A method for positioning a UAV based on TDOA

Abstract

This invention belongs to the field of wireless signal processing technology and provides a UAV positioning method based on TDOA, including: deploying a UAV swarm, establishing communication links between lead UAVs and between lead UAVs and target wingmen; wherein the UAV swarm is divided into several sub-swarms, each sub-swarm including a target wingman, a reference lead UAV, and an auxiliary lead UAV; establishing a coordinate system with the reference lead UAV as the origin; constructing a TDOA equation for obtaining the coordinate vector of the target wingman; solving the TDOA equation to obtain the solution coordinates; filtering out invalid solution coordinates based on a preset error threshold, and retaining the solution coordinates as valid positioning data; averaging the positioning data obtained multiple times, which is the final positioning result of the target wingman. The method provided by this invention for solving the position of UAVs can reduce computation time and does not require prior knowledge of the target state, thus having broad application prospects.

Description

Technical Field

[0001] This invention relates to the field of wireless signal processing technology, and more specifically to a UAV positioning method based on TDOA. Background Technology

[0002] The basic positioning technologies for unmanned aerial vehicles (UAVs) can be divided into two methods: active positioning and passive positioning. Passive positioning systems are popular due to their minimal equipment requirements and high adaptability. Passive positioning systems involve various computational mathematical logics, including Angle of Arrival (AOA), Time of Arrival (TOA), Time Difference of Arrival (TDOA), and Received Signal Strength (RSS). Because TDOA positioning technology can achieve high-precision positioning without strict time synchronization between the target and the positioning-dominant UAV, it is widely used.

[0003] TDOA positioning, also known as hyperbolic positioning, is achieved through solving nonlinear positioning problems. Essentially, it's a method of combining target coordinate parameters with known base station coordinate parameters to formulate equations, requiring additional solution methods to obtain the final positioning result. Extensive research has been conducted on TDOA-based 3D positioning algorithms. Notable basic methods include the Taylor series method and the Chan method. The Taylor series method offers high accuracy, but as an analytical method, it requires complex calculations and may encounter matrix singularity problems in some cases, potentially leading to computational time explosion. Furthermore, the positioning accuracy of the Taylor series method depends heavily on the initial set of estimated positions, which is closely related to the result; without prior information, the accuracy will significantly decrease. Additionally, the Chan method requires at least two weighted least squares processes to guarantee computational accuracy, indicating performance limitations, especially with only four anchor points. Meanwhile, both the Taylor series method and the Chan method are essentially analytical methods with complex algorithm design structures. Their positioning accuracy largely depends on algorithm parameters set based on prior knowledge, and their computation time is also high.

[0004] Therefore, it is essential to study a feasible method to simplify the implementation steps of the solution algorithm, avoid errors caused by setting incorrect parameters due to lack of prior knowledge, and reduce the algorithm's computational cost. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a UAV positioning method based on TDOA to solve the current needs.

[0006] This invention provides a UAV positioning method based on TDOA, comprising:

[0007] Deploy a drone swarm and establish communication links between lead drones and between lead drones and target wingmen; the drone swarm is divided into several sub-swarms, each sub-swarm including the target wingmen, a base lead drone, and an auxiliary lead drone;

[0008] Establish a coordinate system with the reference long machine as the origin;

[0009] Construct the TDOA equation for obtaining the coordinate vector of the target wingman;

[0010] Solve the TDOA equation to obtain the solution coordinates;

[0011] Invalid solution coordinates are filtered out based on a preset error threshold, and the remaining solution coordinates are the valid positioning data.

[0012] The final location result of the target wingman is obtained by averaging the location data obtained from multiple tests.

[0013] Optionally, establishing a coordinate system with the reference long machine as the origin includes:

[0014] Based on the coordinate vector of the reference long machine Determine the coordinates of the auxiliary lead machine; the line connecting one auxiliary lead machine to the reference lead machine is set as the z-axis, and the other auxiliary lead machine is set on the yoz plane. Then the coordinate vectors of the auxiliary lead machines are respectively... , and .

[0015] Optionally, a TDOA equation for obtaining the target wingman's coordinate vector is constructed, including:

[0016] The communication delays between the target wingman, the base wingman, and each auxiliary wingman were obtained through multiple communications. Calculate the distances between the target wingman and each lead aircraft. , C is the speed of light 3 × 10⁻⁶ 8 m / s;

[0017] Obtain the distance differences between the target wingman and the baseline leader, as well as between the target wingman and each auxiliary leader. , , The distance between the target wingman and the baseline lead aircraft. The arrival time difference between the lead aircraft and the auxiliary lead aircraft;

[0018] Based on distance difference Construct the TDOA equation.

[0019] Optionally, the constructed TDOA equation is:

[0020] ,

[0021] Converted to linear algebraic expression as

[0022] ;

[0023] in, ; Indicates the wingman to the subgroup's baseline leader. Distance and to each auxiliary lead aircraft The difference in distance, For the reason The vector formed To make vector The vector formed by squaring all elements in; Let L2 be the coordinate parameter vector of each lead aircraft. ; For all the long-range coordinate vectors The matrix formed; For the wingman's position, among which These are the coordinate parameters of the target wingman on the x, y, and z axes, respectively; Let L be the L2 norm of the wingman's coordinate parameter vector. This represents the L2 norm.

[0024] Optionally, before solving the TDOA equation, the method further includes eliminating... Obtain the equation ;

[0025] in, pass disappear, For the reason The vector formed To assist the difference between the L2 norm of the traverse aircraft coordinate vector and the L2 norm of the reference traverse aircraft coordinate vector, i=2,3,4, that is... , ; For the reason The matrix formed To assist in finding the difference between the lead aircraft's coordinate vector and the reference lead aircraft's coordinate vector, i = 2, 3, 4, i.e. and .

[0026] Optionally, the method for solving the TDOA equation includes:

[0027] The coordinate vector of the target wingman Represented as Where g, h, k, and l are coefficients, respectively denoted as:

[0028] ,

[0029] ,

[0030] ,

[0031] ;

[0032] Will and about Substitute the equation back into the equation Get about The quadratic equation of Where a, b, and c are coefficients, respectively denoted as...

[0033] ,

[0034] ,

[0035] ;

[0036] By solving the equations To obtain the location data of the target wingman.

[0037] Optionally, invalid data can be filtered out based on a preset error threshold, specifically:

[0038] Discriminant based on the roots of the equation Determine the number of solutions to the equation;

[0039] When D≥0, the error threshold is passed. Valid location data must be filtered out; otherwise, valid location data cannot be calculated.

[0040] Optionally, if D≥0, pass the error threshold. Filter out valid location data, including:

[0041] If D>0:

[0042] Obtain the equation Two solution coordinates and ;

[0043] Obtain the distances from the two solution coordinates to the reference long machine. , ;

[0044] like and ,but For valid location data; if and ,but For valid location data;

[0045] If D=0:

[0046] Obtain the equation A solution coordinate ;

[0047] Obtain the distance from the solution coordinates to the reference long machine. , ;

[0048] like ,but For effective location data.

[0049] Optionally, averaging the multiple obtained positioning data includes:

[0050] If the number of positioning attempts k is not less than the preset loop threshold, the average value of the multiple positioning data will be taken; otherwise, the TDOA equation for obtaining the coordinate vector of the target wingman will be reconstructed and solved.

[0051] By adopting the above technical solution, this application has the following beneficial effects:

[0052] The method provided by this invention for solving the position of a UAV can reduce computation time and does not require prior knowledge of the target state, thus having broad application prospects. This invention also ensures the robustness of the positioning results through noise filtering. Attached Figure Description

[0053] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the accompanying drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. In all the drawings, similar elements or parts are generally identified by similar reference numerals. In the drawings, the elements or parts are not necessarily drawn to scale.

[0054] Figure 1 A flowchart of a UAV positioning method based on TDOA provided by an embodiment of the present invention is shown;

[0055] Figure 2 A schematic diagram of the communication link constructed in step S1 according to an embodiment of the present invention is shown;

[0056] Figure 3 A comparison diagram is shown between the final positioning result determined by the method provided in the embodiments of the present invention and the actual location;

[0057] Figure 4 The diagram shows a comparison of the localization results of the method provided in this embodiment of the invention under different noise intensities and existing methods;

[0058] Figure 5A comparison chart of the running time of the method provided in the embodiments of the present invention and existing methods is shown. Detailed Implementation

[0059] The embodiments of the technical solution of the present invention will now be described in detail with reference to the accompanying drawings. These embodiments are only used to more clearly illustrate the technical solution of the present invention and are therefore merely examples, and should not be construed as limiting the scope of protection of the present invention.

[0060] It should be noted that, unless otherwise stated, the technical or scientific terms used in this application should have the ordinary meaning as understood by one of ordinary skill in the art to which this invention pertains.

[0061] This embodiment provides a UAV positioning method based on TDOA, such as Figure 1 As shown, it includes:

[0062] S1. Deploy a swarm of drones and establish communication links between the lead drones and between the lead drones and the target wingmen.

[0063] Specifically, in this embodiment, the drone swarm is divided into several subgroups, each subgroup comprising four lead drones: one base lead drone and three auxiliary lead drones. The fixed positions of the lead drones are... , ;in These represent the coordinate parameters of the lead aircraft on the x, y, and z axes, respectively. Lowercase letters in bold indicate vectors. For example... Figure 2 As shown, target wingmen are assigned to each subgroup as close as possible, and communication links are formed between the lead aircraft and between the lead aircraft and the wingmen.

[0064] S2. Establish a coordinate system with the reference long machine as the origin.

[0065] Specifically, the coordinates of the reference long machine are set as the origin of the coordinate system. If one of the auxiliary lead machines is positioned on the z-axis of the three-dimensional coordinate system, then its coordinates are... If the other auxiliary lead aircraft is set on the yoz plane, then its coordinates are... The coordinates of the last auxiliary lead aircraft are At this time, the target wingman's position is , .

[0066] S3. Construct the TDOA equation for obtaining the target wingman's coordinate vector. This includes the following steps:

[0067] S301. Obtain the communication delay between the target wingman, the base wingman, and each auxiliary wingman through multiple communications. Calculate the distances between the target wingman and each lead aircraft. ,

[0068] ,

[0069] Where C is the speed of light 3 × 10⁻⁶ 8 m / s.

[0070] S302. Obtain the distance differences between the target wingman and the reference lead aircraft, and between the target wingman and each auxiliary lead aircraft. ,

[0071] ,

[0072] Thus, the equation is obtained.

[0073] ,

[0074] The distance between the target wingman and the baseline lead aircraft. This represents the arrival time difference between the lead aircraft and the auxiliary lead aircraft.

[0075] S303. Based on distance difference Construct the TDOA equation.

[0076] Then it is converted into a linear algebraic expression, and taken... It can be obtained

[0077]

[0078] In the formula, This indicates the distance from the target wingman to each lead aircraft within the subgroup. ; Indicates the distance from the target wingman to the subgroup's baseline leader. Distance and to each auxiliary lead aircraft The difference in distance, For the reason The vector formed To make vector The vector formed by squaring all elements in; Let L2 be the coordinate parameter vector of each lead aircraft. ; For all the long-range coordinate vectors The matrix formed; For the wingman's position, among which These are the coordinate parameters of the target wingman on the x, y, and z axes, respectively; Let L be the L2 norm of the wingman's coordinate parameter vector. This represents the L2 norm.

[0079] In the above formula Thus eliminating To obtain a new equation

[0080]

[0081] In the formula, For the reason The vector formed To assist the difference between the L2 norm of the traverse aircraft coordinate vector and the L2 norm of the reference traverse aircraft coordinate vector, i=2,3,4, that is... , ; For the reason The matrix formed To assist in finding the difference between the lead aircraft's coordinate vector and the reference lead aircraft's coordinate vector, i = 2, 3, 4, i.e. and .

[0082] In this step, the coordinates of the three auxiliary lead aircraft have been determined. , and It can be substituted into a new system of equations.

[0083] S4. Solve the TDOA equation to obtain the solution coordinates.

[0084] The target wingman's coordinate parameters Represented as

[0085]

[0086] In the formula, g, h, k, and l are all coefficients, which can be expressed as follows:

[0087] ,

[0088] ,

[0089] ,

[0090] ;

[0091] Will and about Substitution back to equation Get about The quadratic equation of Where a, b, and c are coefficients, respectively denoted as...

[0092] ,

[0093] ,

[0094] ;

[0095] By solving the equations Obtain the solution coordinates of the target wingman.

[0096] S5. Filter out invalid positioning data based on a preset error threshold and retain valid positioning data.

[0097] In this step, an error threshold is introduced. and the discriminant value D for the equation The solution is used to filter out noise.

[0098] According to the discriminant of a quadratic equation Determine the number of roots.

[0099] (1)

[0100] By the discriminant property of a quadratic equation, we know that the equation has two solutions. Therefore, we will obtain two sets of solutions. and This step also presents a method for selecting a solution. Previously, based on arrival time... The distance from the target to the baseline long-range aircraft was calculated as follows:

[0101] ,

[0102] In addition, the coordinates of the reference long machine are preset in step S2. Therefore, the distances from the two sets of coordinate solutions above to the reference long-range aircraft can be obtained. :

[0103]

[0104] Based on this, an error threshold is further given. Used to filter out noise solutions, specifically including the following three cases.

[0105] Case 1: If satisfied ,Right now and Then choose This serves as the location data obtained in this step.

[0106] Case 2: If satisfied ,Right now and Then choose This serves as the location data obtained in this step.

[0107] Case 3: If neither Case 1 nor Case 2 can be satisfied, then the localization solution is considered to have failed. This serves as the location data obtained in this step.

[0108] (2)

[0109] By the discriminant property of a quadratic equation, we know that the equation has only one solution in this case. Then, the solution is... This refers to the location data obtained in this step; otherwise, This serves as the location data obtained in this step.

[0110] (3)

[0111] The equation has two complex solutions, but our positioning coordinates cannot be complex. Therefore, we consider this solution to be a failure and... This serves as the location data obtained in this step.

[0112] S6. Take the average of the multiple location data obtained, which is the final location result of the target wingman.

[0113] The method of averaging multiple location data includes: when the number of location attempts k is not less than a preset loop threshold, the average of multiple location data will be taken.

[0114] Otherwise, return to step S3, reconstruct the equation, and solve it. In this case, increment the positioning count k by 1. Continue this process until the positioning count is not less than the loop threshold. Then, average the positioning data obtained from multiple iterations to ensure the robustness of the positioning data.

[0115] The following verifies the UAV positioning method provided in this embodiment:

[0116] Set the helm aircraft's coordinate position to coordinates. , , and Additional variance is Three different intensities of Gaussian white noise, corresponding to the selected error thresholds are respectively Simulation was performed. The results are as follows: Figure 3 As shown, the target location estimated by this method basically coincides with the actual target location, demonstrating the effectiveness and robustness of this method.

[0117] To compare the accuracy of the localization results with existing algorithms, the root mean square error (RMSE) is introduced as an indicator to evaluate the localization results obtained based on the method provided in this embodiment. Figure 4 As shown, it can be seen that the algorithm proposed in this invention is significantly better than the TDOA algorithm based on the Chan method and can approximate the TDOA algorithm based on the Taylor method.

[0118] To compare the computational efficiency with existing algorithms, time is introduced as a metric, such as... Figure 5The method shown in this embodiment is significantly faster than traditional methods and can completely avoid the problem of time explosion.

[0119] The above embodiments are only used to provide a detailed description of the technical solutions of this application. However, the descriptions of the above embodiments are only for the purpose of helping to understand the methods of the embodiments of the present invention and should not be construed as limiting the embodiments of the present invention. Any variations or substitutions that can be easily conceived by those skilled in the art should be covered within the protection scope of the embodiments of the present invention.

Claims

1. A UAV positioning method based on TDOA, characterized in that, include: Deploy drone swarms and establish communication links between lead drones and between lead drones and target wingmen; The drone swarm is divided into several subgroups, each of which includes a target wingman, a base wingman, and an auxiliary wingman. Establish a coordinate system with the reference long machine as the origin; Construct the TDOA equation for obtaining the target wingman's coordinate vector; including: The communication delays between the target wingman, the base wingman, and each auxiliary wingman were obtained through multiple communications. Calculate the distances between the target wingman and each lead aircraft. , C is the speed of light 3 × 10⁻⁶ 8 m / s; Obtain the distance differences between the target wingman and the baseline leader, as well as between the target wingman and each auxiliary leader. , , The distance between the target wingman and the baseline lead aircraft. The arrival time difference between the lead aircraft and the auxiliary lead aircraft; Based on distance difference Construct the TDOA equation; the constructed TDOA equation is as follows: ， Converted to linear algebraic expression as ； in, ; Indicates the wingman to the subgroup's baseline leader. Distance and to each auxiliary lead aircraft The difference in distance, For the reason The vector formed To make vector The vector formed by squaring all elements in; Let L2 be the coordinate parameter vector of each lead aircraft. ; For all the long-range coordinate vectors The matrix formed; For the wingman's position, among which These are the coordinate parameters of the target wingman on the x, y, and z axes, respectively; Let L be the L2 norm of the wingman's coordinate parameter vector. Represents the L2 norm; Before solving the TDOA equation, the process also includes elimination. Obtain the equation ; in, pass disappear, For the reason The vector formed To assist the difference between the L2 norm of the traverse aircraft coordinate vector and the L2 norm of the reference traverse aircraft coordinate vector, i=2,3,4, that is... , ; For the reason The matrix formed To assist in finding the difference between the lead aircraft's coordinate vector and the reference lead aircraft's coordinate vector, i = 2, 3, 4, i.e. and ; Solve the TDOA equation to obtain the solution coordinates; the method for solving the TDOA equation includes: The coordinate vector of the target wingman Represented as Where g, h, k, and l are coefficients, respectively denoted as: ， ， ， ； Will and about Substitute the equation back into the equation Get about The quadratic equation of Where a, b, and c are coefficients, respectively denoted as... ， ， ； By solving the equations To obtain the location data of the target wingman; Invalid solution coordinates are filtered out based on a preset error threshold, and the remaining solution coordinates are the valid positioning data; The final location result of the target wingman is obtained by averaging the location data obtained from multiple tests.

2. The method according to claim 1, characterized in that, The establishment of a coordinate system with the reference long machine as the origin includes: Based on the coordinate vector of the reference long machine Determine the coordinates of the auxiliary lead machine; the line connecting one auxiliary lead machine to the reference lead machine is set as the z-axis, and the other auxiliary lead machine is set on the yoz plane. Then the coordinate vectors of the auxiliary lead machines are respectively... , and .

3. The method according to claim 2, characterized in that, Invalid data is filtered out based on a preset error threshold, specifically as follows: Discriminant based on the roots of the equation Determine the number of solutions to the equation; When D≥0, the error threshold is passed. Valid location data must be filtered out; otherwise, valid location data cannot be calculated.

4. The method according to claim 3, characterized in that, If D≥0, pass the error threshold. Filter out valid location data, including: If D>0: Obtain the equation Two solution coordinates and ; Obtain the distances from the two solution coordinates to the reference long machine. , ; like and ,but For valid location data; if and ,but For valid location data; If D=0: Obtain the equation A solution coordinate ; Obtain the distance from the solution coordinates to the reference long machine. , ; like ,but For effective location data.

5. The method according to claim 2, characterized in that, The step of averaging the location data obtained multiple times includes: If the number of positioning attempts k is not less than the preset loop threshold, the average value of the positioning data obtained from multiple attempts will be taken; otherwise, the TDOA equation for obtaining the coordinate vector of the target wingman will be reconstructed and solved.

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