A positioning method for the intersection of a direction-finding line and a conical surface

Abstract

The present invention belongs to the technical field of radio direction finding and positioning, and particularly relates to a positioning method for the intersection of a direction finding line and a conical surface. The present invention only requires two direction finding stations, one for one-dimensional direction finding of a radio radiation source and the other for two-dimensional direction finding of the radio radiation source. By using the intersection point of the direction finding line determined by the one-dimensional direction finding station and the conical surface determined by the two-dimensional direction finding station, the three-dimensional rectangular coordinates of the radio radiation source can be determined. Compared with the three-dimensional positioning method that requires both two direction finding stations to perform two-dimensional direction finding on the radio radiation source, and compared with the method that requires at least three direction finding stations to perform one-dimensional direction finding to perform three-dimensional positioning on the radio radiation source, the method of the present invention only requires two direction finding stations, reducing the multi-station cooperation cost and system complexity of direction finding and positioning.

Description

Technical Field

[0001] The present invention belongs to the technical field of radio direction finding and positioning, and particularly relates to a positioning method for the intersection of a direction finding line and a conical surface. Background Art

[0002] In the technical field of radio direction finding and positioning, two-dimensional positioning on a plane requires at least two direction finding stations for one-dimensional direction finding. One-dimensional direction finding of each direction finding station corresponds to a direction finding line. Only through the intersection of the direction finding lines of multiple direction finding stations can it be possible to determine the two-dimensional rectangular coordinates of the radio radiation source on the plane; three-dimensional positioning in a three-dimensional space also requires at least two direction finding stations for two-dimensional direction finding of azimuth and elevation angles. Two-dimensional direction finding of each direction finding station corresponds to a direction finding line. Only through the intersection of the direction finding lines of multiple direction finding stations can it be possible to determine the three-dimensional rectangular coordinates of the radio radiation source in the three-dimensional space.

[0003] Since two-dimensional direction finding is more complex in terms of technical complexity and the maintenance cost of the direction finding system than one-dimensional direction finding, with the increasingly widespread application of platforms such as unmanned aerial vehicles and unmanned vehicles, there is also an increasing demand for miniaturized, lightweight, low-cost, and low-power direction finding stations. Therefore, it is necessary to develop a technology for three-dimensional positioning of radio radiation sources using one-dimensional direction finding.

[0004] For the three-dimensional positioning problem in a three-dimensional space, at least three direction finding stations are required for one-dimensional direction finding. One-dimensional direction finding of each direction finding station determines a conical surface with the direction finding station as the vertex and the direction finding baseline of the direction finding station as the axis. Only through the intersection of the conical surfaces of multiple direction finding stations can it be possible to determine the three-dimensional rectangular coordinates of the radio radiation source in the three-dimensional space. However, since the collaborative direction finding and positioning among three or more direction finding stations is more complex than that between two direction finding stations, it is necessary to develop the collaboration between a direction finding station for one-dimensional direction finding of a radio radiation source and a direction finding station for two-dimensional direction finding, and three-dimensional positioning technology for the radio radiation source through the intersection of the direction finding line and the conical surface of two direction finding stations. Summary of the Invention

[0005] In view of the above problems, the present invention proposes a method for three-dimensional positioning of a radio radiation source by coordinating a direction-finding station for one-dimensional direction finding and a direction-finding station for two-dimensional direction finding, and intersecting the direction-finding lines of the two direction-finding stations with a conical surface. First, set the three-dimensional rectangular coordinates of the direction-finding station for two-dimensional direction finding, the direction-finding station for one-dimensional direction finding, and the direction-finding baseline vector of the direction-finding station for one-dimensional direction finding; the number of distance searches and the searched distance values; secondly, the direction-finding station for one-dimensional direction finding performs one-dimensional direction finding on the radio radiation source to determine the angle between the incoming wave direction of the radio radiation source and the direction-finding baseline of the direction-finding station for one-dimensional direction finding; the direction-finding station for two-dimensional direction finding performs two-dimensional direction finding on the radio radiation source to determine the incoming wave azimuth angle and elevation angle of the radio radiation source; then, based on the three-dimensional rectangular coordinates of the direction-finding station for one-dimensional direction finding, the incoming wave azimuth angle and elevation angle of the radio radiation source determined by the direction-finding station for two-dimensional direction finding, and the search distance, determine the three-dimensional rectangular relative coordinate vector corresponding to the search distance; then, based on the direction-finding baseline vector of the direction-finding station for one-dimensional direction finding and the three-dimensional rectangular relative coordinate vector corresponding to the search distance, determine the angle corresponding to the search distance; then, based on the angle between the incoming wave direction of the radio radiation source determined by the direction-finding station for one-dimensional direction finding and the direction-finding baseline of the direction-finding station for one-dimensional direction finding, and the angle corresponding to the search distance, determine the error corresponding to the search distance; finally, determine the search distance corresponding to the minimum value among all the errors, so as to determine the three-dimensional rectangular coordinates of the radio radiation source, that is, the intersection point between the direction-finding line and the conical surface.

[0006] The technical solution of the present invention is as follows:

[0007] A positioning method for the intersection of a direction-finding line and a conical surface, which uses two direction-finding stations to position a radiation source, wherein one direction-finding station performs one-dimensional direction finding on the radiation source, and the other direction-finding station performs two-dimensional direction finding on the radiation source. The positioning method includes:

[0008] Perform one-dimensional direction finding on the radiation source to obtain the angle between the incoming wave direction of the radiation source and the direction-finding baseline.

[0009] Perform two-dimensional direction finding on the radiation source to obtain the incoming wave azimuth angle and elevation angle of the radiation source.

[0010] According to the coordinates of the direction-finding station for one-dimensional direction finding in the set three-dimensional rectangular coordinates, the search distance, the incoming wave azimuth angle and elevation angle, obtain the relative three-dimensional coordinate vector corresponding to the search distance.

[0011] According to the direction-finding baseline vector of the direction-finding station for one-dimensional direction finding and the relative three-dimensional coordinate vector corresponding to the search distance, obtain the angle corresponding to the search distance.

[0012] According to the angle between the incoming wave direction and the direction-finding baseline of the direction-finding station for one-dimensional direction finding and the angle corresponding to the search distance, obtain the error corresponding to the search distance.

[0013] Based on the search distance corresponding to the minimum value among all errors, the three-dimensional rectangular coordinates of the radiation source are determined, that is, the intersection point between the direction-finding line and the conical surface.

[0014] Furthermore, the expression of the relative three-dimensional coordinate vector corresponding to the search distance is:

[0015]

[0016] where p(r k ) is the relative three-dimensional coordinate vector corresponding to the k-th search distance, r k is the k-th search distance, θ2 and φ2 are the azimuth angle and elevation angle of the incoming wave of the radiation source, (x1, y1, z1) are the three-dimensional rectangular coordinates of the direction-finding station for one-dimensional direction finding, k = 0, 1, 2, …, K - 1, and K is the number of distance searches.

[0017] Furthermore, the expression of the angle corresponding to the search distance is:

[0018]

[0019] where φ(r k ) is the angle corresponding to the k-th search distance, arccos() is the inverse cosine function, q·p(r k ) represents the inner product of vector q and vector p(r k ), q is the baseline vector of the direction-finding station for one-dimensional direction finding, ||p(r k )|| is the norm of vector p(r k ), that is, the distance from vector p(r k ) to the origin of the three-dimensional rectangular coordinate system.

[0020] Furthermore, the expression of the error corresponding to the search distance is:

[0021] g(r k ) = |φ(r k ) - φ1|

[0022] where g(r k ) is the error corresponding to the k-th search distance, and φ1 is the angle between the incoming wave direction of the radiation source and the direction-finding baseline of the direction-finding station for one-dimensional direction finding.

[0023] Furthermore, the expression for determining the three-dimensional rectangular coordinates of the radiation source is (r m cosφ2cosθ2, r m cosφ2sinθ2, r m sinφ2), where m refers to that the minimum value among the K errors is the m-th error, that is, the error corresponding to the m-th search distance r m .

[0024] The beneficial effects of the present invention are as follows: Only two direction-finding stations are required. One is a direction-finding station for one-dimensional direction-finding of a radio radiation source, and the other is a direction-finding station for two-dimensional direction-finding of the radio radiation source. By using the intersection point of the direction-finding line determined by the one-dimensional direction-finding station and the conical surface determined by the two-dimensional direction-finding station, the three-dimensional rectangular coordinates of the radio radiation source can be determined. Compared with the three-dimensional positioning method that requires two direction-finding stations to perform two-dimensional direction-finding on the radio radiation source, the method of the present invention reduces the maintenance cost of the direction-finding system of one direction-finding station and is more suitable for small-sized, lightweight, low-cost, and low-power direction-finding station platforms such as unmanned aerial vehicles and unmanned vehicles. Compared with the method that requires at least three direction-finding stations to perform one-dimensional direction-finding to perform three-dimensional positioning on the radio radiation source, the method of the present invention only requires two direction-finding stations, reducing the multi-station cooperation cost and system complexity of direction-finding and positioning. Specific embodiments

[0025] The practicality of the present invention will be analyzed below in conjunction with embodiments.

[0026] Embodiment

[0027] In this example, the direction-finding station for two-dimensional direction-finding is set as a ground station, which is located at the origin (0, 0, 0) meters of the three-dimensional rectangular coordinate system. The direction-finding station for one-dimensional direction-finding is an unmanned aerial vehicle, and the three-dimensional rectangular coordinates (x1, y1, z1) of the unmanned aerial vehicle are (500, 0, 300) meters. The direction-finding baseline of the unmanned aerial vehicle is placed horizontally, and the angle with the x-axis of the rectangular coordinate system is 10.23 degrees. The direction-finding baseline vector of the direction-finding station for one-dimensional direction-finding is (0.9841, 0.1776, 0); the number of distance searches is K = 991, and the k-th search distance is r k = 10 + k, k = 0, 1, 2,..., 990.

[0028] The specific implementation steps of this example are as follows:

[0029] S1. Set the direction-finding station for two-dimensional direction-finding at the origin of the three-dimensional rectangular coordinate system, the three-dimensional rectangular coordinates of the direction-finding station for one-dimensional direction-finding are (x1, y1, z1), and the direction-finding baseline vector q of the direction-finding station for one-dimensional direction-finding; the number of distance searches is K, and the k-th search distance is r k , k = 0, 1, 2,..., K - 1;

[0030] S2. The direction-finding station for one-dimensional direction-finding performs one-dimensional direction-finding on the radio radiation source to determine that the angle between the incoming wave direction of the radio radiation source and the direction-finding baseline of the direction-finding station for one-dimensional direction-finding is φ1; the direction-finding station for two-dimensional direction-finding performs two-dimensional direction-finding on the radio radiation source to determine that the incoming wave azimuth angle and elevation angle of the radio radiation source are θ2 and φ2 respectively;

[0031] S3. Determine the three-dimensional rectangular relative coordinate vector p(r k ) corresponding to the k-th search distance from the three-dimensional rectangular coordinates of the direction-finding station for one-dimensional direction finding, the azimuth angle and elevation angle of the incoming wave of the radio radiation source determined by the direction-finding station for one-dimensional direction finding, and the k-th search distance r k as follows:

[0032]

[0033] S4. Determine the angle φ(r k ) corresponding to the k-th search distance from the direction-finding baseline vector of the direction-finding station for one-dimensional direction finding and the three-dimensional rectangular relative coordinate vector corresponding to the k-th search distance as follows:

[0034]

[0035] where arccos() is the inverse cosine function, q·p(r k ) represents the inner product of vector q and vector p(r k ), ||p(r k )|| is the norm of the three-dimensional rectangular relative coordinate vector p(r k ), that is, the distance from the three-dimensional rectangular relative coordinate vector p(r k ) to the origin of the three-dimensional rectangular coordinate system;

[0036] S5. Determine the error g(r k ) corresponding to the k-th search distance from the angle between the incoming wave direction of the radio radiation source determined by the direction-finding station for one-dimensional direction finding and the UAV direction-finding baseline and the angle φ(r k ) corresponding to the k-th search distance as follows:

[0037] g(r k ) = |φ(r k ) - φ1|, k = 0, 1, 2, …, K - 1

[0038] S6. Determine that the minimum value among the K errors is the m-th error, which is the error g(r m ) corresponding to the m-th search distance r m ), thereby determining the three-dimensional rectangular coordinates of the radio radiation source, that is, the intersection point between the direction-finding line and the conical surface, as (r m cosφ2cosθ2, r m cosφ2sinθ2, r m sinφ2).

[0039] When the three-dimensional rectangular coordinates of the radio radiation source are (443.8446, 229.9381, 11.4211) meters, the standard deviation of the one-dimensional direction finding of the radio radiation source by the unmanned aerial vehicle is 0.30 degrees, and the standard deviations of the azimuth angle and elevation angle measurements of the radio radiation source by the ground station are both 0.30 degrees, 1000 Monte Carlo simulation experiments are carried out. Using the method of the present invention, three-dimensional positioning of the radio radiation source is carried out by the intersection of the direction finding line and the conical surface, and the average positioning error is 3.8861 meters. By the cooperation between a ground station for two-dimensional direction finding of the radio radiation source and an unmanned aerial vehicle for one-dimensional direction finding, three-dimensional positioning of the radio radiation source is achieved.

Claims

1. A positioning method for the intersection of a direction-finding line and a conical surface, which uses two direction-finding stations to locate a radiation source. One of the direction-finding stations performs one-dimensional direction-finding on the radiation source, and the other direction-finding station performs two-dimensional direction-finding on the radiation source. It is characterized in that The positioning method includes: Performing one-dimensional direction finding on the radiation source to obtain the angle between the incoming wave direction of the radiation source and the direction finding baseline; Performing two-dimensional direction finding on the radiation source to obtain the azimuth angle and elevation angle of the incoming wave of the radiation source; Obtaining the relative three-dimensional coordinate vector corresponding to the search distance according to the coordinates, search distance, incoming wave azimuth angle and elevation angle of the direction finding station performing one-dimensional direction finding in the set three-dimensional rectangular coordinate system; Obtaining the angle corresponding to the search distance according to the direction finding baseline vector of the direction finding station performing one-dimensional direction finding and the relative three-dimensional coordinate vector corresponding to the search distance; Obtaining the error corresponding to the search distance according to the angle between the incoming wave direction and the direction finding baseline of the direction finding station performing one-dimensional direction finding and the angle corresponding to the search distance; Determining the three-dimensional rectangular coordinates of the radiation source, that is, the intersection point between the direction finding line and the conical surface, according to the search distance corresponding to the minimum value among all errors.

2. The positioning method for the intersection of a direction-finding line and a conical surface according to claim 1, characterized in that The expression of the relative three-dimensional coordinate vector corresponding to the search distance is: where p(r k ) is the relative three-dimensional coordinate vector corresponding to the k-th search distance, r k is the k-th search distance, θ2 and φ2 are the azimuth angle and elevation angle of the incoming wave of the radiation source, (x1, y1, z1) are the three-dimensional rectangular coordinates of the direction-finding station for one-dimensional direction finding, k = 0, 1, 2, …, K-1, and K is the number of distance searches.

3. A positioning method for the intersection of a direction-finding line and a conical surface according to claim 2, characterized in that, The expression of the angle corresponding to the search distance is: where φ(r k ) is the angle corresponding to the k-th search distance, arccos() is the inverse cosine function, q·p(r k ) represents the inner product of the vector q and the vector p(r k ), q is the baseline vector of the direction-finding station for one-dimensional direction finding, ||p(r k )|| is the norm of the vector p(r k ), that is, the distance from the vector p(r k ) to the origin of the three-dimensional rectangular coordinate system.

4. A positioning method for the intersection of a direction-finding line and a conical surface according to claim 3, characterized in that The expression of the error corresponding to the search distance is: g(r k ) = |φ(r k ) - φ1| where g(r k ) is the error corresponding to the k-th search distance, and φ1 is the angle between the incoming wave direction of the radiation source and the direction-finding baseline of the direction-finding station for one-dimensional direction finding.

5. A positioning method for the intersection of a direction-finding line and a conical surface according to claim 4, characterized in that The three-dimensional rectangular coordinate expression for determining the radiation source is (r m cosφ2cosθ2, r m cosφ2sinθ2, r m sinφ2), where m refers to the m-th error among the K errors, that is, the m-th search distance r m corresponding error.

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