A virtual anchor point solving method based on indoor multipath characteristics

Abstract

The application discloses a virtual anchor point solving method based on indoor multipath characteristics, which can be applied to a single station single antenna scene, and aims to utilize multipath component delay to realize position calculation of a virtual anchor point in an indoor environment, and gives a method for solving three-dimensional virtual anchor point coordinates from two-dimensional space from the perspective of space projection to cope with the demand of indoor multipath assisted positioning. Firstly, a virtual anchor point model of three-dimensional space is constructed; then, horizontal projection is carried out to solve a virtual anchor point of a two-dimensional horizontal plane; secondly, vertical projection is carried out to solve a virtual anchor point of a two-dimensional vertical plane; finally, similar virtual anchor points are excluded to obtain virtual anchor points corresponding to reflecting surfaces in a three-dimensional closed room. The application avoids extra parameter errors and high hardware costs caused by multi-parameter estimation, and is a multipath assisted mapping method with strong interpretability and simple implementation operation.

Description

Technical Field

[0001] This invention relates to the field of indoor wireless positioning technology, and in particular to a method for solving virtual anchor points based on indoor multipath characteristics. Background Technology

[0002] Location information services have become a basic necessity in people's daily lives. However, in indoor environments, Global Navigation Satellite Systems (GNSS) struggle to provide accurate positioning services. Wireless signals such as Wi-Fi, Bluetooth, and cellular networks are widely used, and indoor positioning technologies based on these signals have enormous potential for integrated sensing and communication. Existing indoor positioning technologies have evolved from multi-station positioning to single-station positioning. Single-station positioning technology focuses on utilizing multipath propagation in the indoor environment to achieve assisted positioning. Indoors, user equipment receives multipath signals from a transmitter. Multipath signals contain rich geometric information. They can be modeled as a superposition of a Line of Sight (LoS) component, several deterministic specular multipath components (SMPC), and random noise components. Among these, SMPC is key to improving positioning performance. In SMPC, a specular reflection that experiences only one reflection within a room is called a first-order specular reflection. The user equipment points towards the transmitter's mirror image in the receiving direction of the first-order specular reflection, i.e., the virtual anchor (VA). Typically, each wall in a room can produce a first-order specular reflection, and each wall can correspond to a virtual anchor point. In a single-station scenario, these virtual anchor points can extend the original single-station positioning to multi-station positioning, thereby achieving assisted positioning and greatly reducing the cost of positioning equipment. Therefore, obtaining accurate virtual anchor points is crucial.

[0003] A key aspect of using virtual anchors for multipath-assisted localization is calculating the coordinates of these virtual anchors. Existing methods for detecting virtual anchor positions mainly fall into two categories: 1. End-to-end learning algorithms: This method uses neural networks to map multipath signals to obtain virtual anchors. It requires a massive amount of data for model training, such as the channel impulse response (CIR)-based virtual anchor mapping proposed by K.-J. Cha, H. Park, and S. Kim in their paper "From Radio Signals to Spatial Maps: End-to-End Learning for Virtual Anchor Mapping". II. Multi-parameter Equation Solving: This method utilizes Time of Arrival (ToA), Time Difference of Arrival (TDoA), or Angle of Arrival (AoA) to construct equations to estimate the coordinates of virtual anchor points. However, the estimation results are highly susceptible to the accuracy of these parameters, typically requiring several GHz of signal bandwidth to achieve high accuracy. Furthermore, AoA estimation necessitates large-scale antenna arrays, resulting in high costs. For example, Ali Yassin et al. presented a multi-parameter virtual anchor point estimation method in "MOSAIC: Simultaneous Localization and Environment Mapping Using mmWave Without A-Priori Knowledge." In light of the above methods, this invention utilizes only multipath component delays to solve for virtual anchor points. However, when using multipath delays to solve for virtual anchor points, it is difficult to achieve a one-to-one correspondence between the multipath component delays obtained from different receivers and multiple reflecting surfaces, thus making the construction of the equation system difficult. This invention uses a grid traversal method to avoid seeking the optimal solution through a system of equations, thus solving the problem of solving for three-dimensional virtual anchor points using multipath component delays. Summary of the Invention

[0004] The purpose of this invention is to utilize the time delay of multipath components to calculate the position of virtual anchor points in an indoor environment, avoiding parameter errors and high hardware costs caused by multi-parameter estimation. It is a multipath-assisted mapping method that is highly interpretable and easy to implement.

[0005] The present invention provides a method for solving virtual anchor points based on indoor multipath characteristics. From the perspective of spatial projection, it presents a method for solving the coordinates of three-dimensional virtual anchor points from two-dimensional space, including the following steps:

[0006] Step 1: Construct a virtual anchor point model in three-dimensional space, and give the rationality of the existence of the virtual anchor points and the necessary conditions for solving them;

[0007] Step 2: Based on the necessary conditions in Step 1, solve for the virtual anchor points on the two-dimensional horizontal plane, specifically including the following steps:

[0008] Step 2 (1) Set up the layout of the transmitter and receiver;

[0009] Step 2 (2): Project the three-dimensional space onto the horizontal plane;

[0010] Step 2 (3): Analyze the multipath components;

[0011] Step 2 (4): Generate the mesh;

[0012] Step 2 (5): Traverse all grids;

[0013] Step 2 (6): Divide the core grid;

[0014] Step 2 (7): Select the center grid;

[0015] Step 3: Based on the necessary conditions in Step 1, solve for the virtual anchor points of the two-dimensional vertical plane, specifically including the following steps:

[0016] Step 3 (1) Change the receiver layout;

[0017] Step 3 (2): Project the three-dimensional space onto the vertical plane;

[0018] Step 3 (3) Analyze the multipath components;

[0019] Step 3 (4): Generate the mesh;

[0020] Step 3 (5): Traverse all grids;

[0021] Step 3 (6): Divide the core grid;

[0022] Step 3 (7): Select the center grid;

[0023] Step 4: Obtain the 3D virtual anchor points. Based on all the central meshes obtained in Steps 2 and 3, obtain the virtual anchor points corresponding to all indoor reflective surfaces.

[0024] Beneficial effects

[0025] 1. Reduce the computational complexity of virtual anchor points and improve computational efficiency: This invention uses a grid traversal method to avoid seeking the optimal solution through a system of equations. It can flexibly control the number of grids traversed and reduce the computational complexity of virtual anchor points by a finite number of grid traversals, thereby improving the computational efficiency of solving multiple virtual anchor points.

[0026] 2. Indiscriminate mesh generation ensures the traversal reachability of multiple virtual anchor points and enables synchronous solving of multiple virtual anchor points: By utilizing the multipath component delay, meshes are generated indiscriminately, ensuring that each virtual anchor point is located within the mesh's neighborhood, thus ensuring that potential virtual anchor points exist within these meshes, and simultaneously covering multiple virtual anchor points to achieve synchronous solving of multiple virtual anchor points.

[0027] 3. Enhanced noise robustness to ensure solution accuracy in complex environments: In complex environments, noise increases the estimation error of the time delay parameters of multipath components by the receiver. This invention ensures the solution accuracy of virtual anchor points in complex environments by associating the grid distribution of multiple receivers and eliminating noisy grids with low interleaving numbers.

[0028] 4. Advantages in adapting to 3D indoor scenes: The virtual anchor point solution method proposed in this invention utilizes the multipath component delay of each receiver to achieve mesh traversal of potential virtual anchor point positions, exhibiting excellent traversal efficiency in a 2D plane. Furthermore, the mapping method from a 3D room to a 2D plane provided by this invention allows the virtual anchor point solution method to be well adapted to 3D indoor scenes, avoiding the direct generation of spherically distributed meshes in 3D space and achieving high traversal efficiency. Attached Figure Description

[0029] Figure 1 A flowchart of the virtual anchor point solution process;

[0030] Figure 2 It is a virtual anchor point model in three-dimensional space, reflecting the multipath characteristics between the transmitter and the receiver;

[0031] Figure 3 This is a schematic diagram of the propagation of a first-order specular reflection signal between a transmitter Tx and a receiver Rx located on the same horizontal plane.

[0032] Figure 4 This is a schematic diagram of the projection result on a two-dimensional horizontal plane;

[0033] Figure 5 This is a schematic diagram of the grid distribution of the four reflecting surfaces in a two-dimensional horizontal plane;

[0034] Figure 6 This is a schematic diagram of the propagation of a first-order specular reflection signal between a transmitter Tx and a receiver Rx located on the same vertical plane.

[0035] Figure 7 This is a schematic diagram of the projection result on a two-dimensional vertical plane.

[0036] Figure 8 This is a schematic diagram of the grid distribution of the four reflecting surfaces in a two-dimensional vertical plane. Detailed Implementation Plan

[0037] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings. The present invention provides a virtual anchor point solution method based on indoor multipath characteristics, such as... Figure 1 As shown, the specific steps include:

[0038] Step 1: Construct a virtual anchor point model in three-dimensional space. Based on... Figure 2 Given the location P of the transmitter, the spatial coordinate relationship between the three mirror transmission points and the three receivers, we can obtain the solution equations for the three-dimensional virtual anchor point:

[0039] (1)

[0040] The virtual anchor point location is The three receiver positions are as follows: , and , , and These are the mirror reflection path lengths of the signal from the transmitter to the three receivers. Equation (1) reveals that a transmitter and a reflecting surface in three-dimensional space must correspond to a virtual anchor point. Solving for the three-dimensional coordinates of this virtual anchor point requires at least three receivers with known coordinates, and the transmitter and receivers must not overlap with each other. In addition, the transmitter and receivers must be on the same side relative to the reflecting surface.

[0041] Step 2: Based on the necessary conditions in Step 1, solve for the virtual anchor points on the two-dimensional horizontal plane, specifically including the following steps:

[0042] Step 2 (1) Set up the receiver layout. In a rectangular enclosed room, the transmitter position is arbitrary. To easily represent the geometric relationship between the transmitter and receiver in the enclosed room, let's assume the transmitter is located at the center of the room, and the number of receivers is set to the minimum requirement of 3. Place the receivers upright on the same horizontal plane S1 as the transmitter, with the receiver's vertical axis parallel to the z-axis. Figure 3 As shown, the transmitter Tx is located at the center of the room, and the first-order specular reflection path of one of the receivers Rx about the six reflective surfaces has been shown;

[0043] Step 2 (2): Project the three-dimensional space onto the horizontal plane. Project the three-dimensional space onto the horizontal plane S1 where the transmitter is located. Since the receivers are all horizontally coplanar with the transmitter, the lengths of the four paths related to the four walls in the six first-order specular reflection paths of one receiver remain consistent with the original lengths and are not affected by the projection angle. For example... Figure 4 As shown, the first-order specular reflection paths of one receiver Rx about the four sides of the enclosed room remain unchanged, while the first-order specular reflection paths corresponding to the other two sides are projected as straight lines, which are invalid reflection paths.

[0044] Step 2 (3): Analyze the multipath component delay. After each receiver receives the multipath signal, it analyzes the delay of the first-order specular reflection signal. Sort the signals in descending order of ray power to characterize the delay of the highest-power signal in the received signal, i.e., the LoS delay, as well as the delay of the first-order specular reflection path, excluding... Figure 4 The invalid reflection path shown is used to obtain the first-order specular reflection signal delay corresponding to the four reflecting surfaces under the horizontal projection view, and thus the path length can be obtained according to the signal propagation rate.

[0045] Step 2 (4) Generate the mesh. Based on the length of each first-order specular reflection path and the receiver coordinates, generate a mesh on the S1 plane with each receiver coordinate as the center and the corresponding first-order specular reflection path length as the radius. For example... Figure 5 As shown, a grid is generated with the coordinates of each receiver Rx as the center and the length of its corresponding first-order specular reflection path as the radius. Grids of the same size are evenly distributed on each circular dashed line. The center-to-center distance between the generated grids is set to half of k, which is the search interval.

[0046] Step 2 (5): Traverse all grids. Determine if the spacing of each grid is less than k. Record the number of grids with a spacing of less than k around each grid as the interlacing number of that grid. Grids with an interlacing number greater than or equal to n-1 are recorded as core grids (n is the number of indoor receivers, which is 3 here).

[0047] Step 2 (6): Divide the core mesh. Determine if the core meshes are adjacent. If the distance between core meshes is less than 2k, they are considered adjacent. Divide each group of adjacent core meshes into a set.

[0048] Step 2 (7) Selecting the central grid. Sort the sets in descending order based on the number of core grids in each set, and select the first m sets (m is the number of reflecting surfaces under the horizontal projection view, which is 4 here). Select the grid with the largest interlacing number from each of these m sets as the central grid. The center coordinates of these m central grids are used as the two-dimensional coordinates of the virtual anchor point corresponding to each reflecting surface (if there is more than one central grid in a set, take the average coordinate as the two-dimensional coordinates of the virtual anchor point of that set), resulting in the following: Figure 5 The four virtual anchor points V1, V2, V3, and V4 are shown in the diagram.

[0049] Step 3: Based on the necessary conditions in Step 1, solve for the virtual anchor points of the two-dimensional vertical plane, specifically including the following steps:

[0050] Step 3 (1) Change the receiver layout. Let S2 be the vertical plane where the transmitter is located. S2 should be parallel to any one of the four walls. Here, we set S2 to be parallel to the yOz plane, and place the three receivers in three different positions on S2, changing the vertical axis of the receivers to be parallel to the x-axis. For example... Figure 6 As shown, six first-order specular reflection paths between one of the receivers Rx and the transmitter Tx have been demonstrated.

[0051] Step 3 (2): Project the three-dimensional space onto the vertical plane. Project this three-dimensional space onto the S2 plane where the transmitter is located. Because the three receivers are located on the same vertical plane as the transmitter, the first-order specular reflection paths of each receiver about the four faces of the enclosed room remain unchanged after projection. Figure 7 As shown, the first-order specular reflection paths of one receiver Rx about the four sides of the enclosed room remain unchanged, while the first-order specular reflection paths corresponding to the other two sides are projected as straight lines and are considered invalid reflection paths.

[0052] Step 3 (3): Analyze the multipath component delay. After each receiver receives the multipath signal, it analyzes the delay of the first-order specular reflection signal. Sort the signals in descending order of ray power to characterize the delay of the highest-power signal in the received signal, i.e., the LoS delay, and the delay of the first-order specular reflection path, excluding... Figure 7 The invalid reflection path is shown. The time delay of the first-order specular reflection signal corresponding to the four reflecting surfaces under the vertical projection view is obtained, and then the path length is obtained according to the signal propagation rate.

[0053] Step 3 (4): Generate the mesh. Based on the length of each first-order specular reflection path and the receiver coordinates, generate a mesh on the S2 plane with each receiver coordinate as the center and the corresponding first-order specular reflection path length as the radius. For example... Figure 8 As shown, a grid is generated with the coordinates of each receiver Rx as the center and the length of its corresponding first-order specular reflection path as the radius. Grids of the same size are evenly distributed on each circular dashed line. The center-to-center distance between the generated grids is set to half of k, which is the search interval.

[0054] Step 3 (5) Traverse all grids. Determine if the spacing of each grid is less than k. Record the number of grids with a spacing of less than k around each grid as the interlacing number of that grid. Grids with an interlacing number greater than or equal to n-1 are recorded as core grids (n is the number of indoor receivers, which is 3 here).

[0055] Step 3 (6): Divide the core mesh. Determine if the core meshes are adjacent. If the distance between core meshes is less than 2k, they are considered adjacent. Divide each group of adjacent core meshes into a set.

[0056] Step 3 (7) Selecting the central grid. Sort the sets in descending order based on the number of core grids in each set, and select the first m sets (m is the number of reflecting surfaces under the vertical projection view, which is 4 here). Select the grid with the largest interlacing number from each of these m sets as the central grid. The center coordinates of these m central grids are used as the virtual anchor point coordinates for each reflecting surface (if there is more than one central grid in a set, take the average coordinates as the virtual anchor point coordinates for that set). Finally, the result is as follows: Figure 8 The four virtual anchor points V1, V4, V5, and V6 are shown in the diagram.

[0057] Step 4: Obtain the coordinates of the 3D virtual anchor points. Based on the 2D coordinates of the virtual anchor points under horizontal and vertical projections, virtual anchor points with corresponding values ​​on the same coordinate axis are supplemented with their corresponding coordinates to obtain the 3D coordinates of some virtual anchor points. For example, the 3D coordinates of virtual anchor points V1 and V4 are obtained. Among the four 2D virtual anchor points obtained under horizontal and vertical projections, two each have the same coordinate value on the y-axis. Therefore, their respective default coordinate axis values ​​are supplemented to obtain the 3D coordinates of two virtual anchor points, namely V1 and V4. Then, based on the coplanar relationship between these virtual anchor points and the remaining virtual anchor points, the default coordinate axis values ​​of the remaining virtual anchor points are filled in to obtain the 3D coordinates of the six virtual anchor points corresponding to the six reflecting surfaces of the 3D enclosed room.

[0058] The above description is merely one specific embodiment of the present invention, and the scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that the present invention can be applied to single-site, single-antenna wireless positioning scenarios. For those skilled in the art, equivalent changes and modifications without departing from the principles of the present invention should still fall within the scope of protection of the present invention.

Claims

1. A method for solving virtual anchor points based on indoor multipath characteristics, characterized in that: a) Construct a three-dimensional virtual anchor point model based on indoor multipath characteristics, and give the rationality of the existence of virtual anchor points and the necessary conditions for solving them; b) From the perspective of spatial projection, derive a method for solving the coordinates of three-dimensional virtual anchor points from two-dimensional space; c) Based on the existence of virtual anchor points, a mesh traversal method for solving a two-dimensional virtual anchor point model is presented.

2. The virtual anchor point solution method based on indoor multipath features according to claim 1, constructing a three-dimensional virtual anchor point model based on multipath features, and providing the rationality of the existence of virtual anchor points and the necessary conditions for their solution, characterized in that... The coordinates of a 3D virtual anchor point can be effectively calculated using the length of a first-order specular reflection path: Based on the propagation relationship of the radio frequency signal between the transmitter Tx, the signal reflection plane S, and the receiver Rx, and the geometric relationship of specular reflection, let the origin of the 3D spatial coordinate system be O, and a receiver be located at point... The point where the radio frequency signal undergoes first-order specular reflection at the reflecting surface S is... The coordinates of the virtual anchor point P' can be obtained: (1)； in, Let O be the vector pointing to P'. Pointed to by O The vector, For the reason point to The vector, For radio frequency signals from Tx via First-order specular reflection occurs The path length; let The coordinates in three-dimensional space are According to equation (1), P' satisfies the condition shown in equation (2) in three-dimensional space: (2)； in, Let P' represent a coordinate in three-dimensional space; in order to determine the position of P' in three-dimensional space, at least three Rx points located at different positions are required to provide the conditions shown in equation (2); with the reflecting surface S as the boundary, suppose there are three points located at different positions on one side of Tx. , and Rx, the radio frequency signal emitted by the transmitter, is reflected by the reflector S and reaches... , and The corresponding path lengths are respectively , and Combining equation (2), we can obtain the system of equations shown in equation (3): (3)； Based on the three-dimensional virtual anchor point model constructed by equation (3), only the lengths of the mirror reflection paths in the multipath signals of three different location points Rx are needed to calculate the mirror image corresponding to Tx, that is, the coordinates of the virtual anchor point P'.

3. The virtual anchor point solution method based on indoor multipath characteristics according to claim 1, derives a method for solving the coordinates of three-dimensional virtual anchor points from a two-dimensional space from the perspective of spatial projection, characterized in that... The ability to reduce a 3D virtual anchor point model to a 2D virtual anchor point model simplifies the model and calculations, and improves solution efficiency includes the following steps: ① Set up the layout of the transmitter and receiver: In a three-dimensional space Ω, there is a reference plane, such as the xOy plane, which is a horizontal plane S1. On this horizontal plane, there is a flat rectangular closed room. At any point in this room, a transmitter Tx and several receivers Rx are placed. The number of Rx is at least 3, and they are on the same horizontal plane as Tx. In this room, there is a signal delay from Tx to Rx through any reflecting surface via a first-order specular reflection path. There are six first-order specular reflection paths between any Rx and Tx. ② Project the space Ω onto the horizontal plane S1: Since the three Rx and one Tx are located on the same horizontal plane, after projection, the first-order specular reflection path of each Rx about the four vertical planes of the closed room remains unchanged; the first-order specular reflection path of each Rx about the four vertical planes of the closed room remains unchanged, only the first-order specular reflection path about the two horizontal planes of the closed room is projected as a straight line, which is an invalid reflection path and is therefore excluded; after projection, equation (3) will be transformed into the system of equations shown in equation (4): (4)； in, , and These are the x-axis coordinates of the three Rx values. , and These are the y-axis coordinates of the three Rx values. , and Let Tx and Rx be the first-order mirror reflection path lengths of the three Rx after projection onto the same reflecting surface in the closed room. Substituting these three first-order mirror reflection path lengths and the projection coordinates of the three Rx into equation (4), the coordinates of the two-dimensional virtual anchor point corresponding to the reflecting surface can be obtained. Since Tx and Rx are coplanar, the coordinates of the virtual anchor point on the z-axis are consistent with Rx. Similarly, the coordinates of the virtual anchor points corresponding to the other three reflecting surfaces can also be obtained, that is, the coordinates of the virtual anchor points corresponding to the other three vertical reflecting surfaces of the closed room. ③ Change the layout of the receivers: Let S2 be the vertical plane where the transmitter Tx is located. S2 is parallel to a vertical plane of the room. Place the three receivers Rx arbitrarily in three different indoor positions on S2. There are six first-order specular reflection paths between each Rx and Tx. ④ Project Ω onto the S2 plane where the transmitter is located: The three receivers Rx and the transmitter Tx are located on the same vertical plane, so after projection, the first-order specular reflection paths of each Rx about the four faces of the enclosed room remain unchanged; the first-order specular reflection paths of each Rx about the four faces of the enclosed room remain unchanged, only the first-order specular reflection paths about the two faces of the enclosed room are projected as straight lines, which are invalid reflection paths and are therefore excluded; after projection, equation (3) will be transformed into the system of equations shown in equation (5): (5)； in, , and Let Rx be the x-axis coordinates of the three Rx values. , and Let Rx be the z-axis coordinates of the three Rx values. , and Let Tx be the first-order mirror reflection path length of the same reflecting surface after the projection of the three Rx onto the closed room; by substituting the signal reflection path lengths received by the three Rx corresponding to the reflecting surface and the projection coordinates of the three Rx into equation (5), the coordinates of the two-dimensional virtual anchor point corresponding to the reflecting surface can be obtained; since Tx and Rx are coplanar, the coordinate value of the virtual anchor point on the y-axis is consistent with that of Rx; similarly, the coordinates of the virtual anchor points corresponding to the other three reflecting surfaces can also be obtained, that is, the coordinates of the four virtual anchor points corresponding to the two walls, the ceiling and the ground; ⑤ Combining the results of steps ② and ④, the average coordinate of virtual anchor points with similar coordinates is used to replace them, thus obtaining six virtual anchor points corresponding to the four walls, ceiling, and floor.

4. The virtual anchor point solution method based on indoor multipath characteristics according to claim 1, which provides a mesh traversal method for solving a two-dimensional virtual anchor point model based on the existence of virtual anchor points, is characterized in that... A method for simultaneously solving multiple virtual anchor points is presented. This method calculates multiple indoor virtual anchor points in one step using only the multipath component time delay. Unlike the equation system solution for virtual anchor points, it avoids the difficulty of constructing the equation system and the need for multiple solution processes. The method specifically includes the following steps: ① Mesh Generation: A mesh is generated based on the two-dimensional virtual anchor point model. Each receiver Rx has a first-order specular reflection path corresponding to each reflecting surface. After each Rx receives a multipath signal, the first-order specular reflection signal delay is extracted, and the length of the first-order specular reflection signal is obtained based on the signal propagation rate. First, for a reflecting surface, a circle is generated with each Rx as the center and the length of a first-order specular reflection path of its corresponding reflecting surface as the radius. Several meshes are evenly distributed on each circle. Similarly, other reflecting surfaces also have the same number of circles as Rx, and several meshes are evenly distributed on each circle. ② Traverse all grids and record the number of interweavings for each grid to obtain the core grid: The number of interweavings of a grid is related to the search interval k, and its initial value is 0; when the distance between one grid and another grid is less than k, the number of interweavings of that grid increases by 1; grids with an interweaving number of not less than n-1 are recorded as core grids (n is the number of indoor Rx, which is 3 here); ③ Divide these core grids and determine whether the core grids are adjacent. If the distance between core grids is less than 2k, they are considered adjacent. Divide each group of adjacent core grids into a set. ④ Selecting the central grid: Sort the sets in descending order based on the number of core grids in each set, and select the first m sets (m is the number of reflecting surfaces under the horizontal projection view, which is 4 here). Select the grid with the largest interlacing number from each of these m sets as the central grid. The center coordinates of these m central grids are used as the virtual anchor point coordinates for each reflecting surface (if there is more than one central grid in a set, take the average coordinate as the virtual anchor point grid for that set). Finally, the virtual anchor point coordinates for the m reflecting surfaces are obtained.

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