A cooperative positioning method fusing land-based navigation and inter-aircraft ranging information

Abstract

The application belongs to the technical field of target positioning, and particularly relates to a cooperative positioning method in a satellite denial environment by fusing land-based navigation and inter-aircraft ranging. The method is mainly applied to cooperative positioning of a UAV group, especially in an environment where satellite signals are blocked or interfered. The scheme of the application is that multiple base stations provide angle of arrival (AOA) and time of arrival (TOA) measurement data, and at the same time, relative distance measurement data between UAVs is combined, a multidimensional scaling (MDS) algorithm and a Procrustes analysis are used to globally optimize the positions of the UAVs. The application not only improves positioning accuracy, but also enhances the robustness and real-time performance of the system, and is particularly suitable for the positioning requirements of a UAV group in a complex environment. The method provides an efficient and reliable solution for high-precision cooperative positioning of a UAV group in a satellite denial environment, and has a wide application prospect.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of target positioning, and particularly relates to a cooperative positioning algorithm of an unmanned aerial vehicle (UAV) fusing land-based navigation and inter-aircraft ranging information under satellite navigation denial conditions. BACKGROUND

[0002] With the rapid development of UAV technology, UAV group cooperation has been widely applied in many fields, such as environmental monitoring, disaster rescue, military reconnaissance, etc. The cooperative positioning technology of UAV group is particularly important in the environment lacking GPS or satellite signal interference. In order to achieve high-precision positioning, many studies based on the measurement guidance information of ground base stations realize the positioning of UAV. Such methods have achieved certain research results, but there are still some key technical bottlenecks:

[0003] (1) The positioning method based on land-based guidance often faces the influence of noise and measurement error. In actual application, due to the sensor precision, environmental complexity and uncertainty of transmission signal, there is a certain error in the land-based measurement value under the condition of long-distance measurement. These errors will cause the deviation of the positioning result, especially in the positioning scene of multiple base stations and multiple UAVs, the error may be amplified, affecting the positioning accuracy.

[0004] (2) The cooperation among UAVs is not fully utilized. The existing technology often only focuses on the measurement data between a single UAV and a base station when positioning the UAV group. Although the relative distance information among the UAV group can be exchanged to improve the positioning accuracy, the existing positioning algorithm usually fails to fully utilize these cooperative information, resulting in that the positioning accuracy of the system is not effectively improved.

[0005] Therefore, although the positioning method based on land-based guidance information under satellite denial environment has made certain progress in some occasions, the existing research has not fully utilized the cooperative information among the UAV group to improve the positioning accuracy. SUMMARY

[0006] In view of the above problems, the application provides a cooperative positioning method using MDS (Multidimensional Scaling) algorithm and Procrustes analysis. By comprehensively considering the AOA and TOA measurement information of the land-based base station and the relative distance data among the UAVs, the MDS algorithm and Procrustes analysis are used to optimize the positioning result, so as to significantly improve the positioning accuracy under the satellite denial environment. Through this method, the influence of measurement error on the positioning accuracy can be effectively reduced, and the cooperative information among the UAV group is utilized to improve the positioning accuracy and system robustness. The method not only improves the positioning accuracy, but also reduces the computational complexity, has higher real-time performance and adaptability.

[0007] The technical scheme adopted by the application is as follows:

[0008] A cooperative positioning method fusing land-based navigation and inter-UAV ranging information, the positioning system comprising a base station and unmanned aerial vehicles (UAVs), the position of the base station is set as bs=(x0, y0), the initial position of the UAVs is set as ms=(x0, y0), and the velocity of the UAVs is set as V=(v0, v0) i i i i xi yi The cooperative positioning method comprises the following steps:

[0009] S1, at each time, the base station measures the UAVs multiple times to obtain the distance between the base station and the UAVs and the angle The inter-UAV ranging information is obtained by simultaneously measuring the distance between the UAVs wherein the superscript m represents a measurement value, j represents the jth measurement, the total number of measurements is defined as M, and the interval time of each measurement is T;

[0010] S2, the measurement data of the base station is used to preliminarily estimate the position of the UAVs, and the linear equation of the measurement information between the base station and the UAVs is defined as:

[0011] G toa YZ0=Y toa ,G aoa YZ0=Y aoa

[0012] wherein Z0 is a position estimation vector, G toa and G aoa are matrices related to TOA and AOA measurements respectively, Y toa and Y aoa are corresponding measurement results, the total number of UAVs is i, the total number of measurement points is M, and the measurement time at each time is represented by j;

[0013] The parameter form of the linear equation is as follows:

[0014] G j_toa =[G T 1j_toa …G T ij_toa ] T

[0015] G ij_TOA =[-2x0 -2y0 -2x0(j-1)T -2y0(j-1)T 1 ((j-1)T) 2 2(j-1)T]

[0016] Y j =[Y​​​​​T ij_toa …Y T ij_toa ] T ,

[0017] G j =[G T 1j_aoa …G T ij_aoa ] T

[0018] Y j =[Y T ij_aoa …Y T ij_aoa ] T ,

[0019] Through the least square method, the preliminary position estimation is performed, and G = [G toa ; G aoa ], Y = [Y toa ; Y aoa ]:

[0020] Z0 = (G T G) -1 G T Y

[0021] S3, using inter-aircraft ranging information to position the unmanned aerial vehicle:

[0022] Define the number of unmanned aerial vehicles as n, and obtain the distance square matrix D from the measured inter-aircraft ranging information:

[0023]

[0024] Construct the centralized matrix J:

[0025]

[0026] Where I n is an n x n identity matrix, and 1 n is an n x 1 all-one column vector;

[0027] Construct the inner product matrix B:

[0028]

[0029] Eigenvalue decomposition is performed on the matrix B to obtain the eigenvalue matrix E and the eigenvector matrix V:

[0030] BV = EV

[0031] The eigenvalues are sorted, and the first two largest eigenvalues and their corresponding eigenvectors are selected to calculate the UAV position:

[0032]

[0033] where V(:,1:2) is the first two eigenvectors, is the square root of the first two largest eigenvalues, and the final estimated UAV position Z mds is an n x 2 matrix.

[0034] S4, fuse the preliminary estimated position signal and the UAV position to realize cooperative positioning and obtain the final UAV positioning information, including:

[0035] Z0 obtained in S2 and Z mds are defined as input matrices X and Y, respectively, and X and Y are centered, i.e., the centroid of each matrix is moved to the origin:

[0036]

[0037] X' and Y' are scaled to unit norm, and Y' and X' are scaled to the same scale through a scaling factor so that their norms are equal:

[0038]

[0039] In order to align Y' and X', a rotation matrix T is required to be solved so that the transformed Y' is closest to X'. The matrix T can be calculated by singular value decomposition (SVD):

[0040] First, the auxiliary matrix A is calculated:

[0041] A = X' T Y'

[0042] Then, A is decomposed by SVD:

[0043] A = UΣV T

[0044] where Σ is a diagonal matrix, and U and V are orthogonal matrices. The rotation matrix T is:

[0045] T = VU T

[0046] Using the rotation matrix T, the transformed Y' is closest to X', and the transformed Y is Y'·T, which can obtain the final positioning result Z:

[0047] Z = b·Y'·T + c

[0048] where b is a scaling factor, T is a rotation matrix, and c is a translation vector.

[0049] The beneficial effects of the present application are: the present application significantly improves the positioning accuracy of the UAV group in the satellite denial or signal interference environment by fusing the angle of arrival (AOA) and time of arrival (TOA) information of the base station and the distance measurement data between the UAVs. The short-time multiple measurement model is adopted, the noise characteristics of multiple measurements are combined, the measurement data is optimized, and the influence of measurement error is effectively reduced. The position information of the UAV group is globally optimized by the MDS algorithm and the Procrustes analysis, and the cooperation information between the UAVs is fully utilized, which not only improves the overall positioning accuracy, but also effectively reduces the influence of single UAV measurement error on the system positioning result. In addition, while improving the accuracy, the robustness of the system is also enhanced, so that it can maintain high-precision positioning in complex environments and has stronger adaptability. Overall, the present application improves the calculation efficiency and real-time performance of the positioning system by optimizing the calculation process and algorithm, and can adapt to the cooperative positioning requirements of larger-scale UAV groups. BRIEF DESCRIPTION OF DRAWINGS

[0050] Figure 1 The model diagram of the cooperative positioning method of fusing land-based navigation and inter-aircraft ranging at a certain time;

[0051] Figure 2 The algorithm core flowchart;

[0052] Figure 3 The positioning accuracy of fusing land-based navigation and inter-aircraft ranging under different short-time measurement points. DETAILED DESCRIPTION

[0053] The technical solutions of the present application will be described in detail below in combination with the drawings and examples.

[0054] The present application provides a cooperative positioning method in a satellite denial environment by fusing land-based navigation and inter-aircraft ranging information. The method uses the measurement data of multiple base stations on the UAV, including time of arrival (TOA) and angle of arrival (AOA) information, combined with the relative distance data between the UAVs, and uses the MDS algorithm and Procrustes analysis for global position optimization. By fusing these information, not only accurate positioning can be performed in the satellite denial or interference environment, but also the positioning accuracy can be optimized by multiple measurements, and the robustness and real-time performance of the system can be improved.

[0055] The general implementation steps of the present application are as follows:

[0056] Step 1: Environment parameter setting: set the base station position, UAV quantity, initial position, speed, measurement point quantity and measurement error standard deviation, etc.

[0057] Step 2: Multiple measurement data generation: Multiple measurements of distance and angle between base station and UAV are taken to simulate measurement noise in reality. From these measurement data, noisy distance and angle measurements are generated.

[0058] Step 3: Position estimation: Preliminary estimation of the position of the UAV is made using the AOA and TOA information measured by the base station. Then, combined with the distance measurement data between UAVs, collaborative positioning is performed through the MDS algorithm.

[0059] Step 4: Optimization and evaluation: Prüfer analysis is used to fuse the relative positions between multiple UAVs and land-based information, calculate the positioning results of both, and evaluate them through root mean square error (RMSE).

[0060] Embodiment

[0061] This embodiment uses a Matlab simulation platform for experiments.

[0062] The specific implementation method of the present application is to perform collaborative positioning of the UAV group in a single land-based base station environment, use the AOA, TOA information of the base station and the relative distance information between UAVs, perform multiple measurements and optimize the global position by combining the MDS algorithm.

[0063] In this example, first, the environmental parameters are set, including the base station position and the initial position and speed of the UAV. It is assumed that in a two-dimensional plane, there is 1 base station and 4 UAVs are randomly distributed. The position of the base station is fixed, and the initial position and speed of all UAVs are obtained by random generation.

[0064] Step 1: Environmental parameter setting

[0065] Base station position: Set a base station with a position of coordinate origin bs = [0, 0].

[0066] Initial position and speed of UAV: Randomly generate the initial positions of 4 UAVs, with positions in the range of [1000, 3000], and the speed of each UAV is randomly generated in the range of -15 to 15 meters / second.

[0067] Noise setting: Define the measurement error standard deviation: base station distance measurement error r1 = 2m, angle error θ = 0.1 degrees, and UAV inter-measurement error is

[0068] Step 2: Generate measurement data

[0069] For each drone and base station distance and angle, the system generates distance and angle data by multiple measurements, with a time measurement interval of 0.5s, sets the number of measurements to 3-8 times, and adds Gaussian noise to these data to simulate the actual measurement process. The measurement data is generated by the following steps:

[0070] (1) Real distance and angle calculation:

[0071] The real distance and angle between each drone and the base station at each measurement time are calculated by geometric relationship. The distance is calculated by Euclidean distance:

[0072] r true (t) = ||ms j (t) - bs i ||

[0073] The angle is calculated by the coordinate difference between the base station and the drone:

[0074]

[0075] (2) Noise measurement data generation:

[0076] On the basis of the real measurement value, noise is randomly added to generate noisy measurement data:

[0077] r(t) = r true (t) + ∈ r , θ(t) = θ true (t) + ∈ θ

[0078] where, and represent measurement errors.

[0079] Step 3: Inter-drone distance measurement

[0080] The relative distance between drones is dynamically calculated by its position change. For any pair of drones, the relative distance at each time is calculated, and an error is added:

[0081] d ij (t) = ||ms i (t) - ms j (t) ||

[0082] After adding the error, the noisy relative distance is obtained:

[0083]

[0084] where, is the distance measurement error.

[0085] Step 4: Preliminary Position Estimation

[0086] The position of each drone is estimated using the least squares method based on the AOA and TOA data from the base stations. The distance and angle values for each measurement point form a linear equation, and based on these measurements, the least squares method is used to obtain a preliminary position estimate Z0. The calculated positions are as follows: [2942.9, 2462.4], [1469.1, 1498.9], [2639, 1260.8], [1048.6, 1966.6].

[0087] Step 5: MDS Algorithm for Multi-Drone Relative Position Optimization

[0088] Based on the relative distance information between drones, the MDS algorithm is used to optimize the global positions of the drones. The specific steps are as follows:

[0089] (1) Construct the distance matrix: For each pair of drones ij, the relative position is calculated to construct the distance matrix.

[0090] (2) Perform eigenvalue decomposition: Perform eigenvalue decomposition on the distance matrix to extract the first two largest eigenvalues and the corresponding eigenvectors.

[0091] (3) Position estimation: Based on the largest eigenvalues and eigenvectors, the positions of the drones are estimated. The results are as follows: [-1011.1, 512.16], [593.9, -204.66], [-519.27, -637.03], [936.5, 329.53].

[0092] Step 6: Procrustes Analysis for Absolute Position Solution

[0093] Based on the MDS results of inter-drone ranging and the preliminary positioning results of land-based, through the calculation of centering and rotation matrix, information fusion and position alignment are achieved. The final position estimate is: [2938.1, 2465.6], [1473 1499.3], [2639.7, 1253.9], [1048.9, 1969.9]. This is closest to the simulated true position [2938, 2468.7], [1471.9, 1495.8], [2641.6, 1253.3], [1047.5, 1966.7], and the effect is relatively ideal.

[0094] Accuracy evaluation of the above scheme:

[0095] The positioning accuracy is evaluated by calculating the root mean square error (RMSE) between the estimated position and the true position. The RMSE calculation formula is as follows:

[0096]

[0097] wherein, is the estimated position, ms i is the actual position.

[0098] Based on the above experimental scene setting, by statistically analyzing the experimental results under different measurement point numbers M, the results of 5000 Monte Carlo experiments show that as the measurement point number increases, the positioning accuracy is significantly improved. Especially after adding the inter-aircraft ranging information through the MDS algorithm and the Procrustes analysis algorithm, the positioning accuracy is significantly improved compared with the single-station AOA+TOA method. This embodies the effectiveness of the method of the present application.

Claims

1. A cooperative positioning method of fusing land-based navigation and inter-vehicle ranging information, the positioning system comprising a base station and a UAV, the position of the base station is set as bs = (x0, y0), the initial position of the UAV is ms = (x0, y0), and the velocity of the UAV is V = (v0, v0). i i i i xi yi The cooperative positioning method comprises the following steps: ​​​​​​ S1, at each time, the base station measures the unmanned aerial vehicle multiple times to obtain the distance between the base station and the unmanned aerial vehicle and angle Simultaneously measure the distance between the unmanned aerial vehicles to obtain inter-aircraft ranging information Wherein, the superscript m represents the measurement value, j represents the jth measurement, the total number of measurements is defined as M, and the interval time of each measurement is T. S2, using the measurement data of the base station to preliminarily estimate the position of the unmanned aerial vehicle, defining a linear equation of measurement information between the base station and the unmanned aerial vehicle as: G toa YZ0 = Y toa ,G aoa YZ0 = Y aoa where Z0is the position estimation vector, G toa and G aoa are matrices related to TOA and AOA measurements, respectively, Y toa and Y aoa are the corresponding measurements, i is the total number of UAVs, M is the total number of measurements, and j denotes the time of each measurement. The parameter form of the linear equation is as follows: G ij_TOA = [-2x0-2y0-2x0(j-1)T-2y0(j-1)T 1((j-1)T) 2 2(j-1)T] Define G = [G toa ; G aoa ], Y = [Y toa ; Y aoa ], and perform a preliminary position estimate by least squares: Z0 = (G T G) -1 G T Y S3, using the inter-vehicle ranging information to position the unmanned aerial vehicle: Defining the number of unmanned aerial vehicles as n, using the inter-vehicle ranging information obtained by measurement to obtain a distance square matrix D as: Constructing a centralization matrix J: where I n is an n x n identity matrix, 1 n is an n x 1 column vector of ones; Constructing an inner product matrix B: Performing eigenvalue decomposition on the matrix B to obtain an eigenvalue matrix E and an eigenvector matrix V: BV=EV Sorting the eigenvalues, selecting the first two largest eigenvalues and the corresponding eigenvectors to calculate the position of the unmanned aerial vehicle: where V(:, 1 :2) is the first two eigenvectors, are the square roots of the first two largest eigenvalues, and the final estimated UAV position Z mds is an n x 2 matrix; S4, fusing the preliminarily estimated position signal and the position of the unmanned aerial vehicle to realize cooperative positioning and obtain final unmanned aerial vehicle positioning information, comprising: Z0 obtained from S2 and Z mds Define input matrices X and Y, respectively, and center them by moving their centroids to the origin: Scaling X' and Y' to unit norm respectively, and scaling Y' and X' to the same scale through a scaling factor, so that their norms are equal: In order to align Y' and X', a rotation matrix T needs to be solved, so that the transformed Y' is closest to X'; the matrix T is calculated through singular value decomposition (SVD): First, an auxiliary matrix A is solved: A = X ′T Y' Then, A is decomposed through SVD: A = UΣV T Wherein, Σ is a diagonal matrix, U and V are orthogonal matrices, and the rotation matrix T is: T = VU T Using the rotation matrix T, the transformed Y' is closest to X', the transformed Y is Y'·T, and the final positioning result Z is obtained: Z=b·Y'·T+c where b is a scaling factor, T is a rotation matrix and c is a translation vector.

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