Dual-station radar collaborative positioning method and system

Abstract

This invention provides a dual-station radar collaborative positioning method and system. This positioning algorithm uses a three-dimensional spatial structure to describe the spatial probability density distribution range of radar measurement errors and the complementary characteristics between the two radar measurement results. It iteratively calculates the intersection of two spheres using a linear weighting method, and then calculates the arc midpoint using a proportional method, ultimately achieving a practical dual-station collaborative target positioning solution. This algorithm is suitable for compressed filtering processing in centralized information fusion for dual-station and multi-station radar collaborative positioning with medium- to long-baseline (20km-100km) configurations. It can significantly improve the accuracy of dual-station radar collaborative target positioning and avoid the systematic errors of the algorithm caused by approximation.

Description

Technical Field

[0001] The present invention relates to the technical field of multi-sensor data fusion, and in particular to a dual-station radar collaborative positioning method and system, and more particularly to a dual-station radar collaborative positioning algorithm for obtaining an arc midpoint based on complementary characteristics of measurement error information and a proportional method. Background Art

[0002] Collaborative detection in modern radar networks has become an inevitable trend, primarily through data-level fusion of detection data from multiple radars to improve target positioning accuracy. Currently, most data-level fusion algorithms utilize only the data itself. Traditional data-level fusion algorithms typically perform a weighted average of radar measurement data without considering the spatial characteristics of the data's error distribution. These algorithms also fail to fully utilize prior information from the measurement process. Therefore, the accuracy of algorithms using data fusion for joint positioning still has room for improvement.

[0003] Patent document CN112526508A (grant number: CN112526508B) discloses a dual-station radar joint target positioning algorithm based on the evaluation of the spatial distribution characteristics of measurement errors. This patent uses a three-dimensional spatial structure to describe the spatial probability density distribution range of radar measurement errors and the complementary characteristics between the two radar measurement results. The optimal estimate of the target position is obtained by solving the center of the overlapping area of ​​the two radar measurement error distributions. The local approximate relationship between the sphere and the tangent plane is used to simplify the solution process of the center of gravity of the overlapping area of ​​the measurement error spatial distribution, ultimately achieving practical dual-station collaborative target positioning. However, this method's measurement results introduce additional range systematic errors in the range dimension, resulting in less accurate target positioning.

[0004] Therefore, it is necessary to propose a new technical solution to improve the above technical problems. Summary of the Invention

[0005] In view of the defects in the prior art, the purpose of the present invention is to provide a dual-station radar collaborative positioning method and system.

[0006] According to the present invention, a dual-station radar collaborative positioning method is provided, the method comprising the following steps:

[0007] Step S1: Set a unified north-east measurement rectangular coordinate system with the fusion center as the origin; select the main observation station radar and the secondary observation station radar and obtain the station coordinates of the two radars. The first radar is the main observation station radar, and its station coordinates are Ω1 (x1, y1, z1); the second radar is the secondary observation station radar, and its station coordinates are Ω2 (x2, y2, z2); the first radar and the second radar simultaneously detect the target T in the airspace and obtain the target measurement result information T respectively. RAE-1 (R1, A1, E1) and T RAE-2(R2, A2, E2); With the help of on-site signal-to-noise ratio data and historical data analysis and modeling, the measurement error distribution characteristics of the first radar of the main observation station to the target are obtained, and the first radar fluctuation error is recorded as (σ R1 ,σ A1 ,σ E1 ), the measurement system error is (δ R1 ,δ A1 ,δ E1 ); the second radar fluctuation error is (σ R2 ,σ A2 ,σ E2 ), the measurement system error is (δ R2 ,δ A2 ,δ E2 );

[0008] Step S2: For the first radar of the main observation station, ignoring the error in the range direction, calculate the target uncertainty range Φ caused by the measurement errors in the azimuth and elevation directions;

[0009] Step S3: In the spherical coordinate system with the second radar station Ω2 as the origin, a spherical surface is constructed with the second radar as the center and R2 as the radius.

[0010] Step S4: using a linear weighted method to iteratively solve the midpoint H of the line segment obtained by the intersection of the spherical surface Γ and the arc surface Φ;

[0011] Step S5: Using the pitch and azimuth directions measured by the two radars for the target as references, the two radar station sites Ω1 and Ω2 as the centers of the circles, and the ranging results R1 and R2 as the radii, draw circles and the intersection line L of the two intersecting circles;

[0012] Step S6: Calculate the intersection coordinates O of the intersection line L of the two intersecting circles and the line Ω1Ω2 connecting the first radar and the second radar sites based on the law of cosines and the proportional method;

[0013] Step S7: Based on point O and point H, the arc point coordinates T(R, A, E) are calculated using the proportional method, which is the positioning result value of the target by the dual-station radar;

[0014] Step S8: Based on the fluctuation error and system error of the second radar, the rationality of the positioning result is judged and the target positioning value is output.

[0015] Preferably, the method for obtaining and specifically calculating the measurement uncertainty range Φ of the target by the radar of the main observation station in step S2 includes the following steps:

[0016] Step S2.1: In a spherical coordinate system with the first radar site as the origin, construct a spherical surface Λ: with the first radar as the center and R1 as the radius;

[0017] Step S2.2: Let ζ be the first radar azimuth The size of the unilateral uncertainty region of the vector measurement result, which is expressed as the combination of the first radar azimuth systematic error and the azimuth fluctuation error:

[0018] ζ=a×δ A1 +b×σ A1 (1)

[0019] Wherein, a is the weight of the first radar azimuth system error, and b is the weight of the first radar azimuth fluctuation error;

[0020] Step S2.3: Similarly, ξ is denoted as the size of the unilateral uncertainty region of the first radar pitch () vector measurement result, which is expressed as the combination of the first radar pitch direction systematic error and the pitch direction heave error:

[0021] ξ=c×δ E41 +d×σ E41 (2)

[0022] Wherein, c is the weight of the first radar's elevation system error, and d is the weight of the first radar's elevation heave error;

[0023] Step S2.4: Create two azimuth planes in a spherical coordinate system with the coordinates of the first radar station as the origin. and Two pitch cones I1:θ=E1-ξ and I2:θ=E1+ξ1; the closed surface on the sphere Λ formed by the planes П1 and Π2 and the intersection lines of the cones I1 and I2 with Λ is denoted as Φ;

[0024] Step S2.5: Also take the first radar as the origin and observe the coordinates of the four vertices of the arc surface Φ in a clockwise direction, which are Φ is the spatial uncertainty range of all targets detected by the first radar, when the range measurement error is ignored and the azimuth and elevation measurement errors exist.

[0025] Preferably, the spherical surface is determined in step S4. The specific method for determining whether the four sides of the arc surface Φ intersect is as follows:

[0026] Step S4.1: At time t, the four points P1, P2, P3, and P4, the coordinates of the first and second radar sites Ω1 and Ω2, and T RAE-1 With T RAE-2 All are transferred to the measurement rectangular coordinate system with the fusion center as the origin;

[0027] Step S4.2: In the spherical coordinate system with the second radar station as the origin, draw a spherical surface with the second radar as the center and R2 as the radius.

[0028] Step S4.3: Starting from point P1, calculate the distances from points P1, P2, P3, and P4 to the center Ω2 of the second radar of the main observation station in clockwise order; if the distance is greater than R2, the point is outside the sphere Γ; if the distance is less than R2, the point is inside the sphere If the distance is equal to R2, the point is on the sphere superior;

[0029] Step S4.4: The positional relationships between the four points P1, P2, P3, and P4 and the sphere Γ are recorded as S1, S2, S3, and S4 respectively. Points outside the sphere are recorded as 1, inside the sphere as -1, and on the sphere as 0. If the product of the positional relationship states of two adjacent points and the sphere Ω2 is -1, then the arc formed by the two points is determined to be adjacent to the sphere. There is an intersection point; or a point and the sphere The position relationship state is equal to 0, then the point is the arc surface Φ and the spherical surface The intersection of .

[0030] Preferably, the specific calculation method of using the cosine theorem and the proportional method in step S6 to obtain the coordinates O of the intersection line L of the two intersecting circles and the line Ω1Ω2 connecting the first radar station site and the second radar station site comprises the following steps:

[0031] Step S6.1: Calculate the distance from the first radar station Ω1 to the second radar station Ω2, denoted as D Ω12 :

[0032]

[0033] Step S6.2: Calculate the distance from O to the first radar station Ω1 using the cosine theorem, denoted as D or1 :

[0034]

[0035] Step S6.3: Calculate the scaling factor k:

[0036]

[0037] Step S6.4: Based on Ω1(x1, y1, z1), Ω2(x2, y2, z2) and k, calculate the coordinates of the intersection point O(x co ,y co ,z co ):

[0038]

[0039] Preferably, the specific calculation method of obtaining the arc point coordinates T(R, A, E) by the proportional method in step S7, that is, the positioning result value of the target by the bistatic radar, includes the following steps:

[0040] Step S7.1: Calculate arc point H p1 (x hp1 ,y hp1 ,z hp1 ) and H p2 (x hp2 ,y hp2 ,z hp2 ) than O(x co ,y co ,z co )'s average radius R ohp12 :

[0041]

[0042]

[0043]

[0044] Step S7.2: Calculate O(x co ,y co ,z co ) to H(x h ,y h ,z h ), denoted as R oh :

[0045]

[0046] Step S7.3: Based on O, H, R ohp12 and R oh , solve the arc point T(R,A,E) using the proportional method:

[0047]

[0048] The present invention also provides a dual-station radar collaborative positioning system, which includes the following modules:

[0049] Module M1: Set a unified north-east measurement rectangular coordinate system with the fusion center as the origin; select the main observation station radar and the secondary observation station radar and obtain the station coordinates of the two radars. The first radar is the main observation station radar, and its station coordinates are Ω1 (x1, y1, z1). The second radar is the secondary observation station radar, and its station coordinates are Ω2 (x2, y2, z2). The first radar and the second radar simultaneously detect the target T in the airspace and obtain the target measurement result information T respectively. RAE-1 (R1, A1, E1) and T RAE-2 (R2, A2, E2); With the help of on-site signal-to-noise ratio data and historical data analysis and modeling, the measurement error distribution characteristics of the first radar of the main observation station to the target are obtained, and the first radar fluctuation error is recorded as (σ R1 ,σA1 ,σ E1 ), the measurement system error is (δ R1 ,δ A1 ,δ E1 ); the second radar fluctuation error is (σ R2 ,σ A2 ,σ E2 ), the measurement system error is (δ R2 ,δ A2 ,δ E2 );

[0050] Module M2: For the first radar of the main observation station, ignoring the error in the range direction, calculate the target uncertainty range Φ caused by the measurement errors in the azimuth and elevation directions;

[0051] Module M3: In the spherical coordinate system with the second radar site Ω2 of the auxiliary observation station as the origin, a spherical surface is constructed with the second radar as the center and R2 as the radius.

[0052] Module M4: Linear weighted iterative solution of spherical surface The midpoint H of the line segment intersecting the arc surface Φ;

[0053] Module M5: Use the pitch and azimuth directions measured by the two radars to measure the target as the reference, the two radar station sites Ω1 and Ω2 as the center of the circle, and the ranging results R1 and R2 as the radius to draw circles and the intersection line L of the two intersecting circles;

[0054] Module M6: Calculate the intersection coordinates O of the intersection line L of the two intersecting circles and the line Ω1Ω2 connecting the first and second radar sites based on the law of cosines and the proportional method;

[0055] Module M7: Based on points O and H, the arc point coordinates T(R, A, E) are calculated using the proportional method, which is the positioning result of the dual-station radar for the target.

[0056] Module M8: Based on the fluctuation error and system error of the second radar, judge the rationality of the positioning result and output the target positioning value.

[0057] Preferably, the system and specific calculation for obtaining the measurement uncertainty range Φ of the target by the radar of the main observation station in the module M2 include the following modules:

[0058] Module M2.1: In the spherical coordinate system with the first radar site as the origin, construct a spherical surface Λ: with the first radar as the center and R1 as the radius;

[0059] Module M2.2: ζ is the first radar azimuth The size of the unilateral uncertainty region of the vector measurement result, which is expressed as the combination of the first radar azimuth systematic error and the azimuth fluctuation error:

[0060] ζ=a×δ A1 +b×σ A1 (1)

[0061] Wherein, a is the weight of the first radar azimuth system error, and b is the weight of the first radar azimuth fluctuation error;

[0062] Module M2.3: Similarly, ξ is denoted as the size of the unilateral uncertainty region of the first radar pitch (θ) vector measurement result, which is expressed as the combination of the first radar pitch systematic error and pitch heave error:

[0063] ξ=c×δ E1 +d×σ E1 (2)

[0064] Wherein, c is the weight of the first radar's elevation system error, and d is the weight of the first radar's elevation heave error;

[0065] Module M2.4: Create a spherical coordinate system with the coordinates of the first radar station as the origin, and then draw two azimuth planes and Two pitch cones I1:θ=E1-ξ and I2:θ=E1+ξ1; the closed surface on the sphere Λ formed by the planes Π1 and Π2 and the intersection lines of the cones I1 and I2 with Λ is denoted as Φ;

[0066] Module M2.5: Also with the first radar as the origin, observe the four vertex coordinates of the arc surface Φ in a clockwise direction, which are Φ is the spatial uncertainty range of all targets detected by the first radar, when the range measurement error is ignored and the azimuth and elevation measurement errors exist.

[0067] Preferably, the module M4 determines the spherical surface The specific judgment system for whether the four sides of the arc surface Φ intersect each other includes the following modules:

[0068] Module M4.1: At time t, the four points P1, P2, P3, P4, the coordinates of the first and second radar sites Ω1 and Ω2, T RAE-1 With T RAE-2 All are transferred to the measurement rectangular coordinate system with the fusion center as the origin;

[0069] Module M4.2: In a spherical coordinate system with the second radar site as the origin, construct a spherical surface Γ with the second radar as the center and R2 as the radius;

[0070] Module M4.3: Starting from point P1, calculate the distances from points P1, P2, P3, and P4 to the center Ω2 of the second radar of the main observation station in clockwise order; if the distance is greater than R2, the point is on the sphere. In addition, if the distance is less than R2, the point is on the sphere If the distance is equal to R2, the point is on the sphere superior;

[0071] Module M4.4: Points P1, P2, P3, P4 and the sphere The positional relationship is recorded as S1, S2, S3, and S4 respectively. The point outside the sphere is recorded as 1, inside the sphere is recorded as -1, and on the sphere is recorded as 0. If the product of the positional relationship between two adjacent points and the sphere Ω2 is -1, then the arc formed by the two points is determined to be There is an intersection point; or a point and the sphere The position relationship state is equal to 0, then the point is the arc surface Φ and the spherical surface The intersection of .

[0072] Preferably, the specific calculation system for calculating the intersection coordinates O of the intersection line L of the two intersecting circles and the line Ω1Ω2 connecting the first radar and the second radar station sites using the cosine theorem and the proportional method in the module M6 includes the following modules:

[0073] Module M6.1: Calculate the distance from the first radar station Ω1 to the second radar station Ω2, denoted as D Ω12 :

[0074]

[0075] Module M6.2: Use the cosine theorem to calculate the distance from O to the first radar station Ω1, denoted as D or1 :

[0076]

[0077] Module M6.3: Calculation of the scaling factor k:

[0078]

[0079] Module M6.4: Based on Ω1(x1,y1,z1), Ω2(x2,y2,z2) and k, calculate the coordinates of the intersection point O(x co ,y co ,z co ):

[0080]

[0081] Preferably, the specific calculation system for obtaining the arc point coordinates T(R, A, E) by the proportional method in the module M7, i.e., the positioning result value of the target by the dual-station radar, includes the following modules:

[0082] Module M7.1: Calculation of arc point H p1 (x hp1 ,y hp1,z hp1 ) and H p2 (x hp2 ,y hp2 ,z hp2 ) than O(x co ,y co ,z co )'s average radius R ohp12 :

[0083]

[0084]

[0085]

[0086] Module M7.2: Calculate O(x co ,y co ,z co ) to H(x h ,y h ,z h ), denoted as R oh :

[0087]

[0088] Module M7.3: Based on O, H, R ohp12 and R oh , solve the arc point T(R,A,E) using the proportional method:

[0089]

[0090] Compared with the prior art, the present invention has the following beneficial effects:

[0091] The present invention is applicable to the compression filtering processing in the coordinated centralized information fusion of dual-station / multi-station radars configured with medium-to-long baselines (20km-100km), which can significantly improve the accuracy of the dual-station radar's coordinated positioning of targets and avoid the systematic error of the algorithm caused by approximation. BRIEF DESCRIPTION OF THE DRAWINGS

[0092] Other features, objects and advantages of the present invention will become more apparent upon reading the detailed description of non-limiting embodiments with reference to the following drawings:

[0093] Figure 1 Flowchart of the dual-station radar collaborative positioning algorithm for finding the arc midpoint based on the complementary characteristics of measurement error information and the proportional method;

[0094] Figure 2 Schematic diagram of the projection of the route on the ZOX plane in an embodiment of the present invention;

[0095] Figure 3 A comparison chart of the R-direction error measured by the first radar and the R-direction error of the existing patent positioning;

[0096] Figure 4 A comparison diagram of the R-direction error measured by the first radar and the R-direction error of the positioning method of the present invention;

[0097] Figure 5 A comparison chart of the R-direction error measured by the second radar and the R-direction error of the existing patent positioning;

[0098] Figure 6 A comparison diagram of the R-direction error measured by the second radar and the R-direction error of the positioning method of the present invention;

[0099] Figure 7 A comparison chart of the R-direction positioning error of the existing patent and the R-direction positioning error of the present invention under the fusion center;

[0100] Figure 8 A comparison chart of the X-direction error measured by the first radar, the X-direction error measured by the second radar, the X-direction error positioned by the existing patent, and the X-direction error positioned by the present invention under the fusion center;

[0101] Figure 9 It is a comparison chart of the Z-direction error measured by the first radar under the fusion center, the Z-direction error measured by the second radar, the Z-direction error positioned by the existing patent, and the Z-direction error positioned by the present invention. DETAILED DESCRIPTION

[0102] The present invention will be described in detail below with reference to specific embodiments. The following examples will help those skilled in the art to further understand the present invention, but are not intended to limit the present invention in any form. It should be noted that, for those skilled in the art, several changes and improvements can be made without departing from the scope of the present invention. These all fall within the scope of protection of the present invention.

[0103] Example 1:

[0104] According to the present invention, a dual-station radar collaborative positioning method is provided, the method comprising the following steps:

[0105] Step S1: Set a unified north-east measurement rectangular coordinate system with the fusion center as the origin; select the main observation station radar and the secondary observation station radar and obtain the station coordinates of the two radars. The first radar is the main observation station radar, and its station coordinates are Ω1 (x1, y1, z1); the second radar is the secondary observation station radar, and its station coordinates are Ω2 (x2, y2, z2); the first radar and the second radar simultaneously detect the target T in the airspace and obtain the target measurement result information T respectively. RAE-1 (R1, A1, E1) and T RAE-2(R2, A2, E2); With the help of on-site signal-to-noise ratio data and historical data analysis and modeling, the measurement error distribution characteristics of the first radar of the main observation station to the target are obtained, and the first radar fluctuation error is recorded as (σ R1 ,σ A1 ,σ E1 ), the measurement system error is (δ R1 ,δ A1 ,δ E1 ); the second radar fluctuation error is (σ R2 ,σ A2 ,σ E2 ), the measurement system error is (δ R2 ,δ A2 ,δ E2 );

[0106] Step S2: For the first radar of the main observation station, ignoring the error in the range direction, calculate the target uncertainty range Φ caused by the measurement errors in the azimuth and elevation directions. The method for calculating and specifically calculating the measurement uncertainty range Φ of the target by the radar of the main observation station includes the following steps:

[0107] Step S2.1: In a spherical coordinate system with the first radar site as the origin, construct a spherical surface Λ with the first radar site as the center and R1 as the radius;

[0108] Step S2.2: Let ζ be the first radar azimuth The size of the unilateral uncertainty region of the vector measurement result, which is expressed as the combination of the first radar azimuth systematic error and the azimuth fluctuation error:

[0109]

[0110] Wherein, a is the weight of the first radar azimuth system error, and b is the weight of the first radar azimuth fluctuation error;

[0111] Step S2.3: Similarly, ξ is denoted as the size of the unilateral uncertainty region of the first radar pitch () vector measurement result, which is expressed as the combination of the first radar pitch direction systematic error and the pitch direction heave error:

[0112] ξ=c×δ E1 +d×σ E1 (2)

[0113] Wherein, c is the weight of the first radar's elevation system error, and d is the weight of the first radar's elevation heave error;

[0114] Step S2.4: Create two azimuth planes in a spherical coordinate system with the coordinates of the first radar station as the origin. and Two pitch cones I1:θ=E1-ξ and I2:θ=E1+ξ1; the closed surface on the sphere Λ formed by the planes Π1 and Π2 and the intersection lines of the cones i1 and i2 with Λ is denoted as Φ;

[0115] Step S2.5: Also take the first radar as the origin and observe the coordinates of the four vertices of the arc surface Φ in a clockwise direction, which are Φ is the spatial uncertainty range of all targets detected by the first radar, when the range measurement error is ignored and the azimuth and elevation measurement errors exist.

[0116] Step S3: In the spherical coordinate system with the second radar station Ω2 as the origin, a spherical surface is constructed with the second radar as the center and R2 as the radius.

[0117] Step S4: Iteratively solve the sphere using the linear weighted method The midpoint H of the line segment obtained by intersecting the arc surface Φ; judge the spherical surface The specific method for determining whether the four sides of the arc surface Φ intersect is as follows:

[0118] Step S4.1: At time t, the four points P1, P2, P3, and P4, the coordinates of the first and second radar sites Ω1 and Ω2, and T RAE-1 With T RAE-2 All are transferred to the measurement rectangular coordinate system with the fusion center as the origin;

[0119] Step S4.2: In the spherical coordinate system with the second radar station as the origin, draw a spherical surface with the second radar as the center and R2 as the radius.

[0120] Step S4.3: Starting from point P1, calculate the distances from points P1, P2, P3, and P4 to the center of the second radar of the main observation station, Ω2, in clockwise order. If the distance is greater than R2, the point is on the sphere. In addition, if the distance is less than R2, the point is on the sphere If the distance is equal to R2, the point is on the sphere superior;

[0121] Step S4.4: Four points P1, P2, P3, and P4 and the sphere The positional relationship is recorded as S1, S2, S3, and S4 respectively. The point outside the sphere is recorded as 1, inside the sphere is recorded as -1, and on the sphere is recorded as 0. If the product of the positional relationship between two adjacent points and the sphere Ω2 is -1, then the arc formed by the two points is determined to be There is an intersection point; or a point and the sphere The position relationship state is equal to 0, then the point is the arc surface Φ and the spherical surface The intersection of .

[0122] Step S5: Using the elevation and azimuth directions of the target measured by the two radars as references, the two radar station sites Ω1 and Ω2 as the centers of the circles, and the ranging results R1 and R2 as the radii, draw circles and the intersection line L of the two intersecting circles;

[0123] Step S6: Calculate the coordinates O of the intersection line L of the two intersecting circles and the line Ω1Ω2 connecting the first and second radar sites based on the cosine theorem and the proportional method. The specific calculation method for calculating the coordinates O of the intersection line L of the two intersecting circles and the line Ω1Ω2 connecting the first and second radar sites based on the cosine theorem and the proportional method includes the following steps:

[0124] Step S6.1: Calculate the distance from the first radar station Ω1 to the second radar station Ω2, denoted as D Ω12 :

[0125]

[0126] Step S6.2: Calculate the distance from O to the first radar station Ω1 using the cosine theorem, denoted as D or1 :

[0127]

[0128] Step S6.3: Calculate the scaling factor k:

[0129]

[0130] Step S6.4: Based on Ω1(x1, y1, z1), Ω2(x2, y2, z2) and k, calculate the coordinates of the intersection point O(x co ,y co ,z co ):

[0131]

[0132] Step S7: Based on point O and point H, the arc point coordinates T(R, A, E) are calculated using the proportional method, which is the positioning result value of the target by the dual-station radar. The specific calculation method for calculating the arc point coordinates T(R, A, E) using the proportional method, which is the positioning result value of the target by the dual-station radar, includes the following steps:

[0133] Step S7.1: Calculate arc point H p1 (x hp1 ,y hp1 ,z hp1 ) and H p2 (x hp2 ,y hp2 ,z hp2 ) than O(x co ,yco ,z co )'s average radius R ohp12 :

[0134]

[0135]

[0136]

[0137] Step S7.2: Calculate O(x co ,y co ,z co ) to H(x h ,y h ,z h ), denoted as R oh :

[0138]

[0139] Step S7.3: Based on O, H, R ohp12 and R oh , solve the arc point T(R,A,E) using the proportional method:

[0140]

[0141] Step S8: Based on the fluctuation error and system error of the second radar, the rationality of the positioning result is judged and the target positioning value is output.

[0142] The present invention also provides a dual-station radar collaborative positioning system, which can be implemented by executing the process steps of the dual-station radar collaborative positioning method. That is, those skilled in the art can understand the dual-station radar collaborative positioning method as a preferred implementation of the dual-station radar collaborative positioning system.

[0143] Example 2:

[0144] The present invention also provides a dual-station radar collaborative positioning system, which includes the following modules:

[0145] Module M1: Set a unified north-east measurement rectangular coordinate system with the fusion center as the origin; select the main observation station radar and the secondary observation station radar and obtain the station coordinates of the two radars. The first radar is the main observation station radar, and its station coordinates are Ω1 (x1, y1, z1). The second radar is the secondary observation station radar, and its station coordinates are Ω2 (x2, y2, z2). The first radar and the second radar simultaneously detect the target T in the airspace and obtain the target measurement result information T respectively. RAE-1 (R1, A1, E1) and T RAE-2(R2, A2, E2); With the help of on-site signal-to-noise ratio data and historical data analysis and modeling, the measurement error distribution characteristics of the first radar of the main observation station to the target are obtained, and the first radar fluctuation error is recorded as (σ R1 ,σ A1 ,σ E1 ), the measurement system error is (δ R1 ,δ A1 ,δ E1 ); the second radar fluctuation error is (σ R2 ,σ A2 ,σ E2 ), the measurement system error is (δ R2 ,δ A2 ,δ E2 );

[0146] Module M2: For the first radar of the main observation station, ignoring the error in the range direction, calculate the target uncertainty range Φ caused by the measurement errors in the azimuth and elevation directions. The system and specific calculations for calculating the measurement uncertainty range Φ of the main observation station radar to the target include the following modules:

[0147] Module M2.1: In the spherical coordinate system with the first radar site as the origin, construct a spherical surface Λ with the first radar as the center and R1 as the radius;

[0148] Module M2.2: ζ is the first radar azimuth The size of the unilateral uncertainty region of the vector measurement result, which is expressed as the combination of the first radar azimuth systematic error and the azimuth fluctuation error:

[0149]

[0150] Wherein, a is the weight of the first radar azimuth system error, and b is the weight of the first radar azimuth fluctuation error;

[0151] Module M2.3: Similarly, ξ is denoted as the size of the unilateral uncertainty region of the first radar pitch () vector measurement result, which is expressed as the combination of the first radar pitch systematic error and pitch heave error:

[0152] ξ=c×δ E1 +d×σ E1 (2)

[0153] Wherein, c is the weight of the first radar's elevation system error, and d is the weight of the first radar's elevation heave error.

[0154] Module M2.4: Create a spherical coordinate system with the coordinates of the first radar station as the origin, and then draw two azimuth planes and Two pitch cones I1:θ=E1-ξ and I2:θ=E1+ξ1; the closed surface on the sphere Λ formed by the planes П1 and П2 and the intersection lines of the cones I1 and I2 with Λ is denoted as Φ;

[0155] Module M2.5: Also with the first radar as the origin, observe the four vertex coordinates of the arc surface Φ in a clockwise direction, which are Φ is the spatial uncertainty range of all targets detected by the first radar, when the range measurement error is ignored and the azimuth and elevation measurement errors exist.

[0156] Module M3: In the spherical coordinate system with the second radar site Ω2 of the auxiliary observation station as the origin, a spherical surface is constructed with the second radar as the center and R2 as the radius.

[0157] Module M4: Linear weighted iterative solution of spherical surface The midpoint H of the line segment obtained by intersecting the arc surface Φ; judge the spherical surface The specific judgment system for whether the four sides of the arc surface Φ intersect each other includes the following modules:

[0158] Module M4.1: At time t, the four points P1, P2, P3, P4, the coordinates of the first and second radar sites Ω1 and Ω2, T RAE-1 With T RAE-2 All are transferred to the measurement rectangular coordinate system with the fusion center as the origin;

[0159] Module M4.2: In the spherical coordinate system with the second radar site as the origin, a spherical surface is constructed with the second radar as the center and R2 as the radius.

[0160] Module M4.3: Starting from point P1, calculate the distances from points P1, P2, P3, and P4 to the center of the second radar of the main observation station, Ω2, in clockwise order. If the distance is greater than R2, the point is on the sphere. In addition, if the distance is less than R2, the point is on the sphere If the distance is equal to R2, the point is on the sphere superior;

[0161] Module M4.4: Points P1, P2, P3, P4 and the sphere The positional relationship is recorded as S1, S2, S3, and S4 respectively. The point outside the sphere is recorded as 1, inside the sphere is recorded as -1, and on the sphere is recorded as 0. If the product of the positional relationship between two adjacent points and the sphere Ω2 is -1, then the arc formed by the two points is determined to be There is an intersection point; or a point and the sphere The position relationship state is equal to 0, then the point is the arc surface Φ and the spherical surface The intersection of .

[0162] Module M5: Use the pitch and azimuth directions measured by the two radars to measure the target as the reference, the two radar station sites Ω1 and Ω2 as the center of the circle, and the ranging results R1 and R2 as the radius to draw circles and the intersection line L of the two intersecting circles;

[0163] Module M6: Calculate the intersection coordinates O of the intersection line L of the two intersecting circles and the line Ω1Ω2 connecting the first and second radar sites based on the cosine theorem and the proportional method. The specific calculation system for calculating the intersection coordinates O of the intersection line L of the two intersecting circles and the line Ω1Ω2 connecting the first and second radar sites based on the cosine theorem and the proportional method includes the following modules:

[0164] Module M6.1: Calculate the distance from the first radar station Ω1 to the second radar station Ω2, denoted as D Ω12 :

[0165]

[0166] Module M6.2: Use the cosine theorem to calculate the distance from O to the first radar station Ω1, denoted as D or1 :

[0167]

[0168] Module M6.3: Calculation of the scaling factor k:

[0169]

[0170] Module M6.4: Based on Ω1(x1,y1,z1), Ω2(x2,y2,z2) and k, calculate the coordinates of the intersection point O(x co ,y co ,z co ):

[0171]

[0172] Module M7: Based on points O and H, the arc point coordinates T(R, A, E) are calculated using the proportional method, which is the positioning result of the dual-station radar for the target. The specific calculation system for calculating the arc point coordinates T(R, A, E) using the proportional method, which is the positioning result of the dual-station radar for the target, includes the following modules:

[0173] Module M7.1: Calculation of arc point H p1 (x hp1 ,y hp1 ,z hp1 ) and H p2 (x hp2 ,y hp2 ,z hp2 ) than O(x co ,yco ,z co )'s average radius R ohp12 :

[0174]

[0175]

[0176]

[0177] Module M7.2: Calculate O(x co ,y co ,z co ) to H(x h ,y h ,z h ), denoted as R oh :

[0178]

[0179] Module M7.3: Based on O, H, R ohP12 and R oh , solve the arc point T(R,A,E) using the proportional method:

[0180]

[0181] Module M8: Based on the fluctuation error and system error of the second radar, judge the rationality of the positioning result and output the target positioning value.

[0182] Example 3:

[0183] The dual-station radar collaborative positioning algorithm is based on the complementary characteristics of measurement error information and the proportional method to obtain the arc midpoint. The method specifically includes:

[0184] Step 1: Set a unified north-east measurement rectangular coordinate system with the fusion center as the origin; select the main observation station radar and the secondary observation station radar and obtain the station coordinates of the two radars. The first radar is the main observation station radar, and its station coordinates are Ω1(x1, y1, z1); the second radar is the secondary observation station radar, and its station coordinates are Ω2(x2, y2, z2); the first radar and the second radar simultaneously detect the target T in the airspace and obtain the target measurement result information T respectively. RAE-1 (R1, A1, E1) and T RAE-2 (R2, A2, E2); With the help of on-site signal-to-noise ratio data and historical data analysis and modeling, the measurement error distribution characteristics of the first radar of the main observation station to the target are obtained, and the first radar fluctuation error is recorded as (σ R1 ,σ A1 ,σ E1 )(Root mean square error), the measurement system error is (δR1 ,δ A1 ,δ E1 ); the second radar fluctuation error is (σ R2 ,σ A2 ,σ E2 )(Root mean square error), the measurement system error is (δ R2 ,δ A2 ,δ E2 ).

[0185] Step 2: For the first radar of the main observation station, ignoring the error in the range direction, calculate the target uncertainty range Φ caused by the measurement errors in the azimuth and elevation directions.

[0186] Step 3: In the spherical coordinate system with the second radar site Ω2 of the secondary observation station as the origin, construct a spherical surface Γ with the second radar as the center and R2 as the radius.

[0187] Step 4: Use the linear weighted method to iteratively solve the midpoint H of the line segment obtained by the intersection of the sphere Γ and the arc surface Φ.

[0188] Step 5: Use the elevation and azimuth measured by the two radars for the target as the reference, the two radar station sites Ω1 and Ω2 as the center of the circle, and the ranging results R1 and R2 as the radius to draw circles and the intersection line L of the two intersecting circles.

[0189] Step 6: Based on the law of cosines and the proportional method, calculate the coordinates O of the intersection line L of the two intersecting circles and the line Ω1Ω2 connecting the first and second radar sites.

[0190] Step 7: Based on point O and point H, use the proportional method to calculate the arc point coordinates T(R, A, E), which is the positioning result value of the dual-station radar for the target.

[0191] Step 8: Based on the fluctuation error and system error of the second radar, judge the rationality of the positioning result and output the target positioning value.

[0192] In step 2, the method for obtaining and specifically calculating the measurement uncertainty range Φ of the target by the radar at the main observation station is as follows:

[0193] (1) In the spherical coordinate system with the first radar site as the origin, draw a spherical surface Λ with the first radar as the center and R1 as the radius.

[0194] (2) Let ζ be the first radar azimuth The size of the unilateral uncertainty region of the vector measurement result can be expressed as the combination of the first radar azimuth systematic error and the azimuth fluctuation error:

[0195] ζ=a×δ A1 +b×σ A1 (1)

[0196] Where a is the weight of the first radar's azimuth system error, and b is the weight of the first radar's azimuth fluctuation error. Generally, a = 1 and b = 4 are sufficient to cover all possible areas where the target may be located in azimuth.

[0197] (3) Similarly, ξ is the size of the unilateral uncertainty region of the first radar pitch (θ) vector measurement result, which can also be expressed as the combination of the first radar pitch direction systematic error and pitch direction heave error:

[0198] ξ=c×δ E1 +d×σ E1 (2)

[0199] Where c is the weighted value of the first radar's elevation error, and d is the weighted value of the first radar's elevation heave error. Generally, c = 1 and d = 4 are sufficient to cover all possible areas where a target may be present in elevation.

[0200] (4) In the spherical coordinate system with the coordinates of the first radar station as the origin, two azimuth planes are drawn. and Two pitch cone surfaces Ι1:θ=E1-ξ and Ι2:θ=E1+ξ1; the closed surface on the spherical surface Λ enclosed by planes Π1 and Π2 and the intersection lines of the cone surfaces Ι1 and Ι2 with Λ is denoted as Φ.

[0201] (5) Also with the first radar as the origin, the coordinates of the four vertices of the arc surface (convex quadrilateral) Φ are observed in the clockwise direction, which are P1(R1,A1-ζ1,E1-ξ1), P2(R1,A1-ζ1,E1+ξ1), P3(R1,A1+ζ1,E1+ξ1), and P4(R1,A1+ζ1,E1-ξ1). Φ is the spatial uncertainty range of all possible targets detected by the first radar when the range measurement error is ignored and the azimuth and elevation measurement errors exist.

[0202] In the step 4, the spherical surface is judged The specific method for determining whether the four sides of the arc surface (convex quadrilateral) Φ intersect is as follows:

[0203] (1) At time t, the four points P1, P2, P3, and P4, the coordinates of the first and second radar sites Ω1 and Ω2, and T RAE-1 With T RAE-2 All are transferred to the measurement rectangular coordinate system with the fusion center as the origin.

[0204] (2) In the spherical coordinate system with the second radar station as the origin, a spherical surface is constructed with the second radar as the center and R2 as the radius.

[0205] (3) Starting from point P1, calculate the distances from points P1, P2, P3, and P4 to the center Ω2 of the second radar of the main observation station in clockwise order. If the distance is greater than R2, the point is on the sphere. In addition, if the distance is less than R2, the point is on the sphere If the distance is equal to R2, the point is on the sphere superior.

[0206] (4) Points P1, P2, P3, and P4 and the sphere The positional relationship is recorded as S1, S2, S3, and S4 respectively. The point outside the sphere is recorded as 1, inside the sphere is recorded as -1, and on the sphere is recorded as 0. If the product of the positional relationship between two adjacent points and the sphere Ω2 is -1, then the arc formed by the two points is determined to be There is an intersection point; or a point and the sphere The position relationship state is equal to 0, then the point is the arc surface (convex quadrilateral) Φ and the spherical surface The intersection of .

[0207] In the fourth step, the linear weighted method is used to iteratively solve the spherical The specific calculation method of the midpoint H of the line segment obtained by intersecting the arc surface Φ is as follows:

[0208] (1) Setting up a point and The line segments and spheres intersect( and is a pair among P1 and P2, P2 and P3, P3 and P4, P4 and P1), then and On the sphere In the measurement rectangular coordinate system with the fusion center as the origin, record and The coordinates are Calculate the difference between the distance from the two points to the center of the second radar station and R2, and record them as D1 and D2:

[0209]

[0210]

[0211] (2) It can be seen that D1·D2<0. Using the linear weighting method to obtain and A point P between o (x o ,y o ,z o ):

[0212]

[0213] (3) Calculate P o The distance to the first radar site Ω1(x1, y1, z1), denoted as D o1 :

[0214]

[0215] (4) Based on the first radar site Ω1, P o , D o1 and the distance measurement R1 of the first radar to the target, solve for the arc point H p (x hp , y hp , z hp ) by the proportional method. H p is a point on the arc side with and as endpoints.

[0216]

[0217] (5) Calculate the difference between the distance from H p to the second radar site Ω2(x2, y2, z2) and R2, denoted as H R (x hr , y hr , z hr ):

[0218]

[0219] (6) Set the threshold value d, which can be taken as 10-4. If H R <d, it can be considered that H p is on the sphere Ω2 and the intersection point has been obtained; if H R ≥d and D1·H R <0, let H p be the new and continue to iterate and update H p until the iteration times are met or H R <d and the iteration ends; if H R ≥d and D2·H R <0, let H p be the new and continue to iterate and update H p until the iteration times are met or H R <d and the iteration ends;

[0220] (7) There is an intersecting arc segment between the arc surface (convex quadrilateral) Φ and the sphere , that is, there are two pairs of combinations that form a line segment that intersects the sphere Intersect, through the above steps, the arc points H at both ends of the intersecting arc segment can be obtained p1 (x hp1 ,y hp1 ,z hp1 ) and H p2 (x hp2 ,y hp2 ,z hp2 ), the midpoint of the line connecting the two arc points is the midpoint of the line connecting the two arc points H(x h ,y h ,z h ).

[0221] In step 6, the specific calculation method for obtaining the intersection coordinates O of the intersection line L of the two intersecting circles and the line Ω1Ω2 connecting the first radar station and the second radar station using the cosine theorem and the proportional method is as follows:

[0222] (1) Calculate the distance from the first radar station Ω1 to the second radar station Ω2, denoted as D Ω12 :

[0223]

[0224] (2) Using the cosine theorem, calculate the distance from O to the first radar station Ω1, denoted as D or1 :

[0225]

[0226] (3) Calculate the scaling factor k:

[0227]

[0228] (4) Based on Ω1(x1, y1, z1), Ω2(x2, y2, z2) and k, the coordinates of the intersection point Ο(x co ,y co ,z co ):

[0229]

[0230] In step 7, the arc point coordinates T(R, A, E) are obtained by the proportional method, which is the specific calculation method of the positioning result value of the dual-station radar for the target as follows:

[0231] (1) Calculate arc point H p1 (x hp1 ,y hp1 ,z hp1 ) and H p2 (x hp2 ,y hp2 ,z hp2 ) than Ο(x co ,yco ,z co )'s average radius R ohp12 :

[0232]

[0233]

[0234]

[0235] (2) Calculate Ο(x co ,y co ,z co ) to H(x h ,y h ,z h ), denoted as R oh :

[0236]

[0237] (3) Based on O, H, R ohp12 and R oh , solve the arc point T(R,A,E) using the proportional method:

[0238]

[0239] When two radars detect the same target and both can obtain the target's three-dimensional measurements of R, A, and E, the present invention provides a dual-station radar collaborative positioning algorithm for obtaining the arc midpoint based on the complementary characteristics of the measurement error information and the proportional method, utilizing the spatial characteristics of the measurement error distribution of the two radars near the target. The algorithm is characterized in that the joint positioning algorithm includes:

[0240] Step 1: Set a unified north-east measurement rectangular coordinate system with the fusion center as the origin; select the main observation station radar and the secondary observation station radar and obtain the station coordinates of the two radars. The first radar is the main observation station radar, and its station coordinates are Ω1(x1, y1, z1); the second radar is the secondary observation station radar, and its station coordinates are Ω2(x2, y2, z2); the first radar and the second radar simultaneously detect the target T in the airspace and obtain the target measurement result information T respectively. RAE-1 (R1, A1, E1) and T RAE-2 (R2, A2, E2); With the help of on-site signal-to-noise ratio data and historical data analysis and modeling, the measurement error distribution characteristics of the first radar of the main observation station to the target are obtained, and the first radar fluctuation error is recorded as (σ R1 ,σ A1 ,σ E1 )(Root mean square error), the measurement system error is (δ R1 ,δ A1 ,δ E1); the second radar fluctuation error is (σ R2 ,σ A2 ,σ E2 )(Root mean square error), the measurement system error is (δ R2 ,δ A2 ,δ E2 ).

[0241] Step 2: For the first radar of the main observation station, ignoring the error in the range direction, calculate the target uncertainty range Φ caused by the measurement errors in the azimuth and elevation directions. The specific calculation method is as follows:

[0242] (1) In the spherical coordinate system with the first radar site as the origin, draw a spherical surface Λ with the first radar as the center and R1 as the radius.

[0243] (2) Let ζ be the first radar azimuth The size of the unilateral uncertainty region of the vector measurement result can be expressed as the combination of the first radar azimuth systematic error and the azimuth fluctuation error:

[0244] ζ=a×δ A1 +b×σ A1 (1)

[0245] Where a is the weight of the first radar's azimuth system error, and b is the weight of the first radar's azimuth fluctuation error. Generally, a = 1 and b = 4 are sufficient to cover all possible areas where the target may be located in azimuth.

[0246] (3) Similarly, ξ is the size of the unilateral uncertainty region of the first radar pitch (θ) vector measurement result, which can also be expressed as the combination of the first radar pitch direction systematic error and pitch direction heave error:

[0247] ξ=c×δ E1 +d×σ E1 (2)

[0248] Where c is the weighted value of the first radar's elevation error, and d is the weighted value of the first radar's elevation heave error. Generally, c = 1 and d = 4 are sufficient to cover all possible areas where a target may be present in elevation.

[0249] (4) In the spherical coordinate system with the coordinates of the first radar station as the origin, two azimuth planes are drawn. and Two pitch cone surfaces Ι1:θ=E1-ξ and Ι2:θ=E1+ξ1; the closed surface on the spherical surface Λ enclosed by planes Π1 and Π2 and the intersection lines of the cone surfaces Ι1 and Ι2 with Λ is denoted as Φ.

[0250] (5) Also with the first radar as the origin, the coordinates of the four vertices of the arc surface (convex quadrilateral) Φ are observed in the clockwise direction, which are P1(R1,A1-ζ1,E1-ξ1), P2(R1,A1-ζ1,E1+ξ1), P3(R1,A1+ζ1,E1+ξ1), and P4(R1,A1+ζ1,E1-ξ1). Φ is the spatial uncertainty range of all possible targets detected by the first radar when the range measurement error is ignored and the azimuth and elevation measurement errors exist.

[0251] Step 3: In the spherical coordinate system with the second radar site Ω2 of the secondary observation station as the origin, draw a spherical surface with the second radar as the center and R2 as the radius.

[0252] Step 4: Linear weighted method iterative solution of sphere The midpoint H of the line segment obtained by intersecting the arc surface Φ, where the spherical surface is determined in step 4 The method for determining whether the four sides of the arc surface (convex quadrilateral) Φ intersect is as follows:

[0253] (1) At time t, the four points P1, P2, P3, and P4, the coordinates of the first and second radar sites Ω1 and Ω2, and T RAE-1 With T RAE-2 All are transferred to the measurement rectangular coordinate system with the fusion center as the origin;

[0254] (2) In the spherical coordinate system with the second radar station as the origin, a spherical surface is constructed with the second radar as the center and R2 as the radius.

[0255] (3) Starting from point P1, calculate the distances from points P1, P2, P3, and P4 to the center Ω2 of the second radar of the main observation station in clockwise order. If the distance is greater than R2, the point is on the sphere. In addition, if the distance is less than R2, the point is on the sphere If the distance is equal to R2, the point is on the sphere superior.

[0256] (4) Points P1, P2, P3, and P4 and the sphere The positional relationship is recorded as S1, S2, S3, and S4 respectively. The point outside the sphere is recorded as 1, inside the sphere is recorded as -1, and on the sphere is recorded as 0. If the product of the positional relationship between two adjacent points and the sphere Ω2 is -1, then the arc formed by the two points is determined to be There is an intersection point; or a point and the sphere The position relationship state is equal to 0, then the point is the arc surface (convex quadrilateral) Φ and the spherical surface The intersection of .

[0257] Finally, in step 4, the linear weighted method is used to iteratively solve the spherical The specific calculation method of the midpoint H of the line segment obtained by intersecting the arc surface Φ is as follows:

[0258] (1) Setting up a point and The line segments and spheres intersect( and is a pair among P1 and P2, P2 and P3, P3 and P4, P4 and P1), then and On the sphere In the measurement rectangular coordinate system with the fusion center as the origin, record and The coordinates are Calculate the difference between the distance from the two points to the center of the second radar station and R2, and record them as D1 and D2:

[0259]

[0260]

[0261] (2) It can be seen that D1·D2<0. Using the linear weighting method to obtain and A point P between o (x o ,y o ,z o ):

[0262]

[0263] (3) Calculate P o The distance to the first radar station Ω1(x1,y1,z1) is denoted as D o1 :

[0264]

[0265] (4) Based on the first radar station Ω1, P o 、D o1 The first radar measures the target distance R1 and the arc point H is solved by the proportional method. p (x hp ,y hp ,z hp ), H p for and A point on the edge of the arc that is the endpoint.

[0266]

[0267] (5) Calculate Hp The difference between the distance to the second radar site Ω2(x2, y2, z2) and R2 is denoted as H R (x hr , y hr , z hr ):

[0268]

[0269] (6) Set the threshold value d, which can be taken as 10-4. If H R < d, it can be considered that H p is on the spherical surface Ω2, and the intersection point has been obtained; if H R ≥ d and D1·H R < 0, let H p be the new Continue to perform iterative update on H according to the above steps p , until the number of iterations is satisfied or H R < d to end the iteration; if H R ≥ d and D2·H R < 0, let H p be the new Continue to perform iterative update on H according to the above steps p , until the number of iterations is satisfied or H R < d to end the iteration;

[0270] (7) There is an intersecting arc segment between the arc surface (convex quadrilateral) Φ and the spherical surface , that is, there are two pairs of The line segments formed by the combination intersect with the spherical surface . Through the above steps, the arc points H p1 (x hp1 , y hp1 , z hp1 ) and H p2 (x hp2 , y hp2 , z hp2 ) can be obtained. The midpoint of the line connecting the two arc points is the midpoint H(x h , y h , z h ).

[0271] Step Five: Respectively take the elevation and azimuth directions of the target measurements by the two radars as the reference, draw circles with the two radar sites Ω1 and Ω2 as the centers and the ranging results R1 and R2 as the radii, and draw the intersection line L of the two intersecting circles;

[0272] Step Six: Based on the cosine theorem and the proportional method, find the intersection coordinates Ο of the intersection line L of the two intersecting circles and the line connecting the first radar and the second radar site Ω1Ω2. The specific calculation method is as follows:

[0273] (1) Calculate the distance from the first radar station Ω1 to the second radar station Ω2, denoted as D Ω12 :

[0274]

[0275] (2) Using the cosine theorem, calculate the distance from O to the first radar station Ω1, denoted as D or1 :

[0276]

[0277] (3) Calculate the scaling factor k:

[0278]

[0279] (4) Based on Ω1(x1, y1, z1), Ω2(x2, y2, z2) and k, the coordinates of the intersection point Ο(x co ,y co ,z co ):

[0280]

[0281] Step 7: Based on point O and point H, use the proportional method to calculate the arc point coordinates T(R, A, E), which is the positioning result of the dual-station radar for the target. The specific calculation method is as follows:

[0282] (1) Calculate arc point H p1 (x hp1 ,y hp1 ,z hp1 ) and H p2 (x hp2 ,y hp2 ,z hp2 ) than Ο(x co ,y co ,z co )'s average radius R ohp12 :

[0283]

[0284]

[0285]

[0286] (2) Calculate Ο(x co ,y co ,z co ) to H(x h ,y h ,z h ), denoted as R oh:

[0287]

[0288] (3) Based on O, H, R ohp12 and R oh , solve the arc point T(R,A,E) using the proportional method:

[0289]

[0290] Step 8: Based on the fluctuation error and system error of the second radar, judge the rationality of the positioning result and output the target positioning value.

[0291] The present invention discloses an embodiment of a dual-station radar collaborative positioning algorithm for obtaining an arc midpoint based on complementary characteristics of measurement error information and a proportional method. The joint positioning algorithm specifically includes the following steps:

[0292] Step 1: Set a unified north-east measurement rectangular coordinate system with the fusion center as the origin; select the main observation station radar and the secondary observation station radar and obtain the station coordinates of the two radars. The first radar is the main observation station radar, and its station coordinates are Ω1(x1, y1, z1); the second radar is the secondary observation station radar, and its station coordinates are Ω2(x2, y2, z2); the first radar and the second radar simultaneously detect the target T in the airspace and obtain the target measurement result information T respectively. RAE-1 (R1, A1, E1) and T RAE-2 (R2, A2, E2); With the help of on-site signal-to-noise ratio data and historical data analysis and modeling, the measurement error distribution characteristics of the first radar of the main observation station to the target are obtained, and the first radar fluctuation error is recorded as (σ R1 ,σ A1 ,σ E1 )(Root mean square error), the measurement system error is (δ R1 ,δ A1 ,δ E1 ); the second radar fluctuation error is (σ R2 ,σ A2 ,σ E2 )(Root mean square error), the measurement system error is (δ R2 ,δ A2 ,δ E2 ).

[0293] Step 2: For the first radar of the main observation station, ignoring the error in the range direction, calculate the target uncertainty range Φ caused by the measurement errors in the azimuth and elevation directions;

[0294] Step 3: In the spherical coordinate system with the second radar site Ω2 of the secondary observation station as the origin, draw a spherical surface with the second radar as the center and R2 as the radius.

[0295] Step 4: Linear weighted method iterative solution of sphere The midpoint H of the line segment intersecting the arc surface Φ;

[0296] Step 5: Use the elevation and azimuth measured by the two radars to determine the target as the reference, the two radar station sites Ω1 and Ω2 as the center of the circle, and the ranging results R1 and R2 as the radius to draw circles and the intersection line L of the two intersecting circles;

[0297] Step 6: Based on the law of cosines and the proportional method, calculate the coordinates O of the intersection line L of the two intersecting circles and the line Ω1Ω2 connecting the first and second radar sites;

[0298] Step 7: Based on point O and point H, use the proportional method to calculate the arc point coordinates T(R, A, E), which is the positioning result of the dual-station radar for the target;

[0299] Step 8: Based on the fluctuation error and system error of the second radar, judge the rationality of the positioning result and output the target positioning value.

[0300] The present invention solves the error distribution space of the primary station radar and approximates it to an arc surface. The distance information of the secondary station radar is used to complement a positioning sphere. The midpoint position of the arc intersected by the arc surface and the sphere is solved based on the proportional method, and this midpoint is used as the optimal estimate of joint positioning.

[0301] The flow chart of the dual-station radar joint positioning algorithm provided by the present invention is as follows: Figure 1 shown.

[0302] In a simulation example, a North-Celestial-East measurement coordinate system is established with the fusion center as the coordinate origin, with the X axis being the north direction, the Z axis being the east direction, and the Y axis being the celestial direction. The target starting coordinates are T (0km, 10km, 300km), the uniform level flight speed is V (0, 0, -100m / s), the simulation duration is 2500s, the sampling interval is 1s, and the horizontal projection diagram of the route on the XOZ plane is shown as follows: Figure 2 As shown in Figure 2, two radar stations, O1 and O2, are located on the X-axis, with coordinates O1 (-20 km, 0, 0) and O2 (20 km, 0, 0). The systematic errors of the first radar's range, azimuth, and elevation dimensions are [10 m, 0.15°, 0.2°], and the heave error is [30 m, 0.25°, 0.2°]. The systematic errors of the second radar's range, azimuth, and elevation dimensions are [8 m, 0.15°, 0.3°], and the heave error is [15 m, 0.15°, 0.25°]. Site errors, Earth curvature, and coordinate axis pointing errors are negligible.

[0303] like Figure 3 and Figure 5 As shown, the existing patent method will introduce systematic errors in the R direction of the first radar and the second radar ranging, such as Figure 4 and Figure 6As shown, the existing method eliminates the distance system error introduced by the existing patent method itself in the distance (R) measured by the first radar and the second radar; Figure 7 As shown, the method of the present invention under the fusion center also eliminates the distance system error introduced by the existing patent method in the R direction. Compared with the existing patent method, the ranging accuracy in the R direction is improved by about 70%; for the X direction, Figure 8 This is a comparison chart of the X-direction error measured by the first radar, the X-direction error measured by the second radar, the X-direction error of the existing patent positioning, and the X-direction error of the positioning of the present invention under the fusion center. The root mean square error of the X-direction of the fusion positioning result of the present invention is slightly reduced by about 20% compared with the existing patent method; for the Z direction, Figure 9 This is a comparison chart of the Z-direction error measured by the first radar under the fusion center, the Z-direction error measured by the second radar, the Z-direction error of the existing patent positioning and the Z-direction error of the positioning of the present invention. The root mean square of the Z-direction error of the fusion positioning result of the present invention is slightly reduced by about 60% compared with the existing patent method.

[0304] In summary, the method of the present invention can effectively improve the Z-direction positioning accuracy of the dual-station radar joint positioning and slightly improve the X-direction positioning accuracy, and effectively eliminate the distance system error introduced by the existing patented method itself in the distance direction.

[0305] Those skilled in the art may understand this embodiment as a more specific description of Embodiment 1 and Embodiment 2.

[0306] Those skilled in the art will appreciate that, in addition to implementing the system and its various devices, modules, and units provided by the present invention in purely computer-readable program code, it is entirely possible to implement the same functions of the system and its various devices, modules, and units provided by the present invention in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers by logically programming the method steps. Therefore, the system and its various devices, modules, and units provided by the present invention can be considered a hardware component, and the devices, modules, and units included therein for implementing various functions can also be considered as structures within the hardware component; the devices, modules, and units for implementing various functions can also be considered as both software modules implementing the method and structures within the hardware component.

[0307] The above describes specific embodiments of the present invention. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art may make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. The embodiments of this application and the features in the embodiments may be combined with each other in any manner unless there is a conflict.

Claims

1. A dual-station radar collaborative positioning method, characterized in that: The method comprises the following steps: Step S1: Set a unified north-east measurement rectangular coordinate system with the fusion center as the origin; select the main observation station radar and the secondary observation station radar and obtain the station coordinates of the two radars. The first radar is the main observation station radar, and its station coordinates are Ω1 (x1, y1, z1); the second radar is the secondary observation station radar, and its station coordinates are Ω2 (x2, y2, z2); the first radar and the second radar simultaneously detect the target T in the airspace and obtain the target measurement result information T respectively. RAE-1 (R1, A1, E1) and T RAE-2 (R2, A2, E2); With the help of on-site signal-to-noise ratio data and historical data analysis and modeling, the measurement error distribution characteristics of the first radar of the main observation station to the target are obtained, and the first radar fluctuation error is recorded as (σ R1 ,σ A1 ,σ E1 ), the measurement system error is (δ R1 ,δ A1 ,δ E1 ); the second radar fluctuation error is (δ R2 ,σ A2 ,σ E2 ), the measurement system error is (δ R2 ,δ A2 ,δ E2 ); Step S2: For the first radar of the main observation station, ignoring the error in the range direction, calculate the target uncertainty range Φ caused by the measurement errors in the azimuth and elevation directions; Step S3: In a spherical coordinate system with the second radar site Ω2 of the secondary observation station as the origin, a spherical surface Γ is constructed with the second radar as the center and R2 as the radius; Step S4: using a linear weighted method to iteratively solve the midpoint H of the line segment obtained by the intersection of the spherical surface Γ and the arc surface Φ; Step S5: Using the elevation and azimuth directions of the target measured by the two radars as references, the two radar station sites Ω1 and Ω2 as the centers of the circles, and the ranging results R1 and R2 as the radii, draw circles and the intersection line L of the two intersecting circles; Step S6: Calculate the intersection coordinates O of the intersection line L of the two intersecting circles and the line Ω1Ω2 connecting the first radar and the second radar sites based on the law of cosines and the proportional method; Step S7: Based on point O and point H, the arc point coordinates T(R, A, E) are calculated using the proportional method, which is the positioning result value of the target by the dual-station radar; Step S8: Based on the fluctuation error and system error of the second radar, determine the rationality of the positioning result and output the target positioning value; The specific calculation method of obtaining the arc point coordinates T(R, A, E) by the proportional method in step S7, i.e., the positioning result value of the target by the dual-station radar, includes the following steps: Step S7.1: Calculate arc point H p1 (x hp1 ,y hp1 ,z hp1 ) and H p2 (x hp2 ,y hp2 ,z hp2 ) to O(x co ,y co ,z co )'s average radius R ohp12 : Step S7.2: Calculate O(x co ,y co ,z co ) to H(x h ,y h ,z h ), denoted as R oh : Step S7.3: Based on O, H, R ohp12 and R oh , solve the arc point T(R,A,E) using the proportional method:

2. The dual-station radar collaborative positioning method according to claim 1, characterized in that: The method for obtaining and specifically calculating the measurement uncertainty range Φ of the target by the radar of the main observation station in step S2 includes the following steps: Step S2.1: In a spherical coordinate system with the first radar site as the origin, construct a spherical surface Λ with the first radar site as the center and R1 as the radius; Step S2.2: Let ζ be the first radar azimuth The size of the unilateral uncertainty region of the vector measurement result, which is expressed as the combination of the first radar azimuth systematic error and the azimuth fluctuation error: ζ=a×δ A1 +b×s A1 (1) Wherein, a is the weight of the first radar azimuth system error, and b is the weight of the first radar azimuth fluctuation error; Step S2.3: Let ξ be the size of the unilateral uncertainty region of the first radar pitch (θ) vector measurement result, which is expressed as the combination of the first radar pitch direction systematic error and pitch direction heave error: ξ=c×δ E1 +d×σ E1 (2) Wherein, c is the weight of the first radar's elevation system error, and d is the weight of the first radar's elevation heave error; Step S2.4: Create two azimuth planes in a spherical coordinate system with the coordinates of the first radar station as the origin. and Two pitch cones I1:θ=E1-ξ and I2:θ=E1+ξ; the closed surface on the sphere Λ formed by the planes ∏1 and ∏2 and the intersection lines of the cones I1 and I2 with Λ is denoted as Φ; Step S2.5: Also with the first radar as the origin, observe the coordinates of the four vertices of the arc surface Φ in a clockwise direction, which are P1(R1,A1-ζ1,E1-ξ1), P2(R1,A1-ζ1,E1+ξ1), P3(R1,A1+ζ1,E1+ξ1), and P4(R1,A1+ζ1,E1-ξ1). Φ is the spatial uncertainty range of all targets detected by the first radar when the range measurement error is ignored and the azimuth and elevation measurement errors exist.

3. The dual-station radar collaborative positioning method according to claim 2, characterized in that: The specific determination method of determining whether the four sides of the spherical surface Γ and the arc surface Φ intersect in step S4 includes the following steps: Step S4.1: At time t, the four points P1, P2, P3, and P4, the coordinates of the first and second radar sites Ω1 and Ω2, and T RAE-1 With T RAE-2 All are transferred to the measurement rectangular coordinate system with the fusion center as the origin; Step S4.2: In a spherical coordinate system with the second radar site as the origin, construct a spherical surface Γ with the second radar as the center and R2 as the radius; Step S4.3: Starting from point P1, calculate the distances from points P1, P2, P3, and P4 to the center Ω2 of the second radar at the main observation station in clockwise order. If the distance is greater than R2, the point is outside the sphere Γ. If the distance is less than R2, the point is inside the sphere Γ. If the distance is equal to R2, the point is on the sphere Γ. Step S4.4: The positional relationships between the four points P1, P2, P3, and P4 and the sphere Γ are recorded as S1, S2, S3, and S4 respectively. A point outside the sphere is recorded as 1, inside the sphere is recorded as -1, and on the sphere is recorded as 0. If the product of the positional relationship states of two adjacent points with the sphere Ω2 is -1, it is determined that the arc formed by the two points has an intersection with the sphere Γ. If the positional relationship state of a point with the sphere Γ is equal to 0, then the point is the intersection of the arc φ and the sphere Γ.

4. The dual-station radar collaborative positioning method according to claim 1, characterized in that: The specific calculation method of the intersection point O of the intersection line L of the two intersecting circles and the line Ω1Ω2 connecting the first radar station and the second radar station using the cosine theorem and the proportional method in step S6 includes the following steps: Step S6.1: Calculate the distance from the first radar station Ω1 to the second radar station Ω2, denoted as D Ω12 : Step S6.2: Calculate the distance from O to the first radar station Ω1 using the cosine theorem, denoted as D or1 : Step S6.3: Calculate the scaling factor k: Step S6.4: Based on Ω1(x1, y1, z1), Ω2(x2, y2, z2) and k, calculate the coordinates of the intersection point O(x co ,y cO ,z co ):

5. A dual-station radar collaborative positioning system, characterized in that: The system includes the following modules: Module M1: Set a unified north-east measurement rectangular coordinate system with the fusion center as the origin; select the main observation station radar and the secondary observation station radar and obtain the station coordinates of the two radars. The first radar is the main observation station radar, and its station coordinates are Ω1 (x1, y1, z1). The second radar is the secondary observation station radar, and its station coordinates are Ω2 (x2, y2, z2). The first radar and the second radar simultaneously detect the target T in the airspace and obtain the target measurement result information T respectively. RAE-1 (R1, A1, E1) and T RAE-2 (R2, A2, E2); With the help of on-site signal-to-noise ratio data and historical data analysis and modeling, the measurement error distribution characteristics of the first radar of the main observation station to the target are obtained, and the first radar fluctuation error is recorded as (σ R1 ,σ A1 ,σ E1 ), the measurement system error is (δ R1 ,δ A1 ,δ E1 ); the second radar fluctuation error is (σ R2 ,σ A2 ,σ E2 ), the measurement system error is (δ R2 ,δ A2 ,δ E2 ); Module M2: For the first radar of the main observation station, ignoring the error in the range direction, calculate the target uncertainty range Φ caused by the measurement errors in the azimuth and elevation directions; Module M3: In the spherical coordinate system with the second radar site Ω2 of the secondary observation station as the origin, a spherical surface Γ is constructed with the second radar as the center and R2 as the radius; Module M4: Iteratively solve the midpoint H of the line segment obtained by the intersection of the sphere Γ and the arc surface Φ using the linear weighted method; Module M5: Use the pitch and azimuth directions measured by the two radars to measure the target as the reference, the two radar station sites Ω1 and Ω2 as the center of the circle, and the ranging results R1 and R2 as the radius to draw circles and the intersection line L of the two intersecting circles; Module M6: Calculate the intersection coordinates O of the intersection line L of the two intersecting circles and the line Ω1Ω2 connecting the first and second radar sites based on the law of cosines and the proportional method; Module M7: Based on points O and H, the arc point coordinates T(R, A, E) are calculated using the proportional method, which is the positioning result of the dual-station radar for the target. Module M8: Based on the fluctuation error and system error of the second radar, judge the rationality of the positioning result and output the target positioning value; The specific calculation system for obtaining the arc point coordinates T(R, A, E) by the proportional method in the module M7, i.e., the positioning result value of the target by the dual-station radar, includes the following modules: Module M7.1: Calculation of arc point H p1 (x hp1 ,y hp1 ,z hp1 ) and H p2 (x hp2 ,y hp2 ,z hp2 ) than O(x co ,y co ,z co )'s average radius R ohp12 : Module M7.2: Calculate O(x co ,y co ,z co ) to H(x h ,y h ,z h ), denoted as R oh : Module M7.3: Based on O, H, R ohp12 and R oh , solve the arc point T(R,A,E) using the proportional method:

6. The dual-station radar collaborative positioning system according to claim 5, characterized in that: The system and specific calculation for obtaining the measurement uncertainty range Φ of the target by the main observation station radar in the module M2 include the following modules: Module M2.1: In the spherical coordinate system with the first radar site as the origin, construct a spherical surface Λ with the first radar as the center and R1 as the radius; Module M2.2: ζ is the first radar azimuth The size of the unilateral uncertainty region of the vector measurement result, which is expressed as the combination of the first radar azimuth systematic error and the azimuth fluctuation error: ζ=a×δ A1 +b×s A1 (1) Wherein, a is the weight of the first radar azimuth system error, and b is the weight of the first radar azimuth fluctuation error; Module M2.3: Let ξ be the size of the unilateral uncertainty region of the first radar pitch (θ) vector measurement result, which is expressed as the combination of the first radar pitch systematic error and pitch heave error: ξ=c×δ E1 +d×σ E1 (2) Wherein, c is the weight of the first radar's elevation system error, and d is the weight of the first radar's elevation heave error; Module M2.4: Create a spherical coordinate system with the coordinates of the first radar station as the origin, and then draw two azimuth planes and Two pitch cones I1:θ=E1-ξ and I2:θ=E1+ξ; the closed surface on the sphere Λ formed by the planes Π1 and Π2 and the intersection lines of the cones I1 and I2 with Λ is denoted as Φ; Module M2.5: Also with the first radar as the origin, observe the coordinates of the four vertices of the arc surface Φ in a clockwise direction, which are P1(R1,A1-ζ1,E1-ζ1), P2(R1,A1-ζ1,E1+ξ1), P3(R1,A1+ζ1,E1+ξ1), and P4(Φ1,A1+ζ1,E1-ξ1). Φ is the spatial uncertainty range of all targets detected by the first radar when the range measurement error is ignored and the azimuth and elevation measurement errors exist.

7. The dual-station radar collaborative positioning system according to claim 6, characterized in that: The specific judgment system for judging whether the four sides of the spherical surface Γ and the arc surface Φ intersect in the module M4 includes the following modules: Module M4.1: At time t, the four points P1, P2, P3, and P4, the coordinates of the first and second radar sites Ω1 and Ω2, and T RAE-1 With T RAE-2 All are transferred to the measurement rectangular coordinate system with the fusion center as the origin; Module M4.2: In a spherical coordinate system with the second radar site as the origin, construct a spherical surface Γ with the second radar as the center and R2 as the radius; Module M4.3: Starting from point P1, calculate the distances from points P1, P2, P3, and P4 to the center Ω2 of the second radar at the main observation station in clockwise order. If the distance is greater than R2, the point is outside the sphere Γ. If the distance is less than R2, the point is inside the sphere Γ. If the distance is equal to R2, the point is on the sphere Γ. Module M4.4: The positional relationships between the four points P1, P2, P3, and P4 and the sphere Γ are denoted as S1, S2, S3, and S4, respectively. A point outside the sphere is denoted as 1, inside the sphere as -1, and on the sphere as 0. If the product of the positional relationship states of two adjacent points with the sphere Ω2 is -1, then it is determined that the arc formed by the two points intersects the sphere Γ. If the positional relationship state of a point with the sphere Γ is equal to 0, then the point is the intersection of the arc φ and the sphere Γ.

8. The dual-station radar collaborative positioning system according to claim 5, characterized in that: The specific calculation system for using the cosine theorem and the proportional method in the module M6 to calculate the coordinates O of the intersection line L of the two intersecting circles and the line Ω1Ω2 connecting the first radar station and the second radar station includes the following modules: Module M6.1: Calculate the distance from the first radar station Ω1 to the second radar station Ω2, denoted as D Ω12 : Module M6.2: Use the cosine theorem to calculate the distance from O to the first radar station Ω1, denoted as D or1 : Module M6.3: Calculation of the scaling factor k: Module M6.4: Based on Ω1(x1,y1,z1), Ω2(x2,y2,z2) and k, calculate the coordinates of the intersection point O(x co ,y co ,z co ):

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