Method for calculating target position in time difference positioning

Abstract

The invention discloses a method for calculating a target position in time difference positioning. The method comprises the following steps: constructing a time difference curve between a main observation station and each auxiliary observation station; obtaining a time difference asymptotic line for time difference positioning calculation according to the time difference curve; based on an intersection point of a straight line where the main observation station and the auxiliary observation station are located and the time difference curve, obtaining a ray according to a ray slope confirmed by a time difference asymptote; taking each boundary region defined by the ray and the time difference asymptote as a position parallelogram for target positioning, and obtaining a target estimation position according to the vertex coordinate value of each position parallelogram; and constructing a quadrilateral iteration adjustment rule based on a position discrimination function, and positioning and obtaining a position area where the target estimation position is located according to the target estimation position in combination with the function value polarity of the discrimination function. According to the method, the technical problem that the position of the target cannot be quickly and accurately solved under the condition that the modern electromagnetic environment is increasingly complicated is solved.

Description

Technical Field

[0001] The present invention relates to the technical field of target position calculation, and in particular to a method for calculating a target position in time difference positioning. Background Art

[0002] Time difference positioning determines the location of the target radiation source by measuring the arrival time difference of the radiation source signal to multiple observation stations. Compared with traditional ranging positioning, its error is smaller, and this technology does not rely on signal strength positioning, so it has strong anti-interference ability. Compared with direction finding positioning, it is not easily affected by the external environment and has stronger adaptability to complex electromagnetic environments. Therefore, time difference positioning is widely used in mobile communications, drone intrusion prevention, electronic countermeasures and other fields.

[0003] At present, in the field of time difference positioning, the target is located at the intersection of multiple sets of hyperbolas corresponding to the measured time difference, and it is usually difficult to directly solve the equations of the two hyperbolas, and the solution cannot be expressed by simple elementary functions. In the increasingly complex modern electromagnetic environment, how to quickly and accurately calculate the target position has become a key issue in time difference positioning technology, and its measurement accuracy and effectiveness play a decisive role in the performance of the positioning system. Summary of the invention

[0004] The present invention provides a method for calculating a target position in time difference positioning to overcome the above technical problems.

[0005] In order to achieve the above object, the technical solution of the present invention is: A method for calculating a target position in time difference positioning comprises the following steps: S1: Set up the main observation station and auxiliary observation station; And the number of the auxiliary observation stations is two; And construct the time difference curve between the main observation station and each auxiliary observation station to calculate the target position by time difference positioning; S2: Obtaining the time difference asymptote for time difference positioning calculation according to the time difference curve; S3: Based on the intersection of the straight line where the station positions of the main observation station and the auxiliary observation station are located and the time difference curve, and according to the slope of the ray confirmed by the time difference asymptote, the ray used for time difference positioning calculation is obtained; Each boundary area enclosed by the ray and the time difference asymptote is used as a position parallelogram for target positioning, and the intersection point of the time difference curve between the main observation station and each auxiliary observation station is located inside each position parallelogram; S4: Obtain the vertex coordinate values ​​of the parallelogram at each position; And obtain the estimated position of the target according to the vertex coordinate values ​​of the parallelogram at each position; S5: constructing a quadrilateral iterative adjustment rule based on the position discriminant function, and locating the position area where the target estimated position is located according to the target estimated position and the function value polarity of the discriminant function; Reconstruct the position parallelogram according to the position area where the target estimated position is located, and repeat step S4 until the difference between the target estimated position of the reconstructed position parallelogram and the target estimated position of the position parallelogram before reconstruction meets the preset error threshold, so as to obtain the intersection coordinates of the time difference curves between the main observation station and each auxiliary observation station, which is the final target estimated position.

[0006] Beneficial effect: The present invention provides a method for calculating the position of a target in time difference positioning, by constructing a time difference curve between a main observation station and each auxiliary observation station to obtain a time difference asymptote for time difference positioning calculation; and based on the intersection of the straight line where the main observation station and the auxiliary observation station are located with the time difference curve, and according to the ray slope confirmed by the time difference asymptote, a ray is obtained, and then the vertex coordinate values ​​of the parallelogram at each position are obtained, and the target estimated position is obtained according to the vertex coordinate values ​​of the parallelogram at each position, and the problem of finding the intersection of two groups of hyperbolas is solved by using a method of iteratively reducing the target area, that is, constructing a quadrilateral iterative adjustment rule based on a position discriminant function, and at the same time, the problem of not being able to obtain real roots by directly solving the equation using a method of approximating the target position with the center value of the parallelogram is solved, and an update iterative method for each vertex of the parallelogram when the target is located at different intersection positions is given, which meets the requirements of quickly and accurately calculating the target position in time difference positioning, solves the problem of not being able to obtain a solution to the hyperbola equation, and has high practical value. BRIEF DESCRIPTION OF THE DRAWINGS

[0007] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0008] Figure 1 A flow chart of a method for calculating a target position in time difference positioning of the present invention; Figure 2 This is a schematic diagram of the initial range of time difference positioning intersection values ​​in this embodiment; Figure 3 4 is a flowchart of the quadrilateral iterative adjustment rule based on the position discriminant function in this embodiment. DETAILED DESCRIPTION

[0009] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0010] This embodiment provides a method for calculating a target position in time difference positioning, comprising the following steps: S1: Set up the main observation station and auxiliary observation station; And the number of the auxiliary observation stations is two; And construct the time difference curve between the main observation station and each auxiliary observation station to calculate the target position by time difference positioning; The specific steps include: S11: Setting up a main observation station and an auxiliary observation station for calculating the target position in time difference positioning; And the auxiliary observation station includes a first auxiliary observation station and a second auxiliary observation station; The distance between the main observation station and the auxiliary observation station is set to ,in Indicates the first auxiliary observation station; Indicates the second auxiliary observation station; Define the time difference between the main observation station and the auxiliary observation station After measurement, confirm that the target is located at For the long axis, The intersection of the two hyperbolas is the location of the target. represents the speed of light constant; S12: Construct the time difference curve between the main observation station and each auxiliary observation station; And the time difference curves include a first set of hyperbolas between the main observation station and the first auxiliary observation station; The second set of hyperbolas between the main observatory and the second auxiliary observatory; S121: The method for constructing the first set of hyperbolas is The main observation station is taken as the origin, and the direction from the main observation station to the first auxiliary observation station is taken as the positive x Axis direction, set the plane rectangular coordinate system; Then based on the plane rectangular coordinate system, the first set of hyperbolas is obtained as (1) Where: represents the major axis of the first set of hyperbolas and ; represents the focal length of the first hyperbola and ; S122: The method for constructing the second set of hyperbolas is Assume that the angle between the straight line where the second auxiliary observation station and the main observation station are located, and the angle between the straight line where the main observation station and the first auxiliary observation station are located is , then the second set of hyperbolas formed by the second auxiliary observation station and the main observation station is (2) Where: represents the major axis of the second set of hyperbolas and ; represents the focal length of the second hyperbola and ; S2: Obtaining the time difference asymptote for time difference positioning calculation according to the time difference curve; According to the characteristics of the hyperbola, the two sets of hyperbolas have four intersection points. To determine the range of the four intersection points, the following straight lines are defined to limit the range: It includes a first asymptote and a second asymptote about the main observation station and the first auxiliary observation station, a third asymptote and a fourth asymptote about the main observation station and the second auxiliary observation station; And the expression of the first asymptote is (3) The expression of the second asymptote is (4) The expression of the third asymptote is (5) The expression of the fourth asymptote is (6) S3: Based on the intersection of the straight line where the main observation station and the auxiliary observation station are located and the time difference curve, and according to the slope of the ray confirmed by the time difference asymptote, the ray used for time difference positioning calculation is obtained; Each boundary area enclosed by the ray and the time difference asymptote is used as a position parallelogram for target positioning, and the intersection point of the time difference curve between the main observation station and each auxiliary observation station is located inside each position parallelogram; The specific steps include: S31: Based on the intersection of the straight line where the main observation station and the auxiliary observation station are located and the time difference curve, and according to the slope of the ray confirmed by the time difference asymptote, a ray for time difference positioning calculation is obtained; Specifically include: confirming the two straight lines where the main observation station and each auxiliary observation station are located; and obtaining the intersection points of each straight line with the corresponding first group of hyperbolas and second group of hyperbolas, and taking each intersection point as the starting point and the slope of the corresponding time difference asymptote as the inclination, obtaining the first ray and the second ray about the main observation station and the first auxiliary observation station, and the third ray and the fourth ray about the main observation station and the second auxiliary observation station; The expression for the first ray is (7) The expression for the second ray is (8) The expression of the third ray is (9) The expression of the fourth ray is (10) S32: using each boundary area enclosed by each ray and the time difference asymptote as a position parallelogram for target positioning, and the intersection point of the first group of hyperbolas and the second group of hyperbolas is located inside each position parallelogram respectively; Among them, for the first curve intersection, the right area of ​​the point does not exceed the left side of the first asymptote, the left area of ​​the point does not exceed the right side of the second ray, the upper area of ​​the point does not exceed the left side of the fourth asymptote, and the lower area of ​​the point does not exceed the right side of the fourth ray; For the intersection point of the second curve, the right area of ​​the point does not exceed the left side of the first ray, the left range of the point does not exceed the right side of the second asymptote, the upper area of ​​the point does not exceed the left side of the third ray 7, and the lower area of ​​the point does not exceed the right side of the third asymptote; For the intersection point of the third curve, the area on the right side of the point does not exceed the left side of the first asymptote, the left side range of the point does not exceed the right side of the second ray, the upper area of ​​the point does not exceed the left side of the second ray, and the lower area of ​​the point does not exceed the right side of the third asymptote; For the intersection point of the fourth curve, the right area of ​​the point does not exceed the left side of the first ray, the left range of the point does not exceed the right side of the second asymptote, the upper area of ​​the point does not exceed the left side of the fourth asymptote, and the lower area of ​​the point does not exceed the right side of the fourth ray 8; S4: Obtain the vertex coordinate values ​​of the parallelogram at each position; And obtain the estimated position of the target according to the vertex coordinate values ​​of the parallelogram at each position; The specific steps include: S41: Assume that the coordinates of a vertex of the position parallelogram are , and the equations of the two adjacent edges of the vertex coordinates are (11) (12) Where: , represents the slope of the equation of the edge; Then the vertex coordinates are obtained by solving the adjacent edge equation, and the expression is: (13) (14) S42: Based on step S41, formulas (3) to (10) are rewritten to solve the coordinates of each vertex of the position parallelogram, and the expression is: (15) (16) (17) (18) (19) (20) (twenty one) (twenty two) S43: Figure 2 As shown, the intersection points of the first set of hyperbolas and the second set of hyperbolas are defined as the first curve intersection point j, the second curve intersection point k, the third curve intersection point l, and the fourth curve intersection point m, respectively; And respectively obtain the vertex coordinate values ​​of the parallelograms at the intersection points of each curve; S431: defining four vertices of a parallelogram at the intersection of the first curve to be a first left vertex, a first right vertex, a first upper vertex, and a first lower vertex; The first left vertex is the intersection of the fourth asymptote and the second ray. Based on formulas (11) to (14), according to formulas (20) and (18), the vertex coordinates of the first left vertex are obtained, and the expression is: (twenty three) (twenty four) The first right vertex is the intersection of the first asymptote and the fourth ray. Based on formulas (11) to (14), according to formulas (22) and (15), the vertex coordinates of the first right vertex are obtained, and the expression is: (25) (26) The first upper vertex is the intersection of the first asymptote and the fourth asymptote. Based on formulas (11) to (14), according to formulas (28) and (15), the vertex coordinates of the first upper vertex are obtained, and the expression is: (27) (28) The first lower vertex is the intersection of the second ray and the fourth ray. Based on formulas (11) to (14), according to formulas (22) and (20), the vertex coordinates of the first lower vertex are obtained, and the expression is: (29) (30) S432: defining four vertices of a parallelogram at the intersection of the second curve, namely a second left vertex, a second right vertex, a second upper vertex, and a second lower vertex; The second left vertex is the intersection of the second asymptote and the third ray. Based on formulas (11) to (14), according to formulas (16) and (21), the vertex coordinates of the second left vertex are obtained, and the expression is: (31) (32) The second right vertex is the intersection of the third asymptote and the first ray. Based on formulas (11) to (14), according to formulas (17) and (19), the vertex coordinates of the second right vertex are obtained, and the expression is: (33) (34) The second upper vertex is the intersection of the first ray and the third ray. Based on formulas (11) to (14), according to formulas (19) and (21), the vertex coordinates of the second upper vertex are obtained, and the expression is: (35) (36) The second lower vertex is the intersection of the second asymptote and the third asymptote. Based on formulas (11) to (14), according to formulas (16) and (17), the vertex coordinates of the second lower vertex are obtained, and the expression is: (37) (38) S433: defining four vertices of the parallelogram at the intersection of the third curve to be a third left vertex, a third right vertex, a third upper vertex, and a third lower vertex; The third left vertex is the intersection of the second ray and the third ray. Based on formulas (11) to (14), the vertex coordinates of the third left vertex are obtained according to formulas (20) and (21). The expression is: (39) (40) The third right vertex is the intersection of the third asymptote and the first asymptote. Based on formulas (11) to (14), according to formulas (17) and (15), the vertex coordinates of the third right vertex are obtained, and the expression is: (41) (42) The third upper vertex is the intersection of the first asymptote and the third ray. Based on formulas (11) to (14), the vertex coordinates of the third upper vertex are obtained according to formulas (15) and (21). The expression is: (43) (44) The third lower vertex is the intersection of the third asymptote and the second ray. Based on formulas (11) to (14), the vertex coordinates of the third lower vertex are obtained according to formulas (17) and (20). The expression is: (45) (46) S434: defining four vertices of the parallelogram at the intersection of the fourth curve to be a fourth left vertex, a fourth right vertex, a fourth upper vertex, and a fourth lower vertex; The fourth left vertex is the intersection of the second asymptote and the fourth asymptote. Based on formulas (11) to (14), the vertex coordinates of the fourth left vertex are obtained according to formulas (16) and (18), and the expression is: (47) (48) The fourth right vertex is the intersection of the first ray and the fourth ray. Based on formulas (11) to (14), the vertex coordinates of the fourth right vertex are obtained according to formulas (19) and (22). The expression is: (49) (50) The fourth upper vertex is the intersection of the fourth asymptote and the first ray. Based on formulas (11) to (14), the vertex coordinates of the fourth upper vertex are obtained according to formulas (18) and (19). The expression is: (51) (52) The fourth lower vertex is the intersection of the second asymptote and the fourth ray. Based on formulas (11) to (14), the vertex coordinates of the fourth lower vertex are obtained according to formulas (22) and (16). The expression is: (53) (54) S44: Obtain the estimated target position according to the vertex coordinates of the parallelogram at each position. The expression is: (55) (56) Where: ; S5: constructing a quadrilateral iterative adjustment rule based on the position discriminant function, and locating the position area where the target estimated position is located according to the target estimated position and the function value polarity of the discriminant function; In this embodiment, the two sets of hyperbolas can divide any parallelogram into four blocks. Although the target estimated position is difficult to be the true value directly, it is definitely located in any of the four blocks. The positional relationship between the target estimated position and the true value is determined according to the position discriminant function to determine in which module the estimated value is located; The constructed position discriminant function includes a first discriminant function about the first set of hyperbolas and a second discriminant function about the second set of hyperbolas; The first discriminant function The expression is (57) The second discriminant function The expression is (58) Reconstruct a position parallelogram according to the position area where the target estimated position is located, and repeat step S4 until the difference between the target estimated position of the reconstructed position parallelogram and the target estimated position of the position parallelogram before reconstruction meets the preset error threshold, so as to obtain the coordinates of the intersection of the time difference curves between the main observation station and each auxiliary observation station, which is the final target estimated position; The quadrilateral iterative adjustment rule based on the position discriminant function is constructed, such as Figure 3 As shown, specifically S51: Substituting the target estimated position obtained according to the vertex coordinates of the parallelogram at the intersection of each curve into the first discriminant function and the second discriminant function respectively to obtain the function value polarity of the first discriminant function and the second discriminant function; S52: Optimize and update the coordinates of each vertex in each position parallelogram according to the polarity of the function value, and reconstruct the position parallelogram; And the optimization and updating method includes replacing vertices, resetting vertices and retaining vertices; And obtain the new target estimated position of the reconstructed position parallelogram; S521: The optimization update rule for the vertices of the parallelogram at the intersection of the first curve is: Confirming the function value polarity of the first discriminant function and the second discriminant function; S5210: If and , the estimated target position is used as the replacement vertex to update the first lower vertex, the first upper vertex is kept unchanged, and the positions of the first left vertex and the first right vertex are reset; S5211: If and , update the first left vertex with the estimated target position as the replacement vertex, keep the first right vertex unchanged, and reset the positions of the first upper vertex and the first lower vertex; S5212: If and and , update the first upper vertex with the estimated target position as the replacement vertex, keep the first lower vertex unchanged, and reset the positions of the first left vertex and the first right vertex; S5213: If and , the target estimated position is used as the replacement vertex to update the first right vertex, and the first left vertex is kept unchanged and the positions of the first upper vertex and the first lower vertex are reset; S522: The optimization update rule for the vertices of the parallelogram at the intersection of the second curve is: Confirming the function value polarity of the first discriminant function and the second discriminant function; S5220: If and , the target estimated position is used as the replacement vertex to update the second upper vertex, and the second lower vertex is kept unchanged and the positions of the second left vertex and the second right vertex are reset; S5221: If and , the target estimated position is used as the replacement vertex to update the second right vertex, and the second left vertex is kept unchanged and the positions of the second upper vertex and the second lower vertex are reset; S5222: If and , the target estimated position is used as the replacement vertex to update the second lower vertex, and the second upper vertex is kept unchanged and the positions of the second left vertex and the second right vertex are reset; S5223: If and , the target estimated position is used as the replacement vertex to update the second left vertex, and the second right vertex is kept unchanged and the positions of the second upper vertex and the second lower vertex are reset; S523: The optimization update rule for the vertices of the parallelogram at the intersection of the third curve is: Confirming the function value polarity of the first discriminant function and the second discriminant function; S5230: If and When , the target estimated position is used as the replacement vertex to update the third left vertex, and the third right vertex is kept unchanged and the positions of the third upper vertex and the third lower vertex are reset; S5231: If and When , the target estimated position is used as the replacement vertex to update the third lower vertex, and the third upper vertex is kept unchanged and the positions of the third left vertex and the third right vertex are reset; S5232: If and When , the target estimated position is used as the replacement vertex to update the third right vertex, and the third left vertex is kept unchanged and the positions of the third upper vertex and the third lower vertex are reset; S5233: If and When , the target estimated position is used as the replacement vertex to update the third upper vertex, and the third lower vertex is kept unchanged and the positions of the third left vertex and the third right vertex are reset; S524: The optimization update rule for the vertices of the parallelogram at the intersection of the fourth curve is: Confirming the function value polarity of the first discriminant function and the second discriminant function; S5240: If and , update the fourth right vertex with the target estimated position as the replacement vertex, keep the fourth left vertex unchanged, and reset the positions of the fourth upper vertex and the fourth lower vertex; S5241: If and , update the fourth upper vertex with the target estimated position as the replacement vertex, keep the fourth lower vertex unchanged, and reset the positions of the fourth left vertex and the fourth right vertex; S5242: If and , update the fourth left vertex with the target estimated position as the replacement vertex, keep the fourth right vertex unchanged, and reset the positions of the fourth upper vertex and the fourth lower vertex; S5243: If and When , the target estimated position is used as the replacement vertex to update the fourth lower vertex, and the fourth upper vertex is kept unchanged and the positions of the fourth left vertex and the fourth right vertex are reset; In this embodiment, the coordinates of each vertex in each position parallelogram are optimized and updated according to the polarity of the function value, and the position parallelogram is reconstructed, as shown in Tables 1 to 4.

[0011]

[0012]

[0013]

[0014]

[0015] S53: Obtaining new target estimated positions of each position parallelogram after reconstruction; and determining whether the difference between the target estimated position and the position parallelogram before reconstruction satisfies a preset error threshold; If satisfied, the new target estimated position of each position parallelogram after reconstruction is used as the final target estimated position; Otherwise, repeat steps S51 to S52 for the reconstructed position parallelogram; In a specific embodiment, the method for resetting the vertex in S52 includes: Reset the first left vertex and the first right vertex based on step S5210: At this time, the first left vertex after reset is the intersection of the fourth asymptote and the straight line passing through the target estimated position point and having the same slope as the first asymptote; The reset first right vertex is the intersection of the first asymptotic line and a straight line passing through the target estimated position point and having the same slope as the fourth asymptotic line; Reset the first upper vertex and the first lower vertex based on step S5211: At this time, the reset first lower vertex is the intersection of the fourth ray and the straight line passing through the estimated target position point and having the same slope as the first asymptote; The reset first upper vertex is the intersection of the first asymptote and a straight line passing through the target estimated position point and having the same slope as the fourth ray; Reset the first left vertex and the first right vertex based on step S5212: At this time, the first left vertex reset is the intersection of the second ray and the straight line passing through the estimated target position point and having the same slope as the fourth ray; The reset first right vertex is the intersection of the fourth ray and the straight line passing through the estimated target position point and having the same slope as the second ray; Reset the first upper vertex and the first lower vertex based on step S5213: At this time, the reset first upper vertex is the intersection of the fourth asymptote and the straight line passing through the target estimated position point and having the same slope as the second ray; The reset first lower vertex is the intersection of the second ray and the straight line passing through the estimated position of the target and having the same slope as the fourth ray; Reset the second left vertex and the second right vertex based on step S5220: At this time, the reset second left vertex is the intersection of the second asymptote and the straight line passing through the target estimated position point and having the same slope as the third asymptote; The reset second right vertex is the intersection of the third asymptote and a straight line passing through the target estimated position point and having the same slope as the second asymptote; Reset the second upper vertex and the second lower vertex based on step S5221: At this time, the reset second upper vertex is the intersection of the third ray and the straight line passing through the estimated position of the target and having the same slope as the second asymptote; The reset second lower vertex is the intersection of the second asymptote and the straight line passing through the estimated target position point and having the same slope as the third ray; Reset the second left vertex and the second right vertex based on step S5222: The reset second left vertex at this time is the intersection of the third ray and the straight line passing through the estimated target position point and having the same slope as the first ray; The reset second right vertex is the intersection of the first ray and the straight line passing through the estimated position of the target and having the same slope as the third ray; Reset the second upper vertex and the second lower vertex based on step S5223: At this time, the reset second upper vertex is the intersection of the first ray and the straight line passing through the estimated position of the target and having the same slope as the third asymptote; The reset second lower vertex is the intersection of the third asymptote and a straight line passing through the estimated target position point and having the same slope as the first ray; Reset the third upper vertex and the third lower vertex based on step S5230: The reset third lower vertex at this time is the intersection of the third asymptote and the straight line passing through the target estimated position point and having the same slope as the first asymptote; The reset third upper vertex is the intersection of the first asymptote and a straight line passing through the target estimated position point and having the same slope as the third asymptote; Reset the third left vertex and the third right vertex based on step S5231: At this time, the reset third left vertex is the intersection of the third ray and the straight line passing through the estimated position of the target and having the same slope as the first asymptote; The reset third right vertex is the intersection of the first asymptote and a straight line passing through the estimated target position point and having the same slope as the third ray; Reset the third upper vertex and the third lower vertex based on step S5232: At this time, the reset third lower vertex is the intersection of the second ray and the straight line passing through the estimated target position point and having the same slope as the third ray; The reset third upper vertex is the intersection of the third ray and the straight line passing through the estimated position of the target and having the same slope as the second ray; Reset the third left vertex and the third right vertex based on step S5233: At this time, the reset third left vertex is the intersection of the third asymptote and the straight line passing through the target estimated position point and having the same slope as the second ray; The reset third right vertex is the intersection of the second ray and the straight line passing through the estimated position of the target and having the same slope as the third asymptote; Reset the fourth upper vertex and the fourth lower vertex based on step S5240: At this time, the reset fourth lower vertex is the intersection of the second asymptote and a straight line passing through the target estimated position point and having the same slope as the fourth asymptote; The reset fourth upper vertex is the intersection of the fourth asymptote and a straight line passing through the target estimated position point and having the same slope as the second asymptote; Reset the fourth left vertex and the fourth right vertex based on step S5241: At this time, the reset fourth left vertex is the intersection of the first ray and the straight line passing through the estimated position of the target and having the same slope as the second asymptote; The reset fourth right vertex is the intersection of the second asymptote and a straight line passing through the estimated target position point and having the same slope as the first ray; Reset the fourth upper vertex and the fourth lower vertex based on step S5242: The fourth lower vertex reset at this time is the intersection of the fourth ray and the straight line passing through the estimated target position point and having the same slope as the first ray; The reset fourth upper vertex is the intersection of the first ray and a straight line passing through the estimated target position point and having the same slope as the fourth ray; Reset the fourth left vertex and the fourth right vertex based on step S5243: At this time, the reset fourth left vertex is the intersection of the fourth asymptote and the straight line passing through the target estimated position point and having the same slope as the first ray; The reset fourth right vertex is the intersection of the first ray and a straight line passing through the estimated target position point and having the same slope as the fourth asymptote.

[0016] This embodiment includes a calculation formula table for resetting the vertex, as shown in Tables 5 to 8, wherein asymptote 1 is the first asymptote, asymptote 2 is the second asymptote, asymptote 3 is the third asymptote, asymptote 4 is the fourth asymptote, ray 5 is the first ray, ray 6 is the second ray, ray 7 is the third ray, and ray 8 is the fourth ray;

[0017]

[0018] In this embodiment, a time difference curve is constructed between the main observation station and each auxiliary observation station to obtain a time difference asymptote for time difference positioning calculation; and based on the intersection of the straight line where the main observation station and the auxiliary observation station are located with the time difference curve, the ray is obtained according to the ray slope confirmed by the time difference asymptote, and then the vertex coordinate values ​​of the parallelogram at each position are obtained, and the target estimated position is obtained according to the vertex coordinate values ​​of the parallelogram at each position. By using the method of iteratively reducing the target area, that is, the iterative adjustment rule of the quadrilateral based on the position discriminant function is constructed, the problem of finding the intersection of two sets of hyperbolas is solved. At the same time, the method of using the center value of the parallelogram to approximate the target position is used to solve the problem that the real root cannot be obtained by directly solving the equation, and a method for updating the vertices of the parallelogram when the target is located at different intersection positions is given, which meets the requirements of quickly and accurately calculating the target position in time difference positioning, solves the problem of not being able to obtain the solution of the hyperbola equation, and has high practical value.

[0019] The verification process in this embodiment is as follows: The input data is the time difference between two sets of primary and secondary station observations, and the output result is the target position. The process diagram of the method is as follows: Figure 2 shown.

[0020] Below millisecond, rice, rice, The implementation process of the present invention is described by taking an example.

[0021] According to Table 1, by the polarity of and , it is judged that the target is located in the lower intersection area (the quadrilateral where the first curve intersection is located). The initial parallelogram range is surrounded by lines 1, 4, 6, and 8. Substitute the horizontal and vertical coordinates and slopes of lines 1, 4, 6, and 8 into formulas (22) to (30) to obtain the coordinates of the four vertices of the parallelogram: the upper vertex, the lower vertex, the left vertex, and the right vertex; calculate the average value of the four vertices, and substitute the coordinate value into the discriminant formulas (57) to (58) to obtain , , that is, the estimated point is located in the upper area of ​​the parallelogram; to replace the upper vertex of the original parallelogram, the lower vertex remains unchanged, the slopes of the four sides remain unchanged, and the new left and right vertex coordinates are reset.

[0022] Repeat the above process of calculating the average value of the four vertices and updating the vertices until the difference between the horizontal and vertical coordinates of the four vertices is less than 0.0001. The estimated value at this time is , which is the required coordinate value. In this example, a total of 21 quadrilateral update iterations were performed.

[0023] In summary, the method of solving the intersection of two sets of hyperbolas based on iterative reduction of the parallelogram range can achieve fast and accurate position calculation, provide method support for achieving efficient positioning, has strong executability and ideal effect.

[0024] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for calculating a target position in time difference positioning, characterized in that: The following steps are involved: S1: Set up the main observation station and auxiliary observation station; And the number of the auxiliary observation stations is two; And construct the time difference curve between the main observation station and each auxiliary observation station to calculate the target position by time difference positioning; S2: Obtaining a time difference asymptote for time difference positioning calculation according to the time difference curve; S3: Based on the intersection of the straight line where the station positions of the main observation station and the auxiliary observation station are located and the time difference curve, and according to the slope of the ray confirmed by the time difference asymptote, the ray used for time difference positioning calculation is obtained; Each boundary area enclosed by the ray and the time difference asymptote is used as a position parallelogram for target positioning; S4: Obtain the vertex coordinate values ​​of the parallelogram at each position; And obtain the estimated position of the target according to the vertex coordinate values ​​of the parallelogram at each position; S5: constructing a quadrilateral iterative adjustment rule based on the position discriminant function, and locating the position area where the target estimated position is located according to the target estimated position and the function value polarity of the discriminant function; Reconstruct the position parallelogram according to the position area where the target estimated position is located, and repeat step S4 until the difference between the target estimated position of the reconstructed position parallelogram and the target estimated position of the position parallelogram before reconstruction meets the preset error threshold, so as to obtain the intersection coordinates of the time difference curves between the main observation station and each auxiliary observation station, which is the final target estimated position.

2. The method for calculating the target position in time difference positioning according to claim 1, characterized in that: The S1 specifically includes the following steps: S11: Setting up a main observation station and an auxiliary observation station for calculating the target position in time difference positioning; And the auxiliary observation station includes a first auxiliary observation station and a second auxiliary observation station; The distance between the main observation station and the auxiliary observation station is set to ,in Indicates the first auxiliary observation station; Indicates the second auxiliary observation station; Define the time difference between the primary and secondary observation stations After measurement, confirm that the target is located at For the long axis, The intersection of the two hyperbolas is the location of the target. represents the speed of light constant; S12: Construct the time difference curve between the main observation station and each auxiliary observation station; And the time difference curves include a first set of hyperbolas between the main observation station and the first auxiliary observation station; The second set of hyperbolas between the main observatory and the second auxiliary observatory; S121: The method for constructing the first set of hyperbolas is The main observation station is taken as the origin, and the direction from the main observation station to the first auxiliary observation station is taken as the positive x Axis direction, set the plane rectangular coordinate system; Based on the plane rectangular coordinate system, the first set of hyperbolas is obtained as （1） Where: represents the major axis of the first set of hyperbolas and ; represents the focal length of the first hyperbola and ; S122: The method for constructing the second set of hyperbolas is Suppose the angle between the straight line where the second auxiliary observation station and the main observation station are located, and the angle between the straight line where the main observation station and the first auxiliary observation station are located is , then the second set of hyperbolas formed by the second auxiliary observation station and the main observation station is （2） Where: represents the major axis of the second set of hyperbolas and ; represents the focal length of the second hyperbola and .

3. The method for calculating the target position in time difference positioning according to claim 2, characterized in that: In S2, a time difference asymptote for time difference positioning calculation is obtained according to the time difference curve, including a first asymptote and a second asymptote about the main observation station and the first auxiliary observation station; The third and fourth asymptotes of the main observation station and the second auxiliary observation station; And the expression of the first asymptote is （3） The expression of the second asymptote is （4） The expression of the third asymptote is （5） The expression of the fourth asymptote is （6）。 4. The method for calculating the target position in time difference positioning according to claim 3, characterized in that: The S3 specifically includes the following steps: S31: Based on the intersection of the straight line where the main observation station and the auxiliary observation station are located and the time difference curve, and according to the ray slope confirmed by the time difference asymptote, a ray for time difference positioning calculation is obtained; Specifically include: confirming the two straight lines where the main observation station and each auxiliary observation station are located; and obtaining the intersection points of each straight line with the corresponding first group of hyperbolas and second group of hyperbolas, and taking each intersection point as the starting point and the slope of the corresponding time difference asymptote as the inclination, obtaining the first ray and the second ray about the main observation station and the first auxiliary observation station, and the third ray and the fourth ray about the main observation station and the second auxiliary observation station; The expression for the first ray is （7） The expression for the second ray is （8） The expression of the third ray is （9） The expression of the fourth ray is （10） S32: using each boundary area enclosed by each ray and the time difference asymptote as a position parallelogram for target positioning; And the intersection points of the first group of hyperbolas and the second group of hyperbolas are respectively located inside the parallelograms at each position.

5. The method for calculating the target position in time difference positioning according to claim 4, characterized in that: The S4 specifically comprises the following steps: S41: Assume that the coordinates of a vertex of the position parallelogram are , and the equations of the two adjacent edges of the vertex coordinates are （11） （12） Where: , represents the slope of the equation of the edge; Then the vertex coordinates are obtained by solving the adjacent edge equation, and the expression is: （13） （14） S42: Based on step S41, formulas (3) to (10) are rewritten to solve the coordinates of each vertex of the position parallelogram, and the expression is: （15） （16） （17） （18） （19） （20） （21） （22） S43: defining the intersection points of the first set of hyperbolas and the second set of hyperbolas as first curve intersection points, second curve intersection points, third curve intersection points, and fourth curve intersection points, respectively; And respectively obtain the vertex coordinate values ​​of the parallelograms at the intersection points of each curve; S431: defining four vertices of a parallelogram at the intersection of the first curve to be a first left vertex, a first right vertex, a first upper vertex, and a first lower vertex; The first left vertex is the intersection of the fourth asymptote and the second ray. Based on formulas (11) to (14), according to formulas (20) and (18), the vertex coordinates of the first left vertex are obtained, and the expression is: （23） （24） The first right vertex is the intersection of the first asymptote and the fourth ray. Based on formulas (11) to (14), according to formulas (22) and (15), the vertex coordinates of the first right vertex are obtained, and the expression is: （25） （26） The first upper vertex is the intersection of the first asymptote and the fourth asymptote. Based on formulas (11) to (14), according to formulas (28) and (15), the vertex coordinates of the first upper vertex are obtained, and the expression is: （27） （28） The first lower vertex is the intersection of the second ray and the fourth ray. Based on formulas (11) to (14), according to formulas (22) and (20), the vertex coordinates of the first lower vertex are obtained, and the expression is: （29） （30） S432: defining four vertices of a parallelogram at the intersection of the second curve as a second left vertex, a second right vertex, a second upper vertex, and a second lower vertex; The second left vertex is the intersection of the second asymptote and the third ray. Based on formulas (11) to (14), according to formulas (16) and (21), the vertex coordinates of the second left vertex are obtained, and the expression is: （31） （32） The second right vertex is the intersection of the third asymptote and the first ray. Based on formulas (11) to (14), according to formulas (17) and (19), the vertex coordinates of the second right vertex are obtained, and the expression is: （33） （34） The second upper vertex is the intersection of the first ray and the third ray. Based on formulas (11) to (14), according to formulas (19) and (21), the vertex coordinates of the second upper vertex are obtained, and the expression is: （35） （36） The second lower vertex is the intersection of the second asymptote and the third asymptote. Based on formulas (11) to (14), according to formulas (16) and (17), the vertex coordinates of the second lower vertex are obtained, and the expression is: （37） （38） S433: defining four vertices of the parallelogram at the intersection of the third curve to be a third left vertex, a third right vertex, a third upper vertex, and a third lower vertex; The third left vertex is the intersection of the second ray and the third ray. Based on formulas (11) to (14), the vertex coordinates of the third left vertex are obtained according to formulas (20) and (21). The expression is: （39） （40） The third right vertex is the intersection of the third asymptote and the first asymptote. Based on formulas (11) to (14), according to formulas (17) and (15), the vertex coordinates of the third right vertex are obtained, and the expression is: （41） （42） The third upper vertex is the intersection of the first asymptote and the third ray. Based on formulas (11) to (14), the vertex coordinates of the third upper vertex are obtained according to formulas (15) and (21). The expression is: （43） （44） The third lower vertex is the intersection of the third asymptote and the second ray. Based on formulas (11) to (14), the vertex coordinates of the third lower vertex are obtained according to formulas (17) and (20). The expression is: （45） （46） S434: defining four vertices of the parallelogram at the intersection of the fourth curve to be a fourth left vertex, a fourth right vertex, a fourth upper vertex, and a fourth lower vertex; The fourth left vertex is the intersection of the second asymptote and the fourth asymptote. Based on formulas (11) to (14), the vertex coordinates of the fourth left vertex are obtained according to formulas (16) and (18), and the expression is: （47） （48） The fourth right vertex is the intersection of the first ray and the fourth ray. Based on formulas (11) to (14), the vertex coordinates of the fourth right vertex are obtained according to formulas (19) and (22). The expression is: （49） （50） The fourth upper vertex is the intersection of the fourth asymptote and the first ray. Based on formulas (11) to (14), the vertex coordinates of the fourth upper vertex are obtained according to formulas (18) and (19). The expression is: （51） （52） The fourth lower vertex is the intersection of the second asymptote and the fourth ray. Based on formulas (11) to (14), the vertex coordinates of the fourth lower vertex are obtained according to formulas (22) and (16). The expression is: （53） （54） S44: Obtain the estimated target position according to the vertex coordinates of the parallelogram at each position. The expression is: （55） （56） Where: .

6. The method for calculating target position in time difference positioning according to claim 5, characterized in that: The position discriminant function constructed in S5 includes a first discriminant function about the first group of hyperbolas and a second discriminant function about the second group of hyperbolas; The first discriminant function The expression is （57） The second discriminant function The expression is （58）。 7. The method for calculating target position in time difference positioning according to claim 6, characterized in that: The quadrilateral iterative adjustment rule based on the position discriminant function constructed in S5 is as follows: S51: Substituting the target estimated position obtained according to the vertex coordinates of the parallelogram at the intersection of each curve into the first discriminant function and the second discriminant function respectively to obtain the function value polarity of the first discriminant function and the second discriminant function; S52: Optimize and update the coordinates of each vertex in each position parallelogram according to the polarity of the function value, and reconstruct the position parallelogram; And the optimization and updating method includes replacing vertices, resetting vertices and retaining vertices; And obtain the new target estimated position of the reconstructed position parallelogram; S521: The optimization update rule for the vertices of the parallelogram at the intersection of the first curve is: Confirming the function value polarity of the first discriminant function and the second discriminant function; S5210: If and , the estimated target position is used as the replacement vertex to update the first lower vertex, the first upper vertex is kept unchanged, and the positions of the first left vertex and the first right vertex are reset; S5211: If and , update the first left vertex with the estimated target position as the replacement vertex, keep the first right vertex unchanged, and reset the positions of the first upper vertex and the first lower vertex; S5212: If and and , the target estimated position is used as the replacement vertex to update the first upper vertex, and the first lower vertex is kept unchanged and the positions of the first left vertex and the first right vertex are reset; S5213: If and , the target estimated position is used as the replacement vertex to update the first right vertex, and the first left vertex is kept unchanged and the positions of the first upper vertex and the first lower vertex are reset; S522: The optimization update rule for the vertices of the parallelogram at the intersection of the second curve is: Confirming the function value polarity of the first discriminant function and the second discriminant function; S5220: If and , the target estimated position is used as the replacement vertex to update the second upper vertex, and the second lower vertex is kept unchanged and the positions of the second left vertex and the second right vertex are reset; S5221: If and , the target estimated position is used as the replacement vertex to update the second right vertex, and the second left vertex is kept unchanged and the positions of the second upper vertex and the second lower vertex are reset; S5222: If and , the target estimated position is used as the replacement vertex to update the second lower vertex, and the second upper vertex is kept unchanged and the positions of the second left vertex and the second right vertex are reset; S5223: If and , the target estimated position is used as the replacement vertex to update the second left vertex, and the second right vertex is kept unchanged and the positions of the second upper vertex and the second lower vertex are reset; S523: The optimization update rule for the vertices of the parallelogram at the intersection of the third curve is: Confirming the function value polarity of the first discriminant function and the second discriminant function; S5230: If and When , the target estimated position is used as the replacement vertex to update the third left vertex, and the third right vertex is kept unchanged and the positions of the third upper vertex and the third lower vertex are reset; S5231: If and When , the target estimated position is used as the replacement vertex to update the third lower vertex, and the third upper vertex is kept unchanged and the positions of the third left vertex and the third right vertex are reset; S5232: If and When , the target estimated position is used as the replacement vertex to update the third right vertex, and the third left vertex is kept unchanged and the positions of the third upper vertex and the third lower vertex are reset; S5233: If and When , the target estimated position is used as the replacement vertex to update the third upper vertex, and the third lower vertex is kept unchanged and the positions of the third left vertex and the third right vertex are reset; S524: The optimization update rule for the vertices of the parallelogram at the intersection of the fourth curve is: Confirming the function value polarity of the first discriminant function and the second discriminant function; S5240: If and , update the fourth right vertex with the target estimated position as the replacement vertex, keep the fourth left vertex unchanged, and reset the positions of the fourth upper vertex and the fourth lower vertex; S5241: If and , update the fourth upper vertex with the target estimated position as the replacement vertex, keep the fourth lower vertex unchanged, and reset the positions of the fourth left vertex and the fourth right vertex; S5242: If and , update the fourth left vertex with the target estimated position as the replacement vertex, keep the fourth right vertex unchanged, and reset the positions of the fourth upper vertex and the fourth lower vertex; S5243: If and When , the target estimated position is used as the replacement vertex to update the fourth lower vertex, and the fourth upper vertex is kept unchanged and the positions of the fourth left vertex and the fourth right vertex are reset; S53: Obtaining new target estimated positions of each position parallelogram after reconstruction; and determining whether the difference between the target estimated position and the position parallelogram before reconstruction satisfies a preset error threshold; If satisfied, the new target estimated position of each position parallelogram after reconstruction is used as the final target estimated position; Otherwise, steps S51 to S52 are repeatedly performed on the reconstructed position parallelogram.

8. The method for calculating target position in time difference positioning according to claim 7, characterized in that: The methods for resetting vertices in S52 include: Reset the first left vertex and the first right vertex based on step S5210: At this time, the first left vertex after reset is the intersection of the fourth asymptote and the straight line passing through the target estimated position point and having the same slope as the first asymptote; The reset first right vertex is the intersection of the first asymptotic line and a straight line passing through the target estimated position point and having the same slope as the fourth asymptotic line; Reset the first upper vertex and the first lower vertex based on step S5211: At this time, the reset first lower vertex is the intersection of the fourth ray and the straight line passing through the estimated target position point and having the same slope as the first asymptote; The reset first upper vertex is the intersection of the first asymptote and a straight line passing through the target estimated position point and having the same slope as the fourth ray; Reset the first left vertex and the first right vertex based on step S5212: At this time, the first left vertex reset is the intersection of the second ray and the straight line passing through the estimated target position point and having the same slope as the fourth ray; The reset first right vertex is the intersection of the fourth ray and the straight line passing through the estimated target position point and having the same slope as the second ray; Reset the first upper vertex and the first lower vertex based on step S5213: At this time, the reset first upper vertex is the intersection of the fourth asymptote and the straight line passing through the target estimated position point and having the same slope as the second ray; The reset first lower vertex is the intersection of the second ray and the straight line passing through the estimated position of the target and having the same slope as the fourth ray; Reset the second left vertex and the second right vertex based on step S5220: At this time, the reset second left vertex is the intersection of the second asymptote and the straight line passing through the target estimated position point and having the same slope as the third asymptote; The reset second right vertex is the intersection of the third asymptote and a straight line passing through the target estimated position point and having the same slope as the second asymptote; Reset the second upper vertex and the second lower vertex based on step S5221: At this time, the reset second upper vertex is the intersection of the third ray and the straight line passing through the estimated position of the target and having the same slope as the second asymptote; The reset second lower vertex is the intersection of the second asymptote and the straight line passing through the estimated target position point and having the same slope as the third ray; Reset the second left vertex and the second right vertex based on step S5222: The reset second left vertex at this time is the intersection of the third ray and the straight line passing through the estimated target position point and having the same slope as the first ray; The reset second right vertex is the intersection of the first ray and the straight line passing through the estimated position of the target and having the same slope as the third ray; Reset the second upper vertex and the second lower vertex based on step S5223: At this time, the reset second upper vertex is the intersection of the first ray and the straight line passing through the estimated position of the target and having the same slope as the third asymptote; The reset second lower vertex is the intersection of the third asymptote and a straight line passing through the estimated target position point and having the same slope as the first ray; Reset the third upper vertex and the third lower vertex based on step S5230: The reset third lower vertex at this time is the intersection of the third asymptote and the straight line passing through the target estimated position point and having the same slope as the first asymptote; The reset third upper vertex is the intersection of the first asymptote and a straight line passing through the target estimated position point and having the same slope as the third asymptote; Reset the third left vertex and the third right vertex based on step S5231: At this time, the reset third left vertex is the intersection of the third ray and the straight line passing through the estimated position of the target and having the same slope as the first asymptote; The reset third right vertex is the intersection of the first asymptote and a straight line passing through the estimated target position point and having the same slope as the third ray; Reset the third upper vertex and the third lower vertex based on step S5232: At this time, the reset third lower vertex is the intersection of the second ray and the straight line passing through the estimated target position point and having the same slope as the third ray; The reset third upper vertex is the intersection of the third ray and the straight line passing through the estimated position of the target and having the same slope as the second ray; Reset the third left vertex and the third right vertex based on step S5233: At this time, the reset third left vertex is the intersection of the third asymptote and the straight line passing through the target estimated position point and having the same slope as the second ray; The reset third right vertex is the intersection of the second ray and the straight line passing through the estimated position of the target and having the same slope as the third asymptote; Reset the fourth upper vertex and the fourth lower vertex based on step S5240: At this time, the reset fourth lower vertex is the intersection of the second asymptote and a straight line passing through the target estimated position point and having the same slope as the fourth asymptote; The reset fourth upper vertex is the intersection of the fourth asymptote and a straight line passing through the target estimated position point and having the same slope as the second asymptote; Reset the fourth left vertex and the fourth right vertex based on step S5241: At this time, the reset fourth left vertex is the intersection of the first ray and the straight line passing through the estimated position of the target and having the same slope as the second asymptote; The reset fourth right vertex is the intersection of the second asymptote and a straight line passing through the estimated target position point and having the same slope as the first ray; Reset the fourth upper vertex and the fourth lower vertex based on step S5242: The fourth lower vertex reset at this time is the intersection of the fourth ray and the straight line passing through the estimated target position point and having the same slope as the first ray; The reset fourth upper vertex is the intersection of the first ray and a straight line passing through the estimated target position point and having the same slope as the fourth ray; Reset the fourth left vertex and the fourth right vertex based on step S5243: At this time, the reset fourth left vertex is the intersection of the fourth asymptote and the straight line passing through the target estimated position point and having the same slope as the first ray; The reset fourth right vertex is the intersection of the first ray and a straight line passing through the estimated position point of the target and having the same slope as the fourth asymptote.

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