Positioning method based on single low-orbit satellite

Abstract

A positioning method based on a single low-earth-orbit satellite relates to the technical field of satellite positioning and comprises the following steps: acquiring orbit data of the single low-earth-orbit satellite; calculating coarse coordinates of the ground station according to the orbit data at the initial moment; calculating frequency data received by the single low-orbit satellite according to the orbit data at the operation moment; performing Taylor series expansion on the frequency data, and obtaining a Doppler observation increment equation in combination with coarse coordinates of the ground station; carrying out iterative positioning calculation on the Doppler observation increment equation by adopting a minimum Newton square method to obtain an estimated value of a ground station coordinate; setting iteration times or iteration conditions, wherein a final iteration result is a final estimation value of the ground station coordinates; the method is used for solving the problems that traditional single-satellite positioning is difficult, and the calculation process is complex.

Description

Technical Field

[0001] The present invention relates to the field of satellite positioning technology, and in particular to a positioning method based on a single low-orbit satellite. Background Art

[0002] With the rapid development of the satellite industry, navigation and positioning technology for medium- and high-orbit satellites has gradually matured. Meeting the growing demand for navigation and positioning has driven the rapid development of low-orbit satellite navigation systems. Single-satellite positioning systems offer a simpler structure than traditional GNSS systems, and their manufacturing costs are significantly lower than those of existing GNSS satellite navigation systems. Because single-satellite positioning systems require only a single satellite to determine the target's position, the hardware development cycle for the entire system is significantly shortened. More importantly, they avoid the stringent requirements of multi-satellite positioning systems for highly synchronized satellite clocks, while also eliminating the complex networking and coordination required.

[0003] Furthermore, due to the influence of satellite orbits and the geographical environment, current single-satellite rapid positioning technology is still primarily in the basic theoretical research stage, mostly verified through experimental simulations. Actual engineering applications are rare and their popularity is limited. However, among the few single-satellite positioning systems already in use, their core technology is still based on simple angle-based positioning theory. This not only fails to meet the needs of future multi-dimensional life scenarios, but also fails to provide high-precision, robust information support for future warfare and emergency response.

[0004] Chinese patent publication number CN 106772502 A discloses a Doppler positioning solution method for a low-orbit satellite backup navigation system. This method utilizes Doppler observation information from low-orbit satellites to achieve user positioning solution, avoiding the system's high-precision time synchronization requirements brought about by pseudorange observations. By flexibly selecting positioning solution observation quantities, this method is suitable for a variety of visible star observation conditions. However, this method uses a large-area grid search method to determine the initial value of the Newton iteration, requiring traversal of a large range of grid points, resulting in a high computational load.

[0005] Therefore, we propose a positioning method that can use a single star for accurate positioning and has a simple calculation process. Summary of the Invention

[0006] The purpose of the present invention is to provide a positioning method based on a single low-orbit satellite, which is used to solve the problems of difficulty and complex calculation process of traditional single-satellite positioning.

[0007] The present invention is achieved through the following technical solutions: A positioning method based on a single low-orbit satellite, specifically comprising: Obtain orbital data of a single low-orbit satellite; Calculate the rough coordinates of the ground station based on the orbit data at the initial moment; Calculate the frequency data received by a single low-orbit satellite based on the orbital data at the time of operation; The frequency data is expanded by Taylor series and combined with the coarse coordinates of the ground station to obtain the Doppler observation increment equation; The least Newton square method is used to iteratively solve the Doppler observation increment equation to obtain the estimated value of the ground station coordinates; Set the number of iterations or iteration conditions, and the final iteration result is the final estimated value of the ground station coordinates.

[0008] Furthermore, the orbital data of the single low-orbit satellite includes the orbital altitude, velocity vector, coordinate data, carrier frequency, observation Doppler frequency and transmission frequency of the ground station of the low-orbit satellite.

[0009] Furthermore, the rough coordinates of the ground station are calculated based on the low-orbit satellite orbit data at the initial moment, and the specific steps are as follows: The rough coordinates of the ground station are defined as , and the initial moment At the bottom, that is, when the ground station first tracks a low-orbit satellite and obtains its orbital data, the angle between the satellite's motion direction and the direction of the line connecting the satellite and the ground station is 90 degrees, and the relative speed between the satellite and the ground station is zero; Construct the Earth radius constraint equation; ； Where, is the radius of the Earth; According to the initial moment The coordinates of the satellite , the satellite's velocity vector and the rough coordinates of the ground station to construct the vertical relationship equation of the satellite velocity; ; Construct the law of cosines equation based on the satellite's coordinates, the ground station's coordinates, the Earth's radius, and the satellite's distance from the Earth's center. ; Where, is the satellite's distance from the Earth's center, and , is the altitude of the satellite; for The distance between the satellite and the ground station at any moment; Construct the Euclidean distance equation based on the satellite's coordinates and the rough coordinates of the ground station; ; The rough coordinates of the ground station are calculated by the equation system composed of the earth radius constraint equation, the satellite velocity vertical relationship equation, the cosine theorem equation and the Euclidean distance equation.

[0010] Further, the running time Orbital data, calculate the frequency data received by a single low-orbit satellite , the formula is: ; Where, for The velocity vector of the satellite at the moment is , for At the moment, the angle between the satellite's motion direction and the direction of the line connecting the satellite and the ground station; is the speed of light, is the transmitting frequency of the ground station, is the measurement error of frequency; The requested position of the ground station , The velocity vector sum of the satellite at the moment The coordinates of the satellite at this moment , substitute the frequency data In the calculation formula, we get: .

[0011] Furthermore, the frequency data is subjected to Taylor series expansion and combined with the coarse coordinates of the ground station to obtain the Doppler observation increment equation. The specific steps are: The frequency data The calculation formula is transformed into: ; The rough coordinates of the ground station Substituting into the equation, expanding it by the first-order Taylor series, and removing the higher-order terms, we get the first-order Taylor expansion: ; ; Substituting the three time points into the first-order Taylor expansion, we get the Taylor expansion equation: ; make , , , ; Converting the Taylor expansion equation into a matrix form, we get the Doppler observation increment equation, which is: .

[0012] Furthermore, the least Newton squares method is used to iteratively solve the Doppler observation increment equation to obtain an estimated value of the ground station coordinates. The specific steps are: Define the variables in the Doppler observation increment equation The iterative equation is: ; Right now ; Where, is the positioning solution result after the i-th iteration; is the correction value of the positioning result of the i+1th iteration; By Newton's least squares method Perform iterative positioning solution, there are; ; First calculate the residual : ; Then construct the Jacobian matrix : ; Where, is the three-dimensional position coordinate of the low-orbit satellite at the jth observation moment; is the three-dimensional velocity of the low-orbit satellite at the jth observation moment; is the carrier frequency of the low-orbit satellite signal; is the observed Doppler frequency of the low-orbit satellite at the jth observation moment; The observed distance between the j-th observation moment of the low-orbit satellite and the i-th position iteration solution result of the user; Finally, according to Iterative equation update .

[0013] Furthermore, the calculation formula for the observed distance between the j-th observation time of the low-orbit satellite and the i-th position iteration solution result of the user is: .

[0014] Furthermore, the set iteration condition is ,and is an infinitesimal real number.

[0015] Furthermore, the set number of iterations is 20 times.

[0016] Furthermore, low-orbit satellites are obtained respectively and The estimated coordinates of the ground station at time t; generate The estimated value at is the two intersection points of the equal-frequency cone lines; generate The estimated value at is the two intersection points of the equal-frequency cone lines; The only common intersection point of the two positioning results is taken as the true position of the ground station to obtain the accurate ground station position coordinates.

[0017] The technical solution of the present invention has at least the following advantages and beneficial effects: The present invention discloses a positioning method based on a single low-orbit satellite. By continuously measuring the frequency of the low-orbit satellite in continuous time periods and then using the Doppler value of the single-satellite frequency measurement for positioning, the method effectively makes up for the defect of requiring multiple satellites for positioning and simplifies the calculation process of the low-orbit satellite.

[0018] In addition, the present invention first calculates the initial position of the ground station, and then brings the initial position into the Taylor series for expansion estimation to calculate the precise ground station position. There is no need to search for the ground station position in a grid divided into equal intervals according to longitude and latitude, thereby saving the algorithm calculation amount, and by setting the number of iterations or iteration conditions as the judgment condition for ending the iteration, the accuracy of the ground station position estimation is improved.

[0019] In addition, the accurate ground station position is further obtained by using two different ground station coordinate estimates to remove the ambiguous position. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 A schematic flow chart of a method of the present invention is shown; Figure 2 This is an example diagram of an error result of the present invention; Figure 3 A schematic diagram of the system structure of the present invention. DETAILED DESCRIPTION

[0021] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions of 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. Generally, the components of the embodiments of the present invention described and shown in the drawings herein can be arranged and designed in various different configurations.

[0022] Example 1 As attached Figure 1 A positioning method based on a single low-orbit satellite is shown. Obtain orbital data of a single low-orbit satellite; In particular, the orbital data of the single low-orbit satellite includes the orbital altitude, velocity vector, coordinate data, carrier frequency, observation Doppler frequency and transmission frequency of the ground station of the low-orbit satellite; Calculate the rough coordinates of the ground station based on the orbit data at the initial moment; In addition, the specific steps are: The rough coordinates of the ground station are defined as , and the initial moment The state when the ground station first tracks a low-orbit satellite and obtains its orbital data is defined as the moment when the satellite's motion direction and the direction between the satellite and the ground station are at an angle of 90 degrees, and the relative speed between the satellite and the ground station is zero. Then construct the Earth radius constraint equation; ; (1) Where, is the radius of the Earth; According to the initial moment The coordinates of the satellite , the satellite's velocity vector and the rough coordinates of the ground station to construct the vertical relationship equation of the satellite velocity; ; (2) Construct the law of cosines equation based on the satellite's coordinates, the ground station's coordinates, the Earth's radius, and the satellite's distance from the Earth's center. ; (3) Where, is the satellite's distance from the Earth's center, and , is the altitude of the satellite; for The distance between the satellite and the ground station at any moment; Construct the Euclidean distance equation based on the satellite's coordinates and the rough coordinates of the ground station; ; (4) The rough coordinates of the ground station are calculated by forming a set of equations consisting of the earth radius constraint equation, the satellite velocity vertical relationship equation, the cosine theorem equation and the Euclidean distance equation. That is, formulas (1)-(4) are constructed into an equation set. According to the known satellite coordinates , the satellite's velocity vector and the height of the satellite to calculate the rough coordinates of the ground station .

[0023] Calculate the frequency data received by a single low-orbit satellite based on the orbital data at the time of operation; When there is relative radial motion between the satellite and the ground station, the signal frequency will shift due to the Doppler effect: That is, when the satellite is far away from the ground station, the satellite's receiving frequency will be lower than the ground station's transmitting frequency; When a satellite is close to a ground station, the satellite's receiving frequency will be higher than the ground station's transmitting frequency; Therefore, according to the formula: ; (5) Where, for The velocity vector of the satellite at the moment is , for At the moment, the angle between the satellite's motion direction and the direction of the line connecting the satellite and the ground station; is the speed of light, is the transmitting frequency of the ground station, is the measurement error of the frequency; the expression of the satellite receiving frequency can be obtained; Then the requested position of the ground station , The velocity vector sum of the satellite at the moment The coordinates of the satellite at this moment , substitute the frequency data In the calculation formula, we get: ; (6) This formula transforms the frequency calculation from a geometric form into a computable form, providing a nonlinear observation equation for subsequent Taylor series expansion and least squares iteration. In addition, this formula is the observation equation for positioning of a single low-orbit satellite, thus getting rid of the dependence on multiple satellites.

[0024] The frequency data is expanded by Taylor series and combined with the coarse coordinates of the ground station to obtain the Doppler observation increment equation; The specific steps are: The frequency data The calculation formula of formula (6) is transformed into the formula containing the ground station coordinates The equation is: ; (7) Then the rough coordinates of the ground station Substituting into the equation, expanding it by the first-order Taylor series, and removing the higher-order terms, we get the first-order Taylor expansion: ; (8) ; (9) Substituting the three time points into the first-order Taylor expansion, we get the Taylor expansion equation: ; (10) make , , , ; Converting the Taylor expansion equation into a matrix form, we get the Doppler observation increment equation, which is: (11).

[0025] The least Newton squares method is used to iteratively solve the Doppler observation increment equation to obtain the estimated value of the ground station coordinates. Each iteration will locate and solve an estimated value of the ground station coordinates. Through continuous iterative solutions, the estimated value of the ground station coordinates can be made closer to the true coordinates. The specific steps are: Define the variables in the Doppler observation increment equation The iterative equation is: ; (12) Right now ; (13) Where, is the positioning solution result after the i-th iteration; is the correction value of the positioning result of the i+1th iteration; By Newton's least squares method , that is, formula (11) is used for iterative positioning solution, and we have; ; (14) First calculate the residual : ; (15) Then construct the Jacobian matrix : ; (16) Where, is the three-dimensional position coordinate of the low-orbit satellite at the jth observation moment; is the three-dimensional velocity of the low-orbit satellite at the jth observation moment; is the carrier frequency of the low-orbit satellite signal; is the observed Doppler frequency of the low-orbit satellite at the jth observation moment; The observed distance between the j-th observation moment of the low-orbit satellite and the i-th position iteration solution result of the user; In particular, the observation distance between the j-th observation time of the low-orbit satellite and the i-th position iteration solution result of the user is calculated as follows: ; (17) Finally, according to Iterative equation update .

[0026] By setting the number of iterations or iteration conditions, when the result of the iterative positioning solution meets the set number of iterations or iteration conditions, the iteration is stopped, and the final iteration result is the final estimated value of the ground station coordinates; In addition, the set iteration condition is ,and is an infinitesimal real number, or the number of iterations is set to 20; that is, the process of iteratively solving the Doppler observation increment equation using the least Newton squares method can be to perform iterative calculations 20 times, or to continue iteratively solving until the solution is obtained. stop.

[0027] Example 2 As an embodiment, when calculating the initial position of the ground station, there may be two real number solutions, one of which is a correct position solution and the other is an ambiguous position; Therefore, after completing the final estimate of the ground station coordinates in Example 1, it is necessary to judge and remove the fuzzy points. The method for eliminating the fuzzy positions is: Get low-orbit satellites separately and The estimated coordinates of the ground station at time t; generate The estimated value at is the two intersection points of the equal-frequency cone lines; generate The estimated value at is the two intersection points of the equal-frequency cone lines; The only common intersection point of the two positioning results is taken as the true position of the ground station to obtain the accurate ground station position coordinates; For example: The trajectory of the satellite on the ground when it passes over the ground station for the first time is satellite trajectory 1. and The intersection points of the isofrequency cones formed by observing the satellite at all times are A and B respectively. At this time, it is impossible to determine which point is the real position of the target. When the low-orbit satellite passes over the ground station for the second time, the track on the ground is satellite track 2. and The intersection points of the isofrequency cones formed by observing the satellites at all times are A and C respectively. The common intersection point A of the two positioning results is the true position of the target, which eliminates the ambiguous position and further improves the accuracy of the calculated ground station coordinates.

[0028] In addition, according to the above-mentioned low-orbit satellite single-star positioning method, the position of the ground station can be calculated by relying on the navigation information and frequency parameters of a single low-orbit satellite that passes quickly, which solves the problem of relying on multiple satellites to obtain the position of the ground station. This method only requires a single low-orbit satellite and does not need to consider the impact of the geometric configuration of multiple satellites on the positioning accuracy of the ground station; in addition, according to this method, an error test is performed, and the error change between the estimated value of the ground station coordinate and the actual value of the ground station is judged by adjusting the value of any combination of the initial position of the ground station, the frequency parameter error or the satellite orbit error. The horizontal axis is the measurement time, the vertical axis is the error, and curves of different colors and shapes represent the error change to construct an attached diagram. Figure 2 , and according to the attached Figure 2 It can be seen intuitively that during the test, the positioning accuracy of the ground station will be significantly affected only after the initial ground position is deviated by 111 km, the frequency parameter error is deviated by 10 Hz, and the satellite orbit error is deviated by 100 m. After adjusting the remaining items, the final ground station coordinates obtained by this method have a small error, so this method can obtain accurate ground station coordinates.

[0029] Example 3 As attached Figure 3 A positioning system based on a single low-orbit satellite is shown, comprising: Data acquisition module, used to obtain orbit data of a single low-orbit satellite; The initial calculation module is used to calculate the rough coordinates of the ground station based on the orbit data at the initial time, and to calculate the frequency data received by a single low-orbit satellite based on the orbit data at the operating time; Taylor expansion module, used to perform Taylor series expansion on the frequency data and combine it with the coarse coordinates of the ground station to obtain the Doppler observation increment equation; Iterative module, used to iteratively solve the Doppler observation increment equation using the least Newton squares method to obtain the estimated value of the ground station coordinates; The judgment module sets the number of iterations or iteration conditions, and the final iteration result is the final estimated value of the ground station coordinates.

[0030] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention shall be included within the scope of protection of the present invention.

Claims

1. A positioning method based on a single low-orbit satellite, characterized in that: Specifically include: Obtain orbital data of a single low-orbit satellite; Calculate the rough coordinates of the ground station based on the orbit data at the initial moment; Calculate the frequency data received by a single low-orbit satellite based on the orbital data at the time of operation; The frequency data is expanded by Taylor series and combined with the coarse coordinates of the ground station to obtain the Doppler observation increment equation; The least Newton square method is used to iteratively solve the Doppler observation increment equation to obtain the estimated value of the ground station coordinates; Set the number of iterations or iteration conditions, and the final iteration result is the final estimated value of the ground station coordinates.

2. The positioning method based on a single low-orbit satellite according to claim 1, characterized in that: The orbital data of the single low-orbit satellite includes the orbital altitude, velocity vector, coordinate data, carrier frequency, observation Doppler frequency and transmission frequency of the ground station of the low-orbit satellite.

3. The positioning method based on a single low-orbit satellite according to claim 2, characterized in that: The specific steps of calculating the rough coordinates of the ground station based on the low-orbit satellite orbit data at the initial moment are as follows: The rough coordinates of the ground station are defined as , and the initial moment At the bottom, that is, when the ground station first tracks a low-orbit satellite and obtains its orbital data, the angle between the satellite's motion direction and the direction of the line connecting the satellite and the ground station is 90 degrees, and the relative speed between the satellite and the ground station is zero; Construct the Earth radius constraint equation; ； Where, is the radius of the Earth; According to the initial time The coordinates of the satellite , the satellite's velocity vector and the rough coordinates of the ground station to construct the vertical relationship equation of the satellite velocity; ； Construct the law of cosines equation based on the satellite's coordinates, the ground station's coordinates, the Earth's radius, and the satellite's distance from the Earth's center. ； Where, is the satellite's distance from the Earth's center, and , is the altitude of the satellite; for The distance between the satellite and the ground station at any moment; Construct the Euclidean distance equation based on the satellite's coordinates and the rough coordinates of the ground station; ； The rough coordinates of the ground station are calculated by the equation system composed of the earth radius constraint equation, the satellite velocity vertical relationship equation, the cosine theorem equation and the Euclidean distance equation.

4. The positioning method based on a single low-orbit satellite according to claim 2, characterized in that: According to the running time Orbital data, calculate the frequency data received by a single low-orbit satellite , the formula is: ； Where, for The velocity vector of the satellite at the moment is , for At the moment, the angle between the satellite's motion direction and the direction of the line connecting the satellite and the ground station; is the speed of light, is the transmitting frequency of the ground station, is the measurement error of frequency; The requested position of the ground station , The velocity vector sum of the satellite at the moment The coordinates of the satellite at this moment , substitute the frequency data In the calculation formula, we get: 。 5. The positioning method based on a single low-orbit satellite according to any one of claims 3 or 4, characterized in that: The frequency data is subjected to Taylor series expansion and combined with the coarse coordinates of the ground station to obtain the Doppler observation increment equation. The specific steps are: The frequency data The calculation formula is transformed into: ； The rough coordinates of the ground station Substituting into the equation, expanding it by the first-order Taylor series, and removing the higher-order terms, we get the first-order Taylor expansion: ； ； Substituting the three time points into the first-order Taylor expansion, we get the Taylor expansion equation: ； make , , , ; Converting the Taylor expansion equation into a matrix form, we get the Doppler observation increment equation, which is: .

6. The positioning method based on a single low-orbit satellite according to claim 5, characterized in that: The least Newton square method is used to iteratively solve the Doppler observation increment equation to obtain the estimated value of the ground station coordinates. The specific steps are: Define the variables in the Doppler observation increment equation The iterative equation is: ； Right now ; Where, is the positioning solution result after the i-th iteration; is the correction value of the positioning result of the i+1th iteration; By Newton's least squares method Perform iterative positioning solution, there are; ； First calculate the residual : ； Then construct the Jacobian matrix : ； Where, is the three-dimensional position coordinate of the low-orbit satellite at the jth observation moment; is the three-dimensional velocity of the low-orbit satellite at the jth observation moment; is the carrier frequency of the low-orbit satellite signal; is the observed Doppler frequency of the low-orbit satellite at the jth observation moment; The observed distance between the j-th observation moment of the low-orbit satellite and the i-th position iteration solution result of the user; Finally, according to Iterative equation update .

7. The positioning method based on a single low-orbit satellite according to claim 6, characterized in that: The calculation formula for the observed distance between the j-th observation time of the low-orbit satellite and the i-th position iteration solution result of the user is: 。 8. The positioning method based on a single low-orbit satellite according to claim 1, wherein: The set iteration condition is ,and is an infinitesimal real number.

9. The positioning method based on a single low-orbit satellite according to claim 1, wherein: The set number of iterations is 20 times.

10. The positioning method based on a single low-orbit satellite according to claim 7, characterized in that: Get low-orbit satellites separately and The estimated coordinates of the ground station at time t; generate The estimated value at is the two intersection points of the equal-frequency cone lines; generate The estimated value at is the two intersection points of the equal-frequency cone lines; The only common intersection point of the two positioning results is taken as the true position of the ground station to obtain the accurate ground station position coordinates.

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