A method for estimating the approximate position of a receiver using visual satellites

Abstract

This invention discloses a method for estimating the approximate location of a receiver using visible satellites. The method includes obtaining the coordinates of the satellites; calculating the maximum time delay from the satellite to the Earth based on the satellite coordinates and the Earth's radius; further obtaining the angle between the maximum Earth distance and the vertical distance; obtaining the center and radius of the projection circle of each satellite onto the Earth based on the angle, the satellite coordinates, and the Earth's radius; selecting two satellites, obtaining the center and radius of their projection circles, and calculating the center of an iterative circle formed by the intersection of the two satellite projection circles on the Earth's surface; determining whether the coordinates of the iterative circle's center are outliers; if not, transforming the coordinates of the iterative circle's center and calculating the radius of the iterative circle, adding the next satellite, and repeating this process until all satellites are added, obtaining the final iterative circle's center and radius as the range center and range of the receiver's approximate location. A simplified projection model and iterative algorithm equations are established using the geometric distribution patterns of satellites to quickly solve for the approximate location result.

Description

Technical Field

[0001] This invention belongs to the technical field of satellite navigation receiver equipment, and in particular relates to a method for estimating the approximate location of a receiver using visible satellites. Background Technology

[0002] In AGPS-assisted positioning algorithms, approximate position and time are typically required as auxiliary information for proper calculation. When receivers in highly dynamic environments need to perform rapid repositioning after loss of lock using AGPS, although the time information is highly accurate, the approximate position information may contain unknowns or have a large range of uncertainty, leading to increased computational complexity and hindering rapid calculation. To address this issue, a method is proposed to estimate the receiver's approximate position using the time and position information of the satellites already acquired by the receiver. The method determines the signal delay range of each satellite near the Earth's surface based on its orbital altitude, calculates the common viewing area covered by the satellite signals, and determines the receiver's position center and the radius of the uncertainty range, i.e., the approximate position information. Compared to traditional projection calculation methods for calculating the common viewing area of ​​satellite signals, this method utilizes the geometric distribution of satellites to establish a simplified projection model and iterative algorithm equations. By appropriately expanding the projection area, the approximate position result can be quickly calculated. Simulations using measured data show that when the satellite navigation receiver receives data from 8 satellites, the position error delay between the calculated center of the position range and the actual receiver coordinates is approximately 4.4 milliseconds, and the radius of the uncertain range is approximately 24 milliseconds. When the satellite navigation receiver acquires more satellite data, the method will achieve even better solution accuracy. Summary of the Invention

[0003] To address the above technical problems, this invention provides a method for estimating the approximate location of a receiver using visual satellites.

[0004] The technical solution adopted by this invention to solve its technical problem is:

[0005] A method for estimating the approximate location of a receiver using visible satellites, the method comprising the following steps:

[0006] S100: Obtain the satellite's coordinates, calculate the maximum time delay of the satellite's distance from Earth based on the satellite's coordinates and Earth's radius, and obtain the angle between the maximum distance from Earth and the vertical distance based on the maximum time delay of the satellite's distance from Earth, the satellite's coordinates, and Earth's radius.

[0007] S200: Based on the included angle, the satellite's coordinates, and the Earth's radius, obtain the center and radius of the circle projected onto the Earth by each satellite;

[0008] S300: Select two satellites, obtain the center and radius of the projection circles of the two satellites, and calculate the center of the iterative circle generated by the intersection of the projection circles of the two satellites on the Earth's surface.

[0009] S400: Determine if the coordinates of the center of the iteration circle are outliers. If not, convert the coordinates of the center of the iteration circle and calculate the radius of the iteration circle.

[0010] S500: Add the next satellite, calculate the center of the new iterative circle formed by the intersection of the satellite projection circle and the iterative circle, determine whether the coordinates of the new iterative circle center are outliers, if not, transform the coordinates of the iterative circle center and calculate the radius of the new iterative circle, repeat this step until all satellites are added, and obtain the final iterative circle center as the center of the approximate location of the receiver, and obtain the final iterative circle radius as the range of the approximate location of the receiver.

[0011] Preferably, S100 includes:

[0012] S110: Obtain the satellite's coordinates, calculate the distance from the satellite to the Earth's center based on the satellite's coordinates, and calculate the maximum time delay between the satellite and the Earth's center based on the distance from the satellite to the Earth's center and the Earth's radius;

[0013] S120: The angle between the maximum distance from the satellite to the Earth and the vertical distance is obtained based on the distance from the satellite to the Earth's center, the Earth's radius, and the maximum time delay of the distance from the satellite to the Earth.

[0014] Preferably, in S110, the satellite's coordinates are obtained, and the distance from the satellite to the Earth's center is calculated based on these coordinates. Specifically:

[0015]

[0016] Among them, (x s y s , z s ) represents the satellite's coordinates, and OS represents the distance from the satellite to the Earth's center;

[0017] S110 calculates the maximum time delay between the satellite and Earth based on the satellite's distance from the Earth's center and the Earth's radius, specifically as follows:

[0018]

[0019] Wherein, CS and DS are schematic lines connecting the maximum time delay of the satellite, and the lines are tangent to the Earth's surface;

[0020] In S120, based on the maximum time delay of the satellite's distance from Earth, the satellite's coordinates, and the Earth's radius, the angle between the maximum distance to Earth and the vertical distance is obtained, specifically:

[0021]

[0022] Where α is the angle between the maximum distance to Earth and the vertical distance.

[0023] Preferably, S200 specifically includes:

[0024]

[0025] Among them, (x A y A , z A () represents the coordinates of the center of the circle;

[0026] According to the arc length calculation formula:

[0027] l AD =∠SOD·R e

[0028] in,

[0029] radius r A The calculation formula is:

[0030]

[0031] Preferably, S300 includes:

[0032] S310: Select two satellites and obtain the centers A and B of the projected circles of the two satellites on the Earth's surface. Reduce the radius of circle B to be equal to the radius of circle A, and then take the center of the resulting circle as B'. Iterate until the center of the circle is taken as the midpoint P of EF, where E and F are the two endpoints of the minor semi-axis of the intersecting portion of the satellite projected circles. If point B is moved to point B', the length of arc BB' is the difference between the radii of circle B and circle A, and the radius of circle B' is equal to the radius of circle A. AP' =l BP' , l AP =l PB' Where P' is the midpoint of the line connecting the centers of the two satellite projection circles on the Earth's surface, according to geometric relationships, we can obtain:

[0033] l BB' =l BP' -l B'P' =l AP' -l B'P' =(l AP +l PP' )-(l PB' -l PP' )=2l PP'

[0034] Among them, l BB' This represents the distance on the Earth's surface between the center of the projection circle with the larger radius of one of the two satellite projection circles and the center of the circle whose radius is reduced to the radius of the smaller projection circle; BP' The middle represents half the distance between the centers of the two satellite projection circles on the Earth's surface; l B'P'This represents the distance on the Earth's surface from the center of the larger of the two satellite projection circles (after its radius is reduced to the smaller radius) to the midpoint of the line connecting the centers of the two satellite projection circles. AP This represents the distance on the Earth's surface between the center of the projection circle with the smaller radius among the two satellite projection circles and the center of the iteration circle in the two-circle iteration; PP' This represents the distance on the Earth's surface between the midpoint of the line connecting the centers of the two satellite projection circles and the center of the iteration circle in the two-circle iteration; l AP' It represents the distance on the Earth's surface from the center of the smaller of the two satellite projection circles to the midpoint of the line connecting the centers of the two satellite projection circles to the Earth's surface.

[0035] S320: According to the arc length formula, we know that:

[0036]

[0037] Where θ represents the angle between the line connecting the midpoint of the line connecting the centers of the two satellite projection circles to the Earth's center, and the line connecting the center of the iterative circle of the two iterations to the Earth's center; r B This represents the radius of the projection circle with the larger radius of coverage between the two satellite projection circles; r A It represents the radius of the projection circle with the smaller radius among the two satellite projection circles;

[0038] S330: To find point P, first calculate point G, and then calculate the coordinates of point G:

[0039]

[0040] Where points A and B are the projected positions of the two satellites on the Earth's surface, with coordinates (x, y, y) respectively. A y A , z A ) and (x B y B , z B Point B's coordinates represent the center coordinates of the projection circle with the larger radius between the two satellite projection circles, and point A's coordinates represent the center coordinates of the projection circle with the smaller radius between the two satellite projection circles. Point G's coordinates are (x... G y G , z G Point G represents the intersection of the line connecting points A and B with the line connecting the Earth's center and the center of the iteration circle. Point G, when projected onto the Earth's surface, becomes point P, which is the center of the iteration circle, with coordinates (x, y). P y P , z P );

[0041] In the formula, Among them, AB can be calculated through the coordinates of points A and B, and the calculation method of AG is as follows:

[0042] OA = OB = R e , Then

[0043]

[0044] Among them, OG represents the connection line between point G and the earth's center, and OH represents the perpendicular line from the earth's center to the connection line between points A and B;

[0045] Among them,

[0046] In △OAG, according to the cosine formula, it can be known that:

[0047]

[0048] Among them, represents the included angle between the connection line between the center of the projection circle with a smaller range radius in the two satellite projections and the earth's center and OG;

[0049] By联立OG and AG 2 's expressions, it can be obtained that:

[0050]

[0051] Among them, 's calculation method is as follows:

[0052] According to the geometric relationship, it can be known that Then:

[0053]

[0054] It can be known from this that:

[0055]

[0056] Preferably, in S400, determining whether the coordinates of the iterative circle center are outliers includes:

[0057] Obtain the distances PA and PB between the iterative circle center and the centers A and B of the circles respectively. If PB > PA, the coordinates of the iterative circle center are normal values. <好的,我将继续为你翻译剩余内容,请你补充完整原文,以便我能准确翻译。

[0058] Preferably, S400 further includes:

[0059] If PB < PA, the coordinates of the iterative circle center are outliers, and return to S300 to recalculate the coordinates of the iterative circle center. Among them, the value of k' is:

[0060] k' = 1 - k.

[0061] Preferably, the transformation of the coordinates of the center of the iteration circle in S400 is specifically as follows:

[0062] Transform point G to point P on the Earth's surface:

[0063]

[0064] Where P represents the center of the iteration circle; R e Represents the Earth's radius.

[0065] Preferably, in S400, the radius of the iterative circle generated by the intersection of the projected circles of the two satellites on the Earth's surface is calculated as follows:

[0066] r P =l PM =r A ·sinγ

[0067] in,

[0068]

[0069]

[0070] Where, r P The radius of the iterative circle, r A The radius AB of circle A represents the straight-line distance between the centers of the two satellite projection circles. AB This represents the surface distance between the centers of the two satellite projection circles, where E and F are the two endpoints of the minor axis of the intersecting portion of the two satellite projection circles. PE and l PF Then, γ represents the distance between the center of the iterative circle and the Earth's surface between these two points, and γ represents the angle between the line connecting any endpoint of the major axis of the intersection of the two satellite projections to the center of the smaller projection circle and the line connecting any endpoint of the minor axis of the intersection of the two satellite projections to the center of the smaller projection circle.

[0071] Preferably, in S500, when adding the next satellite, the center and radius of the new iterative circle generated by the intersection of the satellite's projected circle and the iterative circle are calculated, including:

[0072] Select the satellite whose center is closest to the center of the projection circle in the previous iteration, and determine the positional relationship between the two projected circles;

[0073] If the two projected circles are internally tangent or contained within each other, then the center and radius of the contained projected circle are the center and radius of the new iterated circle.

[0074] If the two circles are intersecting in position, the center and radius of the new iterative circle are calculated based on S300 and S400.

[0075] If the two circular projections are in a positional relationship that is separate, then the satellite projection is not considered and the iteration continues.

[0076] The aforementioned method for estimating the approximate location of a receiver using visible satellites estimates the receiver's location range by utilizing the projection relationships of each satellite on the Earth's surface. Compared to traditional projection algorithms for calculating the shared viewing area of ​​satellite signals, this invention utilizes the geometric distribution patterns of satellites to establish a simplified projection model and iterative algorithm equations. By appropriately expanding the projection area, the approximate location result can be quickly calculated. Attached Figure Description

[0077] Figure 1 This is a flowchart illustrating a method for estimating the approximate location of a receiver using visual satellites, according to an embodiment of the present invention.

[0078] Figure 2 This is a flowchart illustrating a method for estimating the approximate location of a receiver using visual satellites, according to another embodiment of the present invention.

[0079] Figure 3 This is a schematic diagram of the projection of a satellite onto the Earth's surface in one embodiment of the present invention;

[0080] Figure 4 This is a top view of satellite projection iteration in one embodiment of the present invention;

[0081] Figure 5 This is a side view of a satellite projection in one embodiment of the present invention;

[0082] Figure 6 This is a partial top-view view of satellite projection iteration in one embodiment of the present invention;

[0083] Figure 7 This is a schematic diagram showing a special position of the two projection circles in one embodiment of the present invention;

[0084] Figure 8 This is a schematic diagram of the approximate location estimation result of the receiver in one embodiment of the present invention. Detailed Implementation

[0085] To enable those skilled in the art to better understand the technical solution of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings.

[0086] In one embodiment, such as Figure 1 and Figure 2 As shown, a method for estimating the approximate location of a receiver using visual satellites includes the following steps:

[0087] S100: Obtain the satellite's coordinates, calculate the maximum time delay of the satellite's distance from Earth based on the satellite's coordinates and Earth's radius, and obtain the angle between the maximum distance from Earth and the vertical distance based on the maximum time delay of the satellite's distance from Earth, the satellite's coordinates, and Earth's radius.

[0088] Specifically, the BeiDou MEO satellite was selected, with an orbital altitude of approximately 21,528 km.

[0089] In one embodiment, S100 includes:

[0090] S110: Obtain the satellite's coordinates, calculate the distance from the satellite to the Earth's center based on the satellite's coordinates, and calculate the maximum time delay between the satellite and the Earth's center based on the distance from the satellite to the Earth's center and the Earth's radius;

[0091] S120: The angle between the maximum distance from the satellite to the Earth and the vertical distance is obtained based on the distance from the satellite to the Earth's center, the Earth's radius, and the maximum time delay of the distance from the satellite to the Earth.

[0092] In one embodiment, in step S110, the satellite's coordinates are obtained, and the distance from the satellite to the Earth's center is calculated based on these coordinates. Specifically:

[0093]

[0094] Among them, (x s y s , z s ) represents the satellite's coordinates, and OS represents the distance from the satellite to the Earth's center;

[0095] S110 calculates the maximum time delay between the satellite and Earth based on the satellite's distance from the Earth's center and the Earth's radius, specifically as follows:

[0096]

[0097] Wherein, CS and DS are schematic lines connecting the maximum time delay of the satellite, and the lines are tangent to the Earth's surface;

[0098] In S120, based on the maximum time delay of the satellite's distance from Earth, the satellite's coordinates, and the Earth's radius, the angle between the maximum distance to Earth and the vertical distance is obtained, specifically:

[0099]

[0100] Where α is the angle between the maximum distance to Earth and the vertical distance.

[0101] Specifically, a schematic diagram of the satellite's projection onto the Earth's surface is shown below. Figure 3 As shown in the diagram, O represents the Earth's center, S represents the satellite, A represents the satellite's projected position on the Earth's surface, CS and DS represent the tangents from the satellite to the Earth, and the angle between OS and DS is α. Re R represents the Earth's radius. e = 6371.393km. Based on the above relationship, it can be seen that when the receiver receives the satellite S signal, its position near the Earth's surface is a sphere centered at A, with distances to C and D as boundaries. Among these, arcs AC and AD (hereinafter referred to as l) AC With l AD (represented by) is the radius of the satellite's projection onto the Earth.

[0102] S200: Based on the included angle, the satellite's coordinates, and the Earth's radius, obtain the center and radius of the circle projected onto the Earth by each satellite.

[0103] In one embodiment, S200 specifically includes:

[0104]

[0105] Among them, (x A y A , z A () represents the coordinates of the center of the circle;

[0106] According to the arc length calculation formula:

[0107] l AD =∠SOD·R e

[0108] in,

[0109] radius r A The calculation formula is:

[0110]

[0111] S300: Select two satellites, obtain the center and radius of the projection circles of the two satellites, and calculate the center of the iterative circle generated by the intersection of the projection circles of the two satellites on the Earth's surface.

[0112] In one embodiment, S300 includes:

[0113] S310: Select two satellites and obtain the centers A and B of the projected circles of the two satellites on the Earth's surface. Reduce the radius of circle B to be equal to the radius of circle A, and then take the center of the resulting circle as B'. Iterate until the center of the circle is taken as the midpoint P of EF, where E and F are the two endpoints of the minor semi-axis of the intersecting portion of the satellite projected circles. If point B is moved to point B', the length of arc BB' is the difference between the radii of circle B and circle A, and the radius of circle B' is equal to the radius of circle A. AP' =l BP' , l AP =l PB' Where P' is the midpoint of the line connecting the centers of the two satellite projection circles on the Earth's surface, according to geometric relationships, we can obtain:

[0114] l BB' =l BP' -l B'P' =l AP' -l B'P' =(l AP +l PP' )-(l PB' -l PP' )=2l PP'

[0115] Among them, l BB' This represents the distance on the Earth's surface between the center of the projection circle with the larger radius of one of the two satellite projection circles and the center of the circle whose radius is reduced to the radius of the smaller projection circle; BP' The middle represents half the distance between the centers of the two satellite projection circles on the Earth's surface; l B'P' This represents the distance on the Earth's surface from the center of the larger of the two satellite projection circles (after its radius is reduced to the smaller radius) to the midpoint of the line connecting the centers of the two satellite projection circles. AP This represents the distance on the Earth's surface between the center of the projection circle with the smaller radius among the two satellite projection circles and the center of the iteration circle in the two-circle iteration; PP' This represents the distance on the Earth's surface between the midpoint of the line connecting the centers of the two satellite projection circles and the center of the iteration circle in the two-circle iteration; l AP' It represents the distance on the Earth's surface from the center of the smaller of the two satellite projection circles to the midpoint of the line connecting the centers of the two satellite projection circles to the Earth's surface.

[0116] S320: According to the arc length formula, we know that:

[0117]

[0118] Where θ represents the angle between the line connecting the midpoint of the line connecting the centers of the two satellite projection circles to the Earth's center, and the line connecting the center of the iterative circle of the two iterations to the Earth's center; r B This represents the radius of the projection circle with the larger radius of coverage between the two satellite projection circles; r A It represents the radius of the projection circle with the smaller radius among the two satellite projection circles;

[0119] S330: To find point P, first calculate point G, and then calculate the coordinates of point G:

[0120]

[0121] Where points A and B are the projected positions of the two satellites on the Earth's surface, with coordinates (x, y, y) respectively. A y A , zA ) and (x B y B , z B Point B's coordinates represent the center coordinates of the projection circle with the larger radius between the two satellite projection circles, and point A's coordinates represent the center coordinates of the projection circle with the smaller radius between the two satellite projection circles. Point G's coordinates are (x... G y G , z G Point G represents the intersection of the line connecting points A and B with the line connecting the Earth's center and the center of the iteration circle. Point G, when projected onto the Earth's surface, becomes point P, which is the center of the iteration circle, with coordinates (x, y). P y P , z P );

[0122] In the formula, AB can be calculated using the coordinates of points A and B, and AG is calculated as follows:

[0123] OA=OB=R e , but

[0124]

[0125] Where OG represents the line connecting point G to the Earth's center, and OH represents the perpendicular line from the Earth's center to the line connecting points A and B;

[0126] in,

[0127] In △OAG, according to the cosine formula, we know that:

[0128]

[0129] in, This represents the angle between the line connecting the center of the smaller projection circle (within the radius of the two satellite projections) and the Earth's center, and the OG (Optical Point).

[0130] OG and AG 2 From the expression, we can obtain:

[0131]

[0132] in, The calculation method is as follows:

[0133] According to geometric relations, we know but:

[0134]

[0135] Therefore, we can conclude that:

[0136]

[0137] Specifically, the satellite selection strategy for the two preferred satellites is to select the two satellites with the farthest distance between the centers of their projections on the earth's surface, which is to determine the smallest receiver position range.

[0138] Assume that the centers of the projection circles of the two preferred satellites on the earth's surface are A and B respectively, and the top view is as Figure 4 shown. Circle B is the circle after reducing the radius of circle B' to the same length as circle A. The center of the iterative circle is taken as the midpoint P of EF, and the radius of the iterative circle is taken as l PM (or l PN ). In order to calculate the center P, the top view is converted into a side cross-section, as Figure 5 shown.

[0139] S40: Determine whether the coordinates of the center of the iterative circle are outliers. If not, convert the coordinates of the center of the iterative circle and calculate the radius of the iterative circle.

[0140] In one embodiment, determining whether the coordinates of the center of the iterative circle are outliers in S400 includes:

[0141] Obtain the distances PA and PB between the center of the iterative circle and the centers A and B of the circles respectively. If PB > PA, the coordinates of the center of the iterative circle are normal values.

[0142] In one embodiment, S400 further includes:

[0143] If PB < PA, the coordinates of the center of the iterative circle are outliers, and return to S300 to recalculate the coordinates of the center of the iterative circle, where the value of k' is:

[0144] k' = 1 - k.

[0145] Specifically, since the positional relationship between the two projection circles is unknown, the calculated center of the iterative circle should be closer to the center of the projection circle with a smaller radius. Taking the above figure as an example, r B > r A , the relationship between the center P of the iterative circle and A and B should satisfy PB > PA, that is, the center P of the iterative circle is closer to circle A. If the calculated PA and PB conform to this rule, this step can be skipped and proceed to the next step. If the calculated PB < PA, return to S300 to recalculate the coordinates of the center of the iterative circle, where the value of k' is:

[0146] k' = 1 - k.

[0147] In one embodiment, converting the coordinates of the center of the iterative circle in S400 is specifically:

[0148] Convert point G to point P on the earth's surface:

[0149]

[0150] Where P represents the center of the iteration circle; R e Represents the Earth's radius.

[0151] In one embodiment, S400 calculates the radius of the iterative circle generated by the intersection of the projected circles of the two satellites on the Earth's surface, specifically as follows:

[0152] r P =l PM =r A ·sinγ

[0153] in,

[0154]

[0155]

[0156] Where, r P The radius of the iterative circle, r A The radius AB of circle A represents the straight-line distance between the centers of the two satellite projection circles. AB This represents the surface distance between the centers of the two satellite projection circles, where E and F are the two endpoints of the minor axis of the intersecting portion of the two satellite projection circles. PE and l PF Then, γ represents the distance between the center of the iterative circle and the Earth's surface between these two points, and γ represents the angle between the line connecting any endpoint of the major axis of the intersection of the two satellite projections to the center of the smaller projection circle and the line connecting any endpoint of the minor axis of the intersection of the two satellite projections to the center of the smaller projection circle.

[0157] Specifically, by Figure 3 It can be seen that the radius of the iterative circle is l. PM In the diagram, let the radius of circle A be r. A The radius of circle B is r B Point P is the center of the iterative circles of circles A and B. Among them l EF =r A +r B -l AB .

[0158] according to Figure 5 It can be known that

[0159]

[0160] Where β represents the angle between the line connecting the center A of the circle and the Earth's center and the line connecting the center B of the circle and the Earth's center, and AB represents the straight-line distance between the centers of the two satellite projection circles.

[0161] According to the arc length calculation formula:

[0162]

[0163] Among them, l AB This represents the distance between the centers of the two satellite projection circles on the Earth's surface.

[0164] but

[0165]

[0166] Where E and F are the two endpoints of the minor axis of the intersection of the two satellite projection circles, l PE and l PF This represents the distance between the center of the iteration circle and the ground surface between these two points.

[0167] according to Figure 4 Take the projected circle with the smaller radius of the two circles, i.e., circle A, and connect point A and point M as follows. Figure 6 As shown. Assuming that the area of ​​circle A is half the Earth's surface area, then the area of ​​circle A is 2πR. e 2 The area of ​​its corresponding cross-section is equal to the area of ​​the Earth's equatorial plane, i.e., πR. e 2 Assuming circle A is a point on the Earth's surface, and the area of ​​circle A is equal to the area of ​​its cross-section, the ratio of the area of ​​circle A to the area of ​​its cross-section is in the range of (1, 2). Based on the signal delay range of the satellite propagating to the vicinity of the Earth's surface, the common viewing area of ​​the satellite signal, i.e. the projected circle, is calculated. Under this algorithm, based on empirical values, the area ratio can be taken as 1.

[0168] As can be seen from the figure, but

[0169] Iteration circle radius r P The calculation is as follows:

[0170] r P =l PM =r A ·sinγ

[0171] Where, r P Let l represent the radius of the iterative circle, and γ represent the angle between the line connecting any endpoint of the major axis of the intersection of the two satellite projections to the center of the smaller projection circle and the line connecting any endpoint of the minor axis of the intersection to the center of the smaller projection circle. If point M is an endpoint of the major axis of the intersection of the two projection circles, then l PM This represents the distance on the ground from the center of the iterative circle to this endpoint.

[0172] S500: Add the next satellite, calculate the center of the new iterative circle formed by the intersection of the satellite projection circle and the iterative circle, determine whether the coordinates of the new iterative circle center are outliers, if not, transform the coordinates of the iterative circle center and calculate the radius of the new iterative circle, repeat this step until all satellites are added, and obtain the final iterative circle center as the center of the approximate location of the receiver, and obtain the final iterative circle radius as the range of the approximate location of the receiver.

[0173] In one embodiment, when adding the next satellite in S500, the center and radius of the new iterative circle generated by the intersection of the satellite's projection circle and the iterative circle are calculated, including:

[0174] Select the satellite whose center is closest to the center of the projection circle in the previous iteration, and determine the positional relationship between the two projected circles;

[0175] If the two projected circles are internally tangent or contained within each other, then the center and radius of the contained projected circle are the center and radius of the new iterated circle.

[0176] If the two circles are intersecting in position, the center and radius of the new iterative circle are calculated based on S300 and S400.

[0177] If the two circular projections are in a positional relationship that is separate, then the satellite projection is not considered and the iteration continues.

[0178] Specifically, select the satellite whose center of the projection circle is closest to the center of the circle from the previous iteration, and determine the projection relationship between the two circles:

[0179] (a) The two circles are in a positional relationship of being internally tangent or internally contained.

[0180] When the positions of the two projected circles are in the following two cases ( Figure 7 When iterating, the center and radius of the iterated circle are directly equal to the included projected circle. Figure 7 For example, the center and radius of the iterative circle are the center and radius of circle A.

[0181] (b) The two circles are intersecting.

[0182] The method for calculating the center and radius of the iterative circle is the same as that for S300.

[0183] (c) The two circles are in a disjoint position.

[0184] Ignoring the satellite projection, continue the iteration.

[0185] In the above calculations, the positional relationship between the two circles is determined by the distance between their centers and their radii. The formula for calculating the distance between their centers is referenced in [reference needed]. AB Calculation formula.

[0186] Repeat the above steps, and the center of the final iterative circle is the center of the approximate location of the receiver, and the radius is the range of the approximate location of the receiver.

[0187] In a detailed embodiment, satellite data and receiver data in a static scenario are simulated using a GNSS navigation satellite signal simulation source, and the algorithm is used for simulation testing. The projected position of the satellite on the Earth's surface and the receiver position at a certain moment are as follows:

[0188] Table 1 Test Data

[0189]

[0190] In the simulation scenario set in this paper, the receiver position is estimated, and the results are as follows: Figure 8 As shown.

[0191] In the diagram, the dashed sphere represents the Earth, the solid sphere represents the calculated approximate location range of the receiver, and the solid dots represent the actual receiver coordinates. As shown in the diagram, the actual values ​​are included within the estimated range. The receiver location estimation was performed using different numbers of satellites, and the test results are as follows.

[0192] Table 2 Test Results

[0193]

[0194]

[0195] As shown in the table, when using 6 satellites for receiver position estimation, the estimated range radius is about 26.3 ms and the position error is about 13.9 ms. When using 8 satellites for receiver position estimation, the estimated range radius is about 24.3 ms and the position error is about 4.4 ms. The latter reduces the range radius by about 2 ms and the position error by about 9.5 ms compared to the former.

[0196] Therefore, when using this algorithm to estimate the receiver position, the more satellites involved in the calculation, the smaller the estimation radius and the smaller the position error, meaning the more accurate the estimation result and the better the algorithm performance.

[0197] The above-described method for estimating the approximate location of a receiver using visible satellites describes a method for estimating the approximate location of a receiver by utilizing the projection relationships of various satellites on the Earth's surface. Compared with traditional projection algorithms for calculating the common viewing area of ​​satellite signals, this invention utilizes the geometric distribution patterns of satellites to establish a simplified projection model and iterative algorithm equations. By appropriately expanding the projection area, the approximate location result can be quickly calculated.

[0198] The beneficial technical effects of this invention are: in highly dynamic scenarios, this algorithm can quickly estimate the approximate position of the receiver by utilizing the propagation delay range of the captured satellites and their projection relationship on the Earth's surface. Simulation using measured data shows that when the receiver receives data from 8 satellites, the position error delay between the center of the calculated position range and the actual receiver coordinates is approximately 4 milliseconds, and the radius of the uncertain range is approximately 24 milliseconds. When the satellite navigation receiver captures more satellite data, this invention will achieve even better calculation accuracy.

[0199] The foregoing has provided a detailed description of a method for estimating the approximate location of a receiver using visual satellites, as provided by this invention. Specific examples have been used to illustrate the principles and implementation methods of this invention, and the descriptions of these embodiments are merely for the purpose of helping to understand the core ideas of this invention. It should be noted that those skilled in the art can make various improvements and modifications to this invention without departing from its principles, and these improvements and modifications also fall within the protection scope of the claims of this invention.

Claims

1. A method for estimating the approximate location of a receiver using visual satellites, characterized in that, The method includes the following steps: S100: Obtain the coordinates of the satellite, calculate the maximum time delay of the satellite to the Earth according to the coordinates of the satellite and the radius of the Earth, and calculate the angle between the maximum distance from the satellite to the Earth and the vertical distance according to the maximum time delay of the satellite to the Earth, the coordinates of the satellite and the radius of the Earth; S100 includes: S110: Obtain the coordinates of the satellite, and obtain the distance from the satellite to the Earth's center according to the coordinates of the satellite. Specifically: OS= in, Here, OS represents the satellite's coordinates, and OS represents the distance from the satellite to the Earth's center. Calculate the maximum time delay of the satellite to the Earth according to the distance from the satellite to the Earth's center and the radius of the Earth. Specifically: Wherein, CS and DS are schematic lines connecting the maximum time delay of the satellite, and these lines are tangent to the Earth's surface. Indicates the Earth's radius; S120: Obtain the angle between the maximum distance from the satellite to the Earth and the vertical distance according to the distance from the satellite to the Earth's center, the radius of the Earth and the maximum time delay of the satellite to the Earth. Specifically: in, The angle between the maximum distance to Earth and the vertical distance; S200: Obtain the center and radius of the projection of each satellite to the Earth according to the angle, the coordinates of the satellite and the radius of the Earth. Specifically: in,( , , () represents the coordinates of the center of the circle; According to the arc length calculation formula, it can be known that: in, ; radius The calculation formula is: ； S300: Select two satellites, obtain the centers and radii of the projection circles of the two satellites, and calculate the center of the iterative circle generated by the intersection of the projection circles of the two satellites on the Earth's surface; S310: Select two satellites, obtain the centers A and B of the projection circles of the two satellites on the Earth's surface, and the center of the circle obtained by reducing the radius of circle B to the same length as the radius of circle A is B'. The center of the iterative circle is the midpoint P of EF, where E and F are the two endpoints of the short semi-axis of the intersection part of the satellite projection circles. S400: Judge whether the coordinates of the center of the iterative circle are outliers. If not, convert the coordinates of the center of the iterative circle and calculate the radius of the iterative circle. S500: Add the next satellite, calculate the new center of the iterative circle generated by the intersection of the satellite projection circle and the iterative circle, judge whether the coordinates of the new center of the iterative circle are outliers. If not, convert the coordinates of the center of the iterative circle and calculate the radius of the new iterative circle. Repeat this step until all satellites are added, and the final center of the iterative circle is the center of the range of the receiver's approximate position, and the final radius of the iterative circle is the range of the receiver's approximate position.

2. The method according to claim 1, characterized in that, S300 includes: S310 also includes: if point B is moved to point B', the length of arc BB' is the difference between the radii of circle B and circle A, and the radius of circle B' is equal to the radius of circle A. , Where P' is the midpoint of the line connecting the centers of the two satellite projection circles on the Earth's surface, according to geometric relationships, we can obtain: in, This represents the distance on the Earth's surface between the center of the projection circle with the larger radius of the two satellite projection circles and the center of the circle whose radius is reduced to the radius of the smaller projection circle. The distance between the centers of the two satellite projection circles on the Earth's surface is represented by half. This represents the distance on the Earth's surface from the center of the larger satellite projection circle (after its radius is reduced to the smaller radius) to the midpoint of the line connecting the centers of the two satellite projection circles to the Earth's surface. This represents the distance on the Earth's surface between the center of the projection circle with the smaller radius among the two satellite projection circles and the center of the iteration circle of the two iterations; This represents the distance on the Earth's surface between the midpoint of the line connecting the centers of the two satellite projection circles and the center of the iteration circle in the two-circle iteration; It represents the distance on the Earth's surface from the center of the smaller of the two satellite projection circles to the midpoint of the line connecting the centers of the two satellite projection circles to the Earth's surface. S320: According to the arc length formula, it can be known that: in, This represents the angle between the line connecting the midpoint of the line connecting the centers of the two satellite projection circles to the Earth's center, and the line connecting the center of the iterative circle of the two-circle iteration to the Earth's center. It represents the radius of the projection circle with the larger radius of the two satellite projection circles; It represents the radius of the projection circle with the smaller radius among the two satellite projection circles; S330: In order to obtain point P, first calculate point G and calculate the coordinates of point G: Points A and B are the projected positions of the two satellites on the Earth's surface, with coordinates as follows: and Point B's coordinates represent the center coordinates of the projection circle with the larger radius between the two satellite projection circles, and point A's coordinates represent the center coordinates of the projection circle with the smaller radius between the two satellite projection circles. Point G's coordinates are... Point G represents the intersection of the line connecting points A and B with the line connecting the Earth's center and the center of the iteration circle. Point G, when projected onto the Earth's surface, becomes point P, which is the center of the iteration circle, and its coordinates are... ; In the formula, AB can be calculated using the coordinates of points A and B, and AG is calculated as follows: , ,but Among them, OG represents the connection line between point G and the Earth's center, and OH represents the perpendicular line from the Earth's center to the connection line between points A and B. in, ; In △OAG, according to the cosine formula, it can be known that: in, This represents the angle between the line connecting the center of the smaller projection circle (within the radius of the two satellite projections) and the Earth's center, and the OG (Optical Point). United and From the expression, we can obtain: in, The calculation method is as follows: According to geometric relations, we know ,but: From this, it can be known that: 。 3. The method according to claim 2, characterized in that, The judgment of whether the coordinates of the center of the iterative circle are outliers in S400 includes: Obtain the distances PA and PB between the center of the iterative circle and the centers A and B of the circles respectively. If PB>PA, the coordinates of the center of the iterative circle are normal values.

4. The method according to claim 3, characterized in that, S400 also includes: If PB<PA, the coordinates of the center of the iterative circle are outliers, and return to S300 to recalculate the coordinates of the center of the iterative circle, where the value of k' is: 。 5. The method according to claim 4, characterized in that, The conversion of the coordinates of the center of the iterative circle in S400 is specifically: Convert point G to point P on the Earth's surface: Where point P represents the center of the iteration circle; Represents the Earth's radius. .

6. The method according to claim 5, characterized in that, In S400, calculate the radius of the iterative circle generated by the intersection of the projection circles of the two satellites on the Earth's surface. Specifically: in, in, Indicates the radius of the iterative circle. The radius AB of circle A represents the straight-line distance between the centers of the two satellite projection circles. E represents the distance from the centers of the two satellite projection circles to the Earth's surface, and F represents the two endpoints of the minor axis of the intersecting portion of the two satellite projection circles. as well as This represents the distance between the center of the iteration circle and the ground surface between these two points. The angle between the line connecting any endpoint of the major axis of the intersection of the two satellite projections to the center of the smaller projection circle and the line connecting any endpoint of the minor axis of the intersection of the two satellite projections to the center of the smaller projection circle.

7. The method according to claim 6, characterized in that, When adding the next satellite to S500, the center and radius of the new iterative circle generated by the intersection of the satellite's projected circle and the iterative circle are calculated, including: Select the satellite whose center is closest to the center of the projection circle in the previous iteration, and determine the positional relationship between the two projected circles; If the two projected circles are internally tangent or contained within each other, then the center and radius of the contained projected circle are the center and radius of the new iterated circle. If the two circles are intersecting in position, the center and radius of the new iterative circle are calculated based on S300 and S400. If the two circular projections are in a positional relationship that is separate, then the satellite projection is not considered and the iteration continues.

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