UWB base station coordinate reverse resolving method based on TDOA

Abstract

The invention belongs to the technical field of indoor positioning, and discloses a TDOA (time difference of arrival)-based UWB (ultra wide band) base station coordinate reverse resolving method, which comprises the following steps of: acquiring positioning point coordinates of each positioning terminal and distance difference data between the positioning terminal under each positioning point and a plurality of base stations; estimating an initial base station position based on the positioning point coordinates and the distance difference data; for each positioning point, establishing a hyperbolic equation of the positioning point and the coordinates of the base station according to the coordinates of the corresponding positioning point and the measured distance difference information of the base station; and based on the initial base station position, performing iterative solution on a non-hyperbolic equation according to a least square method in combination with a Jacobian matrix and a residual matrix, stopping iteration until a preset termination condition is met, and outputting a final base station position. According to the invention, the coordinates of the base station can be rapidly and accurately solved in real time in a dynamic environment, the accuracy and reliability of a positioning system are remarkably improved, the system deployment is simplified, and the cost is reduced.

Description

Technical Field

[0001] The present invention belongs to the technical field of indoor positioning, and particularly relates to a method for reverse calculation of UWB base station coordinates based on TDOA. Background Art

[0002] Ultra-wideband (UWB) technology has been widely applied in the fields of indoor positioning, asset tracking, robot navigation, etc. Its core is the time difference of arrival (TDOA) technology based on multiple base stations and terminal devices to achieve high-precision positioning. However, in actual scenarios, due to the inaccuracy of the installation position of the base station or the lack of accurate initial coordinates, the positioning accuracy may be affected. Especially in a dynamic environment, this error accumulation will significantly reduce the overall performance of the system.

[0003] Currently, the coordinate measurement of UWB base stations mainly relies on high-precision measurement equipment such as total stations. However, this method is not only costly but also time-consuming. In view of this, it is particularly important to develop a method for reverse calculation of base station coordinates based on portable positioning devices and UWB observation information. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for reverse calculation of UWB base station coordinates based on TDOA to solve the problems existing in the above-mentioned prior art.

[0005] To achieve the above object, the present invention provides a method for reverse calculation of UWB base station coordinates based on TDOA, including:

[0006] Obtaining the positioning point coordinates of each positioning terminal and the distance difference data between the positioning terminal and multiple base stations at each positioning point;

[0007] Estimating the initial base station position based on the positioning point coordinates and the distance difference data;

[0008] For each positioning point, establishing a hyperbolic equation of the positioning point and the base station coordinates according to the corresponding positioning point coordinates and the measured base station distance difference information;

[0009] Based on the initial base station position, iteratively solving the non-hyperbolic equation according to the least squares method in combination with the Jacobian matrix and the residual matrix until the iteration stops when a preset termination condition is reached, and outputting the final base station position.

[0010] Optionally, the obtaining the positioning point coordinates of each positioning terminal and the distance difference data between the positioning terminal and multiple base stations at each positioning point specifically includes:

[0011] Moving the positioning terminal according to a preset trajectory and collecting positioning coordinate information during the movement to obtain the positioning point coordinates;

[0012] The UWB positioning tag is used to receive the ranging information sent by the base station, and the distance difference information between the base station and the positioning point is extracted based on the ranging information.

[0013] Optionally, the positioning terminal adopts a pan-source foot-mounted positioning device.

[0014] Optionally, the hyperbolic equation specifically includes:

[0015]

[0016] In the formula, x i , y i , z i respectively represent the x-axis coordinate, y-axis coordinate and z-axis coordinate of the positioning point i, x 1 , y 1 , z 1 respectively represent the x-axis coordinate, y-axis coordinate and z-axis coordinate of the base station 1, x 2 , y 2 , z 2 respectively represent the x-axis coordinate, y-axis coordinate and z-axis coordinate of the base station 2, L i represents the distance difference between the positioning point i and the base stations 1 and 2.

[0017] Optionally, the iterative solution of the non-hyperbolic equation according to the least squares method in combination with the Jacobian matrix and the residual matrix specifically includes:

[0018] Construct a target optimization function based on the hyperbolic equations of each positioning point;

[0019] For each known positioning point, perform a first-order Taylor expansion on the non-linear part of the distance difference, and approximate the non-linear equation as a linearized equation;

[0020] Rewrite the linearized equation as a matrix equation;

[0021] Solve the matrix equation based on the least squares method to obtain the base station coordinate increment; update the initial base station position based on the base station coordinate increment to obtain the updated base station position;

[0022] Check whether the iteration termination condition is satisfied. If the error tolerance is less than the set value or the maximum number of iterations is reached, stop the iteration and output the final base station position; otherwise, continue the next iteration.

[0023] Optionally, the target optimization function is specifically:

[0024]

[0025] In the formula, f i (.) is the target optimization function, x i , yi , z i respectively represent the x-axis coordinate, y-axis coordinate, and z-axis coordinate of the positioning point i, where x 1 , y 1 , z 1 respectively represent the x-axis coordinate, y-axis coordinate, and z-axis coordinate of base station 1, where x 2 , y 2 , z 2 respectively represent the x-axis coordinate, y-axis coordinate, and z-axis coordinate of base station 2, and L i represents the distance difference between the positioning point i and base stations 1 and 2.

[0026] Optionally, perform a first-order Taylor expansion on the non-linear part of the distance difference. The specific calculation formula is:

[0027]

[0028] In the formula, δ is the base station coordinate increment vector, x 1 , y 1 , z 1 respectively represent the x-axis coordinate, y-axis coordinate, and z-axis coordinate of base station 1, x 2 , y 2 , z 2 respectively represent the x-axis coordinate, y-axis coordinate, and z-axis coordinate of base station 2, L i represents the distance difference between the positioning point i and base stations 1 and 2, ε i is the noise error vector, f i,v is the target optimization function, a i,1 .......a i,6 are the parameters in the target optimization function, and these parameters are used to represent the correction terms in the base station position update process.

[0029] Optionally, solve the matrix equation based on the least squares method, specifically including:

[0030] Rewrite the linearized equation as a matrix equation:

[0031] Hδ = Δf + ε

[0032] In the formula, H is the Jacobian matrix, δ is the base station coordinate increment vector, Δf is the residual vector, and ε is the noise error vector;

[0033] Base station coordinate increment solution:

[0034] δ = (H T H) -1 H T Δf

[0035] In the formula, H T is the transpose of the matrix H;

[0036] Update the initial base station position based on the base station coordinate increment:

[0037] x (t+1) = x (t) + δ

[0038] In the formula, x (t+1) is the updated base station position, and x (t) is the initial base station position.

[0039] The technical effects of the present invention are as follows:

[0040] 1. Flexibility and rapidity: Based on the least squares nonlinear optimization method, the present invention can achieve real-time and rapid solution in a dynamic environment, greatly shortening the positioning time and being able to flexibly adapt to various application scenarios.

[0041] 2. High precision: Through the reverse solution method, this algorithm can significantly eliminate the errors caused by base station installation errors, improve the base station coordinate accuracy to an extremely high level, and thus improve the performance and reliability of the entire positioning system.

[0042] 3. Portability: The present invention does not require external calibration equipment and only needs to provide a preliminary estimate to perform high-precision solution. This simple deployment process not only reduces costs but also increases the portability of the system, making it easy to operate and apply in various environments. Description of the Drawings

[0043] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the embodiments. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0044] The drawings forming a part of this application are used to provide a further understanding of this application. The schematic embodiments of this application and their descriptions are used to explain this application and do not constitute an improper limitation of this application. In the drawings:

[0045] Figure 1 is a method diagram for reverse calculation of UWB base station coordinates based on TDOA provided by an embodiment of the present invention;

[0046] Figure 2 is the horizontal direction UWB base station coordinate calculation result and test trajectory for reverse calculation of UWB base station coordinates based on TODA provided by an embodiment of the present invention;

[0047] Figure 3The vertical coordinate calculation result of the UWB base station for the reverse calculation of the UWB base station coordinates based on TODA provided by the embodiments of the present invention. Detailed implementation manners

[0048] The various exemplary implementation manners of the present invention will now be described in detail. This detailed description should not be considered as a limitation of the present invention, but rather as a more detailed description of certain aspects, features, and implementation schemes of the present invention.

[0049] It should be understood that the terms used in the present invention are only for describing particular implementation manners and are not used to limit the present invention. Additionally, for the numerical ranges in the present invention, it should be understood that each intermediate value between the upper and lower limits of the range is also specifically disclosed. Each intermediate value within any stated value or stated range, as well as each smaller range between any other stated value or intermediate value within the stated range, is also included in the present invention. The upper and lower limits of these smaller ranges may be independently included or excluded from the range.

[0050] Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those of ordinary skill in the art to which the present invention pertains. Although the present invention only describes preferred methods, any method similar or equivalent to those described herein may also be used in the implementation or testing of the present invention. All documents mentioned in this specification are incorporated by reference to disclose and describe the methods related to the documents. In case of conflict with any incorporated document, the content of this specification shall prevail.

[0051] Without departing from the scope or spirit of the present invention, various improvements and changes can be made to the specific implementation manners of the specification of the present invention, which are obvious to those skilled in the art. Other implementation manners obtained from the specification of the present invention are obvious to those skilled in the art. The specification and embodiments of this application are merely exemplary.

[0052] Regarding the terms "comprising", "including", "having", "containing", etc. used herein, they are all open-ended terms, meaning including but not limited to.

[0053] It should be noted that, without conflict, the embodiments in this application and the features in the embodiments can be combined with each other. The following will refer to the drawings and combine the embodiments to detail this application.

[0054] Such as Figure 1 - Figure 3As shown in the figure, in this embodiment, a method for inverse calculation of UWB base station coordinates based on TDOA is provided, including: obtaining the positioning point coordinates of each positioning terminal and the distance difference data between the positioning terminal and multiple base stations at each positioning point; estimating the initial base station position based on the positioning point coordinates and the distance difference data; for each positioning point, establishing a hyperbolic equation of the positioning point and the base station coordinates according to the corresponding positioning point coordinates and the measured base station distance difference information; based on the initial base station position, iteratively solving the non-hyperbolic equation by using the least squares method in combination with the Jacobian matrix and the residual matrix until the iteration stops when the preset termination condition is reached, and outputting the final base station position.

[0055] This embodiment discloses a method for inverse calculation of UWB base station coordinates based on TDOA, belonging to the field of positioning technology, and is used to achieve high-precision positioning when the base station position is unknown or there is a deviation. The method includes the following steps: collecting positioning point coordinates and time difference of arrival (TDOA) data between the positioning point and multiple base stations through terminal devices; setting the initial estimated coordinates of the base station according to the positioning point coordinates and TDOA data, and setting the error tolerance and iteration number limit; constructing a non-linear equation system with the distance difference as a variable, and performing iterative optimization by using the least squares method in combination with the Jacobian matrix and the residual matrix to gradually update the base station coordinates; finally, outputting the optimized base station coordinates. This method can quickly and real-time calculate the base station coordinates with high precision in a dynamic environment, significantly improve the accuracy and reliability of the positioning system, simplify the system deployment, and reduce costs. This embodiment is applicable to fields such as indoor and outdoor positioning, robot navigation, and intelligent logistics.

[0056] This embodiment provides a method for inverse calculation of base station coordinates based on UWB technology, which is used to achieve high-precision calculation of the base station position through measurement data and preliminary estimation when the base station coordinates are unknown or there is a deviation, so as to improve the overall performance of the positioning system.

[0057] The specific implementation process of this embodiment includes:

[0058] S1: Data acquisition: Collecting observation data such as the coordinates of multiple positioning points, the time difference of arrival (TDOA) between each positioning point and multiple base stations, the distance between base stations, the signal strength, and the residual error according to a preset trajectory through a pan-source foot-mounted positioning device and UWB tags.

[0059] S2: Setting initial values: Making a preliminary estimation of the base station position according to the terminal positioning point coordinates and TDOA data, and inputting a roughly estimated initial position coordinate of the base station. And setting the iteration termination conditions, including the error tolerance and the maximum number of iterations, etc.

[0060] S3: Construct equations: Based on the coordinates of the positioning points and the base station distance difference information measured at these points, establish a system of non-linear equations with the coordinates of the base stations to be solved as variables. The number of equations in this system is much larger than the number of unknown base stations to improve the robustness of the algorithm.

[0061] S4: Coordinate calculation: Based on the initial values of the base station coordinates, use the least squares method combined with the Jacobian matrix and the residual matrix to iteratively optimize the system of non-linear equations, and gradually update the base station coordinates until the set calculation accuracy is reached.

[0062] Further, in the step S1, it includes:

[0063] S1-1: The pan-source foot-mounted device collects its own positioning coordinate information; the UWB positioning tag receives the ranging information sent by the base station and extracts the base station distance difference (TDOA) information.

[0064] Further, in the step S2, it includes:

[0065] For the detailed estimation process in the initial value setting stage, the initial position of the base station can be preliminarily estimated using geometric methods based on the terminal positioning point coordinates and TDOA data. Assuming the relative distance differences between multiple positioning points and the base station, the initial position of the base station can be estimated by the weighted average method:

[0066]

[0067] Among them, (x i , y i , z i ) represents the positioning point coordinates, (x 1 , y 1 , z 1 ) represents the coordinates of base station 1, (x 2 , y 2 , z 2 ) represents the coordinates of base station 2, ∑() represents the summation function, and N represents the number of positioning points.

[0068] Further, in the step S3, it includes:

[0069] S3-1: Based on the TDOA positioning method in UWB positioning, establish the hyperbolic equation of the positioning point and the base station coordinates as follows:

[0070]

[0071] Further, construct the objective optimization function f(x) as follows:

[0072]

[0073] Among them, (x i , y i,z i ) represents the coordinates of the positioning point i, (x 1 ,y 1 ,z 1 ) represents the coordinates of base station 1, (x 2 ,y 2 ,z 2 ) represents the coordinates of base station 2, L i represents the distance difference between the positioning point i and base stations 1 and 2.

[0074] Further, in step S4, it includes:

[0075] S4-1: Use the Taylor series expansion method to linearize the non-linear part of the distance difference. For each known positioning point, perform a first-order Taylor expansion on the distance to obtain:

[0076]

[0077] Rewrite it in matrix form:

[0078] Hδ = Δf + ε #(4)

[0079] Among them,

[0080]

[0081] Among them, H is the Jacobian matrix, δ is the base station coordinate increment vector, Δf is the residual vector, ε is the noise error vector, d 1 ,d 2 are the distances from the positioning point to base stations 1 and 2, n is the total number of hyperbola equations, m is the number of base stations to be solved, and j and k are the labels of the base stations to be solved in the equation. The equation can be simplified to:

[0082] δ = (H T H) -1 H T Δf #(9)

[0083] By updating the solution of the base station coordinates with the calculation result, we can obtain:

[0084] x (t+1) = x (t ) + δ #(10)

[0085] That is, the base station coordinates can be iteratively solved. Among them, x (t+1) is the updated base station position, and x (t) is the initial base station position.

[0086] This embodiment exhibits the following significant advantages:

[0087] 1. Flexible speed: Based on the least squares non-linear optimization method, this embodiment can achieve real-time and rapid calculation in a dynamic environment, greatly shortening the time required for positioning and being able to flexibly adapt to a variety of application scenarios.

[0088] 2. High precision: Through the reverse calculation method, this algorithm can significantly eliminate the errors caused by the installation errors of the base stations, improving the coordinate accuracy of the base stations to an extremely high level, thereby enhancing the performance and reliability of the entire positioning system.

[0089] 3. Portability: This embodiment does not need to rely on external calibration equipment and only needs to provide a preliminary estimate to perform high-precision calculation. This simple deployment process not only reduces costs but also increases the portability of the system, making it easy to operate and apply in various environments.

[0090] This embodiment also provides a reverse calculation system for UWB base station coordinates based on TDOA. The system includes a general source foot-mounted device positioning unit, a UWB ranging unit, a base station calculation unit, etc.

[0091] Figure 2 and Figure 3 are respectively schematic diagrams of the calculation results of the reverse calculation method for UWB base station coordinates based on TODA provided by this embodiment in the horizontal and elevation directions. Table 1 is a chart for the error comparison and analysis of the reverse calculation results provided by this embodiment.

[0092] Table 1 Error Comparison and Analysis of Reverse Calculation Results for UWB Base Station Coordinates Based on TODA

[0093]

[0094] As can be seen from Table 1, the base station reverse calculation method proposed in this embodiment can achieve higher positioning accuracy and usability. In the three-axis directions, the method proposed in this embodiment can provide a positioning accuracy better than 1 meter, which reflects the robustness and reliability of this embodiment in performing reverse calculation when the base station coordinates are unknown.

[0095] The above is only a preferred specific embodiment of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by those skilled in the art within the technical scope disclosed in the present application should be covered by the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A UWB base station coordinate inverse solution method based on TDOA, characterized in that: include: Obtaining the coordinates of the positioning points of each positioning terminal and the distance difference data between the positioning terminal and multiple base stations at each positioning point; estimating an initial base station position based on the positioning point coordinates and the distance difference data; For each positioning point, a hyperbolic equation of the positioning point and base station coordinates is established according to the corresponding positioning point coordinates and the measured base station distance difference information; Based on the initial base station position, the non-hyperbolic equation is iteratively solved according to the least squares method in combination with the Jacobian matrix and the residual matrix, until the iteration is stopped when a preset termination condition is reached, and the final base station position is output.

2. The method for inversely calculating the coordinates of a UWB base station based on TDOA according to claim 1, characterized in that: The obtaining of the positioning point coordinates of each positioning terminal and the distance difference data between the positioning terminal and the multiple base stations at each positioning point specifically includes: Move the positioning terminal according to the preset trajectory, and collect positioning coordinate information during the movement to obtain the positioning point coordinates; The UWB positioning tag is used to receive the distance measurement information sent by the base station, and the distance difference information between the base station and the positioning point is extracted based on the distance measurement information.

3. The method for inversely calculating the coordinates of a UWB base station based on TDOA according to claim 2, characterized in that: The positioning terminal adopts the Panyuan foot positioning device.

4. The method for inversely calculating the coordinates of a UWB base station based on TDOA according to claim 1, characterized in that: The hyperbolic equation specifically includes: In the formula, x i ,y i 、z i represent the x-axis coordinate, y-axis coordinate and z-axis coordinate of positioning point i respectively, x1, y1, z1 represent the x-axis coordinate, y-axis coordinate and z-axis coordinate of base station 1 respectively, x2, y2, z2 represent the x-axis coordinate, y-axis coordinate and z-axis coordinate of base station 2 respectively, L i Represents the distance difference between positioning point i and base station 1 and base station 2.

5. The method for inversely calculating coordinates of a UWB base station based on TDOA according to claim 1, characterized in that: The iterative solution of the non-hyperbolic equation according to the least squares method in combination with the Jacobian matrix and the residual matrix specifically includes: Construct the target optimization function based on the hyperbolic equation of each positioning point; For each known positioning point, the nonlinear part of the distance difference is expanded by the first order Taylor, and the nonlinear equation is approximated as a linearized equation; Rewriting the linearized equation into a matrix equation; Solving the matrix equation based on the least square method to obtain a base station coordinate increment; updating the initial base station position based on the base station coordinate increment to obtain an updated base station position; Check whether the iteration termination condition is met. If the error tolerance is less than the set value or the maximum number of iterations is reached, stop the iteration and output the final base station position; otherwise, continue to the next iteration.

6. The method for inversely calculating the coordinates of a UWB base station based on TDOA according to claim 5, characterized in that: The target optimization function is specifically: In the formula, f i (.) is the target optimization function, x i ,y i 、z i represent the x-axis coordinate, y-axis coordinate and z-axis coordinate of positioning point i respectively, x1, y1, z1 represent the x-axis coordinate, y-axis coordinate and z-axis coordinate of base station 1 respectively, x2, y2, z2 represent the x-axis coordinate, y-axis coordinate and z-axis coordinate of base station 2 respectively, L i Represents the distance difference between positioning point i and base station 1 and base station 2.

7. The method for inversely calculating the coordinates of a UWB base station based on TDOA according to claim 5, characterized in that: The nonlinear part of the distance difference is subjected to first-order Taylor expansion, and the specific calculation formula is: Where δ is the base station coordinate increment vector, x1, y1, z1 represent the x-axis coordinate, y-axis coordinate and z-axis coordinate of base station 1 respectively, x2, y2, z2 represent the x-axis coordinate, y-axis coordinate and z-axis coordinate of base station 2 respectively, L i represents the distance difference between positioning point i and base station 1 and base station 2, ε i is the noise error vector, f i,v is the target optimization function, a i,1 .......a i,6 These parameters are used to represent the correction items in the base station location update process.

8. The method for inversely calculating the coordinates of a UWB base station based on TDOA according to claim 5, characterized in that: The solving the matrix equation based on the least squares method specifically includes: Rewrite the linearized equation as a matrix equation: Hδ=Δf+ε Where H is the Jacobian matrix, δ is the base station coordinate increment vector, Δf is the residual vector, and ε is the noise error vector; Incremental solution of base station coordinates: δ=(H T H) -1 H T Δf In the formula, H T is the transpose of the matrix H; Update the initial base station position based on the base station coordinate increment: x (t+1) =x (t) +δ In the formula, x (t+1) is the updated base station position, x (t) is the initial base station position.

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