Relative positioning method and device and storage medium

Abstract

The invention provides a relative positioning method and device and a storage medium, and the method comprises the steps: constructing a first TOA equation and a first AOA equation corresponding to each path according to a path between a first moving body and a second moving body, and a TOA measurement quantity and an AOA measurement quantity corresponding to each path; combining the first TOA equations and the first AOA equations corresponding to all the paths, and solving a weighted least square solution WLS to obtain a first WLS solution; performing error analysis and decorrelation analysis based on the first WLS solution to obtain a first position coordinate of the second moving body relative to the first moving body; and carrying out back substitution solution and error analysis based on the first position coordinates to obtain an orientation angle of the second moving body. According to the invention, high-precision joint estimation of the position and the orientation angle is realized, and the precision of relative positioning is improved.

Description

Technical Field

[0001] The present application relates to the field of positioning, and in particular to a relative positioning method, device and storage medium. Background Art

[0002] The demand for relative positioning between moving objects (e.g., vehicles) has risen sharply, on the one hand because stable and accurate positioning can help perceive and plan trajectories, and on the other hand because the rapidly growing intelligent transportation application systems have driven the demand for precise positioning and tracking.

[0003] Radio-based positioning is usually based on the estimation of distance and angle parameters, including Angle of arrival (AoA) and Time of arrival (ToA), as well as TOA-AOA combined.

[0004] At present, the positioning accuracy of the relative positioning results obtained by using TOA, AOA or TOA-AOA is still insufficient. Summary of the invention

[0005] In view of the problems existing in the prior art, the embodiments of the present application provide a relative positioning method, device and storage medium to solve the problem of insufficient relative positioning accuracy.

[0006] In a first aspect, an embodiment of the present application provides a relative positioning method, including:

[0007] Constructing a first TOA equation and a first AOA equation corresponding to each path according to the path between the first mobile body and the second mobile body and the TOA measurement amount and the AOA measurement amount corresponding to each path;

[0008] The first TOA equation and the first AOA equation corresponding to all paths are combined, and the weighted least square solution WLS is solved to obtain the first WLS solution;

[0009] Perform error analysis and decorrelation analysis based on the first WLS solution to obtain first position coordinates of the second moving object relative to the first moving object;

[0010] Back substitution solution and error analysis are performed based on the first position coordinates to obtain the orientation angle of the second moving body.

[0011] In some embodiments, the first TOA equation is a relationship expression between the path length of the pth path and the position information of the second mobile object; the first AOA equation is θ p The relationship expression between the tangent value of and the position information of the second moving body; p is the angle between the pth path and the positive direction of the X-axis.

[0012] In some embodiments, performing error analysis and decorrelation analysis based on the first WLS solution to obtain the first position coordinates of the second moving object relative to the first moving object includes:

[0013] Performing error analysis on the first TOA equation group and the first AOA equation group respectively to obtain a first covariance matrix and a second covariance matrix; the first TOA equation group includes the first TOA equations corresponding to all paths; the first AOA equation group includes the first AOA equations corresponding to all paths;

[0014] updating the first WLS solution according to the first covariance matrix and the second covariance matrix to obtain a second WLS solution;

[0015] Perform decorrelation analysis based on the second WLS solution to obtain the first position coordinates.

[0016] In some embodiments, performing decorrelation analysis based on the second WLS solution to obtain the first position coordinates includes:

[0017] Establishing a first correlation equation according to a correlation solution in the second WLS solution; the correlation solution is a solution related to the first position coordinates;

[0018] Performing error analysis and WLS solution on the first correlation equation to obtain a first decorrelation WLS solution;

[0019] The first position coordinates are acquired according to the first decorrelated WLS solution and the second WLS solution.

[0020] In some embodiments, performing error analysis and WLS solution on the first correlation equation to obtain a first decorrelation WLS solution includes:

[0021] Performing error analysis on the first correlation equation to obtain a third covariance matrix;

[0022] The first correlation equation is solved by WLS according to the third covariance matrix to obtain the first decorrelation WLS solution.

[0023] In some embodiments, acquiring the first position coordinates according to the first decorrelated WLS solution and the second WLS solution includes:

[0024] Obtaining a third WLS solution according to the first decorrelated WLS solution;

[0025] The solution in the third WLS solution that is closest to the second WLS solution is used as the first position coordinate.

[0026] In some embodiments, performing back substitution solution and error analysis based on the first position coordinates to obtain the orientation angle of the second moving body includes:

[0027] Substituting the first position coordinates back into the first TOA equation and the first AOA equation corresponding to each path to obtain a second TOA equation and a second AOA equation corresponding to each path;

[0028] The second TOA equation and the second AOA equation corresponding to all paths are combined and solved by WLS to obtain a fourth WLS solution;

[0029] An error analysis is performed based on the fourth WLS solution to obtain the orientation angle of the second moving object.

[0030] In some embodiments, performing error analysis based on the fourth WLS solution to obtain the orientation angle of the second moving object includes:

[0031] Performing error analysis on the second TOA equation group and the second AOA equation group respectively to obtain a fourth covariance matrix and a fifth covariance matrix; the second TOA equation group includes the second TOA equations corresponding to all paths; the second AOA equation group includes the second AOA equations corresponding to all paths;

[0032] updating the fourth WLS solution according to the fourth covariance matrix and the fifth covariance matrix to obtain a fifth WLS solution;

[0033] According to the fifth WLS solution, the orientation angle of the second moving object is obtained.

[0034] In some embodiments, after obtaining the orientation angle of the second moving body, the method further includes:

[0035] Back substitution solution, error analysis and decorrelation analysis are performed based on the orientation angle to obtain second position coordinates of the second moving body relative to the first moving body.

[0036] In some embodiments, performing back substitution solution, error analysis, and decorrelation analysis based on the orientation angle to obtain the second position coordinates of the second moving object relative to the first moving object includes:

[0037] Substituting the heading angle back into the first TOA equation and the first AOA equation corresponding to each path to obtain a third TOA equation and a third AOA equation corresponding to each path;

[0038] The third TOA equation and the third AOA equation corresponding to all paths are combined and solved by WLS to obtain a sixth WLS solution;

[0039] Error analysis and decorrelation analysis are performed based on the sixth WLS solution to obtain the second position coordinates.

[0040] In some embodiments, performing error analysis and decorrelation analysis based on the sixth WLS solution to obtain the second position coordinates includes:

[0041] Performing error analysis on the third TOA equation group and the third AOA equation group respectively to obtain a sixth covariance matrix and a seventh covariance matrix; the third TOA equation group includes the third TOA equations corresponding to all paths; the third AOA equation group includes the third AOA equations corresponding to all paths;

[0042] According to the sixth covariance matrix and the seventh covariance matrix, the sixth WLS solution is updated to obtain a seventh WLS solution;

[0043] Decorrelation analysis is performed based on the seventh WLS solution to obtain the second position coordinates.

[0044] In some embodiments, performing decorrelation analysis based on the seventh WLS solution to obtain the second position coordinates includes:

[0045] According to the seventh WLS solution, establishing a second correlation equation;

[0046] performing error analysis and WLS solution on the second correlation equation to obtain a second decorrelation WLS solution;

[0047] The second position coordinates are obtained according to the second decorrelated WLS solution and the seventh WLS solution.

[0048] In a second aspect, an embodiment of the present application further provides an electronic device, including a memory, a transceiver, and a processor:

[0049] A memory for storing a computer program; a transceiver for transmitting and receiving data under the control of the processor; and a processor for reading the computer program in the memory and performing the following operations:

[0050] Constructing a first TOA equation and a first AOA equation corresponding to each path according to the path between the first mobile body and the second mobile body and the TOA measurement amount and the AOA measurement amount corresponding to each path;

[0051] The first TOA equation and the first AOA equation corresponding to all paths are combined, and the weighted least square solution WLS is solved to obtain the first WLS solution;

[0052] Perform error analysis and decorrelation analysis based on the first WLS solution to obtain first position coordinates of the second moving object relative to the first moving object;

[0053] Back substitution solution and error analysis are performed based on the first position coordinates to obtain the orientation angle of the second moving body.

[0054] In some embodiments, the first TOA equation is a relationship expression between the path length of the pth path and the position information of the second mobile object; the first AOA equation is θ p The relationship expression between the tangent value of and the position information of the second moving body; p is the angle between the pth path and the positive direction of the X-axis.

[0055] In some embodiments, performing error analysis and decorrelation analysis based on the first WLS solution to obtain the first position coordinates of the second moving object relative to the first moving object includes:

[0056] Performing error analysis on the first TOA equation group and the first AOA equation group respectively to obtain a first covariance matrix and a second covariance matrix; the first TOA equation group includes the first TOA equations corresponding to all paths; the first AOA equation group includes the first AOA equations corresponding to all paths;

[0057] updating the first WLS solution according to the first covariance matrix and the second covariance matrix to obtain a second WLS solution;

[0058] Perform decorrelation analysis based on the second WLS solution to obtain the first position coordinates.

[0059] In some embodiments, performing decorrelation analysis based on the second WLS solution to obtain the first position coordinates includes:

[0060] Establishing a first correlation equation according to a correlation solution in the second WLS solution; the correlation solution is a solution related to the first position coordinates;

[0061] Performing error analysis and WLS solution on the first correlation equation to obtain a first decorrelation WLS solution;

[0062] The first position coordinates are acquired according to the first decorrelated WLS solution and the second WLS solution.

[0063] In some embodiments, performing error analysis and WLS solution on the first correlation equation to obtain a first decorrelation WLS solution includes:

[0064] Performing error analysis on the first correlation equation to obtain a third covariance matrix;

[0065] The first correlation equation is solved by WLS according to the third covariance matrix to obtain the first decorrelation WLS solution.

[0066] In some embodiments, acquiring the first position coordinates according to the first decorrelated WLS solution and the second WLS solution includes:

[0067] Obtaining a third WLS solution according to the first decorrelated WLS solution;

[0068] The solution in the third WLS solution that is closest to the second WLS solution is used as the first position coordinate.

[0069] In some embodiments, performing back substitution solution and error analysis based on the first position coordinates to obtain the orientation angle of the second moving body includes:

[0070] Substituting the first position coordinates back into the first TOA equation and the first AOA equation corresponding to each path to obtain a second TOA equation and a second AOA equation corresponding to each path;

[0071] The second TOA equation and the second AOA equation corresponding to all paths are combined and solved by WLS to obtain a fourth WLS solution;

[0072] An error analysis is performed based on the fourth WLS solution to obtain the orientation angle of the second moving object.

[0073] In some embodiments, performing error analysis based on the fourth WLS solution to obtain the orientation angle of the second moving object includes:

[0074] Performing error analysis on the second TOA equation group and the second AOA equation group respectively to obtain a fourth covariance matrix and a fifth covariance matrix; the second TOA equation group includes the second TOA equations corresponding to all paths; the second AOA equation group includes the second AOA equations corresponding to all paths;

[0075] updating the fourth WLS solution according to the fourth covariance matrix and the fifth covariance matrix to obtain a fifth WLS solution;

[0076] According to the fifth WLS solution, the orientation angle of the second moving object is obtained.

[0077] In some embodiments, after obtaining the orientation angle of the second moving body, the method further includes:

[0078] Back substitution solution, error analysis and decorrelation analysis are performed based on the orientation angle to obtain second position coordinates of the second moving body relative to the first moving body.

[0079] In some embodiments, performing back substitution solution, error analysis, and decorrelation analysis based on the orientation angle to obtain the second position coordinates of the second moving object relative to the first moving object includes:

[0080] Substituting the heading angle back into the first TOA equation and the first AOA equation corresponding to each path to obtain a third TOA equation and a third AOA equation corresponding to each path;

[0081] The third TOA equation and the third AOA equation corresponding to all paths are combined and solved by WLS to obtain a sixth WLS solution;

[0082] Error analysis and decorrelation analysis are performed based on the sixth WLS solution to obtain the second position coordinates.

[0083] In some embodiments, performing error analysis and decorrelation analysis based on the sixth WLS solution to obtain the second position coordinates includes:

[0084] Performing error analysis on the third TOA equation group and the third AOA equation group respectively to obtain a sixth covariance matrix and a seventh covariance matrix; the third TOA equation group includes the third TOA equations corresponding to all paths; the third AOA equation group includes the third AOA equations corresponding to all paths;

[0085] According to the sixth covariance matrix and the seventh covariance matrix, the sixth WLS solution is updated to obtain a seventh WLS solution;

[0086] Decorrelation analysis is performed based on the seventh WLS solution to obtain the second position coordinates.

[0087] In some embodiments, performing decorrelation analysis based on the seventh WLS solution to obtain the second position coordinates includes:

[0088] According to the seventh WLS solution, establishing a second correlation equation;

[0089] performing error analysis and WLS solution on the second correlation equation to obtain a second decorrelation WLS solution;

[0090] The second position coordinates are obtained according to the second decorrelated WLS solution and the seventh WLS solution.

[0091] In a third aspect, the embodiment of the present application further provides a relative positioning device, including:

[0092] A construction module, configured to construct a first TOA equation and a first AOA equation corresponding to each path according to the path between the first mobile body and the second mobile body and the TOA measurement amount and the AOA measurement amount corresponding to each path;

[0093] A first acquisition module is used to jointly establish a first TOA equation and a first AOA equation corresponding to all paths, and solve a weighted least square solution WLS to obtain a first WLS solution;

[0094] A second acquisition module, configured to perform error analysis and decorrelation analysis based on the first WLS solution to obtain a first position coordinate of the second moving body relative to the first moving body;

[0095] The third acquisition module is used to perform back substitution solution and error analysis based on the first position coordinates to obtain the orientation angle of the second moving body.

[0096] In some embodiments, the first TOA equation is a relationship expression between the path length of the pth path and the position information of the second mobile object; the first AOA equation is θ p The relationship expression between the tangent value of and the position information of the second moving body; p is the angle between the pth path and the positive direction of the X-axis.

[0097] In some embodiments, the second acquisition module includes:

[0098] A first acquisition submodule is used to perform error analysis on the first TOA equation group and the first AOA equation group respectively to obtain a first covariance matrix and a second covariance matrix; the first TOA equation group includes the first TOA equations corresponding to all paths; the first AOA equation group includes the first AOA equations corresponding to all paths;

[0099] A second acquisition submodule, configured to update the first WLS solution according to the first covariance matrix and the second covariance matrix to obtain a second WLS solution;

[0100] The third acquisition submodule is used to perform decorrelation analysis based on the second WLS solution to obtain the first position coordinates.

[0101] In some embodiments, the third acquisition submodule includes:

[0102] An establishing unit, used for establishing a first correlation equation according to a correlation solution in the second WLS solution; the correlation solution is a solution related to the first position coordinates;

[0103] A first acquisition unit, configured to perform error analysis and WLS solution on the first correlation equation to obtain a first decorrelation WLS solution;

[0104] The second acquisition unit is configured to acquire the first position coordinates according to the first decorrelated WLS solution and the second WLS solution.

[0105] In some embodiments, the first acquisition unit includes:

[0106] A first acquisition subunit is used to perform error analysis on the first correlation equation to obtain a third covariance matrix;

[0107] The second acquisition subunit is used to perform WLS solution on the first correlation equation according to the third covariance matrix to obtain the first decorrelation WLS solution.

[0108] In some embodiments, the second acquisition unit includes:

[0109] A third acquisition subunit, configured to obtain a third WLS solution according to the first decorrelated WLS solution;

[0110] The fourth acquisition subunit is configured to use a solution in the third WLS solution that is closest to the second WLS solution as the first position coordinate.

[0111] In some embodiments, the third acquisition module includes:

[0112] A fourth acquisition submodule, used for back-substituting the first position coordinate into the first TOA equation and the first AOA equation corresponding to each path to obtain a second TOA equation and a second AOA equation corresponding to each path;

[0113] A fifth acquisition submodule, configured to jointly solve the second TOA equation and the second AOA equation corresponding to all paths by WLS to obtain a fourth WLS solution;

[0114] The sixth acquisition submodule is used to perform error analysis based on the fourth WLS solution to obtain the orientation angle of the second moving object.

[0115] In some embodiments, the sixth acquisition submodule includes:

[0116] A third acquisition unit is used to perform error analysis on the second TOA equation group and the second AOA equation group respectively to obtain a fourth covariance matrix and a fifth covariance matrix; the second TOA equation group includes the second TOA equations corresponding to all paths; the second AOA equation group includes the second AOA equations corresponding to all paths;

[0117] a fourth acquisition unit, configured to update the fourth WLS solution according to the fourth covariance matrix and the fifth covariance matrix to obtain a fifth WLS solution;

[0118] The fifth acquisition unit is used to obtain the orientation angle of the second moving object according to the fifth WLS solution.

[0119] In some embodiments, the apparatus further comprises:

[0120] A fourth acquisition module is used to perform back substitution solution, error analysis and decorrelation analysis based on the orientation angle to obtain a second position coordinate of the second moving body relative to the first moving body.

[0121] In some embodiments, the fourth acquisition module includes:

[0122] A seventh acquisition submodule, configured to substitute the heading angle back into the first TOA equation and the first AOA equation corresponding to each path to obtain a third TOA equation and a third AOA equation corresponding to each path;

[0123] An eighth acquisition submodule, used for jointly solving the third TOA equation and the third AOA equation corresponding to all paths and performing WLS solution to obtain a sixth WLS solution;

[0124] The ninth acquisition submodule is used to perform error analysis and decorrelation analysis based on the sixth WLS solution to obtain the second position coordinates.

[0125] In some embodiments, the ninth acquisition submodule includes:

[0126] a sixth acquisition unit, configured to perform error analysis on the third TOA equation group and the third AOA equation group, respectively, to obtain a sixth covariance matrix and a seventh covariance matrix; the third TOA equation group includes the third TOA equations corresponding to all paths; the third AOA equation group includes the third AOA equations corresponding to all paths;

[0127] a seventh acquisition unit, configured to update the sixth WLS solution according to the sixth covariance matrix and the seventh covariance matrix to obtain a seventh WLS solution;

[0128] An eighth acquisition unit is configured to perform decorrelation analysis based on the seventh WLS solution to obtain the second position coordinates.

[0129] In some embodiments, the eighth acquisition unit includes:

[0130] an establishing subunit, for establishing a second correlation equation according to the seventh WLS solution;

[0131] a fifth acquisition subunit, configured to perform error analysis and WLS solution on the second correlation equation to obtain a second decorrelation WLS solution;

[0132] The sixth acquisition subunit is configured to obtain the second position coordinates according to the second decorrelated WLS solution and the seventh WLS solution.

[0133] In a fourth aspect, an embodiment of the present application further provides a processor-readable storage medium, wherein the processor-readable storage medium stores a computer program, and the computer program is used to enable the processor to execute the relative positioning method described in the first aspect as described above.

[0134] In a fifth aspect, an embodiment of the present application further provides a computer-readable storage medium, wherein the computer-readable storage medium stores a computer program, and the computer program is used to enable a computer to execute the relative positioning method described in the first aspect as described above.

[0135] In a sixth aspect, an embodiment of the present application further provides a communication device, in which a computer program is stored, and the computer program is used to enable the communication device to execute the relative positioning method described in the first aspect as described above.

[0136] In a seventh aspect, an embodiment of the present application further provides a chip product, wherein a computer program is stored in the chip product, and the computer program is used to enable the chip product to execute the relative positioning method described in the first aspect as described above.

[0137] The relative positioning method, device and storage medium provided in the embodiments of the present application perform error analysis and decorrelation analysis on the basis of the first WLS solution to obtain high-precision first position coordinates, and then perform back substitution and error analysis on the high-precision first position coordinates to obtain high-precision orientation angles, thereby achieving joint estimation of high-precision position and orientation angles, and improving the accuracy of relative positioning. BRIEF DESCRIPTION OF THE DRAWINGS

[0138] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0139] Figure 1 One of the flowcharts of the relative positioning method provided in the embodiment of the present application;

[0140] Figure 2 It is a schematic diagram of the relative positioning scenario provided by this application;

[0141] Figure 3 A second flow chart of the relative positioning method provided in an embodiment of the present application;

[0142] Figure 4 is a schematic diagram of the structure of an electronic device provided in an embodiment of the present application;

[0143] Figure 5It is a schematic diagram of the structure of the relative positioning device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0144] In response to the above technical problems, the embodiments of the present application jointly estimate the position and orientation angle of the moving object to solve the problem of insufficient relative positioning accuracy.

[0145] The following will be combined with the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0146] The first mobile body sends a channel sounding reference signal (SRS), and the second mobile body receives the SRS signal sent by the first mobile body. In one case, the second mobile body reports the measurement value to the location management function (LMF) network element, which performs relative positioning solution, or sends it to other third-party mobile bodies that need to be positioned. In the second case, the second mobile body completes the relative positioning solution by itself.

[0147] Therefore, the relative positioning method provided in the present application can be executed by a LMF network element, a third-party mobile object other than relative positioning, or a second mobile object. The following description will be made by taking the LMF network element as an example.

[0148] Figure 1 is one of the flow charts of the relative positioning method provided in the embodiment of the present application, such as Figure 1 As shown, the embodiment of the present application provides a relative positioning method including:

[0149] Step 110: construct a first TOA equation and a first AOA equation corresponding to each path according to the path between the first mobile body and the second mobile body and the TOA measurement amount and the AOA measurement amount corresponding to each path.

[0150] Specifically, Figure 2 is a schematic diagram of the relative positioning scenario provided by this application, such as Figure 2 As shown, the center of the first moving body V1 is located at the coordinate origin (0,0), the orientation of the first moving body V1 is the X axis, and the direction perpendicular to the orientation of the first moving body V1 is the Y axis. The position of the second moving body V2 is (x, y) and the orientation angle is The orientation angle of the second moving body V2 is the angle between the orientation of the second moving body V2 and the positive direction of the X-axis.

[0151] Four positioning auxiliary units are set at the four corners of the first moving body V1, namely Ant 1-1 、Ant 1-2 、Ant 1-3 and Ant 1-4 The four corners of the second moving body V2 are also equipped with four positioning auxiliary units, namely Ant 2-1 、Ant 2-2 、Ant 2-3 and Ant 2-4 .

[0152] Assume that the size of the first moving body V1 is (2s1, 2w1), that is, the length of the first moving body V1 is 2s1, and the width of the first moving body V1 is 2w1, then Ant 1-1 The location is (-s1, -w1), Ant 1-2 The position of Ant is (s1, -w1), 1-3 The position of Ant is (s1, w1), 1-4 The position is ((-s1, w1)).

[0153] Assume that the size of the second moving body V2 is (2s2, 2w2), that is, the length of the second moving body V2 is 2s2, and the width of the second moving body V2 is 2w2, then Ant 2-1 The location is Ant 2-2 The location is Ant 2-3 The location is Ant 2-4 The location is

[0154] The path between the first moving body V1 and the second moving body V2, namely Ant 1-i (i=1, 2, 3, 4) to Ant 2-j There are 16 paths (j=1, 2, 3, 4). To facilitate matrix representation, the constant terms and positive and negative signs in the 16 path vectors are defined as constant sign vectors Δx1, Δy1, Δx2, Δy 2(x) and Δy 2(y) , Δx1, Δy1, Δx2, Δy 2(x) and Δy 2(y) The expression is as follows:

[0155]

[0156] In the formula, s1 represents 1 / 2 length of the first moving body V1, w1 represents 1 / 2 width of the first moving body V1, s2 represents 1 / 2 length of the second moving body V2, and w2 represents 1 / 2 width of the second moving body V2.

[0157] Among the 16 paths, the pth path is In the formula, Δx 1，p , Δy 1，p , Δx 2，p , Δy 2(x)，p , Δy 2(y)，p Represent vectors Δx1, Δy1, Δx2, Δy 2(x) , Δy 2(y) The pth component of .

[0158] For example, if p is 3, then Δx 1，p = -s1, Δy 1，p = -w1, Δx 2，p is s2, Δy 2(x)，p = -w2, Δy 2(y)，p is w2, that is, the third path is

[0159] Based on TOA, each path is measured to obtain the TOA measurement, that is, the path length r of the pth path. p According to the position information of the second mobile body V2 (i.e. the horizontal coordinate x, the vertical coordinate y and the orientation angle of the second mobile body V2), ) and the path length of the pth path are expressed as follows:

[0160]

[0161] In the formula, the subscript p represents the pth path, Δx 1，p , Δy 1，p , Δx 2，p , Δy 2(x)，p , Δy 2(y)，p Represent vectors Δx1, Δy1, Δx2, Δy 2(x) , Δy 2(y) The pth component of p represents the path length of the pth path, x represents the abscissa of the second moving body V2, y represents the ordinate of the second moving body V2, Indicates the orientation angle of the second moving object V2.

[0162] After simplifying the above formula, we get the first TOA equation corresponding to the pth path. The expression of the first TOA equation is as follows:

[0163]

[0164] In the formula, the subscript p represents the pth path, Δx 1，p , Δy 1，p , Δx 2，p , Δy 2(x)，p , Δy 2(y)，p Represent vectors Δx1, Δy1, Δx2, Δy 2(x) , Δy 2(y) The pth component of p represents the path length of the pth path, x represents the abscissa of the second moving body V2, y represents the ordinate of the second moving body V2, Represents the orientation angle of the second moving body V2; s1 represents 1 / 2 length of the first moving body V1, w1 represents 1 / 2 width of the first moving body V1, s2 represents 1 / 2 length of the second moving body V2, and w2 represents 1 / 2 width of the second moving body V2.

[0165] It can be seen from the first TOA equation that there are 9 variables in the first TOA equation These 9 variables are composed of 4 basic variables Combination, and these four basic variables There are 3 more variables to solve for What is needed.

[0166] Let the angle between the pth path and the positive direction of the X-axis be θ p Based on AOA, each path is measured to obtain the AOA measurement value, that is, the tangent value tanθ of the angle between the pth path and the positive direction of the x-axis p (i.e. the ratio of sine value to cosine value). According to tanθ p The position information of the second mobile body V2 (i.e., the horizontal coordinate x, the vertical coordinate y and the orientation angle of the second mobile body V2) ) is expressed as follows:

[0167]

[0168] Deformation gives:

[0169]

[0170] Simplifying the above formula, we get the first AOA equation corresponding to the pth path. The expression of the first AOA equation is as follows:

[0171]

[0172] In the formula, the subscript p represents the pth path, θ p represents the angle between the pth path and the positive direction of the X-axis, Δx 1，p , Δy 1，p , Δx2，p , Δy 2(x)，p , Δy 2(y)，p Represent vectors Δx1, Δy1, Δx2, Δy 2(x) , Δy 2(y) The pth component of , x represents the abscissa of the second moving body V2, y represents the ordinate of the second moving body V2, Indicates the orientation angle of the second moving object V2.

[0173] From the first AOA equation, we can see that there are 4 variables in the first AOA equation:

[0174] Step 120 , jointly establish the first TOA equation and the first AOA equation corresponding to all paths, and solve the weighted least squares solution WLS to obtain a first WLS solution.

[0175] Specifically, the first TOA equations corresponding to the 16 paths are combined to obtain the first TOA equation group, and the first TOA equation group is rewritten into a matrix form:

[0176] h 1，r =G 1，r z 1，r

[0177] In the formula,

[0178]

[0179]

[0180]

[0181]

[0182]

[0183]

[0184] For h 1，r =G 1，r z 1，r Solve the weighted least squares solution (WLS) and get the WLS solution z corresponding to the first joint TOA 1，r , the WLS solution corresponding to the first combined TOA is z 1，r The expression is as follows:

[0185]

[0186] In the formula, Q r is the diagonal matrix of squared errors of the least squares solution,

[0187] The first AOA equations corresponding to the 16 paths are combined to obtain the first AOA equation group, and the first AOA equation group is rewritten into a matrix form:

[0188] h 1，a =G 1，a z 1，a

[0189] Where:

[0190]

[0191]

[0192]

[0193]

[0194] For h 1，a =G 1，a z 1，a Solve the WLS solution and get the WLS solution z corresponding to the first joint AOA 1，a , the WLS solution corresponding to the first joint AOA is z 1，a The expression is as follows:

[0195]

[0196] In the formula, Q a is the diagonal matrix of squared errors of the least squares solution,

[0197] The first ToA equation group and the first AoA equation group are combined and rewritten into matrix form:

[0198] h1=G1z1

[0199] In the formula,

[0200] G1=[G 1，r ; G 1，a , 0 16×5 ] 32×9

[0201]

[0202] h1=[h 1，r ;h 1.a ] 32×1

[0203] Solving h1=G1z1 for WLS solution, we get the first WLS solution z1. The expression of the first WLS solution z1 is as follows:

[0204]

[0205] In the formula,

[0206]

[0207] Step 130, performing error analysis and decorrelation analysis based on the first WLS solution to obtain first position coordinates of the second moving body relative to the first moving body;

[0208] Specifically, the first two items of the first WLS solution z1 are the first position coordinates (x, y). In order to improve the accuracy of the first position coordinates (x, y), the LWF network element also performs error analysis and decorrelation analysis to update the first WLS solution z1 to obtain high-precision first position coordinates (x, y).

[0209] Step 140, performing back substitution solution and error analysis based on the first position coordinates to obtain the orientation angle of the second moving body.

[0210] Specifically, after obtaining the high-precision first position coordinates (x, y), due to the first WLS solution The first position coordinate (x, y) is used as a known quantity to solve the problem and obtain the direction angle Related WLS solutions.

[0211] The LWF network element also performs error analysis to update the direction angle Correlated WLS solution to obtain high-precision heading angle

[0212] The relative positioning method provided in the embodiment of the present application obtains high-precision first position coordinates by performing error analysis and decorrelation analysis on the basis of the first WLS solution, and then performs back substitution solution and error analysis on the high-precision first position coordinates to obtain high-precision orientation angles, thereby achieving joint estimation of high-precision position and orientation angles, and improving the accuracy of relative positioning.

[0213] In some embodiments, performing error analysis and decorrelation analysis based on the first WLS solution to obtain the first position coordinates of the second moving object relative to the first moving object includes:

[0214] Performing error analysis on the first TOA equation group and the first AOA equation group respectively to obtain a first covariance matrix and a second covariance matrix; the first TOA equation group includes the first TOA equations corresponding to all paths; the first AOA equation group includes the first AOA equations corresponding to all paths;

[0215] According to the first covariance matrix and the second covariance matrix, the first WLS solution is updated to obtain a second WLS solution;

[0216] A decorrelation analysis is performed based on the second WLS solution to obtain the first position coordinates.

[0217] Specifically, the error of the first TOA equation group is analyzed:

[0218]

[0219] In the formula, ψ r represents the first error matrix, represents the true value of the solution to the first TOA system of equations.

[0220] Take a single element for error analysis:

[0221]

[0222] In the formula, the error term is represents the true value of the length of the pth path, r p represents the measured value of the length of the pth path, Δr p Represents the error between the true value and the measured value of the pth path length.

[0223] Then the error ψ of the first TOA equation corresponding to the pth path is r，p for:

[0224]

[0225] In the formula, ψ r，p represents the error of the first TOA equation corresponding to the pth path, represents the true value of the length of the pth path, Δr p Represents the error between the true value and the measured value of the pth path length.

[0226] Ignore the quadratic term of the noise and simplify ψ r，p get:

[0227]

[0228] Therefore, the errors of the first TOA equation corresponding to all paths are combined and rewritten into a matrix form:

[0229] ψ r =2B 2，r ·Δr

[0230] In the formula, ψ r represents the first error matrix, B 2，r is a diagonal matrix consisting of the true values ​​of all path lengths, Δr is a matrix composed of the errors corresponding to all path lengths, Δr = [Δr1, Δr2, ..., Δr 16 ]T .

[0231] In actual calculations, The measured value r p Replacement, due to Δr p by appears in the form of.

[0232] According to the first error matrix ψ r , calculate the first covariance matrix Ψ 2，r :

[0233]

[0234] In the formula, Q r The covariance matrix of r (i.e., the path length measured by TOA) is Q r =E[ΔrΔr T ].

[0235] In fact, For equation h 1，r =G 1，r z 1，r The WLS exact solution, but due to Ψ 2，r In Unknown, need to pass a z r (Generally refers to z 1，r With z 2，r ) to calculate B 2，r .

[0236] Therefore, using the known Q r To approximate Ψ 2，r ,pass Get the initial solution, (z 1，r That is, the ordinary least squares (LS) solution, which is slightly worse than the WLS solution. 2，r , but the accuracy is sufficient as an initial solution), and this is used to calculate Ψ 2，r .

[0237] Analyze the error of the first AOA equation group:

[0238]

[0239] In the formula, ψ a represents the second error matrix, represents the true value of the solution to the first AOA system of equations.

[0240] Perform error analysis on the pth path:

[0241]

[0242] In the formula, the error term is θ p represents the measured value of the angle between the pth path and the positive direction of the X-axis, Represents the true value of the angle between the pth path and the positive direction of the X-axis, Δθ p Represents the error between the measured value and the true value of the angle between the pth path and the positive direction of the X-axis.

[0243] In actual calculations, With the measured value θ p Replacement, due to Δθ p by appears in the form of.

[0244] make:

[0245]

[0246]

[0247] Then the error ψ of the first AOA equation corresponding to the pth path is a，p for:

[0248]

[0249] because:

[0250]

[0251]

[0252] Therefore, the error ψ of the first AOA equation corresponding to the pth path is a，p Simplified to:

[0253]

[0254] Therefore, the errors of the first AOA equation corresponding to all paths are combined and rewritten in matrix form:

[0255] ψ a =B 2，a ·Δθ

[0256] In the formula, ψ a represents the second error matrix, Δθ is a matrix composed of the error angles corresponding to all paths, Δθ = [θ1, ..., θ 16 ].

[0257] According to the second error matrix ψ a , calculate the second covariance matrix Ψ 2，a :

[0258]

[0259] In the formula, Q a The covariance matrix of θ (i.e., the angle measured by AOA) is Q a =E[ΔθΔθ T ].

[0260] In fact, For equation h 1，a =G 1，a z 1，a The WLS exact solution, but due to Ψ 2，a In Unknown quantity Need to pass a z a (Generally refers to z 1，a With z 2，a ) to calculate B 2，a .

[0261] Therefore, using the known Q a To approximate Ψ 2，a ,pass Get the initial solution (z 1，a That is, the ordinary LS solution, which has slightly worse performance than the WLS solution B 2，a , but the accuracy is sufficient as an initial solution), and this is used to calculate Ψ 2，a .

[0262] It should be noted that in actual calculations, B 2，a In By z 1，a Got it.

[0263] The first covariance matrix Ψ 2，r Substitute Q in the Q matrix r , the second covariance matrix Ψ 2，a Substitute Q in the Q matrix a , to update the first WLS solution z1 and obtain the second WLS solution z2. The expression of the second WLS solution z2 is as follows:

[0264]

[0265] In the formula,

[0266]

[0267] Since the second WLS solution z2 is:

[0268]

[0269] It can be seen that the solutions related to the first position coordinate (x, y) in the second WLS solution z2 are the first three solutions [x, y, x 2 +y 2 ], but x, y, x 2 +y 2 There is a correlation between them, therefore, a decorrelation analysis is required to obtain a high-precision first position coordinate (x, y).

[0270] The relative positioning method provided in the embodiment of the present application performs error analysis on the first TOA equation group and the first AOA equation group respectively to obtain a first covariance matrix and a second covariance matrix to update the first WLS solution and obtain a second WLS solution; then, decorrelation analysis is performed based on the second WLS solution to obtain the first position coordinates, thereby further improving the accuracy of the first position coordinates.

[0271] In some embodiments, performing decorrelation analysis based on the second WLS solution to obtain the first position coordinates includes:

[0272] According to the correlation solution in the second WLS solution, a first correlation equation is established; the correlation solution is a solution related to the first position coordinate;

[0273] Perform error analysis and WLS solution on the first correlation equation to obtain the first decorrelation WLS solution;

[0274] A first position coordinate is obtained according to the first decorrelated WLS solution and the second WLS solution.

[0275] Specifically, the correlation refers to the first three terms of z2, namely [x, y, x 2 +y 2 ], x, y and x 2 +y 2 There is a correlation between them, which will lead to a large error in the solution of WLS.

[0276] Considering (x 2 )+(y 2 )=x 2 +y 2 , so only x 2 With y 2 As a new unknown number, a new equation h3=G3z′3 is established and solved, and the obtained x 2 With y 2 These are two unrelated values, and therefore have higher accuracy. This process is called decorrelation.

[0277] According to the first three terms in the second WLS solution z2 [z2(1), z2(2), z2(3)] = [x, y, x 2 +y 2], and establish the first correlation equation. The expression of the first correlation equation is as follows:

[0278] h3=G3z′3

[0279] In the formula,

[0280]

[0281] z3′=[x 2 ,y 2 ] T

[0282]

[0283] An error analysis is performed on the first correlation equation h3=G3z′3, and the WLS solution of the first correlation equation is updated with the error analysis result to obtain a first decorrelation WLS solution.

[0284] After obtaining the first decorrelated WLS solution, a third WLS solution is obtained according to the first decorrelated WLS solution, the third WLS solution is compared with the second WLS solution, and the solution closest to the second WLS solution is selected as the first position coordinate.

[0285] The relative positioning method provided in the embodiment of the present application establishes a first correlation equation based on the second WLS solution; performs error analysis and WLS solution on the first correlation equation to obtain a first decorrelation WLS solution; and obtains first position coordinates based on the first decorrelation WLS solution and the second WLS solution, thereby further improving the accuracy of the first position coordinates.

[0286] In some embodiments, performing error analysis and WLS solution on the first correlation equation to obtain a first decorrelation WLS solution includes:

[0287] Perform error analysis on the first correlation equation to obtain the third covariance matrix;

[0288] The first correlation equation is solved by WLS according to the third covariance matrix to obtain a first decorrelation WLS solution.

[0289] Specifically, an error analysis is performed on the first correlation equation h3=G3z′3, where the error term is:

[0290] x=x 0 +Δx

[0291] y=y 0 +Δy

[0292] x 2 +y 2 =(x 2 +y 2 )0 +Δ(x 2 +y 2 )

[0293] In the formula, x 0 ,y 0 、(x 2 +y 2 ) 0 are the measured values ​​x, y, (x 2 +y 2 ), Δx represents the error of x in the second WLS solution z2, Δy represents the error of y in the second WLS solution z2, Δ(x 2 +y 2 ) represents the second WLS solution z2 in x 2 +y 2 of error.

[0294] Ignoring the quadratic error term, the error of the first correlation equation h3=G3z′3 is:

[0295] ψ 3，1 =(x 0 +Δx) 2 -(x 0 ) 2 ≈2x 0 ·Δx

[0296] ψ 3，2 =(y 0 +Δy) 2 -(y 0 ) 2 ≈2y 0 ·Δy

[0297] ψ 3，3 =(x 2 +y 2 ) 0 +Δ(x 2 +y 2 )-(x 2 +y 2 ) 0 =Δ(x 2 +y 2 )

[0298] In actual calculation, x 0 ,y 0 、(x 2 +y 2 ) 0 The first three terms of the second WLS solution z2 are replaced. Δx, Δy and Δ(x 2 +y 2) appears in the form of a covariance matrix, i.e., cov(z2)=E[Δz2(1:3)·Δz2(1:3) T ].

[0299] Rewrite the above three error equations into matrix form to obtain the third error matrix ψ3:

[0300] ψ3=B3·Δz2(1:3)

[0301] In the formula, B3 = diag (2x 0 , 2y 0 , 1), Δz2 is the error of the second WLS solution z2, and Δz2(1:3) represents the first three dimensions of Δz2 [Δx, Δy, Δ(x 2 +y 2 )] T .

[0302] According to the third error matrix ψ3, calculate the third covariance matrix ψ3:

[0303]

[0304] In the formula, It is obtained by substituting the true value into the coefficient matrix G1.

[0305] According to the third covariance matrix Ψ3, the first correlation equation h3=G3z′3 is solved by WLS to obtain the first decorrelation WLS solution z3′:

[0306]

[0307] The relative positioning method provided in the embodiment of the present application obtains a third covariance matrix by performing error analysis on the first correlation equation, and replaces the matrix in the WLS solution of the first correlation equation with the third covariance matrix to obtain a first decorrelated WLS solution, which is conducive to subsequently obtaining high-precision first position coordinates.

[0308] In some embodiments, obtaining the first position coordinates according to the first decorrelated WLS solution and the second WLS solution includes:

[0309] According to the first decorrelated WLS solution, a third WLS solution is obtained;

[0310] The solution in the third WLS solution that is closest to the second WLS solution is used as the first position coordinate.

[0311] Specifically, due to the first decorrelated WLS solution z′3=[x 2 ,y 2 ] T is a square term, so the third WLS solution z3 = [x, y]T , the expression of the third WLS solution z3 is:

[0312]

[0313] In the formula, z 3，i represents the i-th term in the third WLS solution z3, where the subscript i is an integer from 1 to 2, and z 3，1 ′ represents the first term in the first decorrelated WLS solution z3′, z 3，2 ' represents the second term in the first decorrelated WLS solution z3'.

[0314] The positive and negative values ​​in the third WLS solution z3 are determined according to the result of the second WLS solution z2, and the value closest to the second WLS solution z2 is taken as the first position coordinate.

[0315]

[0316] In the formula, z 3，i represents the i-th term in the third WLS solution z3, z 2，i It represents the i-th term in the second WLS solution z2, where the subscript i is an integer from 1 to 2.

[0317] The relative positioning method provided in the embodiment of the present application avoids a large difference between the two solutions by taking the solution in the third WLS solution that is closest to the second WLS solution as the first position coordinate, thereby ensuring the accuracy of the first position coordinate.

[0318] In some embodiments, performing back substitution and error analysis based on the first position coordinates to obtain the orientation angle of the second moving object includes:

[0319] Substituting the first position coordinates back into the first TOA equation and the first AOA equation corresponding to each path, to obtain the second TOA equation and the second AOA equation corresponding to each path;

[0320] The second TOA equation and the second AOA equation corresponding to all paths are combined and solved by WLS to obtain a fourth WLS solution;

[0321] An error analysis is performed based on the fourth WLS solution to obtain the orientation angle of the second moving object.

[0322] Specifically, the first position coordinates (x, y) obtained by the third WLS solution z3 are used as known quantities and substituted back into the first TOA equation, and the second TOA equation is obtained after simplification:

[0323]

[0324] In the formula, the subscript p represents the pth path, Δx 1，p , Δy 1，p , Δx2，p , Δy 2(x)，p , Δy 2(y)，p Represent vectors Δx1, Δy1, Δx2, Δy 2(x) , Δy 2(y) The pth component of p represents the path length of the pth path, x represents the abscissa of the second moving body V2, y represents the ordinate of the second moving body V2, Represents the orientation angle of the second moving body V2; s1 represents 1 / 2 length of the first moving body V1, w1 represents 1 / 2 width of the first moving body V1, s2 represents 1 / 2 length of the second moving body V2, and w2 represents 1 / 2 width of the second moving body V2.

[0325] The first position coordinates (x, y) obtained by the third WLS solution z3 are used as known quantities and substituted back into the first AOA equation. After simplification, the second AOA equation is obtained:

[0326]

[0327] In the formula, the subscript p represents the pth path, θ p represents the angle between the pth path and the positive direction of the X-axis, Δx 1，p , Δy 1，p , Δx 2，p , Δy 2(x)，p , Δy 2(y)，p Represent vectors Δx1, Δy1, Δx2, Δy 2(x) , Δy 2(y) The pth component of , x represents the abscissa of the second moving body V2, y represents the ordinate of the second moving body V2, Indicates the orientation angle of the second moving object V2.

[0328] The second TOA equation and the second AOA equation corresponding to all paths are combined and rewritten into matrix form:

[0329] h4=G4z4

[0330] Where:

[0331]

[0332]

[0333]

[0334]

[0335] Solving h4=G4z4 with WLS, we obtain the fourth WLS solution z4. The expression of the fourth WLS solution z4 is as follows:

[0336]

[0337] In the formula,

[0338]

[0339]

[0340] After obtaining the fourth WLS solution z4, an error analysis is performed on the fourth WLS solution z4 to obtain a high-precision heading angle

[0341] The relative positioning method provided in the embodiment of the present application obtains the second TOA equation and the second AOA equation corresponding to each path by back-substituting the first position coordinates into the first TOA equation and the first AOA equation corresponding to each path; the second TOA equation and the second AOA equation corresponding to all paths are combined and solved by WLS to obtain a fourth WLS solution; and error analysis is performed based on the fourth WLS solution to obtain the heading angle of the second mobile object, thereby improving the accuracy of the heading angle.

[0342] In some embodiments, performing error analysis based on the fourth WLS solution to obtain the orientation angle of the second moving object includes:

[0343] The second TOA equation group and the second AOA equation group are respectively subjected to error analysis to obtain a fourth covariance matrix and a fifth covariance matrix; the second TOA equation group includes the second TOA equations corresponding to all paths; the second AOA equation group includes the second AOA equations corresponding to all paths;

[0344] According to the fourth covariance matrix and the fifth covariance matrix, the fourth WLS solution is updated to obtain a fifth WLS solution;

[0345] According to the fifth WLS solution, the orientation angle of the second moving object is obtained.

[0346] Specifically, the second TOA equations corresponding to all paths are combined to obtain the second TOA equation group, and the second TOA equation group is rewritten into a matrix form:

[0347] h 4，r =G 4，r z4

[0348] Where:

[0349]

[0350]

[0351]

[0352] Analyze the error of the second TOA equation group:

[0353]

[0354] In the formula, ψ 5，r represents the fourth error matrix, represents the true value of the fourth WLS solution z4.

[0355] Perform error analysis on the pth path:

[0356]

[0357] The error terms include:

[0358]

[0359] x=x 0 +Δx

[0360] y=y 0 +Δy

[0361] In the formula, represents the true value of the length of the pth path, r p represents the measured value of the length of the pth path, Δr p represents the error between the true value and the measured value of the length of the pth path, x 0 and 0 are the true values ​​corresponding to the measured values ​​x and y, respectively. Δx represents the third WLS solution z3 = [x, y] T The error in x, Δy, represents the third WLS solution z3 = [x, y] T The error in y.

[0362] The error ψ corresponding to the pth path 5，r，p The expression is as follows:

[0363]

[0364] Simplify ψ 5，r，p Then we can get:

[0365]

[0366] Combine the errors corresponding to all paths and rewrite them into matrix form:

[0367] ψ 5，r =A5·Δr+B5·Δz3

[0368] In the formula,

[0369] A5=diag(r), r=[r1,…r 16 ] T

[0370]

[0371]

[0372] Δz3=[Δx,Δy] T

[0373] According to the fourth error matrix ψ 5，r , calculate the fourth covariance matrix Ψ 5，r :

[0374]

[0375] In the formula, The calculation method is as follows (directly quoting the conclusion of Chan's algorithm (non-recursive hyperbolic solution)):

[0376]

[0377]

[0378] In the formula,

[0379] B′3=diag(x 0 ,y 0 )

[0380] Therefore, the fourth covariance matrix Ψ 5，r can be simplified to:

[0381]

[0382] Wherein, the first term of the covariance matrix is ​​caused by the measurement error of ToA, and the second term is caused by the estimation error of the third WLS solution z3.

[0383] The second AOA equations corresponding to all paths are combined to obtain the second AOA equation group, and the second AOA equation group is rewritten into matrix form:

[0384] h 4，a =G 4，a z4

[0385] Where:

[0386]

[0387]

[0388]

[0389] Analyzing the Errors of the Second AOA Equations

[0390]

[0391] In the formula, ψ 5，a represents the fifth error matrix, represents the true value of the fourth WLS solution z4.

[0392] Perform error analysis on the pth path:

[0393]

[0394] The error terms include:

[0395]

[0396] x=x 0 +Δx

[0397] y=y 0 +Δy

[0398] In the formula, θ p represents the measured value of the angle between the pth path and the positive direction of the X-axis, Represents the true value of the angle between the pth path and the positive direction of the X-axis, Δθ p represents the error between the measured value and the true value of the angle between the pth path and the positive direction of the X axis, x 0 and 0 are the true values ​​corresponding to the measured values ​​x and y, respectively. Δx represents the third WLS solution z3 = [x, y] T The error in x, Δy, represents the third WLS solution z3 = [x, y] T The error in y.

[0399] The error ψ corresponding to the pth path 5，a，p The expression is as follows:

[0400]

[0401] make:

[0402]

[0403]

[0404] Simplify ψ 5，a，p Then we can get:

[0405] ψ 5，a，p =(a 5，p cosθ p -b 5，p sinθ p )·Δθ p +sinθ p ·Δx-cosθ p ·Δy

[0406] Combine the errors corresponding to all paths and rewrite them into matrix form:

[0407] ψ 5，a =C5·Δθ+D5·Δz3

[0408] In the formula,

[0409] C5=diag(a 5，1 cosθ1-b 5，1 sinθ1,...,a 5，16 cosθ 16 -b 5，16 sinθ 16 )

[0410]

[0411] Δz3=[Δx,Δy] T

[0412] According to the fifth error matrix ψ 5，a , calculate the fifth covariance matrix A 5，a :

[0413]

[0414] Wherein, the first term of the covariance matrix is ​​caused by the measurement error of AoA, and the second term is caused by the estimation error of the third WLS solution z3.

[0415] According to the fourth covariance matrix A 5，r And the fifth covariance matrix A 5，a , update the fourth WLS solution z4, and obtain the fifth WLS solution z5. The expression of the fifth WLS solution z5 is as follows:

[0416]

[0417] In the formula,

[0418]

[0419]

[0420] Therefore, the orientation angle of the second moving body V2 is The value of is:

[0421]

[0422] Wherein, z5(2) represents the second term in the fifth WLS solution z5, and z5(1) represents the first term in the fifth WLS solution z5.

[0423] The relative positioning method provided in the embodiment of the present application, based on the fourth WLS solution, obtains a fourth covariance matrix and a fifth covariance matrix by performing error analysis on the second TOA equation group and the second AOA equation group respectively, so as to update the fourth WLS solution and obtain a fifth WLS solution; according to the fifth WLS solution, the heading angle of the second mobile body is obtained, thereby further improving the accuracy of the heading angle.

[0424] In some embodiments, after obtaining the orientation angle of the second moving body, the method further includes:

[0425] Back substitution solution, error analysis and decorrelation analysis are performed based on the orientation angle to obtain the second position coordinates of the second moving body relative to the first moving body.

[0426] Specifically, Figure 3 This is the second flow chart of the relative positioning method provided in the embodiment of the present application. Figure 3 As shown, the fifth WLS solution z5 gives the heading angle and first position coordinates can be output as optional output.

[0427] In order to further improve the accuracy of the position coordinates, the fifth WLS solution z5 can be used to obtain the heading angle Back-substitution is performed as a known quantity to obtain the sixth WLS solution z6, error analysis is performed based on the sixth WLS solution z6 to obtain the seventh WLS solution z7, ​​decorrelation analysis is performed based on the seventh WLS solution z7 to obtain the eighth WLS solution z8, and the eighth WLS solution z8 is output as the second position coordinate.

[0428] The relative positioning method provided in the embodiment of the present application is to determine the orientation angle of the second moving body. Then, based on the orientation angle By performing back substitution, error analysis and decorrelation analysis, we obtained the second position coordinates with higher accuracy, which further improved the accuracy of relative positioning.

[0429] In some embodiments, performing back substitution solution, error analysis, and decorrelation analysis based on the orientation angle to obtain the second position coordinates of the second moving object relative to the first moving object includes:

[0430] Substituting the heading angle back into the first TOA equation and the first AOA equation corresponding to each path, to obtain a third TOA equation and a third AOA equation corresponding to each path;

[0431] The third TOA equation and the third AOA equation corresponding to all paths are combined and solved by WLS to obtain a sixth WLS solution;

[0432] Error analysis and decorrelation analysis are performed based on the sixth WLS solution to obtain the second position coordinates.

[0433] Specifically, the fifth WLS solution z5 is used to obtain the heading angle As the known quantity, back-substituting it into the first TOA equation, we get the third TOA equation:

[0434]

[0435] In the formula, the subscript p represents the pth path, Δx 1，p , Δy 1，p , Δx 2，p , Δy 2(x)，p , Δy 2(y)，p Represent vectors Δx1, Δy1, Δx2, Δy 2(x) , Δy 2(y) The pth component of p represents the path length of the pth path, x represents the abscissa of the second moving body V2, y represents the ordinate of the second moving body V2, Represents the orientation angle of the second moving body V2; s1 represents 1 / 2 length of the first moving body V1, w1 represents 1 / 2 width of the first moving body V1, s2 represents 1 / 2 length of the second moving body V2, and w2 represents 1 / 2 width of the second moving body V2.

[0436] Solve the fifth WLS for z5 to get the heading angle Substituting the known quantity back into the first AOA equation, we get the third AOA equation:

[0437]

[0438] The third TOA equation and the third AOA equation corresponding to all paths are combined and rewritten into matrix form:

[0439] h6=G6z6

[0440] Where:

[0441]

[0442]

[0443] z6=[x,y,x 2 +y 2 ] T

[0444]

[0445]

[0446]

[0447]

[0448]

[0449] Perform WLS solution on h6=G6z6 to obtain the sixth WLS solution z6. The expression of the sixth WLS solution z6 is as follows:

[0450]

[0451] In the formula,

[0452]

[0453] The relative positioning method provided in the embodiment of the present application obtains the third TOA equation and the third AOA equation corresponding to each path by substituting the heading angle back into the first TOA equation and the first AOA equation corresponding to each path; the third TOA equation and the third AOA equation corresponding to all paths are combined and solved by WLS to obtain a sixth WLS solution; based on the sixth WLS solution, error analysis and decorrelation analysis are performed to obtain the second position coordinates, thereby further improving the accuracy of the second position coordinates.

[0454] In some embodiments, performing error analysis and decorrelation analysis based on the sixth WLS solution to obtain the second position coordinates includes:

[0455] The third TOA equation group and the third AOA equation group are respectively subjected to error analysis to obtain a sixth covariance matrix and a seventh covariance matrix; the third TOA equation group includes the third TOA equations corresponding to all paths; the third AOA equation group includes the third AOA equations corresponding to all paths;

[0456] According to the sixth covariance matrix and the seventh covariance matrix, the sixth WLS solution is updated to obtain the seventh WLS solution;

[0457] A decorrelation analysis is performed based on the seventh WLS solution to obtain the second position coordinates.

[0458] Specifically, the third TOA equations corresponding to all paths are combined to obtain the third TOA equation group, and the third TOA equation group is rewritten into a matrix form:

[0459] h 6，r =G 6，r z 6，r

[0460] Where:

[0461]

[0462]

[0463] z 6，r=[x,y,x 2 +y 2 ] T

[0464]

[0465]

[0466]

[0467] Analyze the error of the third TOA equation group:

[0468]

[0469] In the formula, ψ 7，r represents the sixth error matrix, represents the true value of the solution to the third TOA system of equations.

[0470] Perform error analysis on the pth path:

[0471]

[0472] The error terms include:

[0473]

[0474]

[0475]

[0476] In the formula, represents the true value of the length of the pth path, r p represents the measured value of the length of the pth path, Δr p represents the error between the true value and the measured value of the length of the pth path, Indicates the fifth WLS solution z5 The estimation error of Indicates the measured value The true value of Indicates the measured value The true value of Indicates the fifth WLS solution z5 The estimation error.

[0477] In actual calculations, and Respectively by the fifth WLS , and It appears in the form of a covariance matrix, that is,

[0478] The error ψ corresponding to the pth path 7，r，p The expression is as follows:

[0479]

[0480] make:

[0481] a 7，p =Δx 2，p Δx 1，p +Δy 1，p Δy 2(y)，p -Δx 2，p x-Δx 2，p y

[0482] b 7，p =Δx 1，p Δy 2(x)，p +Δx 2，p Δy 1，p -Δy 2(x)，p x-Δy 2(x)，p y

[0483] Simplify ψ 7，r，p Then we can get:

[0484]

[0485] Combine the errors corresponding to all paths and rewrite them into matrix form:

[0486] ψ 7，r =A7·Δr+B7·Δz5

[0487] In the formula,

[0488] A7=diag(r), r=[r1,…r 16 ] T

[0489]

[0490]

[0491] According to the sixth error matrix ψ 7，r , calculate the sixth covariance matrix Ψ 7，r :

[0492]

[0493] In the formula, The calculation method is as follows (directly quoting the conclusion of Chan algorithm):

[0494]

[0495] Therefore

[0496]

[0497] Wherein, the first term of the covariance matrix is ​​caused by the measurement error of ToA, and the second term is caused by the estimation error of the fifth WLS solution z5.

[0498] The third AOA equations corresponding to all paths are combined to obtain the third AOA equation group, and the third AOA equation group is rewritten into a matrix form:

[0499] h 6，a =G 6，a z 6，a

[0500] Where:

[0501]

[0502] z 6，a =[x,y] T

[0503]

[0504]

[0505]

[0506] Analyze the error of the third AOA equation group:

[0507]

[0508] In the formula, ψ 7，a represents the seventh error matrix, Represents the true value of the solution to the third AOA system of equations.

[0509] Perform error analysis on the pth path:

[0510]

[0511] The error terms include:

[0512]

[0513]

[0514]

[0515] In the formula, θ p represents the measured value of the angle between the pth path and the positive direction of the X-axis, Represents the true value of the angle between the pth path and the positive direction of the X-axis, Δθ pRepresents the error between the measured value and the true value of the angle between the pth path and the positive direction of the X-axis, Indicates the fifth WLS solution z5 The estimation error of Indicates the measured value The true value of Indicates the measured value The true value of Indicates the fifth WLS solution z5 The estimation error.

[0516] The error ψ corresponding to the pth path 7，a，p The expression is as follows:

[0517]

[0518] make:

[0519]

[0520]

[0521]

[0522]

[0523] Keep the first-order error term and simplify ψ 7，a，p Then we can get:

[0524]

[0525] Combine the errors corresponding to all paths and rewrite them into matrix form:

[0526] ψ 7，a =C7·Δθ+D7·Δz5

[0527] In the formula,

[0528] C7=diag(c 7，1 cosθ1-d 7，1 sinθ1,...,c 7，16 cosθ 16 -d 7，16 sinθ 16 )

[0529]

[0530]

[0531] According to the seventh error matrix ψ 7，a , calculate the seventh covariance matrix Ψ 7，a :

[0532]

[0533] Wherein, the first term of the covariance matrix is ​​caused by the measurement error of AoA, and the second term is caused by the estimation error of the fifth WLS solution z5.

[0534] According to the sixth covariance matrix A 7，r and the seventh covariance matrix A 7，a , update the sixth WLS solution to obtain the seventh WLS solution z7. The expression of the seventh WLS solution z7 is as follows:

[0535]

[0536] In the formula,

[0537] z7=[x,y,x 2 +y 2 ] T

[0538]

[0539] The relative positioning method provided in the embodiment of the present application performs error analysis on the third TOA equation group and the third AOA equation group respectively to obtain the sixth covariance matrix and the seventh covariance matrix to update the sixth WLS solution to obtain the seventh WLS solution. Based on the seventh WLS solution, decorrelation analysis is performed to obtain the second position coordinates, thereby further improving the accuracy of the second position coordinates.

[0540] In some embodiments, performing decorrelation analysis based on the seventh WLS solution to obtain the second position coordinates includes:

[0541] According to the seventh WLS solution, the second correlation equation is established;

[0542] Perform error analysis and WLS solution on the second correlation equation to obtain the second decorrelation WLS solution;

[0543] A second position coordinate is obtained according to the second decorrelated WLS solution and the seventh WLS solution.

[0544] Specifically, considering z7=[x, y, x 2 +y 2 ] T The variable correlation in is used to establish the second correlation equation. The expression of the second correlation equation is as follows:

[0545] h8=G8z′8

[0546] In the formula,

[0547]

[0548] z8′=[x 2 ,y 2 ] T

[0549]

[0550] The error analysis of the second correlation equation h8=G8z′8 is performed, and the error term is:

[0551] x=x 0 +Δx

[0552] y=y 0 +Δy

[0553] x 2 +y 2 =(x 2 +y 2 ) 0 +Δ(x 2 +y 2 )

[0554] In the formula, x 0 ,y 0 、(x 2 +y 2 ) 0 are the measured values ​​x, y, (x 2 +y 2 ) corresponds to the true value, Δx represents the error of x in the seventh WLS solution z7, ​​Δy represents the error of y in the seventh WLS solution z7, ​​Δ(x 2 +y 2 ) represents the seventh WLS solution z7 in x 2 +y 2 of error.

[0555] In actual calculation, x 0 ,y 0 、(x 2 +y 2 ) 0 By the seventh WLS solution z7 = [x, y, x 2 +y 2 ] T Δx, Δy and Δ(x 2 +y 2 ) appears in the form of a covariance matrix, i.e., cov(z7)=E[Δz7·Δz7 T ].

[0556] From the error term we can know:

[0557] ψ 8，1 =(x 0 +Δx) 2 -(x0 ) 2 ≈2x 0 ·Δx

[0558] ψ 8，2 =(y 0 +Δy) 2 -(y 0 ) 2 ≈2y 0 ·Δy

[0559] ψ 8，3 =(x 2 +y 2 ) 0 +Δ(x 2 +y 2 )-(x 2 +y 2 ) 0 =Δ(x 2 +y 2 )

[0560] Rewrite the above three error equations into matrix form to obtain the ninth error matrix ψ8:

[0561] ψ8=B8·Δz7

[0562] In the formula,

[0563] B8=diag(2x 0 , 2y 0 , 1)

[0564] According to the eighth error matrix ψ8, the eighth covariance matrix Ψ8 is calculated:

[0565]

[0566] According to the conclusion of Chan algorithm, it is directly given here:

[0567]

[0568] In the formula, It is obtained by substituting the true value into the coefficient matrix G6.

[0569] According to the eighth covariance matrix Ψ8, the second correlation equation h8=G8z′8 is solved by WLS to obtain the second decorrelation WLS solution z8′:

[0570]

[0571] Since the second decorrelated WLS solution z′8=[x 2 ,y 2 ] Tis a square term, therefore, the eighth WLS solution z8 = [x, y] T , the expression of the eighth WLS solution z8 is:

[0572]

[0573] In the formula, z 8，i represents the i-th term in the third WLS solution z8, where the subscript i is an integer from 1 to 2, and z 8，1 ′ represents the first term in the second decorrelated WLS solution z8′, z 8，2 ' represents the second term in the second decorrelated WLS solution z8'.

[0574] The positive and negative values ​​in the eighth WLS solution z8 are determined according to the result of the seventh WLS solution z7, ​​and the value closest to the seventh WLS solution z7 is taken as the second position coordinate.

[0575]

[0576] In the formula, z 8，i Table 8. The i-th term in the WLS solution z8, z 7，i It represents the i-th item in the seventh WLS solution z7, ​​and the subscript i is an integer from 1 to 2.

[0577] The relative positioning method provided in the embodiment of the present application establishes a second correlation equation based on the seventh WLS solution; performs error analysis and WLS solution on the second correlation equation to obtain a second decorrelation WLS solution; obtains second position coordinates based on the second decorrelation WLS solution and the seventh WLS solution, thereby further improving the accuracy of the second position coordinates.

[0578] Figure 4 is a schematic diagram of the structure of an electronic device provided in an embodiment of the present application, such as Figure 4 As shown, the electronic device includes a memory 420, a transceiver 400, and a processor 410, wherein:

[0579] The memory 420 is used to store computer programs; the transceiver 400 is used to send and receive data under the control of the processor 410; the processor 410 is used to read the computer program in the memory 420 and perform the following operations:

[0580] Constructing a first TOA equation and a first AOA equation corresponding to each path according to the path between the first mobile body and the second mobile body and the TOA measurement amount and the AOA measurement amount corresponding to each path;

[0581] The first TOA equation and the first AOA equation corresponding to all paths are combined, and the weighted least square solution WLS is solved to obtain the first WLS solution;

[0582] Perform error analysis and decorrelation analysis based on the first WLS solution to obtain first position coordinates of the second moving object relative to the first moving object;

[0583] Back substitution solution and error analysis are performed based on the first position coordinates to obtain the orientation angle of the second moving body.

[0584] Specifically, the transceiver 400 is used to receive and send data under the control of the processor 410 .

[0585] In the formula, Figure 4 In the embodiment, the bus architecture may include any number of interconnected buses and bridges, specifically linking together various circuits of one or more processors represented by processor 410 and memory represented by memory 420. The bus architecture may also link together various other circuits such as peripherals, voltage regulators, and power management circuits, which are well known in the art and are therefore not further described herein. The bus interface provides an interface. The transceiver 400 may be a plurality of components, namely, a transmitter and a receiver, providing a unit for communicating with various other devices on a transmission medium, which transmission medium may include a wireless channel, a wired channel, an optical cable, and the like. The processor 410 is responsible for managing the bus architecture and general processing, and the memory 420 may store data used by the processor 410 when performing operations.

[0586] The processor 410 may be a central processing unit (CPU), an application specific integrated circuit (ASIC), a field programmable gate array (FPGA) or a complex programmable logic device (CPLD). The processor may also adopt a multi-core architecture.

[0587] In some embodiments, the first TOA equation is a relationship expression between the path length of the pth path and the position information of the second mobile object; the first AOA equation is θ p The relationship expression between the tangent value of and the position information of the second moving body;

[0588] θ p is the angle between the pth path and the positive direction of the X-axis.

[0589] In some embodiments, performing error analysis and decorrelation analysis based on the first WLS solution to obtain the first position coordinates of the second moving object relative to the first moving object includes:

[0590] Performing error analysis on the first TOA equation group and the first AOA equation group respectively to obtain a first covariance matrix and a second covariance matrix; the first TOA equation group includes the first TOA equations corresponding to all paths; the first AOA equation group includes the first AOA equations corresponding to all paths;

[0591] updating the first WLS solution according to the first covariance matrix and the second covariance matrix to obtain a second WLS solution;

[0592] Perform decorrelation analysis based on the second WLS solution to obtain the first position coordinates.

[0593] In some embodiments, performing decorrelation analysis based on the second WLS solution to obtain the first position coordinates includes:

[0594] Establishing a first correlation equation according to a correlation solution in the second WLS solution; the correlation solution is a solution related to the first position coordinates;

[0595] Performing error analysis and WLS solution on the first correlation equation to obtain a first decorrelation WLS solution;

[0596] The first position coordinates are acquired according to the first decorrelated WLS solution and the second WLS solution.

[0597] In some embodiments, performing error analysis and WLS solution on the first correlation equation to obtain a first decorrelation WLS solution includes:

[0598] Performing error analysis on the first correlation equation to obtain a third covariance matrix;

[0599] The first correlation equation is solved by WLS according to the third covariance matrix to obtain the first decorrelation WLS solution.

[0600] In some embodiments, acquiring the first position coordinates according to the first decorrelated WLS solution and the second WLS solution includes:

[0601] Obtaining a third WLS solution according to the first decorrelated WLS solution;

[0602] The solution in the third WLS solution that is closest to the second WLS solution is used as the first position coordinate.

[0603] In some embodiments, performing back substitution solution and error analysis based on the first position coordinates to obtain the orientation angle of the second moving body includes:

[0604] Substituting the first position coordinates back into the first TOA equation and the first AOA equation corresponding to each path to obtain a second TOA equation and a second AOA equation corresponding to each path;

[0605] The second TOA equation and the second AOA equation corresponding to all paths are combined and solved by WLS to obtain a fourth WLS solution;

[0606] An error analysis is performed based on the fourth WLS solution to obtain the orientation angle of the second moving object.

[0607] In some embodiments, performing error analysis based on the fourth WLS solution to obtain the orientation angle of the second moving object includes:

[0608] Performing error analysis on the second TOA equation group and the second AOA equation group respectively to obtain a fourth covariance matrix and a fifth covariance matrix; the second TOA equation group includes the second TOA equations corresponding to all paths; the second AOA equation group includes the second AOA equations corresponding to all paths;

[0609] updating the fourth WLS solution according to the fourth covariance matrix and the fifth covariance matrix to obtain a fifth WLS solution;

[0610] According to the fifth WLS solution, the orientation angle of the second moving object is obtained.

[0611] In some embodiments, after obtaining the orientation angle of the second moving body, the method further includes:

[0612] Back substitution solution, error analysis and decorrelation analysis are performed based on the orientation angle to obtain second position coordinates of the second moving body relative to the first moving body.

[0613] In some embodiments, performing back substitution solution, error analysis, and decorrelation analysis based on the orientation angle to obtain the second position coordinates of the second moving object relative to the first moving object includes:

[0614] Substituting the heading angle back into the first TOA equation and the first AOA equation corresponding to each path to obtain a third TOA equation and a third AOA equation corresponding to each path;

[0615] The third TOA equation and the third AOA equation corresponding to all paths are combined and solved by WLS to obtain a sixth WLS solution;

[0616] Error analysis and decorrelation analysis are performed based on the sixth WLS solution to obtain the second position coordinates.

[0617] In some embodiments, performing error analysis and decorrelation analysis based on the sixth WLS solution to obtain the second position coordinates includes:

[0618] Performing error analysis on the third TOA equation group and the third AOA equation group respectively to obtain a sixth covariance matrix and a seventh covariance matrix; the third TOA equation group includes the third TOA equations corresponding to all paths; the third AOA equation group includes the third AOA equations corresponding to all paths;

[0619] According to the sixth covariance matrix and the seventh covariance matrix, the sixth WLS solution is updated to obtain a seventh WLS solution;

[0620] Decorrelation analysis is performed based on the seventh WLS solution to obtain the second position coordinates.

[0621] In some embodiments, performing decorrelation analysis based on the seventh WLS solution to obtain the second position coordinates includes:

[0622] According to the seventh WLS solution, establishing a second correlation equation;

[0623] performing error analysis and WLS solution on the second correlation equation to obtain a second decorrelation WLS solution;

[0624] The second position coordinates are obtained according to the second decorrelated WLS solution and the seventh WLS solution.

[0625] It should be noted here that the above-mentioned electronic device provided in the embodiment of the present application can implement all the method steps implemented in the above-mentioned method embodiment, and can achieve the same technical effect. The parts and beneficial effects of this embodiment that are the same as the method embodiment will not be described in detail here.

[0626] Figure 5 is a schematic diagram of the structure of the relative positioning device provided in the embodiment of the present application, such as Figure 5 As shown, the embodiment of the present application also provides a relative positioning device including: a construction module 510, a first acquisition module 520, a second acquisition module 530 and a third acquisition module 540; wherein:

[0627] A construction module 510 is used to construct a first TOA equation and a first AOA equation corresponding to each path according to the path between the first mobile body and the second mobile body and the TOA measurement amount and the AOA measurement amount corresponding to each path;

[0628] A first acquisition module 520 is used to jointly establish a first TOA equation and a first AOA equation corresponding to all paths, and solve a weighted least square solution WLS to obtain a first WLS solution;

[0629] A second acquisition module 530, configured to perform error analysis and decorrelation analysis based on the first WLS solution to obtain a first position coordinate of the second moving object relative to the first moving object;

[0630] The third acquisition module 540 is used to perform back substitution solution and error analysis based on the first position coordinates to obtain the orientation angle of the second moving body.

[0631] In some embodiments, the first TOA equation is a relationship expression between the path length of the pth path and the position information of the second mobile object; the first AOA equation is θ p The relationship expression between the tangent value of and the position information of the second moving body; p is the angle between the pth path and the positive direction of the X-axis.

[0632] In some embodiments, the second acquisition module 530 includes:

[0633] A first acquisition submodule is used to perform error analysis on the first TOA equation group and the first AOA equation group respectively to obtain a first covariance matrix and a second covariance matrix; the first TOA equation group includes the first TOA equations corresponding to all paths; the first AOA equation group includes the first AOA equations corresponding to all paths;

[0634] A second acquisition submodule, configured to update the first WLS solution according to the first covariance matrix and the second covariance matrix to obtain a second WLS solution;

[0635] The third acquisition submodule is used to perform decorrelation analysis based on the second WLS solution to obtain the first position coordinates.

[0636] In some embodiments, the third acquisition submodule includes:

[0637] An establishing unit, used for establishing a first correlation equation according to a correlation solution in the second WLS solution; the correlation solution is a solution related to the first position coordinates;

[0638] A first acquisition unit, configured to perform error analysis and WLS solution on the first correlation equation to obtain a first decorrelation WLS solution;

[0639] The second acquisition unit is configured to acquire the first position coordinates according to the first decorrelated WLS solution and the second WLS solution.

[0640] In some embodiments, the first acquisition unit includes:

[0641] A first acquisition subunit is used to perform error analysis on the first correlation equation to obtain a third covariance matrix;

[0642] The second acquisition subunit is used to perform WLS solution on the first correlation equation according to the third covariance matrix to obtain the first decorrelation WLS solution.

[0643] In some embodiments, the second acquisition unit includes:

[0644] A third acquisition subunit, configured to obtain a third WLS solution according to the first decorrelated WLS solution;

[0645] The fourth acquisition subunit is configured to use a solution in the third WLS solution that is closest to the second WLS solution as the first position coordinate.

[0646] In some embodiments, the third acquisition module 540 includes:

[0647] A fourth acquisition submodule, used for back-substituting the first position coordinate into the first TOA equation and the first AOA equation corresponding to each path to obtain a second TOA equation and a second AOA equation corresponding to each path;

[0648] A fifth acquisition submodule, configured to jointly solve the second TOA equation and the second AOA equation corresponding to all paths by WLS to obtain a fourth WLS solution;

[0649] The sixth acquisition submodule is used to perform error analysis based on the fourth WLS solution to obtain the orientation angle of the second moving object.

[0650] In some embodiments, the sixth acquisition submodule includes:

[0651] A third acquisition unit is used to perform error analysis on the second TOA equation group and the second AOA equation group respectively to obtain a fourth covariance matrix and a fifth covariance matrix; the second TOA equation group includes the second TOA equations corresponding to all paths; the second AOA equation group includes the second AOA equations corresponding to all paths;

[0652] a fourth acquisition unit, configured to update the fourth WLS solution according to the fourth covariance matrix and the fifth covariance matrix to obtain a fifth WLS solution;

[0653] The fifth acquisition unit is used to obtain the orientation angle of the second moving object according to the fifth WLS solution.

[0654] In some embodiments, the apparatus further comprises:

[0655] A fourth acquisition module is used to perform back substitution solution, error analysis and decorrelation analysis based on the orientation angle to obtain a second position coordinate of the second moving body relative to the first moving body.

[0656] In some embodiments, the fourth acquisition module includes:

[0657] A seventh acquisition submodule, configured to substitute the heading angle back into the first TOA equation and the first AOA equation corresponding to each path to obtain a third TOA equation and a third AOA equation corresponding to each path;

[0658] An eighth acquisition submodule, used for jointly solving the third TOA equation and the third AOA equation corresponding to all paths and performing WLS solution to obtain a sixth WLS solution;

[0659] The ninth acquisition submodule is used to perform error analysis and decorrelation analysis based on the sixth WLS solution to obtain the second position coordinates.

[0660] In some embodiments, the ninth acquisition submodule includes:

[0661] a sixth acquisition unit, configured to perform error analysis on the third TOA equation group and the third AOA equation group, respectively, to obtain a sixth covariance matrix and a seventh covariance matrix; the third TOA equation group includes the third TOA equations corresponding to all paths; the third AOA equation group includes the third AOA equations corresponding to all paths;

[0662] a seventh acquisition unit, configured to update the sixth WLS solution according to the sixth covariance matrix and the seventh covariance matrix to obtain a seventh WLS solution;

[0663] An eighth acquisition unit is configured to perform decorrelation analysis based on the seventh WLS solution to obtain the second position coordinates.

[0664] In some embodiments, the eighth acquisition unit includes:

[0665] an establishing subunit, for establishing a second correlation equation according to the seventh WLS solution;

[0666] a fifth acquisition subunit, configured to perform error analysis and WLS solution on the second correlation equation to obtain a second decorrelation WLS solution;

[0667] The sixth acquisition subunit is configured to obtain the second position coordinates according to the second decorrelated WLS solution and the seventh WLS solution.

[0668] It should be noted here that the relative positioning device provided in the embodiment of the present application can implement all the method steps implemented in the above-mentioned method embodiment and can achieve the same technical effect. The parts and beneficial effects of this embodiment that are the same as those in the method embodiment will not be described in detail here.

[0669] It should be noted that the division of units / modules in the embodiments of the present application is schematic and is only a logical function division. There may be other division methods in actual implementation. In addition, each functional unit in each embodiment of the present application may be integrated into a processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit. The above-mentioned integrated unit may be implemented in the form of hardware or in the form of a software functional unit.

[0670] If the integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a processor-readable storage medium. Based on this understanding, the technical solution of the present application is essentially or the part that contributes to the prior art or all or part of the technical solution can be embodied in the form of a software product, and the computer software product is stored in a storage medium, including a number of instructions to enable a computer device (which can be a personal computer, server, or network device, etc.) or a processor (processor) to perform all or part of the steps of the method described in each embodiment of the present application. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (Read-Only Memory, ROM), random access memory (Random Access Memory, RAM), disk or optical disk and other media that can store program codes.

[0671] In some embodiments, a non-transitory readable storage medium is also provided, wherein the non-transitory readable storage medium stores a computer program, and the computer program is used to enable a processor to execute the relative positioning method provided by the above-mentioned method embodiments.

[0672] Specifically, the above-mentioned non-transitory readable storage medium provided in the embodiment of the present application can implement all the method steps implemented by the above-mentioned method embodiments, and can achieve the same technical effects. The parts and beneficial effects that are the same as the method embodiments in this embodiment will not be described in detail here.

[0673] It should be noted that the non-transitory readable storage medium can be any available medium or data storage device that can be accessed by the processor, including but not limited to magnetic storage (such as floppy disks, hard disks, magnetic tapes, magneto-optical disks (MO), etc.), optical storage (such as CD, DVD, BD, HVD, etc.), and semiconductor storage (such as ROM, EPROM, EEPROM, non-volatile memory (NAND FLASH), solid-state drive (SSD)), etc.

[0674] In some embodiments, a processor-readable storage medium is also provided, wherein the processor-readable storage medium stores a computer program, and the computer program is used to enable the processor to execute the relative positioning method provided by the above-mentioned method embodiments.

[0675] Specifically, the processor-readable storage medium provided in the embodiment of the present application can implement all the method steps implemented in the above-mentioned method embodiments, and can achieve the same technical effects. The parts and beneficial effects that are the same as those in the method embodiments will not be described in detail herein.

[0676] In some embodiments, a computer-readable storage medium is further provided, wherein the computer-readable storage medium stores a computer program, and the computer program is used to enable a computer to execute the relative positioning method provided by the above-mentioned method embodiments.

[0677] Specifically, the above-mentioned computer-readable storage medium provided in the embodiment of the present application can implement all the method steps implemented by the above-mentioned method embodiments, and can achieve the same technical effect. The parts and beneficial effects of this embodiment that are the same as the method embodiment will not be described in detail here.

[0678] In some embodiments, a communication device is further provided, wherein a computer program is stored in the communication device, and the computer program is used to enable the communication device to execute the relative positioning method provided by the above-mentioned method embodiments.

[0679] Specifically, the above-mentioned communication device provided in the embodiment of the present application can implement all the method steps implemented by the above-mentioned method embodiments, and can achieve the same technical effects. The parts and beneficial effects that are the same as the method embodiments in this embodiment will not be described in detail here.

[0680] In some embodiments, a chip product is further provided, wherein a computer program is stored in the chip product, and the computer program is used to enable the chip product to execute the relative positioning method provided by the above-mentioned method embodiments.

[0681] It should also be noted that the terms "first", "second", etc. in the embodiments of the present application are used to distinguish similar objects, and are not used to describe a specific order or sequence. It should be understood that the terms used in this way can be interchangeable under appropriate circumstances, so that the embodiments of the present application can be implemented in an order other than those illustrated or described here, and the objects distinguished by "first" and "second" are generally of the same type, and the number of objects is not limited. For example, the first object can be one or more.

[0682] In the embodiments of the present application, the term "and / or" describes the association relationship of the associated objects, indicating that three relationships may exist. For example, A and / or B may represent: A exists alone, A and B exist at the same time, and B exists alone. The character " / " generally indicates that the associated objects before and after are in an "or" relationship.

[0683] In the embodiments of the present application, the term "plurality" refers to two or more than two, and other quantifiers are similar.

[0684] "Determine B based on A" in this application means that the factor A should be considered when determining B. It is not limited to "B can be determined based on A alone", but should also include: "Determine B based on A and C", "Determine B based on A, C and E", "Determine C based on A, and further determine B based on C", etc. In addition, it can also include taking A as a condition for determining B, for example, "When A meets the first condition, use the first method to determine B"; for example, "When A meets the second condition, determine B", etc.; for example, "When A meets the third condition, determine B based on the first parameter", etc. Of course, it can also be a condition that takes A as a factor for determining B, for example, "When A meets the first condition, use the first method to determine C, and further determine B based on C", etc.

[0685] The technical solution provided in the embodiment of the present application can be applicable to a variety of systems, especially 5G systems. For example, the applicable system can be a global system of mobile communication (GSM) system, a code division multiple access (CDMA) system, a wideband code division multiple access (WCDMA) general packet radio service (GPRS) system, a long term evolution (LTE) system, a LTE frequency division duplex (FDD) system, a LTE time division duplex (TDD) system, an advanced long term evolution (LTE-A) system, a universal mobile telecommunication system (UMTS), a world-wide interoperability for microwave access (WiMAX) system, a 5G new radio (NR) system, etc. These various systems include terminal equipment and network equipment. The system may also include a core network part, such as an evolved packet system (EPS), a 5G system (5GS), etc.

[0686] The terminal device involved in the embodiment of the present application may be a device that provides voice and / or data connectivity to a user, a handheld device with a wireless connection function, or other processing devices connected to a wireless modem. In different systems, the name of the terminal device may also be different. For example, in a 5G system, the terminal device may be called a user equipment (UE). A wireless terminal device can communicate with one or more core networks (CN) via a radio access network (RAN). The wireless terminal device may be a mobile terminal device, such as a mobile phone (or a "cellular" phone) and a computer with a mobile terminal device. For example, it may be a portable, pocket-sized, handheld, computer-built-in or vehicle-mounted mobile device that exchanges language and / or data with a wireless access network. For example, personal communication service (PCS) phones, cordless phones, session initiation protocol (SIP) phones, wireless local loop (WLL) stations, personal digital assistants (PDAs) and other devices. The wireless terminal device may also be referred to as a system, a subscriber unit, a subscriber station, a mobile station, a mobile station, a remote station, an access point, a remote terminal device, an access terminal device, a user terminal device, a user agent, and a user device, but is not limited in the embodiments of the present application.

[0687] The network device involved in the embodiments of the present application may be a base station, which may include multiple cells providing services for the terminal. Depending on the specific application scenario, the base station may also be called an access point, or may be a device in the access network that communicates with the wireless terminal device through one or more sectors on the air interface, or other names. The network device may be used to interchange received air frames with Internet Protocol (IP) packets, and serve as a router between the wireless terminal device and the rest of the access network, wherein the rest of the access network may include an Internet Protocol (IP) communication network. The network device may also coordinate the attribute management of the air interface. For example, the network device involved in the embodiments of the present application may be a network device (Base Transceiver Station, BTS) in the Global System for Mobile communications (Global System for Mobile communications, GSM) or Code Division Multiple Access (Code Division Multiple Access, CDMA), or a network device (NodeB) in Wide-band Code Division Multiple Access (WCDMA), or an evolutionary network device (evolutional Node B, eNB or e-NodeB) in the long term evolution (long term evolution, LTE) system, a 5G base station (gNB) in the 5G network architecture (next generation system), or a home evolved Node B (Home evolved Node B, HeNB), a relay node, a home base station (femto), a pico base station (pico), etc., which is not limited in the embodiments of the present application. In some network structures, the network device may include a centralized unit (CU) node and a distributed unit (DU) node, and the centralized unit and the distributed unit may also be arranged geographically separately.

[0688] Network devices and terminal devices can each use one or more antennas for multi-input multi-output (MIMO) transmission. MIMO transmission can be single-user MIMO (SU-MIMO) or multi-user MIMO (MU-MIMO). Depending on the form and number of antenna combinations, MIMO transmission can be 2D-MIMO, 3D-MIMO, FD-MIMO or massive-MIMO, or it can be diversity transmission, precoding transmission or beamforming transmission, etc.

[0689] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application may adopt the form of a computer program product implemented on a computer-usable storage medium (including but not limited to a disk storage device and an optical storage device, etc.) that includes a computer-usable program code in one or more formulas.

[0690] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer executable instructions. These computer executable instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0691] These processor executable instructions may also be stored in a processor readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the processor readable memory produce an article of manufacture including an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0692] These processor-executable instructions may also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for executing on the computer or other programmable device to implement the process. Figure 1A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0693] Obviously, those skilled in the art can make various changes and modifications to the present application without departing from the spirit and scope of the present application. Thus, if these modifications and variations fall within the scope of the present application and its equivalent technologies, the present application is also intended to include these modifications and variations.

Claims

1. A relative positioning method, characterized in that: include: Constructing a first TOA equation and a first AOA equation corresponding to each path according to the path between the first mobile body and the second mobile body and the TOA measurement amount and the AOA measurement amount corresponding to each path; The first TOA equation and the first AOA equation corresponding to all paths are combined, and the weighted least square solution WLS is solved to obtain the first WLS solution; Perform error analysis and decorrelation analysis based on the first WLS solution to obtain first position coordinates of the second moving object relative to the first moving object; Back substitution solution and error analysis are performed based on the first position coordinates to obtain the orientation angle of the second moving body.

2. The relative positioning method according to claim 1, characterized in that: The first TOA equation is an expression of the relationship between the path length of the pth path and the position information of the second mobile object; the first AOA equation is θ p The relationship expression between the tangent value of and the position information of the second moving body; p is the angle between the pth path and the positive direction of the X-axis.

3. The relative positioning method according to claim 1, characterized in that: The performing error analysis and decorrelation analysis based on the first WLS solution to obtain the first position coordinates of the second moving body relative to the first moving body includes: Performing error analysis on the first TOA equation group and the first AOA equation group respectively to obtain a first covariance matrix and a second covariance matrix; the first TOA equation group includes the first TOA equations corresponding to all paths; the first AOA equation group includes the first AOA equations corresponding to all paths; updating the first WLS solution according to the first covariance matrix and the second covariance matrix to obtain a second WLS solution; Perform decorrelation analysis based on the second WLS solution to obtain the first position coordinates.

4. The relative positioning method according to claim 3, characterized in that: The performing decorrelation analysis based on the second WLS solution to obtain the first position coordinates includes: Establishing a first correlation equation according to a correlation solution in the second WLS solution; the correlation solution is a solution related to the first position coordinates; Performing error analysis and WLS solution on the first correlation equation to obtain a first decorrelation WLS solution; The first position coordinates are acquired according to the first decorrelated WLS solution and the second WLS solution.

5. The relative positioning method according to claim 4, characterized in that: The performing error analysis and WLS solution on the first correlation equation to obtain a first decorrelation WLS solution includes: Performing error analysis on the first correlation equation to obtain a third covariance matrix; The first correlation equation is solved by WLS according to the third covariance matrix to obtain the first decorrelation WLS solution.

6. The relative positioning method according to claim 4, characterized in that: The acquiring the first position coordinates according to the first decorrelated WLS solution and the second WLS solution includes: Obtaining a third WLS solution according to the first decorrelated WLS solution; The solution in the third WLS solution that is closest to the second WLS solution is used as the first position coordinate.

7. The relative positioning method according to claim 1, characterized in that: The performing back substitution solution and error analysis based on the first position coordinates to obtain the orientation angle of the second moving body includes: Substituting the first position coordinates back into the first TOA equation and the first AOA equation corresponding to each path to obtain a second TOA equation and a second AOA equation corresponding to each path; The second TOA equation and the second AOA equation corresponding to all paths are combined and solved by WLS to obtain a fourth WLS solution; An error analysis is performed based on the fourth WLS solution to obtain the orientation angle of the second moving object.

8. The relative positioning method according to claim 7, characterized in that: The performing error analysis based on the fourth WLS solution to obtain the orientation angle of the second moving object includes: Performing error analysis on the second TOA equation group and the second AOA equation group respectively to obtain a fourth covariance matrix and a fifth covariance matrix; the second TOA equation group includes the second TOA equations corresponding to all paths; the second AOA equation group includes the second AOA equations corresponding to all paths; updating the fourth WLS solution according to the fourth covariance matrix and the fifth covariance matrix to obtain a fifth WLS solution; According to the fifth WLS solution, the orientation angle of the second moving object is obtained.

9. The relative positioning method according to claim 1, characterized in that: After obtaining the orientation angle of the second moving body, the method further includes: Back substitution solution, error analysis and decorrelation analysis are performed based on the orientation angle to obtain second position coordinates of the second moving body relative to the first moving body.

10. The relative positioning method according to claim 9, characterized in that: The performing back substitution solution, error analysis and decorrelation analysis based on the orientation angle to obtain the second position coordinates of the second moving body relative to the first moving body includes: Substituting the heading angle back into the first TOA equation and the first AOA equation corresponding to each path to obtain a third TOA equation and a third AOA equation corresponding to each path; The third TOA equation and the third AOA equation corresponding to all paths are combined and solved by WLS to obtain a sixth WLS solution; Error analysis and decorrelation analysis are performed based on the sixth WLS solution to obtain the second position coordinates.

11. The relative positioning method according to claim 10, characterized in that: The performing error analysis and decorrelation analysis based on the sixth WLS solution to obtain the second position coordinates includes: Performing error analysis on the third TOA equation group and the third AOA equation group respectively to obtain a sixth covariance matrix and a seventh covariance matrix; the third TOA equation group includes the third TOA equations corresponding to all paths; the third AOA equation group includes the third AOA equations corresponding to all paths; According to the sixth covariance matrix and the seventh covariance matrix, the sixth WLS solution is updated to obtain a seventh WLS solution; Decorrelation analysis is performed based on the seventh WLS solution to obtain the second position coordinates.

12. The relative positioning method according to claim 11, characterized in that: The performing decorrelation analysis based on the seventh WLS solution to obtain the second position coordinates includes: According to the seventh WLS solution, establishing a second correlation equation; performing error analysis and WLS solution on the second correlation equation to obtain a second decorrelation WLS solution; The second position coordinates are obtained according to the second decorrelated WLS solution and the seventh WLS solution.

13. An electronic device, characterized in that: Including memory, transceiver, processor: A memory for storing a computer program; a transceiver for transmitting and receiving data under the control of the processor; and a processor for reading the computer program in the memory and performing the following operations: Constructing a first TOA equation and a first AOA equation corresponding to each path according to the path between the first mobile body and the second mobile body and the TOA measurement amount and the AOA measurement amount corresponding to each path; The first TOA equation and the first AOA equation corresponding to all paths are combined, and the weighted least square solution WLS is solved to obtain the first WLS solution; Perform error analysis and decorrelation analysis based on the first WLS solution to obtain first position coordinates of the second moving object relative to the first moving object; Back substitution solution and error analysis are performed based on the first position coordinates to obtain the orientation angle of the second moving body.

14. The electronic device according to claim 13, characterized in that: The first TOA equation is an expression of the relationship between the path length of the pth path and the position information of the second mobile object; the first AOA equation is θ p The relationship expression between the tangent value of and the position information of the second moving body; p is the angle between the pth path and the positive direction of the X-axis.

15. The electronic device according to claim 13, characterized in that: The performing error analysis and decorrelation analysis based on the first WLS solution to obtain the first position coordinates of the second moving body relative to the first moving body includes: Performing error analysis on the first TOA equation group and the first AOA equation group respectively to obtain a first covariance matrix and a second covariance matrix; the first TOA equation group includes the first TOA equations corresponding to all paths; the first AOA equation group includes the first AOA equations corresponding to all paths; updating the first WLS solution according to the first covariance matrix and the second covariance matrix to obtain a second WLS solution; Perform decorrelation analysis based on the second WLS solution to obtain the first position coordinates.

16. The electronic device according to claim 15, characterized in that: The performing decorrelation analysis based on the second WLS solution to obtain the first position coordinates includes: Establishing a first correlation equation according to a correlation solution in the second WLS solution; the correlation solution is a solution related to the first position coordinates; Performing error analysis and WLS solution on the first correlation equation to obtain a first decorrelation WLS solution; The first position coordinates are acquired according to the first decorrelated WLS solution and the second WLS solution.

17. The electronic device according to claim 16, characterized in that: The performing error analysis and WLS solution on the first correlation equation to obtain a first decorrelation WLS solution includes: Performing error analysis on the first correlation equation to obtain a third covariance matrix; The first correlation equation is solved by WLS according to the third covariance matrix to obtain the first decorrelation WLS solution.

18. The electronic device according to claim 16, characterized in that: The acquiring the first position coordinates according to the first decorrelated WLS solution and the second WLS solution includes: Obtaining a third WLS solution according to the first decorrelated WLS solution; The solution in the third WLS solution that is closest to the second WLS solution is used as the first position coordinate.

19. The electronic device according to claim 13, characterized in that: The performing back substitution solution and error analysis based on the first position coordinates to obtain the orientation angle of the second moving body includes: Substituting the first position coordinates back into the first TOA equation and the first AOA equation corresponding to each path to obtain a second TOA equation and a second AOA equation corresponding to each path; The second TOA equation and the second AOA equation corresponding to all paths are combined and solved by WLS to obtain a fourth WLS solution; An error analysis is performed based on the fourth WLS solution to obtain the orientation angle of the second moving object.

20. The electronic device according to claim 19, characterized in that: The performing error analysis based on the fourth WLS solution to obtain the orientation angle of the second moving object includes: Performing error analysis on the second TOA equation group and the second AOA equation group respectively to obtain a fourth covariance matrix and a fifth covariance matrix; the second TOA equation group includes the second TOA equations corresponding to all paths; the second AOA equation group includes the second AOA equations corresponding to all paths; updating the fourth WLS solution according to the fourth covariance matrix and the fifth covariance matrix to obtain a fifth WLS solution; According to the fifth WLS solution, the orientation angle of the second moving object is obtained.

21. The electronic device according to claim 13, characterized in that: After obtaining the orientation angle of the second moving body, the method further includes: Back substitution solution, error analysis and decorrelation analysis are performed based on the orientation angle to obtain second position coordinates of the second moving body relative to the first moving body.

22. The electronic device according to claim 21, characterized in that: The performing back substitution solution, error analysis and decorrelation analysis based on the orientation angle to obtain the second position coordinates of the second moving body relative to the first moving body includes: Substituting the heading angle back into the first TOA equation and the first AOA equation corresponding to each path to obtain a third TOA equation and a third AOA equation corresponding to each path; The third TOA equation and the third AOA equation corresponding to all paths are combined and solved by WLS to obtain a sixth WLS solution; Error analysis and decorrelation analysis are performed based on the sixth WLS solution to obtain the second position coordinates.

23. The electronic device according to claim 22, characterized in that: The performing error analysis and decorrelation analysis based on the sixth WLS solution to obtain the second position coordinates includes: Performing error analysis on the third TOA equation group and the third AOA equation group respectively to obtain a sixth covariance matrix and a seventh covariance matrix; the third TOA equation group includes the third TOA equations corresponding to all paths; the third AOA equation group includes the third AOA equations corresponding to all paths; According to the sixth covariance matrix and the seventh covariance matrix, the sixth WLS solution is updated to obtain a seventh WLS solution; Decorrelation analysis is performed based on the seventh WLS solution to obtain the second position coordinates.

24. The electronic device according to claim 23, characterized in that: The performing decorrelation analysis based on the seventh WLS solution to obtain the second position coordinates includes: According to the seventh WLS solution, establishing a second correlation equation; performing error analysis and WLS solution on the second correlation equation to obtain a second decorrelation WLS solution; The second position coordinates are obtained according to the second decorrelated WLS solution and the seventh WLS solution.

25. A relative positioning device, characterized in that: include: A construction module, configured to construct a first TOA equation and a first AOA equation corresponding to each path according to the path between the first mobile body and the second mobile body and the TOA measurement amount and the AOA measurement amount corresponding to each path; A first acquisition module is used to jointly establish a first TOA equation and a first AOA equation corresponding to all paths, and solve a weighted least square solution WLS to obtain a first WLS solution; A second acquisition module, configured to perform error analysis and decorrelation analysis based on the first WLS solution to obtain a first position coordinate of the second moving body relative to the first moving body; The third acquisition module is used to perform back substitution solution and error analysis based on the first position coordinates to obtain the orientation angle of the second moving body.

26. A non-transitory readable storage medium, characterized in that The non-transitory readable storage medium stores a computer program, and the computer program is used to enable a processor to execute the relative positioning method according to any one of claims 1 to 12.

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