A method for calculating time difference positioning measurement error

Abstract

The present invention belongs to the technical field of time difference positioning error measurement and discloses a method for calculating time difference positioning measurement error, comprising the following steps: S1: establishing a time difference positioning error calculation model and determining a fuzzy area; S2: calculating the time difference between observations of a primary station and a secondary station to determine the fuzzy area to which the observed target belongs; S3: forming a discrimination area; S4: generating a number of sampling points within the discrimination area and performing a formula discrimination on each sampling point to determine the number of sampling points located within the fuzzy area to which the observed target belongs; and S5: calculating the area of the fuzzy area to which the observed target belongs based on the number of sampling points within the fuzzy area to which the observed target belongs. The present invention measures the accuracy of time difference positioning by the fuzzy area, solves the error estimation problem during the dynamic change of observation station position parameters and measurement parameters, and simultaneously utilizes the change in the fuzzy area to guide the primary observation station to timely direct and adjust the relative station position, providing a basis for the primary and secondary stations to cooperate in achieving optimal value positioning.

Description

Technical Field

[0001] The present 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 dilution 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. Moreover, using 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 it 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 existing technology.

[0005] In order to achieve the above object, the technical solution of the present invention is:

[0006] A method for calculating time difference positioning measurement error, comprising the following steps:

[0007] S1: Establishing a time difference positioning error calculation model, and determining several fuzzy areas based on the time difference positioning error calculation model, including:

[0008] 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, wherein the time difference line is a hyperbola;

[0009] A first hyperbolic belt and a second hyperbolic belt are formed based on an error range defining the hyperbola, wherein the first hyperbolic belt and the second hyperbolic belt intersect with each other to form four closed surfaces, and the four closed surfaces are respectively defined as four fuzzy areas;

[0010] S2: Calculate the time difference between the observations of the primary station and several secondary stations, and determine the fuzzy region to which the observed target belongs based on the polarity of the time difference;

[0011] 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, including:

[0012] S31: Delineating the outer boundary of the fuzzy region to which the observed target belongs using the set asymptote and ray equation;

[0013] The set asymptote equations include a first asymptote, a second asymptote, a third asymptote and a fourth asymptote;

[0014] The set ray equation includes the fifth ray, the sixth ray, the seventh ray and the eighth ray;

[0015] S32: Based on the set asymptotes and ray equations, the coordinates of the outer boundary intersection points of the fuzzy area to which the observed target belongs are respectively calculated;

[0016] S33: Obtaining a rectangular area based on the extreme values of the horizontal and vertical coordinates of the outer boundary intersection coordinates of the fuzzy area to which the observation target belongs;

[0017] 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;

[0018] S5: Calculate the area of the fuzzy region to which the observation target belongs based on the number of sampling points in the fuzzy region to which the observation target belongs. The area of the fuzzy region to which the observation target belongs is the measurement error of the time difference positioning.

[0019] Furthermore, a time difference positioning error calculation model is established, and based on the time difference positioning error calculation model, several fuzzy areas are determined, including:

[0020] S11: Let the distance between the master station and the first and second slave stations be d i The time difference between the master station and the first and second slave stations is Δt i , then the observed target is located at is the long axis, On the two sets of hyperbolas with minor axes, i = 1, 2; c is the speed of light constant;

[0021] S12: Establishing the coordinate system

[0022] With the master station as the origin and the direction from the master station to the first slave station as the positive x-axis, a plane rectangular coordinate system is established;

[0023] 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;

[0024] The time difference line formed by the master station and the first slave station is denoted as hyperbola P, and its formula is as follows:

[0025]

[0026] Where x is the horizontal coordinate of the observation target; y is the vertical coordinate of the observation target;

[0027] Assuming that the angle formed by the second secondary station, the main station, and the first secondary station is β, the hyperbola Q formed by the second secondary station and the main station is expressed as:

[0028]

[0029] In formulas (1) and (2),

[0030] S14: Define the error range of hyperbola P and Q

[0031] Assume a i The error is ±d, then the two sets of hyperbolas determined by a1±d are recorded as hyperbolas ① and ②, and their equations are:

[0032]

[0033] Hyperbolas ① and ② are located on the inner and outer sides of hyperbola P respectively, forming the first hyperbolic band;

[0034] Similarly, the two sets of hyperbolas determined by a2±d are recorded as hyperbolas ③ and ④, and their equations are:

[0035]

[0036] Hyperbolas ③ and ④ are located on the inner and outer sides of hyperbola Q respectively, forming the second hyperbolic band;

[0037] S15: The first hyperbolic band and the second hyperbolic band intersect with each other to form four closed surfaces. Let the axis of symmetry of the hyperbola P be line m, and the axis of symmetry of the hyperbola Q be line n. The equations are:

[0038] x=c1 (11)

[0039] ysinβ+xcosβ=c2 (12)

[0040] From the origin to the intersection O' of line m and line n, the four closed surfaces are defined as the upper fuzzy area, the lower fuzzy area, the right fuzzy area and the left fuzzy area according to their positions relative to O'.

[0041] Furthermore, calculating the time difference between the observations of the primary station and several secondary stations, and judging the fuzzy region to which the observed target belongs based on the polarity of the time difference includes:

[0042] S21: Calculate the time differences Δt1 and Δt2 observed between the master station and the first and second slave stations. The formula is:

[0043] Δt1=t0-t1

[0044] Δt2=t0-t2

[0045] Among them, t0 is the time value observed by the primary station, t1 and t2 are the time values observed by the first and second secondary stations respectively;

[0046] S22: Determine the fuzzy region to which the observed target belongs based on the polarity of Δt1 and Δt2, including:

[0047] When Δt1≥0 and Δt2≥0, the observed target is located in the upper fuzzy area;

[0048] When Δt1<0, Δt2<0, the observed target is located in the lower fuzzy area;

[0049] When Δt1≥0 and Δt2<0, the observed target is located in the right fuzzy area;

[0050] When Δt1<0 and Δt2≥0, the observed target is located in the left fuzzy area.

[0051] Furthermore, in S31, using the set asymptotes and ray equations to delineate the outer boundary of the fuzzy region to which the observed target belongs includes:

[0052] The equations of the first asymptote, the second asymptote, the third asymptote and the fourth asymptote are:

[0053]

[0054] Where (x1, y1), (x2, y2), (x3, y3), and (x4, y4) are the coordinates of the points on the first, second, third, and fourth asymptotes, respectively;

[0055] The equations of the fifth ray, the sixth ray, the seventh ray and the eighth ray are respectively:

[0056]

[0057]

[0058] Where (x5, y5), (x6, y6), (x7, y7), and (x8, y8) are the coordinates of the points on the fifth, sixth, seventh, and eighth rays, respectively;

[0059] Delineating the outer boundary of the fuzzy area to which the observed target belongs, including:

[0060] If the fuzzy area to which the observed target belongs is an upper fuzzy area, delineating an outer boundary of the upper fuzzy area based on the second asymptote, the third asymptote, the fifth ray, and the seventh ray;

[0061] If the fuzzy area to which the observed target belongs is a lower fuzzy area, delineating an outer boundary of the lower fuzzy area based on the first asymptote, the fourth asymptote, the sixth ray, and the eighth ray;

[0062] 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;

[0063] If the fuzzy area to which the observed target belongs is a right fuzzy area, the outer boundary of the right fuzzy area is defined based on the second asymptote, the fourth asymptote, the fifth ray and the eighth ray.

[0064] Furthermore, respectively obtaining the coordinates of the outer boundary intersection points of the fuzzy region to which the observed target belongs based on the set asymptotes and ray equations includes:

[0065] 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, respectively:

[0066]

[0067] y 上 =k a2 (x 上 -c1-a1-d) (30)

[0068]

[0069] y 下 =k a1 (x 下 -c1) (32)

[0070]

[0071] y 左 =k a1 (x 左 -c1) (34)

[0072]

[0073] y 右 =k a2 (x 右 -c1-a1-d) (36)

[0074] 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 using the equations of the first asymptote, the fourth asymptote, the sixth ray, and the eighth ray, which are respectively:

[0075]

[0076] y' 上 =-k a1 (x' 上 -c1) (38)

[0077]

[0078] y' 左 =-k a2 (x' 左 -c1+a1+d) (40)

[0079]

[0080] y' 右 =-k a1 (x' 右 -c1) (42)

[0081]

[0082] y' 下 =-k a2 (x' 下 -c1+a1+d) (44)

[0083] 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, respectively:

[0084]

[0085] y” 上 =k a2 (x” 上 -c1-a1-d) (46)

[0086]

[0087] y” 右 =k a2 (x” 右 -c1-a1-d) (48)

[0088]

[0089] y” 左 =k a1 (x” 左 -c1) (50)

[0090]

[0091] y”下 =k a1 (x” 下 -c1) (52)

[0092] 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, respectively:

[0093]

[0094] y"' 右 =-k a1 (x”' 右 -c1) (54)

[0095]

[0096] y"' 下 =-k a2 (x”' 下 -c1+a1+d) (56)

[0097]

[0098] y"' 左 =-k a2 (x”' 左 -c1+a1+d) (58)

[0099]

[0100] y"' 上 =-k a1 (x”' 上 -c1) (60)

[0101] Where,

[0102] Furthermore, generating a plurality of sampling points within the discrimination area and performing a formula discrimination on each of the sampling points to determine the number of sampling points located within the fuzzy area to which the observed target belongs includes:

[0103] A Monte Carlo random algorithm is used to generate a number of sampling points in the discrimination area;

[0104] Substitute each of the sampling points into the following discriminant formula in turn, including:

[0105] The first point in the hyperbolic band (x # ,y # ) satisfies the formula:

[0106]

[0107] The points (x^,y^) in the second hyperbolic band satisfy the formula:

[0108]

[0109] The points in the upper fuzzy area satisfy the formula:

[0110] x 1 上 -c1>0 (13)

[0111] y 1 上 sinβ-x 1 上 cosβ-c2>0 (14)

[0112] The points in the lower fuzzy area satisfy the formula:

[0113] x 1 下 -c1<0 (15)

[0114] y 1 下 sinβ-x 1 下 cosβ-c2<0 (16)

[0115] The points in the left fuzzy area satisfy the formula:

[0116] x 1 左 -c1<0 (17)

[0117] y 1 左 sinβ-x 1 左 cosβ-c2>0 (18)

[0118] The points in the right fuzzy area satisfy the formula:

[0119] x 1 右 -c1>0 (19)

[0120] y 1 右 sinβ-x 1 右 cosβ-c2<0 (20)

[0121] If the sampling point satisfies formulas (5), (6), (9), (10), (13) and (14), then the sampling point is located in the upper fuzzy area;

[0122] If the sampling point satisfies formulas (5), (6), (9), (10), (15) and (16), then the sampling point is located in the lower fuzzy area;

[0123] If the sampling point satisfies formulas (5), (6), (9), (10), (17) and (18), then the sampling point is located in the left fuzzy area;

[0124] If the sampling point satisfies formulas (5), (6), (9), (10), (19) and (20), then the sampling point is located in the right fuzzy area;

[0125] After judging each sampling point in turn, the number of sampling points located in the fuzzy area to which the observation target belongs is obtained.

[0126] Furthermore, 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:

[0127]

[0128] Among them, n 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 x min and x max They are the extreme values of the horizontal coordinates of the outer boundary intersection point coordinates of the fuzzy area to which the observation target belongs, y min and y max They are respectively the extreme values of the ordinates of the outer boundary intersection points of the fuzzy area to which the observed target belongs.

[0129] 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 the time difference positioning. The present invention measures the accuracy of time difference positioning by the 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 in the fuzzy area can guide the main observation station to timely command and adjust the relative station position, providing a basis for the main and secondary stations to cooperate to achieve optimal value positioning, and has high practical value. BRIEF DESCRIPTION OF THE DRAWINGS

[0130] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following is a brief introduction to 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 any creative labor.

[0131] Figure 1 This is a first flow chart of a method for calculating time difference positioning measurement error in the present invention;

[0132] Figure 2 This is a second flow chart of a method for calculating time difference positioning measurement error in the present invention;

[0133] Figure 3 Schematic diagram of a time difference positioning error calculation model in an embodiment of the present invention;

[0134] Figure 4 Schematic diagram of the outer boundaries of each fuzzy area in an embodiment of the present invention.

[0135] 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;

[0136] A. Main station; B. First secondary station; C. Second secondary station. DETAILED DESCRIPTION

[0137] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0138] In time-of-day positioning, the primary source of error is the time difference measured between the primary and secondary observation stations. Fluctuations in the time difference cause the hyperbola determined by the time difference to shift left and right relative to the centerlines of the primary and secondary stations. The two sets of hyperbolas corresponding to the time difference error can be used to determine the positioning error of one set of primary and secondary stations as a hyperbolic surface. Similarly, another set of hyperbolic surfaces for the primary and secondary stations can be taken. The intersection of these two hyperbolic surfaces is the positioning ambiguity area. The size of the ambiguity area directly reflects positioning accuracy: larger areas indicate lower positioning accuracy, while smaller areas indicate higher positioning accuracy. The core concept of calculating time-of-day positioning error based on the ambiguity area is to use current observation parameters to assess positioning accuracy. Due to the dynamic nature of combat operations, the layout of observation stations is constantly changing, and the measurement errors corresponding to different observation parameters are constantly changing. Keeping track of current measurement errors is key to optimizing and adjusting observation station layouts. Especially in coordinated operations, utilizing real-time calculations of time-of-day positioning errors can ensure that primary and secondary stations work together to achieve optimal positioning.

[0139] Based on the above principles, this embodiment provides a method for calculating the time difference positioning measurement error. On the basis of clarifying the boundary conditions of the positioning ambiguity zone, the area of the ambiguity 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:

[0140] 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;

[0141] In a specific embodiment, establishing a time difference positioning error calculation model, and determining a number of fuzzy areas based on the time difference positioning error calculation model includes:

[0142] S11: Let the distance between the master station and the first and second slave stations be d i The time difference between the master station and the first and second slave stations is Δt i , then the observed target is located at is the long axis, On the two sets of hyperbolas with minor axes, i = 1, 2; c is the speed of light constant;

[0143] S12: Establishing the coordinate system

[0144] With the master station as the origin and the direction from the master station to the first slave station as the positive x-axis, a plane rectangular coordinate system is established;

[0145] 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;

[0146] The time difference line formed by the master station and the first slave station is denoted as hyperbola P, and its formula is as follows:

[0147]

[0148] Where x is the horizontal coordinate of the observation target; y is the vertical coordinate of the observation target;

[0149] Assuming that the angle formed by the second secondary station, the main station, and the first secondary station is β, the hyperbola Q formed by the second secondary station and the main station is expressed as:

[0150]

[0151] In formulas (1) and (2),

[0152] S14: Define the error range of hyperbola P and Q

[0153] Assume a i The error is ±d, then the two sets of hyperbolas determined by a1±d are recorded as hyperbolas ① and ②, and their equations are:

[0154]

[0155] Hyperbolas ① and ② are located on the inner and outer sides of hyperbola P respectively, forming the first hyperbolic band;

[0156] Similarly, the two sets of hyperbolas determined by a2±d are recorded as hyperbolas ③ and ④, and their equations are:

[0157]

[0158] Hyperbolas ③ and ④ are located on the inner and outer sides of hyperbola Q respectively, forming the second hyperbolic band;

[0159] S15: Figure 3 As shown, the first hyperbolic belt and the second hyperbolic belt intersect with each other to form four closed surfaces. Let the symmetry axis of the hyperbola P be line m, and the symmetry axis of the hyperbola Q be line n. The equations are:

[0160] x=c1 (11)

[0161] ysinβ+xcosβ=c2 (12)

[0162] From the origin to the intersection O' of line m and line n, the four closed surfaces are defined as the upper fuzzy area, the lower fuzzy area, the right fuzzy area and the left fuzzy area according to their positions relative to O'. Each fuzzy area is surrounded by hyperbolas ①, ②, ③ and ④, and the relationship between the points in each fuzzy area and line m and line n is different.

[0163] In a specific embodiment, in S2, calculating the time difference between the observations of 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:

[0164] S21: Calculate the time differences Δt1 and Δt2 observed between the master station and the first and second slave stations. The formula is:

[0165] Δt1=t0-t1

[0166] Δt2=t0-t2

[0167] Among them, t0 is the time value observed by the primary station, t1 and t2 are the time values observed by the first and second secondary stations respectively;

[0168] S22: Determine the fuzzy region to which the observed target belongs based on the polarity of Δt1 and Δt2, including:

[0169] When Δt1≥0 and Δt2≥0, the observed target is located in the upper fuzzy area;

[0170] When Δt1<0, Δt2<0, the observed target is located in the lower fuzzy area;

[0171] When Δt1≥0 and Δt2<0, the observed target is located in the right fuzzy area;

[0172] When Δt1<0 and Δt2≥0, the observed target is located in the left fuzzy area.

[0173] 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;

[0174] 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:

[0175] S31: If Figure 4 As shown, the outer boundary of the fuzzy area to which the observed target belongs is delineated by using the set asymptotes and ray equations;

[0176] The set asymptote equations include a first asymptote, a second asymptote, a third asymptote and a fourth asymptote;

[0177] The set ray equation includes the fifth ray, the sixth ray, the seventh ray and the eighth ray;

[0178] In a specific embodiment, in S31, using the set asymptote and ray equation to delineate the outer boundary of the fuzzy region to which the observed target belongs includes:

[0179] The equations of the first asymptote, the second asymptote, the third asymptote and the fourth asymptote are:

[0180]

[0181]

[0182] Where (x1, y1), (x2, y2), (x3, y3), and (x4, y4) are the coordinates of the points on the first, second, third, and fourth asymptotes, respectively;

[0183] The equations of the fifth ray, the sixth ray, the seventh ray and the eighth ray are respectively:

[0184]

[0185] Where (x5, y5), (x6, y6), (x7, y7), and (x8, y8) are the coordinates of the points on the fifth, sixth, seventh, and eighth rays, respectively;

[0186] Delineating the outer boundary of the fuzzy area to which the observed target belongs, including:

[0187] 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;

[0188] If the fuzzy area to which the observed target belongs is a lower fuzzy area, the outer boundary of the lower fuzzy area is delineated based on the first asymptote 1, the fourth asymptote 4, the sixth ray 6 and the eighth ray 8;

[0189] If the fuzzy area to which the observed target belongs is the 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;

[0190] If the fuzzy area to which the observed target belongs is a right fuzzy area, the outer boundary of the right fuzzy area is defined based on the second asymptote 2 , the fourth asymptote 4 , the fifth ray 5 and the eighth ray 8 .

[0191] S32: Based on the set asymptotes and ray equations, the coordinates of the outer boundary intersection points of the fuzzy area to which the observed target belongs are respectively calculated;

[0192] In a specific embodiment, in S32, respectively calculating the coordinates of the outer boundary intersection points of the fuzzy region to which the observed target belongs based on the set asymptotes and ray equations includes:

[0193] 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, respectively:

[0194]

[0195] y 上 =k a2 (x 上 -c1-a1-d) (30)

[0196]

[0197] y 下 =k a1 (x 下 -c1) (32)

[0198]

[0199] y 左 =k a1 (x 左 -c1) (34)

[0200]

[0201] y 右 =k a2 (x 右 -c1-a1-d) (36)

[0202] 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 using the equations of the first asymptote, the fourth asymptote, the sixth ray, and the eighth ray, which are respectively:

[0203]

[0204] y' 上 =-k a1 (x' 上 -c1) (38)

[0205]

[0206] y' 左 =-k a2 (x' 左 -c1+a1+d) (40)

[0207]

[0208] y' 右 =-k a1 (x' 右 -c1) (42)

[0209]

[0210] y' 下 =-k a2 (x' 下-c1+a1+d) (44)

[0211] 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, respectively:

[0212]

[0213] y” 上 =k a2 (x” 上 -c1-a1-d) (46)

[0214]

[0215] y” 右 =k a2 (x” 右 -c1-a1-d) (48)

[0216]

[0217] y” 左 =k a1 (x” 左 -c1) (50)

[0218]

[0219] y” 下 =k a1 (x” 下 -c1) (52)

[0220] 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, respectively:

[0221]

[0222] y"' 右 =-k a1 (x”' 右 -c1) (54)

[0223]

[0224] y"' 下 =-k a2 (x”' 下 -c1+a1+d) (56)

[0225]

[0226] y"' 左 =-k a2 (x”' 左 -c1+a1+d) (58)

[0227]

[0228] y"' 上 =-k a1 (x”' 上 -c1) (60)

[0229] Where,

[0230] S33: Obtain a rectangular area based on the extreme values of the horizontal and vertical coordinates of the outer boundary intersection coordinates of the fuzzy area to which the observation target belongs.

[0231] Specifically, since the outer boundaries of the four fuzzy regions do not intersect with each other, and the largest rectangular region formed by the vertices of the four fuzzy regions do not overlap, to simplify the calculation, this embodiment uses the Monte Carlo randomization 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 a uniform distribution.

[0232] 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;

[0233] 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.

[0234] In a specific embodiment, in S4, generating a plurality 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 includes:

[0235] A Monte Carlo random algorithm is used to generate a number of sampling points in the discrimination area;

[0236] Substitute each of the sampling points into the following discriminant formula in turn, including:

[0237] The first point in the hyperbolic band (x # ,y # ) satisfies the formula:

[0238]

[0239] The points (x^,y^) in the second hyperbolic band satisfy the formula:

[0240]

[0241] The points in the upper fuzzy area satisfy the formula:

[0242] x 1 上 -c1>0 (13)

[0243] y 1 上 sinβ-x 1 上 cosβ-c2>0 (14)

[0244] The points in the lower fuzzy area satisfy the formula:

[0245] x 1 下 -c1<0 (15)

[0246] y 1 下 sinβ-x 1 下 cosβ-c2<0 (16)

[0247] The points in the left fuzzy area satisfy the formula:

[0248] x 1 左 -c1<0 (17)

[0249] y 1 左 sinβ-x 1 左 cosβ-c2>0 (18)

[0250] The points in the right fuzzy area satisfy the formula:

[0251] x 1 右 -c1>0 (19)

[0252] y 1 右 sinβ-x 1 右 cosβ-c2<0 (20)

[0253] If the sampling point satisfies formulas (5), (6), (9), (10), (13) and (14), then the sampling point is located in the upper fuzzy area;

[0254] If the sampling point satisfies formulas (5), (6), (9), (10), (15) and (16), then the sampling point is located in the lower fuzzy area;

[0255] If the sampling point satisfies formulas (5), (6), (9), (10), (17) and (18), then the sampling point is located in the left fuzzy area;

[0256] If the sampling point satisfies formulas (5), (6), (9), (10), (19) and (20), then the sampling point is located in the right fuzzy area;

[0257] Specifically, each sampling point in the blurred area satisfies formulas (5), (6), (9) and (10).

[0258] After judging each sampling point in turn, the number of sampling points located in the fuzzy area to which the observation target belongs is obtained.

[0259] S5: Calculate the area of the fuzzy region to which the observation target belongs based on the number of sampling points in the fuzzy region to which the observation target belongs. The area of the fuzzy region to which the observation target belongs is the measurement error of the time difference positioning.

[0260] 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:

[0261]

[0262] Among them, n 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 x min and x max They are the extreme values of the horizontal coordinates of the outer boundary intersection point coordinates of the fuzzy area to which the observation target belongs, y min and y max They are respectively the extreme values of the ordinates of the outer boundary intersection points of the fuzzy area to which the observed target belongs.

[0263] In a specific embodiment, in order to verify the effectiveness of the method proposed in this embodiment, the observation time difference between the two sets 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. The following is based on Δt1=Δt2=-0.16667 milliseconds, c1=c2=100 meters, d1=d2=200 meters, error d=5 meters, The implementation process of the present invention is described with an example.

[0264] According to Table 1, based on the polarity of Δt1 and Δt2, it is determined that the fuzzy area to which the observed target belongs is the lower fuzzy area. Figure 4The outer boundary lines of the lower fuzzy region are determined as follows: 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), and (89.1664, 41.9585). The horizontal and vertical coordinate extreme values of the four intersection points define the judgment region, that is, the rectangular region of x∈(41.9585, 89.1664) and y∈(41.9585, 89.1664). The Monte Carlo random algorithm is used to generate random sampling points in the judgment region. Each sampling point is judged by formulas (5), (6), (9), (10), (15), and (16). The point where all six formulas are true is the point in the lower fuzzy region.

[0265] Table 1:

[0266]

[0267] By counting all sampling points within the lower ambiguity region, the area of the lower ambiguity region can be calculated from the ratio of the number of sampling points to the number of Monte Carlo random points. Using a time-of-day positioning error calculation method based on the ambiguity area, quantitative error calculation can be achieved with real-time updating of measurement parameters. This provides a theoretical basis for dynamically adjusting the resource allocation of passive positioning sensors, demonstrating strong feasibility and achieving ideal results.

[0268] 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 above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above 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 several fuzzy areas based on the time difference positioning error calculation model, including: 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, wherein the time difference line is a hyperbola; A first hyperbolic belt and a second hyperbolic belt are formed based on an error range defining the hyperbola, wherein the first hyperbolic belt and the second hyperbolic belt intersect with each other to form four closed surfaces, and the four closed surfaces are respectively defined as four fuzzy areas; S2: Calculate the time difference between the observations of the primary station and several secondary stations, and determine the fuzzy region 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, including: S31: Delineating the outer boundary of the fuzzy region to which the observed target belongs 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 equation includes the fifth ray, the sixth ray, the seventh ray and the eighth ray; S32: Based on the set asymptotes and ray equations, the coordinates of the outer boundary intersection points of the fuzzy area to which the observed target belongs are respectively calculated; S33: Obtaining a rectangular area based on the extreme values of the horizontal and vertical coordinates of the outer boundary intersection coordinates of the fuzzy area to which the observation target belongs; 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: Calculate the area of the fuzzy region to which the observation target belongs based on the number of sampling points in the fuzzy region to which the observation target belongs. The area of the fuzzy region to which the observation target belongs is the measurement error of the time difference positioning.

2. The method for calculating time difference positioning measurement error according to claim 1, characterized in that: In S1, a time difference positioning error calculation model is established, and several fuzzy areas are determined based on the time difference positioning error calculation model, including: S11: Let the distance between the master station and the first and second slave stations be d i The time difference between the master station and the first and second slave stations is Δt i , then the observed target is located at is the long axis, On the two sets of hyperbolas with minor axes, i = 1, 2; c is the speed of light constant; S12: Establishing the coordinate system With the master station as the origin and the direction from the master station to the first slave station as the positive x-axis, a plane rectangular coordinate system is established; 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 denoted as hyperbola P, and its formula is as follows: Where x is the horizontal coordinate of the observation target; y is the vertical coordinate of the observation target; Assuming that the angle formed by the second secondary station, the main station, and the first secondary station is β, the hyperbola Q formed by the second secondary station and the main station is expressed as: In formulas (1) and (2), S14: Define the error range of hyperbola P and Q Assume a i The error is ±d, then the two sets of hyperbolas determined by a1±d are recorded as hyperbolas ① and ②, and their equations are: Hyperbolas ① and ② are located on the inner and outer sides of hyperbola P respectively, forming the first hyperbolic band; Similarly, the two sets of hyperbolas determined by a2±d are recorded as hyperbolas ③ and ④, and their equations are: Hyperbolas ③ and ④ are located on the inner and outer sides of hyperbola Q respectively, forming the second hyperbolic band; S15: The first hyperbolic band and the second hyperbolic band intersect with each other to form four closed surfaces. Let the axis of symmetry of the hyperbola P be line m, and the axis of symmetry of the hyperbola Q be line n. The equations are: x=c1 (11) ysinβ+xcosβ=c2 (12) From the origin to the intersection O' of line m and line n, the four closed surfaces are defined as the upper fuzzy area, the lower fuzzy area, the right fuzzy area and the left fuzzy area according to their positions relative to O'.

3. The method for calculating 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 differences Δt1 and Δt2 observed between the master station and the first and second slave stations. The formula is: Δt1=t0-t1 Δt2=t0-t2 Among them, t0 is the time value observed by the primary station, t1 and t2 are the time values observed by the first and second secondary stations respectively; S22: Determine the fuzzy region to which the observed target belongs based on the polarity of Δt1 and Δt2, including: When Δt1≥0 and Δt2≥0, the observed target is located in the upper fuzzy area; When Δt1<0, Δt2<0, the observed target is located in the lower fuzzy area; When Δt1≥0 and Δt2<0, the observed target is located in the right fuzzy area; When Δt1<0 and Δt2≥0, the observed target is located in the left fuzzy area.

4. The method for calculating time difference positioning measurement error according to claim 3, characterized in that: In S31, the outer boundary of the fuzzy area to which the observed target belongs is delineated using the set asymptotes and ray equations, including: The equations of the first asymptote, the second asymptote, the third asymptote and the fourth asymptote are: Where (x1, y1), (x2, y2), (x3, y3), and (x4, y4) are the coordinates of the points on the first, second, third, and fourth asymptotes, respectively; The equations of the fifth ray, the sixth ray, the seventh ray and the eighth ray are respectively: Where (x5, y5), (x6, y6), (x7, y7), and (x8, y8) are the coordinates of the points on the fifth, sixth, seventh, and eighth rays, respectively; Delineating 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, delineating 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, delineating 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 fuzzy area to which the observed target belongs is a right fuzzy area, the outer boundary of the right fuzzy area is defined based on the second asymptote, the fourth asymptote, the fifth ray and the eighth ray.

5. The method for calculating time difference positioning measurement error according to claim 4, characterized in that: In S32, based on the set asymptotes and ray equations, 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, respectively: y 上 =k a2 (x 上 -c1-a1-d) (30) y 下 =k a1 (x 下 -c1) (32) y 左 =k a1 (x 左 -c1) (34) y 右 =k a2 (x 右 -c1-a1-d) (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 using the equations of the first asymptote, the fourth asymptote, the sixth ray, and the eighth ray, which are respectively: y' 上 =-k a1 (x' 上 -c1) (38) y' 左 =-k a2 (x' 左 -c1+a1+d) (40) y' 右 =-k a1 (x' 右 -c1) (42) y' 下 =-k a2 (x' 下 -c1+a1+d) (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, respectively: y” 上 =k a2 (x” 上 -c1-a1-d) (46) y” 右 =k a2 (x” 右 -c1-a1-d) (48) y” 左 =k a1 (x” 左 -c1) (50) y” 下 =k a1 (x” 下 -c1) (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, respectively: y”' 右 =-k a1 (x”' 右 -c1) (54) y”' 下 =-k a2 (x”' 下 -c1+a1+d) (56) y”' 左 =-k a2 (x”' 左 -c1+a1+d) (58) y”' 上 =-k a1 (x”' 上 -c1) (60) Where, 6. The method for calculating time difference positioning measurement error according to claim 5, 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: The first point in the hyperbolic band (x # ,y # ) satisfies the formula: The points (x^,y^) in the second hyperbolic band satisfy the formula: The points in the upper fuzzy area satisfy the formula: x 1 上 -c1>0 (13) y 1 上 sinβ-x 1 上 cosβ-c2>0 (14) The points in the lower fuzzy area satisfy the formula: x 1 下 -c1<0 (15) y 1 下 sinβ-x 1 下 cosβ-c2<0 (16) The points in the left fuzzy area satisfy the formula: x 1 左 -c1<0 (17) y 1 左 sinβ-x 1 左 cosβ-c2>0 (18) The points in the right fuzzy area satisfy the formula: x 1 右 -c1>0 (19) y 1 右 sinβ-x 1 右 cosβ-c2<0 (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 observation target belongs is obtained.

7. The method for calculating time difference positioning measurement error according to claim 6, 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. The calculation formula is: Among them, n 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 x min and x max They are the extreme values of the horizontal coordinates of the outer boundary intersection point coordinates of the fuzzy area to which the observation target belongs, y min and y max They are respectively the extreme values of the ordinates of the outer boundary intersection points of the fuzzy area to which the observed target belongs.

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