Heterogeneous networked radar spatial registration method based on adaptive grid reconstruction

Abstract

The application discloses a heterogeneous networked radar space registration method based on adaptive grid reconstruction, which comprises the following steps: 1, constructing a radar network system model, presetting related parameters of the radar network system, and initializing the related parameters; 2, obtaining a space sampling unit association group of each grid, and merging grids with the same space sampling unit association group into a reconstructed overlapping area; 3, obtaining a space sampling unit association group of each reconstructed overlapping area, and forming a set; according to the set, an average registration rate of a plurality of randomly distributed point targets is obtained, and a local mismatch rate of each radar station and other radar stations is obtained; if the average registration rate is greater than or equal to a preset average registration rate threshold value, and the local mismatch rate is less than or equal to a preset local mismatch rate threshold value, the optimal grid side length is determined; 4, obtaining a calibration point of the reconstructed overlapping area corresponding to the optimal grid side length. The application effectively improves the registration accuracy.

Description

Technical Field

[0001] This invention belongs to the field of radar technology, specifically relating to a heterogeneous networked radar spatial registration method based on adaptive grid reconstruction. Background Technology

[0002] Networked radar spatial registration correlates observations of the same target from different radar stations, which is an important prerequisite for ensuring the accurate implementation of fusion detection.

[0003] Currently, spatial registration methods based on raster partitioning face problems such as excessive repetition in data association and combination, non-optimal selection of raster calibration points, and lack of solutions for finding the optimal raster size under certain spatial registration evaluation indicators. These problems can lead to large registration errors, excessive computational burden on the system, and loss of fusion detection performance in practical applications.

[0004] Therefore, there is an urgent need to provide a radar spatial registration method to reduce registration errors in practical applications. Summary of the Invention

[0005] To address the aforementioned problems in the existing technology, this invention provides a heterogeneous networked radar spatial registration method based on adaptive grid reconstruction. The technical problem to be solved by this invention is achieved through the following technical solution:

[0006] In a first aspect, the present invention provides a heterogeneous networked radar spatial registration method based on adaptive grid reconstruction, comprising:

[0007] Step 1: Construct a radar network system model, preset the relevant parameters of the radar network system, and initialize the relevant parameters; wherein, the radar network system model includes multiple radar stations and a common monitoring area monitored by multiple radar stations, and the common monitoring area is rasterized, and the relevant parameters include the side length of the raster and the preset raster search step size.

[0008] Step 2: Obtain the spatial sampling unit association group for each grid, and merge grids with the same spatial sampling unit association group into a reconstructed overlapping area;

[0009] Step 3: Obtain the spatial sampling unit association group for each reconstructed overlapping region and form a set; obtain the average registration rate of multiple randomly distributed point targets based on the set, and obtain the local mismatch rate of each radar station not paired with other radar stations; compare the average registration rate with a preset average registration rate threshold, and compare the local mismatch rate with a preset local mismatch rate threshold; if the average registration rate is greater than or equal to the preset average registration rate threshold, and the local mismatch rate is less than or equal to the preset local mismatch rate threshold, determine the optimal grid side length; otherwise, compare the grid side length with a preset grid search step size; if the grid side length is less than or equal to the preset grid search step size, decrease the preset grid search step size and return to step 1 until the optimal grid side length is determined; otherwise, update the grid side length and return to step 2 until the optimal grid side length is determined.

[0010] Step 4: Obtain the calibration points of the reconstructed overlapping region corresponding to the optimal grid side length.

[0011] The beneficial effects of this invention are:

[0012] This invention provides a heterogeneous networked radar spatial registration method based on adaptive grid reconstruction. By gridding the common monitoring area of ​​networked radars, the overlapping area of ​​spatial sampling units of local radar stations is approximately reconstructed, thereby reducing the computational burden. Fermat points at the centers of grids with repeated registrations are searched as calibration points for the reconstructed area to optimize the registration error. Then, by introducing the average registration rate and local mismatch rate as registration performance evaluation indicators, an optimization model that comprehensively considers the computational burden and spatial registration performance is given to achieve the optimization of grid side length.

[0013] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0014] Figure 1 This is a flowchart of a heterogeneous networked radar spatial registration method based on adaptive grid reconstruction provided in an embodiment of the present invention;

[0015] Figure 2 This is a schematic diagram of the average registration rate as a function of grid side length provided in an embodiment of the present invention;

[0016] Figure 3 This is a schematic diagram of the local mismatch rate of Radar 1 as a function of grid side length provided in an embodiment of the present invention;

[0017] Figure 4 This is a distribution map of the reconstructed overlapping regions provided in an embodiment of the present invention;

[0018] Figure 5(a) is a schematic diagram of the registration position distribution corresponding to different average registration rates when each local mismatch rate is fixed at 0, provided by an embodiment of the present invention.

[0019] Figure 5(b) is another schematic diagram of the registration position distribution corresponding to different average registration rates when each local mismatch rate is fixed at 0, provided by an embodiment of the present invention.

[0020] Figure 5(c) is another schematic diagram of the registration position distribution corresponding to different average registration rates when the local mismatch rate is fixed at 0, provided by an embodiment of the present invention. Detailed Implementation

[0021] The present invention will be further described in detail below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.

[0022] To address the shortcomings of existing spatial registration techniques, this invention proposes a heterogeneous networked radar spatial registration method based on adaptive grid reconstruction. This method reduces computational burden by approximating the overlapping areas of local radar station spatial sampling units in the shared monitoring area of ​​networked radars using a grid. Furthermore, it optimizes registration errors by searching for Fermat points at the centers of registered duplicate grids as calibration points for the reconstructed area. Finally, by introducing average registration rate and local mismatch rate as performance evaluation indicators, an optimization model considering both computational burden and spatial registration performance is provided, achieving optimal grid side length.

[0023] Please see Figure 1 , Figure 1 This is a flowchart of a heterogeneous networked radar spatial registration method based on adaptive grid reconstruction provided by an embodiment of the present invention. The heterogeneous networked radar spatial registration method based on adaptive grid reconstruction provided by the present invention includes:

[0024] Step 1: Construct a radar network system model, preset the relevant parameters of the radar network system, and initialize the relevant parameters; wherein, the radar network system model includes multiple radar stations and a common monitoring area monitored by multiple radar stations, the common monitoring area is rasterized, and the relevant parameters include the side length of the raster and the preset raster search step size.

[0025] Specifically, in this embodiment, N radar stations are set according to usage requirements, and the location coordinates of each radar station are set. Distance sampling unit size Δρ i and the size of the angle sampling unit Δθ i The number of discrete distances and scanning angles K in the common monitoring area i D i The set of discrete distances and discrete scanning angles is Input average registration rate and local mismatch rate thresholds and Set the grid search step size to Δq; initialize the grid side length to a large value q = q s A large number of test points are randomly set and their coordinates are input into the radar network system model.

[0026] Step 2: Obtain the spatial sampling unit association group for each raster, and merge rasters with the same spatial sampling unit association group into a reconstructed overlapping area.

[0027] Specifically, in this embodiment, obtaining the spatial sampling unit association group for each grid, and merging grids with the same spatial sampling unit association group into a reconstructed overlapping region, includes:

[0028] The common surveillance area is rasterized into G square grids with side length q. Assuming that there is a point target at the center of each grid, the distance ρ between the center of the point target at the center of the j-th grid and the center of the i-th radar station is obtained. ij and azimuth θ ij Their expressions are as follows:

[0029]

[0030] The center position of the j-th grid cell is represented as The location of the i-th radar station is represented as follows: N represents the total number of radar stations;

[0031] Based on the distance ρ of the point target at the center of the j-th grid to the i-th radar station. ij and azimuth θ ij Obtain the range cell index k in the station-center coordinate system of the i-th radar station, which maps the point target at the center of the j-th grid. ij and angle unit index d ij Their expressions are as follows:

[0032]

[0033] Among them, K i D represents the number of discrete distances between the shared surveillance areas. i This indicates the number of discrete scanning angles. Represents discrete distance, Indicates the discrete scanning angle;

[0034] Based on the point target at the center of the j-th grid, map it to the range cell index k in the station-centered coordinate system of the i-th radar station. ij and angle unit index d ij Obtain the spatial sampling unit associated group c for each raster. j Its expression is:

[0035] c j={(k ij ,d ij |i = 1, 2, ..., N};

[0036] Because the grid is small, there may be cases where different grids correspond to the same spatial sampling unit association group. In this case, these grids are classified into the same set, and the grids in the same classification set are merged and reconstructed into an approximate spatial unit overlapping region. That is, grids with the same spatial sampling unit association group are merged into a reconstructed overlapping region.

[0037] Step 3: Obtain the spatial sampling unit association group for each reconstructed overlapping region and form a set; obtain the average registration rate of multiple randomly distributed point targets based on the set, and obtain the local mismatch rate of each radar station not paired with other radar stations; compare the average registration rate with a preset average registration rate threshold, and compare the local mismatch rate with a preset local mismatch rate threshold; if the average registration rate is greater than or equal to the preset average registration rate threshold, and the local mismatch rate is less than or equal to the preset local mismatch rate threshold, determine the optimal grid side length; otherwise, compare the grid side length with a preset grid search step size; if the grid side length is less than or equal to the preset grid search step size, decrease the preset grid search step size and return to step 1 until the optimal grid side length is determined; otherwise, update the grid side length and return to step 2 until the optimal grid side length is determined.

[0038] Specifically, in this embodiment, spatial sampling unit association groups for each reconstructed overlapping region are obtained and formed into a set, including:

[0039] Obtain the spatial sampling unit association group r for each reconstructed overlapping region t Its expression is:

[0040] r t ={(k it ,d it )|i=1,2,…,N},t=1,2,…,T;

[0041] Where t represents the index of the reconstructed overlapping region, and T represents the total number of reconstructed overlapping regions;

[0042] Associating all the spatial sampling units of the reconstructed overlapping regions into a set Its expression is:

[0043]

[0044] The average registration rate of multiple randomly distributed point targets is obtained from the set, including:

[0045] Obtain the spatial sampling unit association group s corresponding to Z randomly distributed point targets. zIts expression is:

[0046] s z ={(k iz ,d iz )|i=1,2,…,N},z=1,2,…,Z;

[0047] Where z represents the index of a randomly distributed point target;

[0048] The spatial sampling units corresponding to the Z point targets in the set and random distribution are associated with group s. z The average registration rate is obtained by the following expression:

[0049]

[0050] in, Represents the characteristic function.

[0051] It should be noted that the average registration rate η represents the spatial sampling unit association group corresponding to a randomly occurring point target within the common monitoring area appearing in the spatial unit resolution group set. The probability of it.

[0052] Obtain the local mismatch rate of each radar station that is not paired with other radar stations, including:

[0053] Obtain the set Φ of spatial sampling cells of the i-th radar station in the common surveillance area. i Its expression is:

[0054]

[0055] Among them, H i This represents the number of spatial sampling units of the i-th radar station in the common surveillance area. This indicates that the i-th radar station is in the h-th common surveillance area. i One spatial sampling unit, Indicates the h-th i Distance index corresponding to each spatial sampling unit Indicates the h-th i Angle index of each spatial sampling unit;

[0056] The spatial sampling units in all the reconstructed overlapping regions are grouped together to form a set. In the diagram, the set of spatial sampling units ψ of the i-th radar station i The expression is:

[0057] ψ i ={(k it ,d it |t=1,2,…,T};

[0058] Based on the spatial sampling unit set Φ of the i-th radar station in the common surveillance area i and the set of spatial sampling units ψ of the i-th radar station i Obtain the local mismatch rate μ i Its expression is:

[0059]

[0060] in, Represents the characteristic function.

[0061] It should be noted that the local mismatch rate μ i This represents the ratio of the spatial sampling units of the i-th local radar station within the common surveillance area that are not paired with the spatial sampling units of the remaining N-1 radar stations.

[0062] Updating the side length of the grid includes:

[0063] The updated grid's side length is equal to the initial grid's side length minus the preset grid search step size, expressed as:

[0064] q = q - Δq;

[0065] Where Δq represents the preset grid search step size.

[0066] In this embodiment, the calculated average registration rate η and local mismatch rate μ are used as the basis for the calculation. i Compared with the threshold value, when and If q ≤ Δq, proceed to step 4; otherwise, if q ≤ Δq, return to step 1 and decrease the search step size; otherwise, let q = q - Δq and return to step 2.

[0067] Step 4: Obtain the calibration points of the reconstructed overlapping region corresponding to the optimal grid side length.

[0068] Specifically, in this embodiment, the method further includes: optimizing the coordinates of the calibration points of the reconstructed overlapping region corresponding to the side length of the optimal grid;

[0069] The reconstructed overlapping region is defined as having L grid cells, denoted as n1, n2, ..., n L The set of center coordinates of L grid cells is S = {g l |l=n1,n2,…,n L}, reconstruct the coordinates of the calibration points in the overlapping region m = (m x ,m y ) is a function of S;

[0070] The registration error value E of the calibration points in the reconstructed overlapping region is obtained, and its expression is:

[0071]

[0072] in,

[0073] Obtain the minimum value m of the registration error E. opt ,Right now:

[0074]

[0075] Where F represents the two-dimensional coordinate space of the jointly monitored area, and m is the minimum value of the registration error E. opt The solution is the famous Fermat point in mathematics. Since it is difficult to find the closed-form solution of the Fermat point when L≥3, search algorithms (such as simulated annealing and ant colony algorithm) can be used to find the approximate numerical solution of the Fermat point.

[0076] It should be noted that the registration error value represents the average difference between the actual position of the point target that randomly appears in the reconstructed overlapping area and the distance between the calibration point in the reconstructed overlapping area.

[0077] In an optional embodiment of the present invention, it further includes: returning a spatial registration information retrieval table, reconstructing an overlapping region distribution map and a registration location distribution map;

[0078] Based on the calibration points of each reconstructed overlapping region and the spatial sampling unit association group of each reconstructed overlapping region, a spatial registration information retrieval table is obtained;

[0079] By testing multiple randomly distributed point targets in a radar network system model, the distribution maps of reconstructed overlapping areas and registration locations are obtained.

[0080] It should be noted that the reconstructed overlapping region distribution map is an image that intuitively displays the overlapping areas of the reconstructed spatial sampling units. Regions corresponding to the same spatial unit sampling group are filled with the same color. The registration position distribution map is an image that intuitively represents the distribution of registered and unregistered positions.

[0081] In an optional embodiment of the present invention, the beneficial effects of the heterogeneous networked radar spatial registration method based on adaptive grid reconstruction provided in the above embodiment are verified by simulation experiments, specifically as follows:

[0082] I. Simulation Conditions

[0083] The experiment employed three heterogeneous, off-site radars: Radar 1, Radar 2, and Radar 3, with coordinates of (0km, 0km), (5km, 0km), and (-5km, 0km), respectively. The range sampling frequencies were 20MHz, 30MHz, and 50MHz, and the angle sampling units were 0.5°, 0.5°, and 0.5°, respectively. The common monitoring area was a square centered at (50km, 50km) with sides of 1km. Additionally, 4×10... 6 Several test points are used to evaluate registration performance metrics.

[0084] II. Simulation Content

[0085] Simulation 1: Relationship between average registration rate, local mismatch rate, and grid side length;

[0086] Based on the above-mentioned parameters, simulation experiments were conducted, and the relationship curve between the average registration rate and the grid side length was obtained as follows: Figure 2 As shown, Figure 2 This is a schematic diagram of the average registration rate as a function of grid side length provided in an embodiment of the present invention. Consistent with the above analysis, increasing the grid side length makes the reconstructed overlapping area coarser, and the spatial sampling unit associated set... With fewer elements, the spatial sampling unit association group corresponding to the point target cannot appear. In this case, the average registration rate will decrease.

[0087] The relationship between the local mismatch rate and the grid side length of Radar 1 is shown in the curve below. Figure 3 As shown, Figure 3 This is a schematic diagram of the local mismatch rate of Radar 1 as a function of grid side length provided in an embodiment of the present invention. As the grid side length increases, the number of spatial sampling unit set elements for the i-th local radar station in the spatial sampling unit association set also decreases, causing some spatial sampling units to be unable to pair with the spatial sampling units of other local radar stations, thereby increasing the local mismatch rate.

[0088] Simulation 2: Registration information table and reconstruction overlap region distribution map;

[0089] Based on the above simulation conditions, with the local mismatch rate fixed at 0 and the average registration rate η = 0.9019, some information in the spatial registration information table is shown in Table 1. The reconstructed overlapping region distribution map is shown in Table 1. Figure 4 As shown, Figure 4 This is a distribution map of the reconstructed overlapping regions provided in an embodiment of the present invention.

[0090] Table 1 Spatial Registration Information

[0091]

[0092]

[0093] Simulation 3: Registration position distribution diagram;

[0094] When the average registration rate is less than 1, some locations in the common monitoring area will not be correctly registered, meaning that the spatial sampling unit association group corresponding to the point target at that location is not in the spatial sampling unit association group set. In this case, a registration position distribution map can be used to show which point targets cannot be registered. Figure 5 is a registration position distribution map corresponding to different average registration rates when the local mismatch rate is fixed at 0, provided by an embodiment of the present invention. The positions corresponding to the yellow parts can be correctly registered, while the remaining positions cannot be correctly registered. It can be seen that as the average registration rate increases, the grid gradually decreases, the overlapping area reconstructed by the grid becomes more refined, and more and more positions can be correctly registered.

[0095] It should be noted that, in this document, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations are intended to cover non-exclusive inclusion, such that an article or device comprising a list of elements includes not only those elements but also other elements not expressly listed. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the article or device comprising said element. Terms such as "connected" or "linked" are not limited to physical or mechanical connections but can include electrical connections, whether direct or indirect. The orientations or positional relationships indicated by terms such as "upper," "lower," "left," and "right" are based on the orientations or positional relationships shown in the accompanying drawings and are used only for the convenience of describing the invention and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be construed as limiting the invention.

[0096] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features or characteristics described may be combined in any suitable manner in one or more embodiments or examples. In addition, those skilled in the art can combine and integrate the different embodiments or examples described in this specification.

[0097] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A heterogeneous networked radar spatial registration method based on adaptive grid reconstruction, characterized in that, include: Step 1: Construct a radar network system model, preset relevant parameters of the radar network system, and initialize the relevant parameters; wherein, the radar network system model includes multiple radar stations and a common monitoring area monitored by multiple radar stations, the common monitoring area is rasterized, and the relevant parameters include the side length of the raster and the preset raster search step size; Step 2: Obtain the spatial sampling unit association group for each grid, and merge grids with the same spatial sampling unit association group into a reconstructed overlapping region; Step 3: Obtain the spatial sampling unit association group for each of the reconstructed overlapping regions and form a set; obtain the average registration rate of multiple randomly distributed point targets based on the set, and obtain the local mismatch rate of each radar station not paired with other radar stations; compare the average registration rate with a preset average registration rate threshold, and compare the local mismatch rate with a preset local mismatch rate threshold; if the average registration rate is greater than or equal to the preset average registration rate threshold, and the local mismatch rate is less than or equal to the preset local mismatch rate threshold, determine the optimal grid side length; otherwise, compare the grid side length with a preset grid search step size; if the grid side length is less than or equal to the preset grid search step size, decrease the preset grid search step size and return to step 1 until the optimal grid side length is determined; otherwise, update the grid side length and return to step 2 until the optimal grid side length is determined. Step 4: Obtain the calibration points of the reconstructed overlapping region corresponding to the side length of the optimal grid; The step of obtaining the average registration rate of multiple randomly distributed point targets based on the set includes: Obtain random distribution Spatial sampling unit association group corresponding to each point target Its expression is: ； in, Indices representing randomly distributed point targets. Indicates the total number of radar stations; Based on the set and the random distribution Spatial sampling unit association group corresponding to each point target Obtain the average registration rate Its expression is: ； in, This represents the set of spatial sampling units associated with all reconstructed overlapping regions; The step of obtaining the local mismatch rate of each radar station that is not paired with other radar stations includes: Get the A set of spatial sampling units of radar stations in the common surveillance area Its expression is: ； in, Indicates the first The number of spatial sampling units per radar station in the common surveillance area. Indicates the first The radar station is located in the common surveillance area. One spatial sampling unit, Indicates the first Distance index corresponding to each spatial sampling unit Indicates the first Angle index of each spatial sampling unit; The spatial sampling units associated with all the reconstructed overlapping regions form a set. In the middle, the first spatial sampling unit set of radar stations The expression is: ； in, This indicates the total number of reconstructed overlapping regions; According to the first A set of spatial sampling units of radar stations in the common surveillance area and the first spatial sampling unit set of radar stations To obtain the local mismatch rate Its expression is: ； in, Represents the characteristic function.

2. The heterogeneous networked radar spatial registration method based on adaptive grid reconstruction according to claim 1, characterized in that, The step of obtaining the spatial sampling unit association group for each raster and merging rasters with the same spatial sampling unit association group into a reconstructed overlapping region includes: The common monitoring area is rasterized as follows The side length is The square grid, get the first The target point at the center of the first grid cell is for the... Distance between the centers of the radar stations and azimuth Their expressions are as follows: ； Among them, the The center position of each grid cell is represented as , No. The location of each radar station is represented as follows: , Indicates the total number of radar stations; According to the first The target point at the center of the first grid cell is for the... Distance between radar stations and azimuth , obtain the The point target at the center of the first grid cell is mapped to the first... Range cell index in the station-centered coordinate system of each radar station and angle unit index Their expressions are as follows: ； in, This indicates the number of discrete distances between the shared monitoring areas. This indicates the number of discrete scanning angles. Represents discrete distance, Indicates the discrete scanning angle; According to the first The point target at the center of the first grid cell is mapped to the first... Range cell index in the station-centered coordinate system of each radar station and angle unit index Obtain the spatial sampling unit association group for each grid. Its expression is: ； The spatial sampling units with the same grid group are merged into a reconstructed overlapping region.

3. The heterogeneous networked radar spatial registration method based on adaptive grid reconstruction according to claim 1, characterized in that, The step of obtaining the spatial sampling unit association group for each of the reconstructed overlapping regions and forming a set includes: Obtain the spatial sampling unit association group for each of the reconstructed overlapping regions. Its expression is: ； in, Indicates the index of the reconstructed overlapping region. This indicates the total number of reconstructed overlapping regions; Associating all the spatial sampling units of the reconstructed overlapping regions into a set Its expression is: 。 4. The heterogeneous networked radar spatial registration method based on adaptive grid reconstruction according to claim 1, characterized in that, Updating the side length of the grid includes: The updated grid's side length is equal to the initial grid's side length minus the preset grid search step size, expressed as: ； in, This indicates the preset grid search step size.

5. The heterogeneous networked radar spatial registration method based on adaptive grid reconstruction according to claim 1, characterized in that, Also includes: The coordinates of the calibration points in the reconstructed overlapping region corresponding to the side length of the optimal grid are optimized; The reconstructed overlapping region is defined as including Each grid is a separate grid. The The set of center coordinates of each grid is The coordinates of the calibration points in the reconstructed overlapping region It is about The function; Obtain the registration error value of the calibration points in the reconstructed overlapping region. Its expression is: ； in, ; Obtain the registration error value minimum value ,Right now: ； in, The two-dimensional coordinate space representing the shared monitoring area.

6. The heterogeneous networked radar spatial registration method based on adaptive grid reconstruction according to claim 1, characterized in that, Also includes: Return the spatial registration information retrieval table, the reconstructed overlapping region distribution map, and the registration location distribution map; Based on the calibration points of each of the reconstructed overlapping regions and the spatial sampling unit association group of each of the reconstructed overlapping regions, the spatial registration information retrieval table is obtained; By testing multiple randomly distributed point targets in the radar network system model, the distribution map of the reconstructed overlapping area and the distribution map of the registration position are obtained.

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