Method for calculating time difference positioning measurement error

Abstract

The invention belongs to the technical field of time difference positioning error measurement, and discloses a method for calculating a time difference positioning measurement error, which comprises the following steps: S1, establishing a time difference positioning error calculation model, and determining a fuzzy region; s2, calculating an observation time difference between the main station and the auxiliary station, and judging a fuzzy region to which an observation target belongs; s3, forming a discrimination area; s4, generating a plurality of sampling points in the discrimination region, and performing formula discrimination on each sampling point to determine the number of the sampling points in the fuzzy region to which the observation target belongs; and S5, calculating the area of the fuzzy region to which the observation target belongs based on the number of the sampling points in the fuzzy region to which the observation target belongs. According to the method, the accuracy degree of time difference positioning is measured through the fuzzy area, the error estimation problem in the dynamic change process of observation station position parameters and measurement parameters is solved, meanwhile, the main observation station is guided to command and adjust the relative station distribution position in time through the change condition of the fuzzy area, and a basis is provided for optimal value positioning through cooperation of the main station and the auxiliary station.

Description

Technical Field

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

[0002] In the field of time difference positioning, especially in modern complex electromagnetic environments, the number of target radiation sources is large and their distribution is wide, and passive positioning of targets faces many challenges. How to evaluate the accuracy of target positioning by passive positioning sensor resources is an important measurement factor in electronic countermeasure reconnaissance technology, and it is also the core issue that needs to be solved first to solve the problem of limited sensor resource allocation.

[0003] The analysis and research on time difference positioning error or feasibility issues often use circular probability error or geometric precision factor as methods to measure positioning accuracy. However, the parameter expressions obtained by these methods are usually complex parameter matrices, and the matrix parameters are not intuitive measured values ​​or known quantities, but relative values ​​or differential forms. In addition, the use of these parameter matrices to explore the station layout problem of time difference positioning is usually carried out under special circumstances such as controlling certain parameters or setting the station layout shape. It is difficult to directly judge the error of the current state and is not conducive to finding the global optimal station layout plan. Summary of the invention

[0004] The present invention provides a method for calculating a time difference positioning measurement error, so as to overcome the technical problem that it is difficult to directly judge the error of the current state by using the prior art.

[0005] In order to achieve the above object, the technical solution of the present invention is: A method for calculating a time difference positioning measurement error, the specific steps comprising: S1: establishing a time difference positioning error calculation model, and determining a number of fuzzy areas based on the time difference positioning error calculation model; S2: Calculate the time difference between the observations of the primary station and several secondary stations, and determine the fuzzy area to which the observed target belongs based on the polarity of the time difference; S3: forming a rectangular area based on the fuzzy area to which the observed target belongs, and using the rectangular area as a discrimination area; S4: generating a number of sampling points in the discrimination area, and performing a formula discrimination on each of the sampling points to determine the number of sampling points located in the fuzzy area to which the observed target belongs; S5: The area of ​​the fuzzy region to which the observed target belongs is calculated based on the number of sampling points in the fuzzy region to which the observed target belongs. The area of ​​the fuzzy region to which the observed target belongs is the measurement error of the time difference positioning.

[0006] Furthermore, in S1, a time difference positioning error calculation model is established, and a number of fuzzy areas are determined based on the time difference positioning error calculation model, including: S11: Assume that the distance between the master station and the first and second slave stations is , the time difference observed between the master station and the first and second slave stations is , then the observed target is located at is the long axis, On two sets of hyperbolas with minor axes, ; c is the speed of light constant; S12: Establishing the coordinate system Taking the master station as the origin, the direction from the master station to the first slave station is positive. x Axis, establish plane rectangular coordinate system; S13: establishing a time difference line between the master station and the first slave station and a time difference line between the master station and the second slave station based on the plane rectangular coordinate system; The time difference line formed by the master station and the first slave station is recorded as hyperbola P, and its formula is as follows: (1) In the formula, is the horizontal coordinate of the observed target; is the ordinate of the observed target; Assume that the angle formed by the second auxiliary station, the main station, and the first auxiliary station is , then the hyperbola Q formed by the second secondary station and the primary station is expressed as: (2) In formulas (1) and (2), , ; S14: Define the error range of hyperbola P and Q set up The error is ,but The two sets of hyperbolas determined are recorded as hyperbolas ① and ②, and their equations are: (3) (4) Hyperbolas ① and ② are located on the inner and outer sides of hyperbola P respectively, forming the first hyperbolic belt; Same reason The two sets of hyperbolas determined are recorded as hyperbolas ③ and ④, and their equations are: (7) (8) Hyperbolas ③ and ④ are located on the inner and outer sides of hyperbola Q respectively, forming the second hyperbolic belt; S15: The first hyperbolic belt and the second hyperbolic belt intersect each other to form four closed surfaces. Assume that the axis of symmetry of the hyperbola P is line m, and the axis of symmetry of the hyperbola Q is line n. The equations are: (11) (12) From the origin to the intersection of line m and line n Direction, according to the four closed faces relative to The position of the fuzzy area is defined as the upper fuzzy area, the lower fuzzy area, the right fuzzy area and the left fuzzy area respectively.

[0007] Furthermore, in S2, calculating the time difference observed between the primary station and the plurality of secondary stations, and judging the fuzzy region to which the observed target belongs based on the polarity of the time difference includes: S21: Calculate the time difference between the master station and the first and second slave stations and , the formula is: , ,in, is the time value observed by the master station, and are the time values ​​observed by the first and second secondary stations, respectively; S22: Based on and The polarity of determines the fuzzy area to which the observed target belongs, including: when , When , the observed target is located in the upper fuzzy area; when , When , the observed target is located in the lower fuzzy area; when , When , the observed target is located in the right fuzzy area; when , , the observed target is located in the left fuzzy area.

[0008] Further, in S3, forming a rectangular area based on the fuzzy area to which the observed target belongs, and using the rectangular area as the discrimination area includes: S31: Using the set asymptote and ray equation to define the outer boundary of the fuzzy area to which the observed target belongs; The set asymptote equations include a first asymptote, a second asymptote, a third asymptote and a fourth asymptote; The set ray equations include a fifth ray, a sixth ray, a seventh ray and an eighth ray; S32: based on the set asymptote and ray equation, respectively obtain the coordinates of the outer boundary intersection points of the fuzzy area to which the observed target belongs; S33: Obtaining a rectangular area based on the coordinates of the outer boundary intersection points of the fuzzy area to which the observed target belongs, including: The coordinates of the outer boundary intersection points of the fuzzy area to which the observation target belongs and the coordinates of the outer boundary intersection points of other fuzzy areas are calculated to obtain a rectangular area.

[0009] Furthermore, in S31, using the set asymptote and ray equation to define the outer boundary of the fuzzy area to which the observed target belongs includes: The equations of the first asymptote, the second asymptote, the third asymptote and the fourth asymptote are respectively: (twenty one) (twenty two) (twenty three) (twenty four) In the formula, , , and are the coordinates of points on the first asymptote, the second asymptote, the third asymptote, and the fourth asymptote, respectively; The equations of the fifth ray, the sixth ray, the seventh ray and the eighth ray are respectively: (25) (26) (27) (28) In the formula, , , and are the coordinates of points on the fifth, sixth, seventh and eighth rays respectively; Defining the outer boundary of the fuzzy area to which the observed target belongs, including: If the fuzzy area to which the observed target belongs is an upper fuzzy area, defining an outer boundary of the upper fuzzy area based on the second asymptote, the third asymptote, the fifth ray and the seventh ray; If the fuzzy area to which the observed target belongs is a lower fuzzy area, defining an outer boundary of the lower fuzzy area based on the first asymptote, the fourth asymptote, the sixth ray and the eighth ray; If the fuzzy area to which the observed target belongs is a left fuzzy area, then defining an outer boundary of the left fuzzy area based on the first asymptote, the third asymptote, the sixth ray and the seventh ray; If the blurred area to which the observed target belongs is a right blurred area, the outer boundary of the right blurred area is defined based on the second asymptote, the fourth asymptote, the fifth ray and the eighth ray.

[0010] Further, in S32, respectively obtaining the coordinates of the outer boundary intersection points of the fuzzy area to which the observed target belongs based on the set asymptote and ray equation includes: If the fuzzy area to which the observed target belongs is the upper fuzzy area, the coordinates of the outer boundary intersection point of the upper fuzzy area are obtained by the equations of the second asymptote, the third asymptote, the fifth ray and the seventh ray, which are respectively: (29) (30) (31) (32) (33) (34) (35) (36) If the fuzzy area to which the observed target belongs is the lower fuzzy area, the coordinates of the outer boundary intersection point of the lower fuzzy area are obtained by the equations of the first asymptote, the fourth asymptote, the sixth ray and the eighth ray, which are respectively: (37) (38) (39) (40) (41) (42) (43) (44) If the fuzzy area to which the observed target belongs is the right fuzzy area, the coordinates of the outer boundary intersection point of the right fuzzy area are obtained by the equations of the second asymptote, the fourth asymptote, the fifth ray and the eighth ray, which are respectively: (45) (46) (47) (48) (49) (50) (51) (52) If the fuzzy area to which the observed target belongs is the left fuzzy area, the coordinates of the outer boundary intersection point of the left fuzzy area are obtained by the equations of the first asymptote, the third asymptote, the sixth ray and the seventh ray, which are respectively: (53) (54) (55) (56) (57) (58) (59) (60) In the formula, , , , .

[0011] Further, in S4, a plurality of sampling points are generated in the discrimination area, and a formula discrimination is performed on each of the sampling points to determine the number of sampling points located in the fuzzy area to which the observed target belongs, including: A Monte Carlo random algorithm is used to generate a number of sampling points in the discrimination area; Substitute each of the sampling points into the following discriminant formula in turn, including: Points in the first hyperbolic band Satisfy the formula: (5) (6) Points in the second hyperbolic band Satisfy the formula: (9) (10) The points in the upper fuzzy region satisfy the formula: (13) (14) The points in the lower fuzzy region satisfy the formula: (15) (16) The points in the left fuzzy area satisfy the formula: (17) (18) The points in the right fuzzy area satisfy the formula: (19) (20) If the sampling point satisfies formulas (5), (6), (9), (10), (13) and (14), then the sampling point is located in the upper fuzzy area; If the sampling point satisfies formulas (5), (6), (9), (10), (15) and (16), then the sampling point is located in the lower fuzzy area; If the sampling point satisfies formulas (5), (6), (9), (10), (17) and (18), then the sampling point is located in the left fuzzy area; If the sampling point satisfies formulas (5), (6), (9), (10), (19) and (20), then the sampling point is located in the right fuzzy area; After judging each sampling point in turn, the number of sampling points located in the fuzzy area to which the observed target belongs is obtained.

[0012] Further, in S5, the area of ​​the fuzzy region to which the observation target belongs is calculated based on the number of sampling points in the fuzzy region to which the observation target belongs, and the calculation formula is: (61) in, is the number of sampling points in the fuzzy area to which the observed target belongs, N is the number of sampling points in the rectangular area, and are the abscissa extreme values ​​of the four intersection points between the first hyperbolic band and the second hyperbolic band, and are the ordinate extreme values ​​of the four intersection points between the first hyperbolic band and the second hyperbolic band.

[0013] Beneficial effects: The present invention obtains several fuzzy areas by establishing a time difference positioning error calculation model, determines the fuzzy area to which the observation target belongs based on the calculated time difference, and forms a discrimination area; generates several sampling points in the discrimination area, and performs formula discrimination on each sampling point to determine the number of sampling points located in the fuzzy area to which the time difference belongs; calculates the area of ​​the fuzzy area to which the observation target belongs based on the number of sampling points in the fuzzy area to which the observation target belongs, and the area of ​​the fuzzy area to which the observation target belongs is the measurement error of time difference positioning. The present invention measures the accuracy of time difference positioning by fuzzy area, realizes direct judgment of the error of the current state, solves the error estimation problem in the process of dynamic change of observation station position parameters and measurement parameters, and at the same time, the subsequent use of the change of fuzzy area can guide the main observation station to timely command and adjust the relative station position, providing a basis for the coordination and cooperation between the main and auxiliary stations to achieve optimal value positioning, and has high practical value. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] 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.

[0015] Figure 1 A first flow chart of a method for calculating a time difference positioning measurement error in the present invention; Figure 2 A second flow chart of a method for calculating a time difference positioning measurement error in the present invention; Figure 3 Schematic diagram of a time difference positioning error calculation model in an embodiment of the present invention; Figure 4 Schematic diagram of the outer boundaries of each fuzzy area in an embodiment of the present invention.

[0016] In the figure: 1, first asymptote; 2, second asymptote; 3, third asymptote; 4, fourth asymptote; 5, fifth ray; 6, sixth ray; 7, seventh ray; 8, eighth ray; A. Main station; B. First secondary station; C. Second secondary station. DETAILED DESCRIPTION

[0017] 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.

[0018] In time difference positioning, the main error comes from the time difference measured by the main and auxiliary observation stations. When the time difference fluctuates, the hyperbola determined by the time difference will shift left and right relative to the center line of the main and auxiliary stations. The two sets of hyperbolas corresponding to the time difference error can determine the positioning error of a set of main and auxiliary stations as a hyperbolic surface. Similarly, another set of main and auxiliary station hyperbolic surfaces are taken. The intersection of the two hyperbolic surfaces is the positioning fuzzy area. The size of the fuzzy area directly reflects the positioning accuracy. The larger the area, the lower the positioning accuracy, and vice versa. The core idea of ​​the calculation of time difference positioning error based on fuzzy area is to use the current observation parameters to evaluate the accuracy of the current positioning. Due to the dynamic characteristics of the combat process, the layout of the observation station is also changing at all times. The measurement errors corresponding to different observation parameters change at any time. Timely grasping the current measurement error is the key to optimizing the layout of the observation station. Especially in coordinated operations, the use of real-time calculated time difference positioning errors can ensure that the main and auxiliary stations work together to achieve the optimal value positioning.

[0019] Based on the above principle, this embodiment provides a method for calculating the measurement error of the time difference positioning. On the basis of clarifying the boundary conditions of the positioning fuzzy zone, the area of ​​the fuzzy zone is determined to measure the error size of the time difference positioning, such as Figure 1 and Figure 2 As shown, the specific steps include: S1: establishing a time difference positioning error calculation model, and determining a number of fuzzy areas based on the time difference positioning error calculation model; In a specific embodiment, a time difference positioning error calculation model is established, and a number of fuzzy areas are determined based on the time difference positioning error calculation model, including: S11: Assume that the distance between the master station and the first and second slave stations is , the time difference observed between the master station and the first and second slave stations is , then the observed target is located at is the long axis, On two sets of hyperbolas with minor axes, ; c is the speed of light constant; S12: Establishing the coordinate system Taking the master station as the origin, the direction from the master station to the first slave station is positive. x Axis, establish plane rectangular coordinate system; S13: establishing a time difference line between the master station and the first slave station and a time difference line between the master station and the second slave station based on the plane rectangular coordinate system; The time difference line formed by the master station and the first slave station is recorded as hyperbola P, and its formula is as follows: (1) In the formula, is the horizontal coordinate of the observed target; is the ordinate of the observed target; Assume that the angle formed by the second auxiliary station, the main station, and the first auxiliary station is , then the hyperbola Q formed by the second secondary station and the primary station is expressed as: (2) In formulas (1) and (2), , ; S14: Define the error range of hyperbola P and Q set up The error is ,but The two sets of hyperbolas determined are recorded as hyperbolas ① and ②, and their equations are: (3) (4) Hyperbolas ① and ② are located on the inner and outer sides of hyperbola P respectively, forming the first hyperbolic belt; Same reason The two sets of hyperbolas determined are recorded as hyperbolas ③ and ④, and their equations are: (7) (8) Hyperbolas ③ and ④ are located on the inner and outer sides of hyperbola Q respectively, forming the second hyperbolic belt; S15: Figure 3 As shown, the first hyperbolic belt and the second hyperbolic belt intersect each other to form four closed surfaces. Assuming that the axis of symmetry of the hyperbola P is line m, and the axis of symmetry of the hyperbola Q is line n, the equations are: (11) (12) From the origin to the intersection of line m and line n Direction, according to the four closed faces relative to , and define four closed surfaces as upper fuzzy area, lower fuzzy area, right fuzzy area and left fuzzy area respectively. Each fuzzy area is surrounded by hyperbolas ①, ②, ③ and ④, and the relationships of the points in each fuzzy area with respect to line m and line n are different.

[0020] S2: Since the coordinate value of the observed target can only be located in a certain fuzzy area, the time difference between the observation of the primary station and the first secondary station and the second secondary station is calculated, and the fuzzy area to which the observed target belongs is determined based on the polarity of the time difference; In a specific embodiment, in S2, calculating the time difference observed between the primary station and the plurality of secondary stations, and judging the fuzzy region to which the observed target belongs based on the polarity of the time difference includes: S21: Calculate the time difference between the master station and the first and second slave stations and , the formula is: , ,in, is the time value observed by the master station, and are the time values ​​observed by the first and second secondary stations, respectively; S22: Based on and The polarity of determines the fuzzy area to which the observed target belongs, including: when , When , the observed target is located in the upper fuzzy area; when , When , the observed target is located in the lower fuzzy area; when , When , the observed target is located in the right fuzzy area; when , , the observed target is located in the left fuzzy area.

[0021] S3: forming a rectangular area based on the fuzzy area to which the observed target belongs, and using the rectangular area as a discrimination area; In a specific embodiment, in S3, forming a rectangular area based on the fuzzy area to which the observed target belongs, and using the rectangular area as the discrimination area includes: S31: Figure 4 As shown, the outer boundary of the fuzzy area to which the observed target belongs is delineated by using the set asymptote and ray equation; The set asymptote equations include a first asymptote, a second asymptote, a third asymptote and a fourth asymptote; The set ray equations include a fifth ray, a sixth ray, a seventh ray and an eighth ray; In a specific embodiment, in S31, using the set asymptote and ray equation to define the outer boundary of the fuzzy area to which the observed target belongs includes: The equations of the first asymptote, the second asymptote, the third asymptote and the fourth asymptote are respectively: (twenty one) (twenty two) (twenty three) (twenty four) In the formula, , , and are the coordinates of points on the first asymptote, the second asymptote, the third asymptote, and the fourth asymptote, respectively; The equations of the fifth ray, the sixth ray, the seventh ray and the eighth ray are respectively: (25) (26) (27) (28) In the formula, , , and are the coordinates of points on the fifth, sixth, seventh and eighth rays respectively; Defining the outer boundary of the fuzzy area to which the observed target belongs, including: If the fuzzy area to which the observed target belongs is an upper fuzzy area, the outer boundary of the upper fuzzy area is delineated based on the second asymptote 2, the third asymptote 3, the fifth ray 5 and the seventh ray 7; If the blurred area to which the observed target belongs is a lower blurred area, the outer boundary of the lower blurred area is delineated based on the first asymptote 1, the fourth asymptote 4, the sixth ray 6 and the eighth ray 8; If the fuzzy area to which the observed target belongs is a left fuzzy area, the outer boundary of the left fuzzy area is delineated based on the first asymptote 1, the third asymptote 3, the sixth ray 6 and the seventh ray 7; If the blurred area to which the observed target belongs is a right blurred area, the outer boundary of the right blurred area is defined based on the second asymptote 2 , the fourth asymptote 4 , the fifth ray 5 and the eighth ray 8 .

[0022] S32: based on the set asymptote and ray equation, respectively obtain the coordinates of the outer boundary intersection points of the fuzzy area to which the observed target belongs; In a specific embodiment, in S32, respectively obtaining the coordinates of the outer boundary intersection points of the fuzzy area to which the observed target belongs based on the set asymptote and ray equation includes: If the fuzzy area to which the observed target belongs is the upper fuzzy area, the coordinates of the outer boundary intersection point of the upper fuzzy area are obtained by the equations of the second asymptote, the third asymptote, the fifth ray and the seventh ray, which are respectively: (29) (30) (31) (32) (33) (34) (35) (36) If the fuzzy area to which the observed target belongs is the lower fuzzy area, the coordinates of the outer boundary intersection point of the lower fuzzy area are obtained by the equations of the first asymptote, the fourth asymptote, the sixth ray and the eighth ray, which are respectively: (37) (38) (39) (40) (41) (42) (43) (44) If the fuzzy area to which the observed target belongs is the right fuzzy area, the coordinates of the outer boundary intersection point of the right fuzzy area are obtained by the equations of the second asymptote, the fourth asymptote, the fifth ray and the eighth ray, which are respectively: (45) (46) (47) (48) (49) (50) (51) (52) If the fuzzy area to which the observed target belongs is the left fuzzy area, the coordinates of the outer boundary intersection point of the left fuzzy area are obtained by the equations of the first asymptote, the third asymptote, the sixth ray and the seventh ray, which are respectively: (53) (54) (55) (56) (57) (58) (59) (60) In the formula, , , , .

[0023] S33: Obtaining a rectangular area based on the coordinates of the outer boundary intersection points of the fuzzy area to which the observed target belongs, including: The coordinates of the outer boundary intersection points of the fuzzy area to which the observation target belongs and the coordinates of the outer boundary intersection points of other fuzzy areas are calculated to obtain a rectangular area.

[0024] Specifically, since the outer boundaries of the four fuzzy regions do not intersect each other, and the maximum rectangular region formed by the vertices of the four fuzzy domains do not overlap, in order to simplify the calculation, this embodiment uses the rectangular region defined by the maximum horizontal and vertical coordinate difference of each fuzzy region as the discrimination region, and uses the Monte Carlo random algorithm in MATLAB to generate a number of sampling points in the rectangular region, and the number of generated sampling points is proportional to the area of ​​the rectangular region, that is, the larger the number of generated sampling points, the closer the points in the rectangular region are to uniform distribution.

[0025] S4: generating a number of sampling points in the discrimination area, and performing a formula discrimination on each of the sampling points to determine the number of sampling points located in the fuzzy area to which the observed target belongs; Specifically, since solving the set of equations established by two sets of hyperbolas is usually very complicated, this embodiment adopts a method of performing formula judgment on the points in each fuzzy area to determine the number of sampling points located in the fuzzy area to which the observation target belongs, thereby calculating the area of ​​the fuzzy area to which the observation target belongs.

[0026] In a specific embodiment, in S4, a plurality of sampling points are generated in the discrimination area, and a formula discrimination is performed on each of the sampling points to determine the number of sampling points located in the fuzzy area to which the observed target belongs, including: A Monte Carlo random algorithm is used to generate a number of sampling points in the discrimination area; Substitute each of the sampling points into the following discriminant formula in turn, including: Points in the first hyperbolic band Satisfy the formula: (5) (6) Points in the second hyperbolic band Satisfy the formula: (9) (10) The points in the upper fuzzy region satisfy the formula: (13) (14) The points in the lower fuzzy region satisfy the formula: (15) (16) The points in the left fuzzy area satisfy the formula: (17) (18) The points in the right fuzzy area satisfy the formula: (19) (20) If the sampling point satisfies formulas (5), (6), (9), (10), (13) and (14), then the sampling point is located in the upper fuzzy area; If the sampling point satisfies formulas (5), (6), (9), (10), (15) and (16), then the sampling point is located in the lower fuzzy area; If the sampling point satisfies formulas (5), (6), (9), (10), (17) and (18), then the sampling point is located in the left fuzzy area; If the sampling point satisfies formulas (5), (6), (9), (10), (19) and (20), then the sampling point is located in the right fuzzy area; Specifically, each sampling point in the blurred area satisfies formulas (5), (6), (9) and (10).

[0027] After judging each sampling point in turn, the number of sampling points located in the fuzzy area to which the observed target belongs is obtained.

[0028] S5: The area of ​​the fuzzy region to which the observed target belongs is calculated based on the number of sampling points in the fuzzy region to which the observed target belongs. The area of ​​the fuzzy region to which the observed target belongs is the measurement error of the time difference positioning.

[0029] In a specific embodiment, in S5, the area of ​​the fuzzy region to which the observation target belongs is calculated based on the number of sampling points in the fuzzy region to which the observation target belongs, and the calculation formula is: (61) in, is the number of sampling points in the fuzzy area to which the observed target belongs, N is the number of sampling points in the rectangular area, and are the horizontal coordinate extreme values ​​of the four intersection points between the first hyperbolic band and the second hyperbolic band, that is, the horizontal coordinate extreme values ​​of the four intersection points between the first hyperbolic band and the second hyperbolic band, and They are respectively the ordinate extreme values ​​of the four intersection points between the first hyperbolic belt and the second hyperbolic belt, that is, the ordinate extreme values ​​of the four intersection points between the first hyperbolic belt and the second hyperbolic belt.

[0030] In a specific embodiment, in order to verify the effectiveness of the method proposed in this embodiment, the observation time difference between two groups of primary and secondary stations is obtained, and the distribution, area and target position estimation of the fuzzy area are obtained based on this method. millisecond, rice, d 1= d 2 = 200 meters, error d = 5 meters, The implementation process of the present invention is described by taking an example.

[0031] According to Table 1, , The polarity of is used to judge that the fuzzy area to which the observed target belongs is the lower fuzzy area. Figure 4 The outer boundary lines of the lower fuzzy area are determined as: the first asymptote 1, the fourth asymptote 4, the sixth ray 6 and the eighth ray 8. Substitute the four outer boundary line equations into formulas (37)-(44) to obtain the coordinates of the four intersection points, which are: (79.4787, 79.4787), (53.2528, 53.2528), (41.9585, 89.1664), (89.1664, 41.9585). The horizontal and vertical coordinate extreme values ​​of the four intersection points are used to define the judgment area, that is, , In the judgment area, the Monte Carlo random algorithm is used to generate random sampling points. Formulas (5), (6), (9), (10), (15) and (16) are used to judge each sampling point. The points where all six formulas are true are the points in the lower fuzzy area.

[0032] Table 1:

[0033] The number of sampling points in the lower fuzzy area is counted, and the area of ​​the lower fuzzy area can be calculated by the ratio of the number of sampling points to the number of Monte Carlo random points. The time difference positioning error calculation method based on the fuzzy area can realize the quantitative calculation of the error of real-time update of measurement parameters, provide a theoretical basis for the dynamic adjustment of passive positioning sensor resource configuration, and has strong executability and ideal effect.

[0034] 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 time difference positioning measurement error, characterized in that: The specific steps include: S1: establishing a time difference positioning error calculation model, and determining a number of fuzzy areas based on the time difference positioning error calculation model; S2: Calculate the time difference between the observations of the primary station and several secondary stations, and determine the fuzzy area to which the observed target belongs based on the polarity of the time difference; S3: forming a rectangular area based on the fuzzy area to which the observed target belongs, and using the rectangular area as a discrimination area; S4: generating a number of sampling points in the discrimination area, and performing a formula discrimination on each of the sampling points to determine the number of sampling points located in the fuzzy area to which the observed target belongs; S5: The area of ​​the fuzzy region to which the observed target belongs is calculated based on the number of sampling points in the fuzzy region to which the observed target belongs. The area of ​​the fuzzy region to which the observed target belongs is the measurement error of the time difference positioning.

2. The method for calculating the time difference positioning measurement error according to claim 1, characterized in that: In S1, a time difference positioning error calculation model is established, and a number of fuzzy areas are determined based on the time difference positioning error calculation model, including: S11: Assume that the distance between the master station and the first and second slave stations is , the observed time difference between the master station and the first and second slave stations is , then the observed target is located at is the long axis, On two sets of hyperbolas with minor axes, ; c is the speed of light constant; S12: Establishing the coordinate system Taking the master station as the origin, the direction from the master station to the first slave station is positive. x Axis, establish plane rectangular coordinate system; S13: establishing a time difference line between the master station and the first slave station and a time difference line between the master station and the second slave station based on the plane rectangular coordinate system; The time difference line formed by the master station and the first slave station is recorded as hyperbola P, and its formula is as follows: （1） In the formula, is the horizontal coordinate of the observed target; is the ordinate of the observed target; Assume that the angle formed by the second auxiliary station, the main station, and the first auxiliary station is , then the hyperbola Q formed by the second secondary station and the primary station is expressed as: （2） In formulas (1) and (2), , ; Defining the error range of hyperbola P and Q set up The error is ,but The two sets of hyperbolas determined are recorded as hyperbolas ① and ②, and their equations are: （3） （4） Hyperbolas ① and ② are located on the inner and outer sides of hyperbola P respectively, forming the first hyperbolic belt; Same reason The two sets of hyperbolas determined are recorded as hyperbolas ③ and ④, and their equations are: （7） （8） Hyperbolas ③ and ④ are located on the inner and outer sides of hyperbola Q respectively, forming the second hyperbolic belt; S15: The first hyperbolic belt and the second hyperbolic belt intersect each other to form four closed surfaces. Assume that the axis of symmetry of the hyperbola P is line m, and the axis of symmetry of the hyperbola Q is line n. The equations are: （11） （12） From the origin to the intersection of line m and line n Direction, according to the four closed faces relative to The position of the fuzzy area is defined as the upper fuzzy area, the lower fuzzy area, the right fuzzy area and the left fuzzy area respectively.

3. The method for calculating the time difference positioning measurement error according to claim 2, characterized in that: In S2, the time difference between the observations of the primary station and several secondary stations is calculated, and the fuzzy area to which the observed target belongs is determined based on the polarity of the time difference, including: S21: Calculate the time difference between the master station and the first and second slave stations and , the formula is: , ,in, is the time value observed by the master station, and are the time values ​​observed by the first and second secondary stations, respectively; S22: Based on and The polarity of determines the fuzzy area to which the observed target belongs, including: when , When , the observed target is located in the upper fuzzy area; when , When , the observed target is located in the lower fuzzy area; when , When , the observed target is located in the right fuzzy area; when , , the observed target is located in the left fuzzy area.

4. The method for calculating the time difference positioning measurement error according to claim 3, characterized in that: In S3, forming a rectangular area based on the fuzzy area to which the observed target belongs, and using the rectangular area as a discrimination area includes: S31: Using the set asymptote and ray equation to define the outer boundary of the fuzzy area to which the observed target belongs; The set asymptote equations include a first asymptote, a second asymptote, a third asymptote and a fourth asymptote; The set ray equations include a fifth ray, a sixth ray, a seventh ray and an eighth ray; S32: based on the set asymptote and ray equation, respectively obtain the coordinates of the outer boundary intersection points of the fuzzy area to which the observed target belongs; S33: Obtaining a rectangular area based on the coordinates of the outer boundary intersection points of the fuzzy area to which the observed target belongs, including: The coordinates of the outer boundary intersection points of the fuzzy area to which the observation target belongs and the coordinates of the outer boundary intersection points of other fuzzy areas are calculated to obtain a rectangular area.

5. The method for calculating the time difference positioning measurement error according to claim 4, characterized in that: In S31, using the set asymptote and ray equation to define the outer boundary of the fuzzy area to which the observed target belongs includes: The equations of the first asymptote, the second asymptote, the third asymptote and the fourth asymptote are respectively: （21） （22） （23） （24） In the formula, , , and are the coordinates of points on the first asymptote, the second asymptote, the third asymptote, and the fourth asymptote, respectively; The equations of the fifth ray, the sixth ray, the seventh ray and the eighth ray are respectively: （25） （26） （27） （28） In the formula, , , and are the coordinates of points on the fifth, sixth, seventh and eighth rays respectively; Defining the outer boundary of the fuzzy area to which the observed target belongs, including: If the fuzzy area to which the observed target belongs is an upper fuzzy area, defining an outer boundary of the upper fuzzy area based on the second asymptote, the third asymptote, the fifth ray and the seventh ray; If the fuzzy area to which the observed target belongs is a lower fuzzy area, defining an outer boundary of the lower fuzzy area based on the first asymptote, the fourth asymptote, the sixth ray and the eighth ray; If the fuzzy area to which the observed target belongs is a left fuzzy area, then defining an outer boundary of the left fuzzy area based on the first asymptote, the third asymptote, the sixth ray and the seventh ray; If the blurred area to which the observed target belongs is a right blurred area, the outer boundary of the right blurred area is defined based on the second asymptote, the fourth asymptote, the fifth ray and the eighth ray.

6. The method for calculating the time difference positioning measurement error according to claim 5, characterized in that: In S32, based on the set asymptote and ray equation, respectively calculating the coordinates of the outer boundary intersection points of the fuzzy area to which the observed target belongs includes: If the fuzzy area to which the observed target belongs is the upper fuzzy area, the coordinates of the outer boundary intersection point of the upper fuzzy area are obtained by the equations of the second asymptote, the third asymptote, the fifth ray and the seventh ray, which are respectively: （29） （30） （31） （32） （33） （34） （35） （36） If the fuzzy area to which the observed target belongs is the lower fuzzy area, the coordinates of the outer boundary intersection point of the lower fuzzy area are obtained by the equations of the first asymptote, the fourth asymptote, the sixth ray and the eighth ray, which are respectively: （37） （38） （39） （40） （41） （42） （43） （44） If the fuzzy area to which the observed target belongs is the right fuzzy area, the coordinates of the outer boundary intersection point of the right fuzzy area are obtained by the equations of the second asymptote, the fourth asymptote, the fifth ray and the eighth ray, which are respectively: （45） （46） （47） （48） （49） （50） （51） （52） If the fuzzy area to which the observed target belongs is the left fuzzy area, the coordinates of the outer boundary intersection point of the left fuzzy area are obtained by the equations of the first asymptote, the third asymptote, the sixth ray and the seventh ray, which are respectively: （53） （54） （55） （56） （57） （58） （59） （60） In the formula, , , , .

7. The method for calculating the time difference positioning measurement error according to claim 6, characterized in that: In S4, a number of sampling points are generated in the discrimination area, and a formula discrimination is performed on each of the sampling points to determine the number of sampling points located in the fuzzy area to which the observed target belongs, including: A Monte Carlo random algorithm is used to generate a number of sampling points in the discrimination area; Substitute each of the sampling points into the following discriminant formula in turn, including: Points in the first hyperbolic band Satisfy the formula: （5） （6） Points in the second hyperbolic band Satisfy the formula: （9） （10） The points in the upper fuzzy region satisfy the formula: （13） （14） The points in the lower fuzzy region satisfy the formula: （15） （16） The points in the left fuzzy area satisfy the formula: （17） （18） The points in the right fuzzy area satisfy the formula: （19） （20） If the sampling point satisfies formulas (5), (6), (9), (10), (13) and (14), then the sampling point is located in the upper fuzzy area; If the sampling point satisfies formulas (5), (6), (9), (10), (15) and (16), then the sampling point is located in the lower fuzzy area; If the sampling point satisfies formulas (5), (6), (9), (10), (17) and (18), then the sampling point is located in the left fuzzy area; If the sampling point satisfies formulas (5), (6), (9), (10), (19) and (20), then the sampling point is located in the right fuzzy area; After judging each sampling point in turn, the number of sampling points located in the fuzzy area to which the observed target belongs is obtained.

8. The method for calculating the time difference positioning measurement error according to claim 7, characterized in that: In S5, the area of ​​the fuzzy region to which the observation target belongs is calculated based on the number of sampling points in the fuzzy region to which the observation target belongs, and the calculation formula is: （61） in, is the number of sampling points in the fuzzy area to which the observed target belongs, N is the number of sampling points in the rectangular area, and are the abscissa extreme values ​​of the four intersection points between the first hyperbolic band and the second hyperbolic band, and are the ordinate extreme values ​​of the four intersection points between the first hyperbolic band and the second hyperbolic band.

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