Optical Navigation and Positioning Method Based on Geometric Measurement Information of Low Earth Orbit Satellite Constellation

Abstract

The present invention provides an optical navigation and positioning method based on geometric measurement information of a low-earth orbit satellite constellation, which includes: generating a database of satellite geometric configurations and positioning errors; analyzing the first-layer screening indexes of the satellite geometric configurations obtained from data; extracting the satellite geometric configuration parameters that mainly affect the positioning error; quantifying and dimensionlessizing the satellite geometric configuration parameters and calculating the weights of each parameter; obtaining an evaluation function and calculating the availability of different satellite geometric configurations; obtaining the second-layer screening indexes according to the distribution of the availability of the satellite geometric configurations; evaluating the geometric configuration of each star point and determining whether to retain the data of this shot; positioning all the data with excellent satellite geometric configurations through the P3P algorithm and calculating the average value as the final positioning result. The present invention realizes optical navigation and positioning by observing low-earth orbit satellites using the P3P algorithm. The positioning method is fast and efficient, and effectively solves the problem of poor positioning accuracy of the P3P algorithm for observing long-distance targets.

Description

Technical Field

[0001] The present invention relates to the technical field of optical navigation and geometric positioning, and particularly relates to an optical navigation and positioning method based on geometric measurement information of a low-Earth orbit satellite constellation. Background Art

[0002] In recent years, the technology of low-Earth orbit satellite constellations has developed rapidly. Since 2020, major well-known enterprises including SpaceX in the United States have successively applied for and deployed commercial very low-Earth orbit satellite systems, involving from ten to tens of thousands of satellites, such as Starlink, OneWeb, "Hongyan Constellation", "Hongyun Project", etc. With the improvement of optical observation technology, if the space navigation information source is expanded from traditional stars to a large number of on-orbit satellites, it will be able to enrich the technical connotation of optical navigation. Moreover, compared with stellar targets, the relative distance between artificial satellites and carriers is limited, and their position information can be calculated through ephemeris data, providing feasibility for precise positioning.

[0003] The P3P technology, namely the three-point perspective calibration technology, uses the two-dimensional image coordinates of image feature points and the three-dimensional coordinates of target points in the Earth coordinate system to calculate the pose relationship between the camera coordinate system and the Earth coordinate system, so as to achieve the positioning function. The positioning method based on the P3P problem has the advantages of simple structure, high calculation efficiency, and mature related algorithms. Combining with the current development trend of Starlink satellites, it is very feasible to perform positioning in the future by simultaneously observing 3 or more satellites in combination with the P3P problem.

[0004] However, since the traditional P3P positioning method is suitable for short-distance positioning, and satellites are generally far apart, if the traditional method based on the P3P problem is used for positioning, the positioning error is too large to provide accurate information. Therefore, the present invention starts from the geometric configuration of the three observed satellites, studies the influence of the satellite geometric configuration on the positioning error, establishes an evaluation function, and thus screens out a better positioning result. The present invention expands the P3P positioning algorithm to the field of observing satellites, enriching the application of the P3P algorithm; the present invention greatly improves the positioning accuracy of the traditional P3P algorithm for observing long-distance targets, and at the same time also has the advantages of simplicity and high efficiency of the P3P algorithm. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to construct an optical navigation and positioning method based on geometric measurement information of a low-Earth orbit satellite constellation, integrate the P3P algorithm into the observation of long-distance targets, determine the geometric configuration of low-Earth orbit satellites, establish an evaluation function and evaluate its geometric configuration through the evaluation function, perform screening of information sources, and finally realize the optical navigation and positioning of geometric measurement information of a low-Earth orbit satellite constellation.

[0006] To solve the above problems, the present invention provides a navigation and positioning method based on observing geometric measurement information of a low-Earth orbit satellite constellation, which includes the following steps:

[0007] S1. Generate a database of satellite geometric configurations and positioning errors: With the aid of Monte Carlo simulation, generate a database of satellite observation information, geometric configurations, and positioning results according to the distribution of three star points in the pixel coordinate system;

[0008] S2. Analyze respectively the relationship between the satellite geometric configuration and the positioning error in the database of satellite geometric configurations and positioning errors under different distributions of star points in the coordinate quadrants, extract data to obtain the influence effect of the quadrant position distribution of satellite star points in the pixel coordinate system on the positioning error, and use it as the first-level screening index;

[0009] S21. Set the positioning error into 5 intervals, specifically: less than 100m, 100m - 300m, 300m - 500m, 500m - 700m, and greater than 700m;

[0010] S22. Statistically analyze the distribution of the positioning errors of 20,000 simulation results under each distribution in the 5 intervals in step S21 and their corresponding geometric configurations;

[0011] S23. Determine the first-level screening index according to the relationship between the positioning error and the satellite geometric configuration;

[0012] S3. Extract the satellite geometric configuration parameters that affect the positioning error, and statistically analyze the influence relationship between each parameter and the positioning error;

[0013] S4. Quantify and dimensionless each satellite geometric configuration parameter that affects the positioning error, establish an evaluation function, and calculate the weight of each parameter;

[0014] S41. Quantify and dimensionless the satellite geometric configuration parameters that affect the positioning error;

[0015] S42. Construct an evaluation function:

[0016]

[0017] where Q i is the availability of the geometric configuration, w j is the weight corresponding to the jth parameter, X ij represents the jth parameter of the ith data, and m represents the number of parameters;

[0018] S43. Calculate the weight of each parameter by using the entropy weight method;

[0019] S431. Calculate the ratio Y ij of the value of the jth parameter of the ith group of data to the sum of the first j parameters by means of the data after dimensionless processing:

[0020]

[0021] S432. Calculate the entropy value e of the j-th parameter j :

[0022]

[0023] where ln() represents the logarithmic operation;

[0024] S433. Calculate the comprehensive weight w corresponding to each parameter j :

[0025]

[0026] S5. With the help of the evaluation function, calculate the availability of the satellite geometric configuration, and calculate the distributions of the availability of the satellite geometric configuration under different distributions and different positioning errors respectively;

[0027] S6. According to the availability distribution of the geometric configuration under different positioning errors obtained in step S5, obtain the second-layer screening index;

[0028] S7. Result verification: Evaluate the geometric configuration of the star points obtained by shooting. If it meets the first-layer and second-layer screening indexes, confirm the geometric configuration, save the current data and use the P3P algorithm for positioning; otherwise, reject the current data;

[0029] S8. After positioning the data of the geometric configurations obtained in multiple steps S7, calculate the average value of multiple groups of positioning results to obtain the final positioning result.

[0030] Furthermore, the star points described in step S1 refer to the points where the satellite appears in the satellite photo taken by the camera.

[0031] Furthermore, the database parameters of the satellite geometric configuration and positioning error described in step S1 include: the position vector of the satellite in the world coordinate system; the pixel coordinates of the satellite star points in the pixel coordinate system; the area, angle of the triangle formed by the satellite star points in the pixel coordinate system, the distance from the centroid to the origin of the image coordinate system, and the positioning error.

[0032] Furthermore, the different distributions described in step S2 are specifically as follows: there are four distributions of three satellite star points in the pixel coordinate system, namely, the three star points are located in the same quadrant, the three star points are located in two adjacent quadrants, the three star points are located in two non-adjacent quadrants, and the three star points are located in three different quadrants.

[0033] Preferably, the geometric configuration extraction parameters described in step S3 are the angle difference between the maximum angle and the minimum angle of the triangle, the area of the triangle, whether the projection of the camera optical center in the pixel coordinate system falls inside the triangle, and the distance between it and the centroid of the triangle.

[0034] Preferably, step S41 specifically includes the following steps:

[0035] S411. Perform dimensionless processing on the angle difference JDC between the maximum angle and the minimum angle of the triangle formed by three star points i :

[0036]

[0037] where JD i represents the angle difference between the maximum angle and the minimum angle of the triangle formed by three star points after dimensionless processing, JD represents the matrix composed of JD i , i represents the number of groups in the total data, and n represents the total number of data;

[0038] S412. Perform dimensionless processing on the area M of the triangle formed by three star points i :

[0039]

[0040] where S i represents the area of the triangle formed by three star points after the i-th dimensionless processing, S represents the matrix composed of all area data, width represents the horizontal pixels of the star map, and height represents the vertical pixels of the star map;

[0041] S413. Perform dimensionless processing on the positional relationship I between the optical center and the triangle formed by three star points i :

[0042]

[0043] where D i represents the distance between the optical center and the centroid of the triangle formed by three star points, and I represents the matrix composed of all processed I i data.

[0044] Compared with the prior art, the present invention has the following beneficial effects:

[0045] 1. Starting from the geometric configuration of the satellite constellation composed of three or more observed satellites, the present invention studies the influence of the satellite geometric configuration on the positioning error, establishes an evaluation function, and thus screens out a better positioning result.

[0046] 2. The present invention extends the P3P positioning algorithm to the field of observed satellites, enriches the application of the P3P algorithm, greatly improves the positioning accuracy of the traditional P3P algorithm for observing long-distance target positioning, and at the same time has the advantages of simplicity and high efficiency of the P3P algorithm.

[0047] 3. When the number of low-earth orbit satellites is sufficient, positioning can be achieved by observing three or more satellites, providing a fast and efficient positioning method for the spatial navigation and positioning of aircraft, and expanding the methods of aircraft spatial navigation and positioning. Description of the Drawings

[0048] Figure 1 Schematic diagram of the optical navigation and positioning method based on the geometric measurement information of the low-earth orbit satellite constellation of the present invention in the ECEF and ENU coordinate systems;

[0049] Figure 2 Schematic diagram of the camera coordinate system, image coordinate system and pixel coordinate system of the present invention;

[0050] Figure 3 Flowchart of the optical navigation and positioning method based on the geometric measurement information of the low-earth orbit satellite constellation of the present invention;

[0051] Figure 4 Schematic diagram of the simulation observation platform of the example of the present invention;

[0052] Figures 5a - 5b Schematic diagram of the four position distributions of three satellites in the pixel coordinate system in the example of the present invention;

[0053] Figures 6a - 6d Schematic diagram of the relationship between the area of the triangle formed by three satellites in the pixel coordinate system and the positioning error in the example of the present invention;

[0054] Figures 7a - 7e Schematic diagram of the availability distribution under different positioning errors when three satellites are located in different quadrants in the pixel coordinate system in the example of the present invention;

[0055] Figure 8 Schematic diagram of the comparison between the positioning error under the method of the present invention and the original positioning error. Detailed Embodiment

[0056] The following further details the present application in conjunction with the drawings and embodiments. It should be understood that the specific embodiments described herein are only for explaining the relevant invention and not for limiting the invention. Additionally, it should be noted that for the sake of description, only parts related to the relevant invention are shown in the drawings. Without conflict, the embodiments in the present application and the features in the embodiments can be combined with each other.

[0057] Before specifically elaborating on the examples of the present invention, the coordinate systems mentioned in the present invention are described. As Figure 1The following shows a schematic diagram of the optical navigation and positioning method based on the geometric measurement information of the low-earth orbit satellite constellation in the ECEF and ENU coordinate systems. ECEF represents the Earth-centered inertial coordinate system, also known as the world coordinate system, with the Earth's center as the origin, the X-axis pointing to the point with longitude and latitude of 0, the Z-axis pointing to the Earth's North Pole, and the Y-axis in the equatorial plane and determined by the right-hand rule. ENU represents the geographical coordinate system, that is, the northeast celestial coordinate system, with the centroid of the carrier as the origin, the X-axis pointing east, the Y-axis pointing north, and the Z-axis vertically pointing to the sky.

[0058] As Figure 2 The following shows a schematic diagram of the camera coordinate system, image coordinate system, and pixel coordinate system of the present invention. ox e y e z e represents the camera coordinate system, and the origin of the camera coordinate system is taken at the optical center position of the camera. For simplicity in the examples of the present invention, it is considered that the camera coordinate system coincides with the geographical coordinate system, that is, the camera is located at the origin of the geographical coordinate system, and the optical axis of the camera vertically points to the sky along the Z-axis of the northeast celestial coordinate system. uov represents the pixel coordinate system, which is a two-dimensional plane rectangular coordinate system. The u-axis is parallel to the x e axis, and the v-axis is parallel to the y e axis. In the present invention, the pixel coordinate system is transformed, that is, xoy.

[0059] Figure 3 The following shows a flowchart of the optical navigation and positioning method based on the geometric measurement information of the low-earth orbit satellite constellation, which specifically includes the following steps:

[0060] S1. Generate a database of satellite geometric configurations and positioning errors: With the aid of Monte Carlo simulation, generate a database of satellite observation information, geometric configurations, and positioning results according to the distribution of three star points in the pixel coordinate system, including the position vector of the satellite in the world coordinate system, the pixel coordinates of the satellite star points in the pixel coordinate system, the area, angle, and distance from the centroid of the triangle formed by the satellite star points in the pixel coordinate system to the origin of the image coordinate system, and the positioning error.

[0061] S2. There are four distributions of three satellite star points in the pixel coordinate system, namely, the three star points are in the same quadrant, the three star points are in two adjacent quadrants, the three star points are in two non-adjacent quadrants, and the three star points are in three different quadrants. Analyze the relationship between the satellite geometric configuration data and the positioning error in the satellite geometric configuration and positioning error database under different distributions respectively, and obtain the first-layer screening indicators.

[0062] S21. Set the positioning error into 5 intervals, specifically: less than 100m, 100m - 300m, 300m - 500m, 500m - 700m, and greater than 700m.

[0063] S22. Statistically analyze the distribution of the positioning errors in the five intervals in step S21 and their corresponding geometric configurations for 20,000 simulations or multiple simulations set as needed for each distribution.

[0064] S23. Determine the first-layer screening indicators based on the relationship between the positioning error and the satellite geometric configuration.

[0065] S3. Extract the parameters of the satellite geometric configuration that affect the positioning error, including the angular difference between the maximum and minimum angles of the triangle, the area of the triangle, whether the projection of the camera optical center in the pixel coordinate system falls inside the triangle, and the distance between it and the centroid of the triangle, and statistically analyze the influence relationship between each parameter and the positioning error.

[0066] S4. Quantify and dimensionlessize the parameters of the satellite geometric configuration that affect the positioning error, establish an evaluation function, and calculate the weights of each parameter.

[0067] S41. Quantify and dimensionlessize the parameters of the satellite geometric configuration that affect the positioning error.

[0068] S411. Perform dimensionless processing on the angular difference JDC between the maximum and minimum angles of the triangle formed by three star points i :

[0069]

[0070] where JD i represents the angular difference between the maximum and minimum angles of the triangle formed by three star points after dimensionless processing, JD represents the matrix composed of JD i , i represents the number of groups in the total data, and n represents the total number of data.

[0071] S412. Perform dimensionless processing on the area M of the triangle formed by three star points i :

[0072]

[0073] where S i represents the area of the triangle formed by three star points after dimensionless processing for the i-th one, S represents the matrix composed of all area data, width represents the horizontal pixels of the star map, and height represents the vertical pixels of the star map.

[0074] S413. Perform dimensionless processing on the positional relationship I between the optical center and the triangle formed by three star points i :

[0075]

[0076] where D iIt represents the distance between the optical center and the centroid of the triangle formed by three star points, and I represents the matrix formed by all processed I data. i Data.

[0077] S42. Construct an evaluation function:

[0078]

[0079] Among them, Q i is the availability of the geometric configuration, w j is the weight corresponding to the j-th parameter, X ij represents the j-th parameter of the i-th data, and m represents the number of parameters.

[0080] S43. Calculate the weights of each parameter using the entropy weight method.

[0081] S431. Calculate the ratio Y of the value of the j-th parameter of the i-th group of data to the sum of the first j parameters using the data after dimensionless processing of the data: ij :

[0082]

[0083] S432. Calculate the entropy value e of the j-th parameter: j :

[0084]

[0085] Among them, ln() represents the logarithmic operation.

[0086] S433. Calculate the comprehensive weight w corresponding to each parameter: j :

[0087]

[0088] S5. Calculate the availability of the satellite geometric configuration using the evaluation function, and calculate the distribution of the availability of the satellite geometric configuration under different distributions and different positioning errors respectively.

[0089] S6. Obtain the second-layer screening index according to the availability distribution of the geometric configuration under different positioning errors calculated in step S5.

[0090] S7. Result verification. Evaluate the geometric configuration of the star points obtained by shooting. If it meets the first-layer and second-layer screening indexes, it is considered that the geometric configuration is good, save the current data and use the P3P algorithm for positioning; otherwise, reject the current data.

[0091] S8. After positioning the data with good geometric configurations multiple times, that is, after positioning the data with geometric configurations obtained in multiple steps S7, calculate the average value of multiple groups of positioning results to obtain the final positioning result. Calculate the average value of multiple groups of positioning results to obtain the final positioning result.

[0092] The following uses an example to illustrate this. In the working condition of the present invention, the camera is located on the ground, that is, observing the satellite constellation on the ground for self-positioning. The satellite orbits are distributed at an altitude of 500 km - 600 km. The resolution is set to 2048×2048, and the field of view of the star sensor is 60°×60°, as Figure 4 shown. Gaussian noise with a mean of 0.04 and a variance of 0.004 is added to the image plane. The present invention adds pixel noise to simulate a situation closer to real shooting, and the added noise is small to reduce the impact of noise on geometric configuration analysis. Figure 4 In the figure, A is the target satellite and B is the camera.

[0093] S1. Conduct 4 groups of simulations respectively. Each group conducts 20,000 Monte Carlo simulations. The generated satellite geometric configuration parameters include the positions of three satellites in the world coordinate system, the pixel coordinates of the three satellites, the single positioning error, and the area, angle, and centroid pixel coordinates of the triangle formed by the three satellites. As Figures 5a - 5b shown, for the observation satellites generated in the first group, their projections on the image plane are distributed in 3 different quadrants of the image plane; for the observation satellites generated in the second group, two of them are in the third quadrant of the image plane and the other is in the first quadrant; for the observation satellites generated in the third group, two of them are in the third quadrant of the image plane and the other is in the second quadrant; for the observation satellites generated in the fourth group, the projections of the three satellites on the image plane are all in the third quadrant.

[0094] S2. Conduct statistical analysis on the four groups of simulation results obtained in step S1 according to the positioning error respectively.

[0095] S21. Set the positioning error to 5 intervals: less than 100 m, 100 m - 300 m, 300 m - 500 m, 500 m - 700 m, and greater than 700 m.

[0096] S22. Statistically analyze the distribution of the positioning errors of 20,000 simulation results in each group in these 5 intervals. Conduct statistics on the 4 groups of simulations respectively. For the fourth group, that is, when the projections of the three satellites on the image plane are in the same quadrant, the proportion of the positioning error less than 100 m is less than 1%, and the proportion less than 300 m is less than 10%.

[0097] S23. Therefore, it can be considered that the configuration is poor when the planar projections of three satellites are in the same quadrant. When such an image is captured, it can be considered that the positioning result obtained based on this image is inaccurate. Similarly, for the third group, that is, when three satellites are in two adjacent quadrants, the proportion of positioning errors less than 100 m is less than 2%. Therefore, similar to the above, it can also be considered that when such an image is captured, the positioning result is inaccurate. Therefore, such images can be directly excluded. Therefore, the above two situations are used as the first-level screening criteria.

[0098] S3. Process the simulation results of the first group and the second group in step S1 respectively. According to the 5 positioning error intervals in step S2, divide 20,000 positioning data into 5 categories, and statistically analyze the distributions of the triangle area, angle, and the distance between the triangle centroid and the optical center under these 5 categories. When there are overly large or overly small angles in the triangle angles, the positioning error is often too large. Therefore, the present invention selects the difference between the maximum angle and the minimum angle of the triangle as the first measurement parameter. Analyze this parameter, and it is obtained that this parameter is positively correlated with the positioning error, that is, the smaller the angle difference, the smaller the positioning error tends to be. Through data processing and drawing analysis, it is found that the triangle area is negatively correlated with the positioning error, that is, the larger the triangle area, the smaller the positioning error tends to be, as Figures 6a - 6d shown. Therefore, the present invention selects the area as the second measurement parameter; according to the position distribution of the triangle in the image plane, it is found that when the positioning error is less than 100 m, the probability that the optical center is inside the triangle is greater than 60%, while when the positioning error is greater than 700 m, the optical center is inside the triangle by 20%. When the optical center is outside the triangle, the farther the optical center is from the triangle centroid, the greater the positioning error tends to be. Therefore, whether the optical center is inside the triangle or the distance from the triangle centroid when it is outside the triangle is also the third parameter for measuring the configuration.

[0099] S4. Quantify and dimensionlessize the satellite geometric configuration parameters that affect the positioning error, establish an evaluation function, and calculate the weights of each parameter.

[0100] S41. Taking the case where three star points are respectively in three quadrants in the first group as an example, perform quantification and dimensionlessization processing on the 3 parameters selected in step S3.

[0101] S411. Perform dimensionlessization processing on the angle difference JDC i between the maximum angle and the minimum angle of the triangle formed by the three star points:

[0102]

[0103] where JD i represents the angle difference between the maximum angle and the minimum angle of the triangle formed by the three star points after dimensionlessization, JD represents the matrix composed of JD i , i represents the number of groups in the total data, and n represents the total number of data.

[0104] S412. Dimensionless processing is performed on the area M of the triangle formed by three star points i as follows:

[0105]

[0106] where S i represents the area of the triangle formed by three star points after dimensionless processing for the i-th time, S represents the matrix composed of all area data, width represents the horizontal pixels of the star map, and height represents the vertical pixels of the star map.

[0107] S413. Dimensionless processing is performed on the positional relationship I of the triangle formed by the optical center and three star points i as follows:

[0108]

[0109] where D i represents the distance between the optical center and the centroid of the triangle formed by three star points, and I represents the matrix composed of all processed I i data.

[0110] S42. Construct an evaluation function;

[0111]

[0112] where Q i is the availability of the geometric configuration, w j is the weight corresponding to the j-th parameter, X ij ' represents the j-th parameter of the i-th data, and m represents the number of parameters.

[0113] S43. The entropy weight method is used to calculate the weights of each parameter.

[0114] S431. The dimensionless results of the obtained data are combined into a matrix C:

[0115] C = [JD S I] = [X’ ij n×m , i = 1, 2, …n, j = 1, 2,..., m, m = 3.

[0116] The ratio Y of the value of the j-th parameter to the sum of the j-th parameters of the i-th group of data is calculated for the data after dimensionless processing ij as follows:

[0117]

[0118] S432. Calculate the entropy value e of the j-th parameter j as follows:

[0119] ​

[0120] S433. Calculate the comprehensive weight w corresponding to each parameter j :

[0121]

[0122] According to the method described above, in this example, the weights of the parameters corresponding to the three points in the first group located in three quadrants are calculated as w = [0.35 0.45 0.2]; it can be seen that the area S formed by the triangle has the greatest influence on the configuration (positioning error).

[0123] S5. The distribution of the availability obtained according to the 5 intervals in step S2 is as Figures 7a - 7e shown. There are more data with positioning errors in the interval less than 300m and greater than 700m, and the availability of data with positioning errors greater than 300m is mostly less than 0.5, which is different from the situation where the positioning error is less than 300m. Therefore, the positioning data can be evaluated and screened according to the defined availability interval.

[0124] S6. Combining the availability distributions of the three satellites in the pixel coordinate system under different positioning errors in three quadrants respectively in Figures 7a - 7e , it can be clearly seen from the figure that the availability Q of 0.5 can clearly distinguish different levels of positioning errors, but setting the availability to 0.5 will also eliminate many data less than 300m. Therefore, in order to increase the proportion of data with positioning errors less than 300m and minimize the proportion of data greater than 700m to the greatest extent, the evaluation function availability of 0.4 is selected as the second-level screening index.

[0125] S7. Set to take 30 star map pictures on the ground in total. After extracting the star points in a single captured picture, first judge the positions of the three star points. If the three star points are all in the same quadrant and two adjacent quadrants, then this group of positioning data is eliminated. If the first group of indicators is satisfied, it enters the second-level screening. Calculate the three parameters of the triangle area, angle difference, and the distance between the triangle centroid and the optical center from the star point coordinate information, and substitute them into the evaluation function obtained in step S5 to calculate the availability. If the screening index is satisfied, the data of this capture is retained; if not, it is eliminated.

[0126] S8. Use the Kneip algorithm of P3P to solve the single positioning result for the data obtained in step 7, and take the average of the comprehensive multiple positioning results to obtain the final positioning result. The results of taking the average of the 30 groups of original positioning data and the results of taking the average of the positioning results of the screened data are as Figure 8As shown, it can be seen that by evaluating the geometric configuration of a single satellite, removing the shooting data with poor configuration, and retaining the good configuration data for positioning, the statistical curve after positioning is the positioning result curve of the present invention. It is entirely below the original positioning error curve, and the error value is greatly reduced. The average positioning error obtained by positioning the original data is 730.27 m, and the average positioning error obtained by positioning using the present invention is 122.102 m. Therefore, the present invention can greatly improve the positioning accuracy of the P3P algorithm for observing and positioning distant targets.

[0127] The beneficial technical effects of this application are as follows:

[0128] 1. Starting from the geometric configuration of the three observed satellites, after studying the influence of the satellite geometric configuration on the positioning error, it is concluded that the positioning errors in two cases where the three satellites are in the same quadrant and two adjacent quadrants in the pixel coordinate system are generally large. When evaluating, the positions of the three star points are used as the first-layer screening index; then three parameters are extracted, an evaluation function is established, and the availability of the configuration is calculated. In the example of the present invention, the availability of 0.4 is selected as the second-layer screening index, that is, the positioning data with an availability less than 0.4 is excluded, so as to screen out a better configuration.

[0129] 2. In the example of the present invention, the average positioning error using the P3P algorithm for positioning is 122.102 m, which is much smaller than the average error of 730.27 m obtained by directly using the P3P positioning algorithm for positioning, improving the positioning accuracy of the P3P positioning algorithm applied to observing and positioning distant targets.

[0130] 3. The present invention evaluates and screens the configuration of the observed satellite constellation and then uses the P3P positioning algorithm for positioning, expanding the method of aircraft spatial navigation and positioning. Moreover, because the P3P algorithm itself is efficient, the algorithm of the present invention also inherits its advantages.

[0131] The embodiments described above are only descriptions of the preferred implementation manners of the present invention, and do not limit the scope of the present invention. Without departing from the design spirit of the present invention, various deformations and improvements made by those of ordinary skill in the art to the technical solutions of the present invention shall fall within the protection scope determined by the claims of the present invention.

Claims

1. An optical navigation and positioning method based on the geometric measurement information of a low-earth orbit satellite constellation, characterized in that, It includes the following steps: S1. Generate a database of satellite geometric configurations and positioning errors: With the help of Monte Carlo simulation, generate a database of satellite observation information, geometric configurations, and positioning results according to the distribution of three star points in the pixel coordinate system; S2. Analyze the relationship between the satellite geometric configuration and the positioning error in the database of satellite geometric configurations and positioning errors under different distributions of star points in the coordinate system quadrants respectively, extract data to obtain the influence effect of the quadrant position distribution of satellite star points in the pixel coordinate system on the positioning error, and use it as the first-level screening index; S21. Set the positioning error into 5 intervals, specifically: less than 100m, 100m - 300m, 300m - 500m, 500m - 700m, and greater than 700m; S22. Statistically analyze the distribution of the positioning error of 20,000 simulation results under each distribution in the 5 intervals in step S21 and its corresponding geometric configuration; S23. Determine the first-level screening index according to the relationship between the positioning error and the satellite geometric configuration; S3. Extract the satellite geometric configuration parameters that affect the positioning error, and statistically analyze the influence relationship between each parameter and the positioning error; S4. Quantify and dimensionless the satellite geometric configuration parameters that affect the positioning error, establish an evaluation function, and calculate the weights of each parameter; S41. Quantify and dimensionless the satellite geometric configuration parameters that affect the positioning error; S42. Construct an evaluation function: Among them, Q i is the availability of the geometric configuration, w j is the weight corresponding to the j-th parameter, X ij represents the j-th parameter of the i-th data, and m represents the number of parameters; S43. Use the entropy weight method to calculate the weights of each parameter; S431. Calculate the ratio Y of the j-th parameter value of the i-th group of data to the sum of the first j parameters using the data after dimensionless processing of the data ij : S432. Calculate the entropy value e of the j-th parameter j :[[]]END]] where, ln() represents the logarithmic operation; S433. Calculate the comprehensive weight w corresponding to each parameter j : S5. With the help of the evaluation function, calculate the availability of the satellite geometric configuration, and calculate the distribution of the availability of the satellite geometric configuration under different distributions and different positioning errors respectively; S6. According to the availability distribution of the geometric configuration based on different positioning errors calculated in step S5, obtain the second-level screening index; S7. Result verification: Evaluate the geometric configuration of the star points obtained by shooting. If it meets the first-level and second-level screening indexes, confirm the geometric configuration, save the current data, and use the P3P algorithm for positioning; otherwise, reject the current data; S8. After positioning the data of the geometric configurations obtained in multiple steps S7, calculate the average value of multiple groups of positioning results to obtain the final positioning result.

2. The optical navigation and positioning method based on the geometric measurement information of the low-earth orbit satellite constellation according to claim 1, wherein The star points described in step S1 refer to the points where the satellite appears in the satellite photo taken by the camera.

3. The optical navigation and positioning method based on the geometric measurement information of a low-earth orbit satellite constellation according to claim 1, wherein The database parameters of the satellite geometric configuration and positioning error described in step S1 include: the position vector of the satellite in the world coordinate system; the pixel coordinates of the satellite star points in the pixel coordinate system; the area, angle, and the distance from the centroid of the triangle formed by the satellite star points in the pixel coordinate system to the origin of the image coordinate system, and the positioning error.

4. The optical navigation and positioning method based on the geometric measurement information of the low-earth orbit satellite constellation according to claim 1, wherein The different distributions described in step S2 are specifically: there are four distributions of three satellite star points in the pixel coordinate system, namely, the three star points are located in the same quadrant, the three star points are located in two adjacent quadrants, the three star points are located in two non-adjacent quadrants, and the three star points are located in three different quadrants.

5. The optical navigation and positioning method based on the geometric measurement information of the low-earth orbit satellite constellation according to claim 1, wherein The geometric configuration extraction parameters described in step S3 are the angle difference between the maximum angle and the minimum angle of the triangle, the area of the triangle, whether the projection of the camera optical center in the pixel coordinate system falls inside the triangle, and the distance between the camera optical center and the centroid of the triangle.

6. The optical navigation and positioning method based on the geometric measurement information of a low-earth orbit satellite constellation according to claim 1, wherein The specific steps of step S41 include the following steps: S411. Dimensionless processing is performed on the angle difference JDC between the maximum angle and the minimum angle of the triangle formed by three star points. i Specifically: Among them, JD i represents the angular difference between the maximum angle and the minimum angle of the triangle formed by three star points after dimensionlessization. JD represents the matrix composed of JD i . i represents the number of groups in the total data, and n represents the total number of data; S412. Nondimensionalize the area M of the triangle formed by three star points i as follows: Among them, S i represents the area of the triangle formed by the three dimensionless star points at the i-th position, S represents the matrix composed of all area data, width represents the horizontal pixels of the star map, and height represents the vertical pixels of the star map; S413. The positional relationship I of the triangle formed by the optical center and three star points i Perform dimensionless processing: Among them, D i represents the distance between the optical center and the centroid of the triangle formed by three star points, and I represents the matrix formed by all processed I i data.

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