A one-dimensional search conical positioning method

Abstract

This invention discloses a one-dimensional search method for conical positioning. By setting the number of direction-finding stations, their position coordinates, and the angle between the horizontally placed linear array of the direction-finding stations and the positive direction of the X-axis; and by setting the number of coordinate values ​​and the set of coordinate values ​​for the one-dimensional search, this method addresses how to utilize the one-dimensional direction finding of the horizontally arranged linear array of each direction-finding station for conical positioning using a one-dimensional search when there are few direction-finding stations. Compared with three-dimensional search methods for conical positioning, this method achieves less positioning accuracy loss while quickly determining the three-dimensional position coordinates of the target. Compared to three-dimensional search methods that search for 101 values ​​per dimension, this method requires less than one-hundredth of the computation time. Compared to pseudo-linear conical positioning methods, this method requires a minimum of 4 direction-finding stations, while the pseudo-linear conical positioning method requires a minimum of 7. This method has a wider range of applications.

Description

Technical Field

[0001] This invention belongs to the field of passive direction finding and positioning technology, specifically relating to a method for three-dimensional positioning using one-dimensional direction finding and one-dimensional search of a target. Background Technology

[0002] In the field of radio positioning, the method of locating a target using direction finding from multiple direction finding stations is widely used. When a direction finding station can simultaneously measure the target's azimuth and elevation in two-dimensional direction finding, the direction finding lines from multiple stations often do not intersect at a single point due to measurement noise. Therefore, it is necessary to determine the target's three-dimensional position coordinates by solving an optimization problem. For example, determining the point with the minimum sum of distances from the direction finding lines of multiple stations is the target's positioning result. Although the relationship between the target's three-dimensional position coordinates and the two-dimensional direction finding of the target's azimuth and elevation is non-linear, the problem of solving for the target's three-dimensional position coordinates can be transformed into a linear problem using the sine and cosine functions of the two-dimensional direction finding of the target's azimuth and elevation.

[0003] With the increasing application of small, lightweight, and low-power direction-finding stations such as drones and unmanned vehicles, it is necessary to simplify two-dimensional direction finding using area arrays to one-dimensional direction finding using linear arrays. In one-dimensional direction finding where the direction-finding station only measures the angle between the target's incoming wave direction and the linear array used by the station, the one-dimensional direction finding of a single station can determine a direction-finding cone, with the station's linear array located on the central axis of the cone. Due to measurement noise, the direction-finding cones of multiple stations often do not intersect at a single point, requiring the solution of an optimization problem to determine the target's location. For example, determining the point with the minimum sum of distances to the direction-finding cones of multiple stations as the target's location. Since the relationship between the target's three-dimensional coordinates and its one-dimensional direction finding is more complex and nonlinear, it is difficult to transform the problem of determining the target's three-dimensional coordinates into a linear problem using the sine and cosine functions of the target's one-dimensional direction finding.

[0004] To determine the nonlinear conic positioning result using one-dimensional direction finding from multiple direction finding stations, a direct search can be performed on the three-dimensional coordinates of the target position within a limited positioning area. The point with the minimum sum of distances to the direction finding conic surfaces of multiple stations can be identified as the target's positioning result. However, this exhaustive method is computationally intensive and cannot meet the requirements of low power consumption and real-time target positioning. Based on the local linearization approximation using Taylor series expansion, iterative search can replace the exhaustive search. However, during the iterative search, problems such as local convergence and initial position selection are often encountered, leading to numerous inconveniences in practical applications. Furthermore, by introducing redundant parameters, the nonlinear conic positioning problem can be transformed into a pseudolinear conic positioning problem, significantly reducing the computational load. However, to ensure that the number of pseudolinear equations exceeds the number of unknown parameters, including the target's three-dimensional position coordinates and redundant parameters, more direction finding stations are needed to provide more one-dimensional direction finding to guarantee the uniqueness of the pseudolinear conic positioning result. This makes the pseudolinear conic positioning method unsuitable for situations with a limited number of direction finding stations. Summary of the Invention

[0005] The purpose of this invention is to solve the problem of how to use the one-dimensional direction finding of the horizontally arranged linear array of each direction finding station to perform conical positioning through one-dimensional search when there are few direction finding stations. Compared with the three-dimensional search conical positioning method, the positioning accuracy loss is small, while the three-dimensional position coordinates of the target are quickly determined.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] A one-dimensional search conical positioning method first sets the number of direction-finding stations, their three-dimensional position coordinates, and the angle between the horizontally placed linear array of the direction-finding stations and the positive direction of the X-axis; then sets the number of coordinate values ​​for the one-dimensional search and the set of coordinate values ​​for the one-dimensional search; next, it determines the position coordinate vector and direction vector of the linear array, as well as the search parameter matrix; then, it determines the direction finding of the linear array by using the position coordinates of the direction-finding stations, the angle between the linear array and the positive direction of the X-axis, the search parameter matrix, and the direction finding of the linear array of the direction-finding stations to determine the coefficient matrix corresponding to the coordinate values ​​in the set of coordinate values ​​for the one-dimensional search; then, it determines the coefficient vector corresponding to the coordinate values ​​in the set of coordinate values ​​for the one-dimensional search; finally, it uses the coefficient matrix and coefficient... The process begins by determining the fitted vector corresponding to the coordinate values ​​in the set of coordinate values ​​from the one-dimensional search. Then, using the coordinate values ​​and their corresponding fitted vectors, the three-dimensional position coordinate vectors corresponding to the coordinate values ​​in the set of coordinate values ​​are determined. Next, the fitted orientation of each linear array corresponding to the coordinate values ​​in the set of coordinate values ​​is determined. From the fitted orientations corresponding to the coordinate values ​​in the set of coordinate values, the cost value corresponding to the coordinate values ​​in the set of coordinate values ​​is determined, thus determining the cost value set. Finally, the cost value corresponding to the coordinate value of the maximum value in the cost value set is determined, and finally, the three-dimensional position coordinates of the cone positioning in the one-dimensional search are determined.

[0008] This invention includes the following steps:

[0009] S1. Set the number of direction finding stations to K (K≥4), and the three-dimensional position coordinates of the k-th direction finding station are [x...]. k y k , z k The linear array of the direction-finding station is placed horizontally, with an angle φ between it and the positive direction of the X-axis of the coordinate system. k k = 1, 2, ..., K; set the number of coordinates in the one-dimensional search to N, and the set of coordinates in the one-dimensional search to {ρ1, ρ2, ..., ρ...} N}; and then determine the three-dimensional position coordinate vector of the k-th direction finding station as s k =[x k y k , z k The search parameter matrix is ​​η, and the element in the k-th row and n-th column is η. k (ρ n )=ρ n cosφ k -x k cosφ k -y k sinφ k k = 1, 2, ..., K, n = 1, 2, ..., N; determine the direction vector of the linear array of the k-th direction-finding station as follows:

[0010]

[0011] S2. Determine the linear array direction finding of the k-th direction finding station as θ. k The nth coordinate value ρ in the coordinate set of the one-dimensional search is determined by the position coordinates of the direction finding station, the angle between the linear array and the positive direction of the X-axis, the search parameter matrix, and the direction finding of the linear array of the direction finding station. n The corresponding coefficient matrix Q(ρ) n )for

[0012] Q(ρ n )=[q1 q2(ρ n ) q3 q4]

[0013] Where n = 1, 2, ..., N,

[0014]

[0015]

[0016]

[0017]

[0018] S3. Determine the nth coordinate value ρ in the set of coordinate values ​​for the one-dimensional search. n The corresponding coefficient vector q5(ρ) n )for

[0019]

[0020] Where n = 1, 2, ..., N;

[0021] S4, from the coefficient matrix Q(ρ) n ) and coefficient vector q5(ρ n Determine the nth coordinate value ρ in the set of coordinate values ​​for the one-dimensional search. n The corresponding fitted vector q6(ρ) n )for

[0022]

[0023] Where n = 1, 2, ...; N, This indicates the generalized inverse of a matrix.

[0024] S5. The nth coordinate value ρ from the set of coordinate values ​​obtained from the one-dimensional search. n and its corresponding fitting vector q6(ρ n Determine the nth coordinate value ρ in the set of coordinate values ​​for the one-dimensional search. n The corresponding three-dimensional position coordinate vector q7(ρ) n )=[ρ n q 62 (ρn ), q 64 (ρ n )], where q 62 (ρ n ) and q 64 (ρ n ) are the fitted vectors q6(ρ) n The second and fourth elements of ) are used to determine the nth coordinate value ρ in the set of coordinate values ​​for the one-dimensional search. n The fitted orientation of the corresponding k-th linear array for

[0025]

[0026] Where k = 1, 2, ..., K, n = 1, 2, ..., N

[0027] S6. The nth coordinate value ρ in the set of coordinate values ​​from the one-dimensional search. n Corresponding fitting orientation Determine the nth coordinate value ρ in the set of coordinate values ​​for a one-dimensional search. n The corresponding cost f(ρ) i )for

[0028]

[0029] Where n = 1, 2, ..., N; and then determine the value set {f(ρ1), f(ρ2), ..., f(ρ)}. N )};

[0030] S7. Determine the set of values ​​{f(ρ1), f(ρ2), ..., f(ρ)}. N The maximum value in )} is the m-th coordinate value ρ m The corresponding cost f(ρ) m ), thereby determining the cone positioning of the one-dimensional search as the three-dimensional position coordinates q7(ρ) determined in step S5. m )=[ρ m q 62 (ρ m ), q 64 (ρ m )], where q 62 (ρ m ) and q 64 (ρ m ) are the fitted vectors q6(ρ) m The second and fourth elements of ).

[0031] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are:

[0032] This invention provides a method for achieving conical positioning using a one-dimensional direction finding system (DOS) through a horizontally arranged linear array of DOS stations, even with a limited number of DOS stations. Compared to a three-dimensional conical positioning method that searches for 101 values ​​per dimension, this invention requires less than one-hundredth of the computation time. Furthermore, compared to a pseudo-linear conical positioning method, this invention requires a minimum of 4 DOS stations, while the pseudo-linear conical positioning method requires a minimum of 7 DOS stations, thus broadening the applicability of this invention. Detailed Implementation

[0033] All features disclosed in this specification, or all steps in all disclosed methods or processes, may be combined in any way, except for mutually exclusive features and / or steps.

[0034] Any feature disclosed in this specification (including any appended claims and abstract) may be replaced by other equivalent or similar features, unless specifically stated otherwise. That is, unless specifically stated otherwise, each feature is merely one example of a series of equivalent or similar features.

[0035] The number of direction finding stations is set to 4, and the three-dimensional position coordinates of the direction finding stations are [0, 0, 0], [399.9741, 10.3281, 119.2989], [897.8337, 300.0498, 16.6261] and [-398.8564, 398.1783, 90.2969] meters, respectively. The linear array of the direction finding stations is placed horizontally, and the angles with the positive X-axis of the coordinate system are -4.94, 18.83, 15.40 and -9.64 degrees, respectively. The number of coordinates for the one-dimensional search is 101, with an adjacent interval of 0.1 meters, and the coordinate set for the one-dimensional search is {71.0, 71.1, 71.2, ..., 80.8, 80.9, 81.0} meters.

[0036] With the target's three-dimensional position coordinates at [76.0270, 168.6041, 75.7072] meters and a one-dimensional direction finding error standard deviation of 0.1° for the linear array, 1000 Monte Carlo experiments were conducted. The target was located using both a three-dimensional search (searching 101 points for each of the target's three-dimensional position coordinates, with an adjacent interval of 0.1 meters) conical positioning method and the one-dimensional search conical positioning method of this invention. Using the same computer, the average time for the three-dimensional search conical positioning method was 4.0748 seconds, with a positioning error of less than 1.2329 meters in 80% of cases. The average time for the one-dimensional search conical positioning method of this invention was 0.0154 seconds, less than 1 / 264th of the average time of the three-dimensional search conical positioning method, with a positioning error of less than 2.1402 meters in 80% of cases. This demonstrates that, with a limited number of direction finding stations, the goal of rapidly determining the target's three-dimensional position coordinates using a horizontally arranged linear array for one-dimensional direction finding is achieved.

[0037] This invention is not limited to the specific embodiments described above. The invention extends to any new feature or combination disclosed in this specification, as well as any new method or process step or combination disclosed herein.

Claims

1. A one-dimensional search method for cone positioning, characterized in that: By setting the parameters of the direction finding stations, the number of direction finding stations, the three-dimensional position coordinates, the angle between the horizontally placed linear array of the direction finding stations and the positive direction of the X-axis of the coordinate system, and the search parameter matrix are determined. The coefficient matrix corresponding to the coordinate values ​​in the one-dimensional search coordinate value set is determined by the parameters of the direction finding stations and the direction finding of the linear array. The fitting vector corresponding to the coordinate values ​​in the one-dimensional search coordinate value set is determined by the coefficient matrix and the coefficient vector. The three-dimensional position coordinate vector corresponding to the coordinate values ​​in the one-dimensional search coordinate value set is determined by the fitting vector. Then, the fitting orientation of each linear array corresponding to the coordinate values ​​in the one-dimensional search coordinate value set is determined. The cost value corresponding to the coordinate values ​​in the one-dimensional search coordinate value set is determined. The cost value corresponding to the coordinate value of the maximum value in the cost value set is determined. Finally, the three-dimensional position coordinates of the conical positioning in the one-dimensional search are determined. Includes the following steps: S1: Set the number of direction finding stations to... The three-dimensional position coordinates of the k-th direction finding station are: The angle between the linear array placed horizontally and the positive direction of the X-axis of the coordinate system is... Set the number of coordinate values ​​for the one-dimensional search to N, and the set of coordinate values ​​for the one-dimensional search to be N. Determine the first The three-dimensional position coordinate vector of each direction finding station Determine the search parameter matrix , its first Line number The elements of the column are Determine the first The direction vector of the linear array of each direction finding station is ; S2: Determine the first The linear array direction finding of each direction finding station is The first position of the coordinates in the one-dimensional search is determined by the three-dimensional position coordinates of the direction finding station, the angle between the linear array and the positive direction of the X-axis, the search parameter matrix, and the direction finding of the linear array of the direction finding station. coordinate values The corresponding coefficient matrix is: ； S3: Determine the first element in the set of coordinate values ​​for the one-dimensional search. coordinate values Corresponding coefficient vector for: ； S4: From the coefficient matrix sum coefficient vector Determine the first coordinate value in the set of coordinate values ​​for a one-dimensional search. coordinate values Corresponding fitted vector for: ; S5: The first value in the set of coordinates from a one-dimensional search. coordinate values and its corresponding fitted vector Determine the first coordinate value in the set of coordinate values ​​for a one-dimensional search. coordinate values The corresponding three-dimensional position coordinate vector ,in and These are the fitted vectors. The 2nd and 4th elements; thus determining the first element in the set of coordinate values ​​for the one-dimensional search. coordinate values The corresponding number Fitting orientation of each linear array for: ； S6: The first value in the set of coordinates from a one-dimensional search. coordinate values Corresponding fitting orientation Determine the first coordinate value in the set of coordinate values ​​for a one-dimensional search. coordinate values Corresponding cost for: ; S7. Determine the value set The maximum value in is the first coordinate values Corresponding cost Therefore, the cone positioning of the one-dimensional search is determined as the three-dimensional position coordinates determined in step S5. ,in and These are the fitted vectors. The 2nd and 4th elements; In the above formula, , , This indicates the generalized inverse of a matrix.

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