A dual-station 3D cross-location method based on grid search

Abstract

This invention discloses a dual-station three-dimensional cross-location method based on grid search, belonging to the field of electronic countermeasures reconnaissance technology. Based on the azimuth-elevation angle vectors measured by reconnaissance equipment at two stations (air or ground), the direction-finding vectors of the corresponding radiation sources at each station are transformed into a northeast-sky coordinate system with their respective stations as the origin. Then, the dual-station direction-finding vectors are transformed into the same coordinate system using a coordinate system transformation method. The coordinates of the radiation sources are searched using a grid search method that minimizes the straight-line distance between opposite planes. Finally, the coordinates of the radiation sources searched multiple times are clustered to obtain the optimal positioning coordinates.

Description

Technical Field

[0001] This invention relates to electronic countermeasures reconnaissance technology, specifically to a dual-station three-dimensional cross-location method based on grid search. Background Technology

[0002] Direction-finding cross-location is a method that uses a single, mobile station to measure azimuth multiple times at different locations. Positioning is then achieved by intersecting the direction-finding vectors obtained from time-division reconnaissance equipment, or by intersecting the direction-finding vectors simultaneously measured by multiple air or ground-based reconnaissance stations. Single-station positioning requires accumulating multiple measurement results, making it slow and inaccurate. However, multi-station direction-finding cross-location systems offer advantages such as speed, longer detection range, and stronger anti-interference capabilities.

[0003] Common direction-finding and localization algorithms utilize a set of measurement equations containing target coordinates to solve for the location information of the radiation source. A commonly used algorithm is the simplified weighted least squares localization algorithm. The paper "Application of Direction-Finding Cross-Localization Method in Engineering" introduces a bi-station cross-localization method based on weighted least squares, but this method suffers from problems such as large matrix inversion computation, high computational resource consumption, long radiation source localization time, and difficulty in engineering implementation, making it unsuitable for applications requiring real-time performance. This paper proposes a method to determine the location information of the radiation source using the spatial geometric relationship of the direction-finding vectors of bi-station reconnaissance equipment. This method offers high real-time performance and is easy to implement in engineering. Summary of the Invention

[0004] This invention proposes a dual-station three-dimensional cross-location method based on grid search, which has high real-time performance and is easy to implement in engineering.

[0005] The technical solution for realizing the present invention is as follows: a dual-station three-dimensional cross-positioning method based on grid search, the steps of which are as follows: Step 1: The reconnaissance equipment of the two stations uses a passive method to measure the azimuth-elevation angle of the radiation source respectively.

[0006] Step 2: Each of the two stations establishes a northeast-sky coordinate system with its self-positioning coordinates as the origin. In their respective coordinate systems, the azimuth-elevation angle of the radiation source is converted into the direction-finding vector of the radiation source.

[0007] Step 3: Using the conversion relationship between the northeast celestial coordinate system and the geocentric coordinate system, convert the self-positioning coordinates of the two stations and the direction finding vector of the radiation source to the geocentric coordinate system.

[0008] Step 4: By roughly presetting the coordinate position of the radiation source, establish the northeast-sky coordinate system based on the coordinates. Through the transformation relationship between the geocentric coordinate system and the northeast-sky coordinate system, transform the self-positioning coordinates of the two stations and the direction finding vector of the radiation source in the geocentric coordinate system into the same coordinate system.

[0009] Step 5: Based on the principle of minimizing the distance from the radiation source to the dual-station direction finding vector, divide the three-dimensional space into grid nodes and calculate the spatial distance from the grid to the direction finding vector. Take the grid node with the shortest spatial distance as the coordinate of the radiation source for this positioning.

[0010] Step 6: Cluster the multiple radiation source location coordinates using a least squares-based clustering method to obtain the final radiation source location coordinates.

[0011] Compared with the prior art, the significant advantages of this invention are:

[0012] (1) The least squares localization algorithm uses a set of measurement equations containing the target coordinates to solve for the location information of the radiation source. However, it suffers from problems such as large computational load, high computational resource consumption, and difficulty in engineering implementation, making it difficult to meet real-time requirements. The localization method in this paper can quickly locate the radiation source using a set of bi-station direction-finding results. Compared with the traditional method of solving a set of equations to calculate the coordinates of the radiation source, the proposed method of dividing the grid nodes for radiation source coordinate search is easier to implement in embedded software.

[0013] (2) The spacing of the grid nodes can be selected according to the positioning accuracy requirements. When estimating the coordinates of the radiation source, the spacing of the grid nodes can be set to several kilometers or even tens of kilometers. A rough coordinate of the radiation source can be obtained through a pre-positioning, and then fine grid nodes can be selected for precise positioning. This method allows for flexible selection between rough and precise positioning.

[0014] (3) The search grid node spacing and search range can be adjusted according to the actual engineering application and the positioning accuracy to reduce the radiation source positioning time. Based on engineering practice, the positioning results of this invention can be achieved in microseconds at the fastest. The radiation source positioning results can guide other devices in the system to detect and interfere with the radiation source in real time. Attached Figure Description

[0015] Figure 1 This is a flowchart of the dual-station three-dimensional cross-location method based on grid search according to the present invention.

[0016] Figure 2 This is a schematic diagram of a two-site orientation-based cross-location system.

[0017] Figure 3 The figure shows the simulation results of the bi-station 3D cross-location method based on grid search. Detailed Implementation

[0018] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0019] It should be noted that all directional indications (such as up, down, left, right, front, back, etc.) in the embodiments of the present invention are only used to explain the relative positional relationship and movement of each component in a certain specific posture (as shown in the figure). If the specific posture changes, the directional indication will also change accordingly.

[0020] Furthermore, in this invention, descriptions involving "first," "second," etc., are for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this invention, "a plurality of" means at least two, such as two, three, etc., unless otherwise explicitly and specifically defined.

[0021] The technical solutions of the various embodiments of the present invention can be combined with each other, but only if they can be implemented by those skilled in the art. When the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such combination of technical solutions does not exist and is not within the scope of protection claimed by the present invention.

[0022] The following section will further introduce the specific implementation method, as well as the technical difficulties and inventive points of this invention, using this design example as an example.

[0023] Combination Figure 1 and Figure 2 A bi-station 3D cross-location method based on grid search includes the following steps:

[0024] Step 1: The reconnaissance equipment at both stations conducts reconnaissance of the radiation source direction. The reconnaissance equipment at the first and second stations uses passive angle measurement to measure the azimuth-elevation angles of the radiation source (β1, ε1) and (β2, ε2), respectively. The azimuth-elevation angle measurement error is...

[0025] Step 2: Establish a northeast-sky coordinate system for each of the two stations, using their self-positioning coordinates as the origin. Set the azimuth-elevation angle (0°, 0°) of the reconnaissance equipment to point due north. In their respective coordinate systems, convert the azimuth-elevation angles (β1, ε1) and (β2, ε2) of the radiation source into the direction-finding vector e of the radiation source. S1 e S2 :

[0026] e S1 =[cosε1*sinβ1cosε1*cosβ1sinε1]

[0027] e S2 =[cosε2*sinβ2cosε2*cosβ2sinε2]

[0028] Step 3: The two direction-finding vectors obtained above are not in the same coordinate system, which facilitates calculation. Next, we will transform the self-positioning coordinates and direction-finding vectors of the two stations into one coordinate system. Using the transformation relationship between the Northeast-Northeast coordinate system and the geocentric coordinate system, combined with the self-positioning coordinates S of the first station in the geocentric coordinate system... g1 (x g1 y g1 z g1 (Self-positioning coordinates obtained via BeiDou positioning) The radiation source direction finding vector in the northeast celestial coordinate system is transformed to the geocentric coordinate system. After transformation, the radiation source direction finding vector of the first station is e. g-S1 =[l g1 m g1 n g1 Similarly, based on the self-positioning coordinates S of the second station in the geocentric coordinate system... g2 (x g2 y g2 z g2 ), thus obtaining the radiation source direction finding vector e of the second station after conversion. g-S2 =[l g2 m g2 n g2 ]. l ga This represents the x-direction component of the radiation source direction-finding vector at station a after transformation, corresponding to the coordinate system; m ga n represents the y-direction component of the radiation source direction-finding vector at station a after transformation, corresponding to the coordinate system. ga This represents the z-direction component of the radiation source direction finding vector of station a after transformation, corresponding to the coordinate system. The station number is a = 1, 2.

[0029] Step 4: Due to the excessively large coordinate values ​​in the geocentric coordinate system, the station coordinates and direction-finding vectors in the geocentric coordinate system are transformed to the Northeast Altitude Coordinate System for easier calculation. The radiation source coordinates are roughly preset to O = (x0 y0 z0), or a rough position O = (x0 y0 z0) is obtained through a large-scale search using the positioning method described in this paper. The Northeast Altitude Coordinate System is then established with this coordinate as the origin. Through the transformation relationship between the Northeast Altitude Coordinate System and the geocentric coordinate system, the self-positioning coordinates S of the first station in this Northeast Altitude Coordinate System are obtained. O-1 (x O1 y O1 z O1 The self-positioning coordinates S of the second stationO-2 (x O2 y O2 z O2 ), and the radiation source direction finding vector e measured at the first station. O-S1 =[l O1 m O1 n O1 The radiation source direction finding vector e measured at the second station. O-S2 =[l O2 m O2 n O2 ], where, where, l Oa m represents the x-direction component of the direction-finding vector of the radiation source measured at station a, corresponding to the coordinate system; Oa Let n represent the y-direction component of the coordinate system corresponding to the radiation source direction-finding vector measured at station a. Oa The z-direction component of the radiation source direction finding vector measured at station a, corresponding to the coordinate system, where station number a = 1, 2.

[0030] Step 5: If the reconnaissance equipment at both sites has no direction-finding errors, then the intersection of the two direction-finding vectors is the coordinate of the radiation source. However, in reality, both the self-positioning coordinates and azimuth-elevation angle measurements of the reconnaissance equipment at each site have errors. These errors cause the two direction-finding vectors to not intersect in three-dimensional space. Therefore, this paper uses the principle of minimizing the distance from the radiation source coordinates to the direction-finding vectors of the two sites. It divides the three-dimensional space into grid nodes with equal intervals Δl, then calculates the sum of the spatial distances from each grid node to the two direction-finding vectors, and takes the grid node with the shortest sum of spatial distances as the search result for the radiation source coordinates. Grid node coordinates T ijk (x i y j z k ), i=1,2...I, j=1,2...J, k=1,2...K. x i y j , z k The step value is Δl, and the values ​​of I, J, and K determine the search range in three-dimensional space.

[0031] The vector e from the first station to the grid node T-S1 :

[0032] e T-S1 =[l i m j n k ] = [x i -x O1 y j -y O1 z k -z O1 ];

[0033] The distance d1 from the grid node to the first station's direction-finding vector space is calculated using the vector cross product principle:

[0034]

[0035] Distance d2 in the direction-finding vector space from the grid node to the second station:

[0036]

[0037] Iterate through all grid nodes and take the grid node T corresponding to the minimum value of d1+d2. ijk (x i y j z k (T1) is used as the coordinate of the radiation source in this study.

[0038] Two stations perform N cross-locations of the radiation source, obtaining N location results T. n (x n y n z n ), n=1,2,3...N.

[0039] Step 6: Since the single cross-location results of the radiation source from the two stations have large errors, this section clusters the N radiation source location coordinates based on the shortest distance principle to obtain an optimal location result. The process is as follows:

[0040] In practical engineering, direction-finding vectors with significant errors may occur. First, abnormal positioning results are discarded. Calculate the positioning results T from N attempts. n (x n y n z n The mean point of ) Calculate the result T of N positioning attempts. n to the mean point distance l n According to the angle measurement error and the distance from the radiation source to the first site S1 Calculate positioning error Eliminate l based on experience value n Location coordinates of anomalies with a distance ≥10*Δd.

[0041] Cluster the remaining M location coordinates and calculate the sum of squared distances from each coordinate to the other M-1 coordinates. The current coordinates are m0 = 1, 2, 3...M. Finally, the minimum sum of squared distances is taken. Corresponding coordinates As the optimal coordinates for locating the radiation source.

[0042] Down Figure 3The simulation of the cross-positioning method presented in this paper is based on actual measurement results in the project. The self-positioning coordinates of the first station are (118.913216 / 180*π, 31.955966 / 180*π, 64.8847), and the azimuth and elevation angles are (β1, ε1) = (-9.0°, 9.1°). The self-positioning coordinates of the second station are (118.913766 / 180*π, 31.958927 / 180*π, 36.9), and the azimuth and elevation angles are (β2, ε2) = (21°, 11.8°). The station self-positioning error is 5 meters, and the direction finding error of the reconnaissance equipment is... With a grid node spacing Δl = 2 meters and preset radiation source coordinates (118.919804 / 180*π, 31.956680 / 180*π, 170), two stations perform N = 100 cross-location operations on the radiation source. Using a northeast-sky coordinate system with the radiation source as the origin, the optimal location result after clustering is obtained (18, 22, -1), with a spatial distance error better than 5 meters from the actual location (22, 22, 0). The grid search method described in this paper is suitable for pipelined computation on an FPGA, and can complete a location calculation in microseconds.

Claims

1. A bi-station three-dimensional cross-location method based on grid search, characterized in that, Includes the following steps: Step 1: The reconnaissance equipment at both stations conducts reconnaissance of the radiation source direction. The reconnaissance equipment at the first and second stations uses passive angle measurement to measure the azimuth-elevation angles of the radiation source (β1, ε1) and (β2, ε2), respectively. The angle measurement error is... Step 2: Establish a northeast-sky coordinate system for each of the two stations, using their self-positioning coordinates as the origin. Set the azimuth-elevation angle (0°, 0°) of the reconnaissance equipment to point due north. In this coordinate system, convert the azimuth-elevation angles (β1, ε1) and (β2, ε2) of the radiation source into the direction-finding vector e of the radiation source. S1 e S2 : e S1 =[cosε1*sinβ1 cosε1*cosβ1 sinε1] e S2 =[cosε2*sinβ2 cosε2*cosβ2 sinε2] Step 3: Through the transformation relationship between the northeast celestial coordinate system and the geocentric coordinate system, combined with the self-positioning coordinates S of the first station in the geocentric coordinate system... g1 (x g1 y g1 z g1 Transform the radiation source direction finding vector in the northeast celestial coordinate system to the geocentric coordinate system. After transformation, the radiation source direction finding vector e of the first station is obtained. g-S1 =[l g1 m g1 n g1 Similarly, based on the self-positioning coordinates S of the second station in the geocentric coordinate system... g2 (x g2 y g2 z g2 ), thus obtaining the radiation source direction finding vector e of the second station after conversion. g-S2 =[l g2 m g2 n g2 ];l ga This represents the x-direction component of the radiation source direction-finding vector at station a after transformation, corresponding to the coordinate system; m ga n represents the y-direction component of the radiation source direction-finding vector at station a after transformation, corresponding to the coordinate system. ga This represents the z-direction component of the radiation source direction finding vector of the a-th station in the corresponding coordinate system after the transformation, where the station number is a = 1, 2; Step 4: By roughly presetting the coordinate position of the radiation source O = (x0 y0 z0), establish a northeast-sky coordinate system with this coordinate as the origin. Through the transformation relationship between the northeast-sky coordinate system and the geocentric coordinate system, obtain the self-positioning coordinates S of the first station under this northeast-sky coordinate system. O-1 (x O1 y O1 z O1 The self-positioning coordinates S of the second station O-2 (x O2 y O2 z O2 ), and the radiation source direction finding vector e measured at the first station. O-S1 =[l O1 m O1 n O1 The radiation source direction finding vector e measured at the second station. O-S2 =[l O2 m O2 n O2 ], where l Oa m represents the x-direction component of the direction-finding vector of the radiation source measured at station a, corresponding to the coordinate system; Oa Let n represent the y-direction component of the coordinate system corresponding to the radiation source direction-finding vector measured at station a. Oa The z-direction component of the radiation source direction finding vector measured at station a, corresponding to the coordinate system; station number a = 1, 2. Step 5: Based on the principle of minimizing the distance between the radiation source coordinates and the direction-finding vectors of the two stations, divide the three-dimensional space into grid nodes with equal spacing Δl, then calculate the spatial distance from the grid to the direction-finding vector, and take the grid node corresponding to the shortest spatial distance as the search result for the radiation source coordinates; grid node coordinates T ijk (x i y j z k ), i=1,2…I, j=1,2…J, k=1,2…K; x i y j , z k The step value is Δl, and the values ​​of I, J, and K determine the search range in three-dimensional space; The vector e from the first station to the grid node T-S1 : e T-S1 =[l i m j n k ]=[x i -x O1 y j -y O1 z k -z O1 ]; The distance d1 from the grid node to the first station's direction-finding vector space is calculated using the vector cross product principle: Distance d2 in the direction-finding vector space from the grid node to the second station: Iterate through all grid nodes and take the grid node T corresponding to the minimum value of d1+d2. ijk (x i y j z k (T1) is used as the coordinate of the radiation source in this study; Two stations perform N cross-locations of the radiation source, obtaining N location results T. n (x n y n z n ), n = 1, 2, 3…N; Step 6: Cluster the N radiation source location coordinates based on the shortest distance principle to obtain an optimal location result.

2. The dual-station three-dimensional cross-location method based on grid search according to claim 1, characterized in that, In step 6, the N radiation source location coordinates are clustered based on the shortest distance principle to obtain an optimal location result, as follows: Find the result T of N positioning attempts. n (x n y n z n The mean point of ) Calculate the result T of N positioning attempts. n to the mean point distance l n According to the angle measurement error and the distance from the radiation source to the first site S1 Calculate positioning error Eliminate l based on experience value n Location coordinates of anomalies with a distance ≥10*Δd; Cluster the remaining M location coordinates and calculate the sum of squared distances from each coordinate to the other M-1 coordinates. Take the minimum sum of squared distances The corresponding coordinates are the optimal coordinates for locating the radiation source.

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