energy distribution matrix. ; S104: Hard truncation of side lobes, which achieves hard truncation of spatial side lobes through local peak detection mechanism in the image domain; S105: Strong multipath extraction, which achieves deterministic extraction of the coordinates of strong multipath scattering centers by performing pixel energy saliency sorting on the radar imaging matrix; S106: Topological association hypothesis. A set of association hypotheses between multipath and physical reflector is constructed based on enumeration. The optimal multipath combination is determined by the candidate physical propagation paths within the known scene. Match physical propagation path labels to generate multipath correlation mapping vectors. ; S107: Virtual source inverse calculation: Perform mirror inverse calculation on the strong multipath coordinates based on the multipath correlation mapping vector to solve for the virtual source spatial coordinates under each assumption. ; S108: Global coherence optimization calculates the coherence energy spectrum of the virtual source under all association assumption combinations, and uses the spatial coordinates corresponding to the global maximum coherence energy as the final localization result for non-line-of-sight targets. .

2. The non-line-of-sight target single-station localization method based on angle-constrained back projection according to claim 1, characterized in that: The receiving matrix in step S101 The representation method is as follows: ； in, Represents the number of array elements. This represents the length of the discrete time delay sequence. The background clutter suppression method for the received signal is as follows: ； ； ； in, The raw signal received by the radar. Indicates the clutter suppression power threshold. This indicates the effective dynamic tolerance in decibels (dB).

3. The non-line-of-sight target single-station localization method based on angle-constrained back projection according to claim 1, characterized in that: The spatial arrival angle estimation method for the multipath components in step S102 is as follows: ； ； in, The spatial angular energy spectrum reconstructed based on Angle-FFT; The phase coherence index term is used to compensate for the spatial path difference between antenna array elements; The wavelength of the signal; The element spacing is used. The method for determining the spatial angle confidence interval of the multipath components is as follows: ； ； in, For the array in the estimated angle Physical Rayleigh resolution limit in direction (unit: degrees). Adjust the expansion coefficient for the preset confidence level (typically ranging from 100 to 100%). This coefficient is adaptively configured based on the system's empirical tolerance for the angle of arrival estimation error; This is the boundary of the angle confidence domain corresponding to the finally established multipath component.

4. The non-line-of-sight target single-station localization method based on angle-constrained back projection according to claim 1, characterized in that: In step S103, the back projection radar imaging steps based on angle constraints are as follows: First, considering the actual detection coverage of the radar system, the physical boundary of the continuous three-dimensional observation scene is defined as follows: , as well as The discrete search grid is constructed based on the spatial step size as follows: ； ； ； ； in, , as well as The coordinates of the initial geometric boundary of the observed scene; , as well as This refers to the resolution size of the three-dimensional spatial grid. The preset spatial grid scaling factor; Indicates the speed of signal propagation; The sampling frequency of the receiving system; Next, the energy of each imaging grid is calculated using angular constraints, as follows: ； ； ； ； ； in, This represents the angle constraint factor for each grid cell. For the position index of the grid, Indicates the time delay index of the grid. as well as Let represent the theoretical angle of arrival and theoretical time delay of the grid, respectively. The calculation steps are as follows: ； ； in, Let be the location coordinates of the receiving base station, and be a known quantity. The normal installation angle of the receiving base station, such as when the array normal is parallel to the x-axis, then .

5. The non-line-of-sight target single-station localization method based on angle-constrained back projection according to claim 1, characterized in that: In step S104, a spatial sliding window neighborhood is introduced. The energy spectrum is traversed pixel by pixel, and only the center pixel whose energy equals the maximum energy within the sliding window is retained; otherwise, its energy is set to zero. The specific steps are as follows: ； ； in, This represents the peak energy of the multipath after detection. This is the set of discrete candidate scattering centers after removing side lobes.

6. The non-line-of-sight target single-station localization method based on angle-constrained back projection according to claim 1, characterized in that: In step S105, after obtaining the discrete candidate feature point set... Subsequently, to further remove background noise and high-order weak clutter from the image, this method introduces a preset multipath constraint factor. Energy optimization processing is performed on the candidate feature point set to obtain the energy-optimal multipath combination. The steps are as follows: ； in, Let be the energy constraint threshold of the imaging matrix, and be... The Middle High power values; thus, several strong multipaths can be extracted from complex received signals.

7. The non-line-of-sight target single-station localization method based on angle-constrained back projection according to claim 1, characterized in that: In step S106, the set of candidate physical propagation topology states contained in the known observation scene is first defined: ； in, Representative physical wall surface First-order reflection; To construct the set of assumptions relating multipath and physical reflector, the system employs a full permutation traversal strategy to construct the associated mapping state vector: ； in, Representative at the Under this combination of assumptions, forcibly assigning the first Multipath features The specific physical propagation topology; The total number of combinations in the entire hypothesis space; if each multipath has Given the possible wall association states, under a full permutation traversal without pruning, assuming the total dimension of the space is... .

8. The non-line-of-sight target single-station localization method based on angle-constrained back projection according to claim 1, characterized in that: In step S107, for any candidate combination The system employs a multipath inverse solution module; if this hypothesis combination determines a certain multipath feature point... For physical wall surface For the first reflection path, the system will retrieve the three-dimensional geometric feature parameters of the wall and perform a mirror-symmetric inverse transformation on the multipath coordinates; Based on the principle of mirror projection, multipath feature points Back-derived to the virtual source isomorphic coordinates under the corresponding assumption Its algebraic mapping operator satisfies: ； in, This indicates the physical wall surface Spatial normal eigenvectors Let represent the spatial intercept constant of the geometric equation of the wall, and let represent the absolute physical distance of the wall relative to the observation origin. The square of the Euclidean norm of the normal vector.

9. The non-line-of-sight target single-station localization method based on angle-constrained back projection according to claim 1, characterized in that: In step S108, the virtual source mapping coordinates of all multipaths under any combination are obtained. Subsequently, the system performs coherent superposition within a continuous three-dimensional physical computation domain to generate the scene energy spectrum for this specific combination: ； in, The square of the Euclidean norm represents spatial distance; To control the Gaussian kernel smoothing factor of the energy focusing range, express The corresponding power; The system iterates through and calculates all The system calculates the spatial energy spectrum corresponding to various combinations of assumptions and constructs an optimization objective function. Since a correct physical scattering topology causes the coordinates of each virtual source to overlap, resulting in a large energy peak, the system selects the optimal combination of topological assumptions by solving for the global maximum. Its decision formula satisfies: ； Based on the above global optimization results, the system extracts the optimal combination of hypotheses. The spatial coordinates at which the spatial energy peak is reached. The system directly uses these peak coordinates as the target position estimate under the current non-line-of-sight occlusion environment. The steps are as follows: 。

Images