A method of astronomical positioning and navigation based on optical observation

Abstract

The present invention provides an astronomical positioning and navigation method based on optical observation, comprising: screening and sorting observation targets to be observed based on the platform's initial conditions and the ephemeris of the observation targets to form an observation task list; driving the optical telescope to steer and collect observation images based on the observation task list; matching the constellations in the observation images with a star catalog to calculate the observed celestial coordinates of each constellation; extracting moving targets as observation targets by changes in the constellations in multiple frames of observation images to obtain the motion trajectory of the observation targets; and performing platform position resolution. The astronomical positioning and navigation method of the present invention integrates optical observation data of stars and observation targets to complete platform attitude and position resolution, enabling autonomous navigation and positioning of the platform in the absence of GNSS signals.

Description

Technical Field

[0001] The present invention belongs to the field of astronomical observation, and in particular relates to an astronomical positioning and navigation method based on optical observation. Background Art

[0002] Modern navigation and positioning technologies include GNSS (Global Navigation Satellite System) navigation technology, inertial navigation technology, astronomical navigation technology, etc. Currently, the status quo and challenges of modern navigation and positioning technologies are as follows:

[0003] 1. Widespread application and limitations of GNSS navigation technology:

[0004] GNSS (Global Navigation Satellite System) provides high-precision position and time services and is widely used in land, ocean, aviation and space.

[0005] However, the following scenarios pose significant challenges to GNSS technology:

[0006] 1) Signal jamming and denial: In military battlefields or strategic environments, GNSS signals may be jammed, spoofed, or even completely denied.

[0007] 2) Limited coverage: GNSS signals cannot effectively cover deep space probes and high-orbit satellites.

[0008] 3) High dependence: The high dependence on satellite signals makes the system prone to failure under interference conditions.

[0009] 2. Application and problems of inertial navigation technology:

[0010] Inertial Navigation Systems (INS) provide navigation capabilities independent of external signals through accelerometers and gyroscopes and are widely used in high-dynamic scenarios such as spacecraft and missiles.

[0011] The problem with inertial navigation technology is that errors (drift) will accumulate over time, making it unable to meet long-term high-precision positioning requirements; in addition, vibration and noise interference in high-dynamic environments exacerbate errors.

[0012] 3. Current status and limitations of astronomical navigation technology:

[0013] Astronomical navigation technology uses observation data of stars or artificial celestial bodies, combined with accurate celestial ephemeris or star catalog information, to provide independent high-precision reference for navigation systems.

[0014] The limitations of traditional astronomical navigation include: 1) Orientation-focused: Traditional star-based astronomical navigation techniques primarily calculate the platform's attitude (orientation), but cannot directly determine its position. 2) Lack of multi-target positioning capabilities: Navigation methods that rely solely on stars cannot incorporate reference targets with known positions in space (such as artificial celestial bodies) to resolve the platform's three-dimensional coordinates.

[0015] At present, positioning technologies based on artificial celestial body observations mainly include stellar navigation and orientation technology, and artificial celestial body radio navigation technology.

[0016] The principle of stellar navigation and orientation technology is to use star sensors to observe the positions of stars in the celestial coordinate system and calculate the platform's attitude by matching them with a star catalog (attitude solution). Its application scenarios include spacecraft attitude determination (such as adjusting the direction of the probe's antenna or camera) and autonomous orientation missions for deep space exploration. However, its limitation is that it cannot directly calculate the platform's specific position in space using stellar data, and positioning must be combined with other navigation technologies (such as radio ranging) to achieve positioning.

[0017] The principle of radio navigation technology for artificial celestial bodies is to observe artificial celestial bodies (such as orbiting satellites) with known ephemeris and calculate their relative positions using their precise orbital information and ground base station data. Application scenarios include real-time position calculation of orbiting spacecraft. However, its limitations are that, on the one hand, traditional implementations of radio navigation technology for artificial celestial bodies rely on radio signal ranging (measuring the distance from the platform to the artificial celestial body) and the Doppler effect to calculate the platform's position, which is susceptible to electromagnetic interference. On the other hand, a single observation object cannot meet the precise navigation requirements of multiple platforms and multiple scenarios.

[0018] Currently, specific implementation plans at home and abroad include NASA's star navigation system, ESA's autonomous navigation technology, and China's deep space exploration astronomical navigation system.

[0019] NASA's stellar navigation system uses star sensors to observe stars and achieve autonomous spacecraft orientation through star catalog matching. Combined with inertial navigation, it assists with course adjustments in deep space. Application examples include NASA's deep space probes (such as Cassini) using stellar navigation for flight attitude control. However, a limitation of stellar navigation is that its core function is orientation, not positioning. Without external reference information (such as radio ranging), it cannot independently calculate the platform's position.

[0020] ESA's autonomous navigation technology combines star observation and radio ranging techniques, using the precise position of target celestial bodies to calculate the platform's relative position. Optimized algorithms and filtering techniques enhance positioning accuracy. Applications include ESA's Mars exploration missions. However, its limitations include frequent reliance on data updates from ground control, and a lack of complete autonomy.

[0021] China's deep-space exploration astronomical navigation system, based on star observation and combined with inertial navigation, provides autonomous orientation and rough positioning for deep-space probes. An example of its application is the attitude adjustment system combining astronomical and inertial navigation used in the Chang'e lunar exploration program. However, its limitations include its reliance on the inertial navigation system for positioning accuracy and insufficient long-term stability.

[0022] In summary, the disadvantage of traditional stellar navigation is that it can only achieve orientation, not positioning. Specifically, stellar navigation primarily calculates the platform's attitude (orientation) by observing the relative positions of stars, but the platform's absolute position cannot be determined through star observation alone. For scenarios requiring high-precision three-dimensional position resolution (such as deep space exploration and GNSS signal-denied environments), stellar navigation alone cannot meet the requirements.

[0023] The disadvantage of radio navigation technology based on artificial celestial bodies is its high reliance on radio signals. Existing artificial celestial body navigation technologies often use radio ranging or the Doppler effect to determine relative position. These methods are highly dependent on signal quality and are susceptible to interference, obstruction, and spoofing attacks. Summary of the Invention

[0024] The purpose of the present invention is to propose an astronomical positioning and navigation method based on optical observation to achieve three-dimensional position solution and rely only on optical observation, thereby improving the applicability of multiple scenarios.

[0025] To achieve the above objectives, the present invention provides an astronomical positioning and navigation method based on optical observation, comprising:

[0026] S1: Input the platform's position and attitude as initial conditions to provide a high-precision reference time for timestamps;

[0027] S2: Based on the initial conditions of the platform and the ephemeris of the observation target, according to a fixed rule, the observation targets to be observed are screened and sorted to form the observation task list;

[0028] S3: Drive the two-dimensional turntable of the optical telescope to steer and collect observation images according to the observation task list, and use the observation images and their timestamps as observation data;

[0029] S4: Match the stars in the observed image with the star catalog to calculate the observed celestial coordinates of each star;

[0030] S5: extracting a moving target as an observation target by observing the star image changes in multiple frames of observation images, and obtaining the motion trajectory of the observation target. The motion trajectory of the observation target includes the observation time t and the observed celestial coordinates (α, δ);

[0031] S6: Calculate the platform position, including: using the observed celestial coordinates (α, δ) of the observed target and the theoretical position (X i ,Y i ,Z i ) Establish the observation equation; solve the observation equation to obtain the three-dimensional position (X, Y, Z) of the platform.

[0032] The observation targets include artificial celestial bodies, natural celestial bodies with ephemeris, or specific reflective objects or landmarks fixed on the ground.

[0033] The step S2 specifically includes:

[0034] S21: Determine the constraints according to the platform type, and then screen all the observation targets that meet the constraints as observable targets;

[0035] S22: Determine the observation priority of the observable targets and sort them according to a fixed rule based on the observation priority;

[0036] S23: Generate an observation task list according to the sorting result, wherein the observation task list includes an observation window and a pointing parameter of each observation target to be observed.

[0037] In step S21, when the platform type is a ground-based platform, the constraints include a minimum elevation angle constraint and a sky light and earth shadow constraint for excluding observation targets whose angular distance from the sun is less than an angular distance threshold; when the platform type is a space-based platform, the constraints include an earth shadow constraint for excluding observation targets in the Earth's umbra and a sun / moon avoidance constraint for excluding observation targets whose angular distance from the sun or moon is less than an angular distance threshold; and / or in step S22, the observation priority of the observation target includes a magnitude priority and a geometric configuration priority; and the observation priority of the observation target is sorted according to a fixed rule, specifically including:

[0038] S221: Select the brightest m targets from the set of observable targets;

[0039] S222: Select n targets from the m targets and calculate the value of the position precision dilution;

[0040] S223: Select n targets with the smallest position precision factor values ​​as the observation targets to be observed.

[0041] The step S3 specifically includes:

[0042] S31: driving the two-dimensional turntable of the optical telescope to rotate to the direction of the observation target to be observed according to the observation task list and the current posture of the platform;

[0043] S32: Use the imaging equipment of the optical telescope to collect observation images.

[0044] Step S31 specifically includes:

[0045] S311: Obtain the current attitude of the platform from the initial conditions, obtain the celestial coordinates of the target to be observed from the observation task list, and convert them into the observation direction of the target to be observed in the platform coordinate system;

[0046] S312: determining the pitch angle and azimuth angle of the two-dimensional turntable of the optical telescope according to the observation direction of the observation target to be observed in the platform coordinate system, and sending a command to the two-dimensional turntable of the optical telescope to drive the two-dimensional turntable of the optical telescope to turn; and / or

[0047] In step S32, a suitable image acquisition mode is selected according to the dynamic characteristics of the target to be observed and the platform capabilities, and exposure parameters are adjusted to complete the observation image acquisition; the image acquisition mode includes a short exposure staring mode and a tracking shooting mode.

[0048] The step S4 specifically includes:

[0049] S41: extracting pixel coordinates of stars from the observed image;

[0050] S42: Performing preliminary coordinate conversion; that is, establishing a preliminary mapping relationship between the observed image coordinates and the celestial coordinates based on the platform attitude and imaging parameters when the observed image is collected;

[0051] S43: matching the celestial coordinates of each candidate star with the preliminary celestial coordinates of the star image by calculating the angular distance, wherein the preliminary celestial coordinates of the star image are obtained based on a preliminary mapping relationship from the observed image coordinates to the celestial coordinates;

[0052] S44: Correcting the conversion parameters according to the matching results, and fitting a conversion formula from the coordinates of the observed image to the celestial coordinates, which serves as an accurate mapping relationship from the coordinates of the observed image to the celestial coordinates;

[0053] S45: Determine the observed celestial coordinates of all the stars in the observed image based on the precise mapping relationship between the coordinates of the observed image and the celestial coordinates.

[0054] The step S4 satisfies at least one of the following:

[0055] a1) Step S41 further includes: after extracting the pixel coordinates (x, y) of the star image, screening the star image with a high signal-to-noise ratio;

[0056] a2) Step S42 further includes: determining a search range for celestial coordinates based on a preliminary mapping relationship between image coordinates and celestial coordinates and a coordinate range of the observed image; and selecting candidate stars within the search range for celestial coordinates from a star catalog;

[0057] a3) In step S43, the angular distance θ between the candidate star and the constellation is:

[0058] cosθ=sinδ1sinδ2+cosδ1cosδ2cos(α1-α2),

[0059] Among them, (α1, δ1) is the celestial coordinate of the star, and (α2, δ2) is the preliminary celestial coordinate of the candidate star;

[0060] a4) in step S44, obtaining a conversion formula from the coordinates of the observed image to the celestial coordinates based on polynomial or linear model fitting;

[0061] a5) In step S42, the preliminary mapping relationship between the coordinates of the observation image and the celestial coordinates is obtained by:

[0062] S421: Define the image coordinate system (u, v), platform coordinate system (X c ,Y c ,Z c ), celestial coordinate system (α, δ);

[0063] S422: Obtain pixel coordinates (u, v) in the image coordinate system to coordinates (X c ,Y c ,Z c )

[0064] S423: Determine the posture matrix according to the posture of the imaging device, and obtain the coordinates of the platform coordinate system (X c ,Y c ,Z c ) to the coordinates (α, δ) of the celestial coordinate system;

[0065] S424: Comprehensively obtain a preliminary mapping relationship between the coordinates of the observed image and the celestial coordinates.

[0066] The step S5 specifically includes:

[0067] S51: comparing the position changes of the stars in the multiple frames of observation images to screen out moving targets;

[0068] S52: Calculate the theoretical celestial coordinates (α theo ,δ theo );

[0069] S53: Compare the celestial coordinates (α, δ) of the multi-frame observation of the moving target with the theoretical celestial coordinates (α theo ,δ theo ) is matched by calculating the angular distance to confirm whether it is the observed target.

[0070] The step S6 specifically includes:

[0071] S61: Based on the observation of two or more observation targets, the observed celestial coordinates (α, δ) of the observation targets and the theoretical positions (X i ,Y i ,Z i ) Establish the observation equation;

[0072] S62: According to the observation equation, the three-dimensional position (X, Y, Z) of the platform is obtained by solving the least squares method;

[0073] The step S62 specifically includes:

[0074] S621: Obtain the initial value of the three-dimensional position (X0, Y0, Z0) according to the initial conditions of the platform;

[0075] S622: Using the initial value of the three-dimensional position (X0, Y0, Z0) as the initial solution of the observation equation, the observation equation is iteratively solved until the residual vector meets the accuracy requirements. At this time, the three-dimensional position (X, Y, Z) of the platform is obtained by solution.

[0076] The astronomical positioning and navigation method of the present invention combines astronomical positioning (orientation) of stars with observational positioning of artificial celestial bodies. Through multi-target collaborative observation, it achieves the three-dimensional position calculation of the platform, overcoming the limitation of traditional stellar navigation that can only determine orientation but not calculate position. Specifically, the astronomical positioning and navigation method of the present invention uses star catalog matching to complete the preliminary determination of the platform's attitude, and then uses the ephemeris information of artificial celestial bodies to establish observation equations to solve the platform's absolute position.

[0077] At the same time, the present invention uses autonomous timekeeping technology and optical observation to achieve fully autonomous navigation, does not require external signal support, and is adaptable to environments where GNSS signals are interfered with, deceived or denied, or where the coverage of GNSS signals is limited. It solves the problem that existing navigation technologies are difficult to operate normally and provide reliable navigation services in environments where GNSS signals are interfered with, deceived or completely denied, or where the coverage of GNSS signals is limited, such as scenarios outside the Earth's orbit or deep space exploration, military battlefields or strategic protection areas, and other special scenarios.

[0078] In addition, the present invention comprehensively utilizes the observation data of stars and artificial celestial bodies, significantly improving the adaptability of the navigation system in complex and changeable scenarios, supporting multi-scenario applications of ground-based, sea-based, air-based and space-based platforms, and meeting the needs of various complex tasks.

[0079] In addition, the present invention uses multi-frame correlation technology to separate moving targets from dynamic backgrounds and extract the star images of artificial celestial bodies; it utilizes the trajectory characteristics of the moving targets (such as angular distance changes and position correlation) to accurately distinguish between stars and artificial celestial bodies, thereby reducing the error rate.

[0080] When using star catalog matching to complete the preliminary determination of the platform's attitude, the present invention establishes a conversion model between image coordinates and celestial coordinates based on the optical characteristics of the observation equipment and the initial attitude of the platform; then, through star catalog matching, errors are corrected and the mapping relationship between the image and the celestial sphere is optimized, which greatly reduces the amount of calculation and speeds up the calculation process.

[0081] In summary, the astronomical positioning and navigation method of the present invention completes the attitude and position calculation of the platform by integrating the optical observation data of stars and artificial celestial bodies, and realizes the autonomous navigation and positioning of the platform in the absence of GNSS signals. BRIEF DESCRIPTION OF THE DRAWINGS

[0082] Figure 1 It is a structural block diagram of the astronomical positioning and navigation system adopted by the astronomical positioning and navigation method based on optical observation of the present invention.

[0083] Figure 2 It is a flow chart of the astronomical positioning and navigation method based on optical observation of the present invention.

[0084] Figure 3 This is a schematic diagram of the positional relationship between the sun, the earth and the earth's umbra. DETAILED DESCRIPTION

[0085] The present invention will be further described below with reference to specific examples. It should be understood that the following examples are only used to illustrate the present invention and are not intended to limit the scope of the present invention.

[0086] Figure 1 This is a structural block diagram of the astronomical positioning and navigation system used in the astronomical positioning and navigation method based on optical observation of the present invention. Figure 1 As shown, the astronomical positioning and navigation system is integrated on the platform, including optical observation equipment 10, auxiliary equipment 20, and computer 30, covering hardware facilities and software systems to ensure high-precision navigation and positioning functions under GNSS signal denial conditions.

[0087] The optical observation device 10 is configured to acquire images of artificial celestial bodies and stars, thereby providing stable observation data.

[0088] In this embodiment, the optical observation device 10 includes an optical telescope 11 and an auxiliary time synchronization system 12 .

[0089] Among them, the optoelectronic telescope includes a two-dimensional turntable, an optical system installed on the two-dimensional turntable, and an imaging device.

[0090] The optical system is used to collect external light and image it onto the imaging device. The optical system is preferably a lens assembly with a high-resolution optical design suitable for visible light or infrared observation, optimized for capturing dim targets, and supporting short-exposure and tracking photography.

[0091] The 2D turntable is used to direct the optical system and imaging equipment toward the target. Specifically, the 2D turntable calculates the azimuth and pitch angles of the artificial celestial object relative to the turntable based on the position of the artificial celestial object and the turntable's rough position and attitude. A motor then drives the turntable to the desired angle. The 2D turntable is preferably a high-precision, high-response motor-driven turntable, capable of rapidly pointing to the target and meeting the needs of sequential multi-target observation, with tracking accuracy reaching arcseconds.

[0092] The imaging device is used to capture images, which is preferably a CMOS or CCD camera with high sensitivity and low noise imaging performance, and supports short exposure mode and tracking shooting mode.

[0093] The auxiliary timing system 12 is configured to receive trigger signals from the imaging device and record a timestamp when the imaging device captures an image. This serves as the image acquisition timestamp. The auxiliary timing system 12 provides high-precision self-timekeeping, ensuring microsecond-level time accuracy without external timing. It also ensures the accuracy of image timestamps, providing a precise time reference for multi-frame correlation, object separation, and position calculation.

[0094] The auxiliary equipment 20 is used to support the operation of the observation equipment and provide necessary reference and supplementary information for system data processing. The auxiliary equipment 20 includes a star catalog and ephemeris database 21 and a control and power supply module 22.

[0095] The star catalog and ephemeris database 21 includes star catalogs and ephemeris for artificial celestial bodies. The star catalog contains information on the right ascension, declination, and magnitude of stars, used for astronomical positioning and image correction. The ephemeris for artificial celestial bodies includes orbital information for the mission planning unit 32 and theoretical position verification; theoretical position verification is used to confirm that the target extracted from the image is the artificial celestial body being observed.

[0096] The control and power module 22 is used to provide stable power support for the imaging device and two-dimensional turntable of the optical telescope 11 of the optical observation device 10. Furthermore, the control and power module 2230 can be configured to minimize environmental interference (such as temperature and electromagnetic waves) during device operation. In this embodiment, the control and power module 22 includes a refrigeration device installed at the imaging device to precisely control temperature, as well as a storage area for temperature-sensitive devices such as the computer and the auxiliary time system 12 of the optical observation device 10. Hardware devices such as the camera, computer, and auxiliary time system 12 are covered with a metal sheath to shield them from interference from external electromagnetic waves.

[0097] Computer 30 is used to realize data processing, task planning and real-time control functions, and is the core computing unit of the system.

[0098] The computer 30 is equipped with a data processing unit 31 , a mission planning unit 32 and a control and communication unit 33 .

[0099] The data processing unit 31 includes: an image processing module, which is used to realize functions such as star extraction and astronomical positioning; a target separation module, which uses multi-frame correlation technology and artificial celestial body ephemeris data to accurately separate artificial celestial body stars and output the right ascension and declination of the observed target (i.e., the observed artificial celestial body); a position solution module, which is used to establish observation equations and solve them to obtain the platform position based on the right ascension, declination and ephemeris data of at least two observed targets, and supports real-time position updates in dynamic scenarios.

[0100] The mission planning unit 32 is used to screen and sort the artificial celestial bodies to be observed according to a fixed rule based on the initial conditions of the platform and the ephemeris of the artificial celestial bodies, as an observation task list. Specifically, the mission planning unit 32 is configured to: predict the set of observable artificial celestial bodies based on the initial conditions and the ephemeris of the artificial celestial bodies (the initial conditions include the rough position and attitude information of the two-dimensional turntable of the optical telescope 11, which can be automatically or manually input by the gyroscope from an external system); generate an observation task list based on the magnitude priority and geometric configuration optimization sorting. The observation list is a list of planned artificial celestial bodies to be observed, so that the two-dimensional turntable rotates to the direction of the artificial celestial bodies to be observed in sequence according to the observation list for observation; and dynamically update the observation task list to adapt to the changing needs of the mobile platform.

[0101] The control and communication unit 33 is configured as follows:

[0102] 1) According to the observation task list, the 2D turntable is driven to the direction of the artificial celestial body to be observed, and the observation direction is adjusted in real time. When photographing artificial celestial bodies, stars will also be included in the image, so there is no need to observe stars separately.

[0103] 2) Support data interaction between the platform and external systems, such as receiving the initial conditions of the platform, sending position solution results, etc. Specifically, data can be received and sent through the serial port.

[0104] 3) Provide a graphical user interface to implement task management and status monitoring.

[0105] Figure 2 This is a flow chart of the astronomical positioning and navigation method based on optical observation of the present invention. Figure 2 As shown, the astronomical positioning and navigation method based on optical observation of the present invention specifically includes the following steps:

[0106] Step S1: Initial preparation, including: inputting the position and attitude of the platform as initial conditions to provide a high-precision reference time for the timestamp;

[0107] The position and attitude of the platform are input as initial conditions, including:

[0108] The initial conditions of the platform are provided by the user or an external system, including position (X0, Y0, Z0), attitude (φ, θ, ψ) and velocity (V x ,V y ,V z ).

[0109] Here the position (X0, Y0, Z0), attitude (φ, θ, φ) and velocity (V x ,V y ,V z ) are coordinates in the celestial coordinate system. The accuracy of the initial conditions can be rough, for example, within tens of kilometers, as long as the observed artificial celestial object is within the field of view of the telescope. For example, the accuracy of the current attitude of the platform (φ, θ, ψ) is better than one-fifth of the field of view size.

[0110] Providing a high-precision reference time for timestamps involves activating and synchronizing auxiliary time systems to ensure a high-precision reference time T0 for timestamps. Time accuracy must reach microseconds to ensure accurate timestamps for observation data.

[0111] Step S2: Perform mission planning. This involves screening and sorting the artificial celestial bodies to be observed based on the platform's initial conditions and the ephemeris of the artificial celestial bodies, according to a fixed rule, to form an observation mission list. The goal is to screen and sort the set of artificial celestial bodies to be observed.

[0112] The step S2 specifically includes:

[0113] Step S21: Observability screening; that is, determining the constraints according to the platform type, and then screening all artificial celestial bodies that meet the constraints as observable targets;

[0114] Step S22: sorting observable targets; that is, determining the observation priority of the observable targets and sorting them according to a fixed rule based on the observation priority;

[0115] Step S23: Generate an observation task list; that is, generate an observation task list according to the sorting result, wherein the observation task list includes the observation window and pointing parameters of each artificial celestial body to be observed.

[0116] Therefore, mission planning ensures the rapid switching of the steering platform's direction, which is beneficial to subsequent functions such as star extraction and astronomical positioning.

[0117] In step S21, when the platform type is a ground-based platform, the constraints include a minimum elevation angle constraint and a constraint for excluding an artificial celestial body from the sun whose angular distance is less than an angular distance threshold θ. min When the platform type is space-based platform, the constraints include the shadow constraint for excluding artificial celestial bodies in the Earth's umbra and the shadow constraint for excluding artificial celestial bodies with an angular distance from the sun or the moon less than the angular distance threshold θ. min The artificial celestial body Sun / Moon circumvents constraints.

[0118] The constraint formula used is derived from the actual requirements of optical observation to ensure that occlusion or interference factors are eliminated.

[0119] For ground-based platforms, the minimum elevation angle constraint includes: To avoid ground obstruction and atmospheric interference, the formula for the minimum elevation angle constraint is:

[0120] h≥h min

[0121] Where h is the elevation angle of the artificial celestial body, h min It is the lowest elevation angle (usually 20°~30°).

[0122] Sky and Earth shadow constraints: Considering the relative position of the sun and the earth, exclude artificial celestial bodies whose angular distance from the sun is less than the angular distance threshold θ min artificial celestial bodies.

[0123] The formula for skylight and ground shadow constraints is:

[0124] θ>θ min ,

[0125] cosθ=cosδcosδ sun cos(α-α sun )+sinδsinδ sun ,

[0126] Where θ is the angular distance between the target artificial celestial body and the sun, and θ>θ min , usually 20°; δ,α are the declination and right ascension of the target artificial celestial body; δ sun ,α sun is the declination and right ascension of the sun. That is, θ is the calculated angular distance, θ>θ min The condition is used to exclude artificial celestial bodies that are directly exposed to sunlight or in the shadow of the earth.

[0127] For space-based platforms, such as Figure 3 As shown, the Earth's shadow constraints include: excluding artificial celestial bodies in the Earth's umbra.

[0128] The calculation method for whether an artificial celestial body (such as a satellite) is in the Earth's umbra is as follows:

[0129] Step A1: Define key parameters of the Earth, the Sun, and artificial celestial bodies;

[0130] The key parameters are as follows:

[0131] R E : Earth's radius (average value 6378km)

[0132] R S : Radius of the Sun (approximately 696,340 km)

[0133] d ES : The distance from the Earth to the Sun (approximately 1 AU = 149,597,870 km)

[0134] h: Orbital altitude of artificial celestial body (relative to the Earth's surface)

[0135] d: The distance from the artificial celestial body to the center of the Earth (d = R E +h).

[0136] Step A2: Calculate the opening angle θ of the umbra cone;

[0137] The umbra cone angle θ is calculated from the relationship between similar triangles:

[0138]

[0139] For the Earth, the calculated value of the umbra cone angle θ is approximately:

[0140]

[0141] Step A3: Calculate the distance L between the end of the umbra and the center of the earth U ;

[0142] The umbra is the area where the Earth completely blocks sunlight, extending along the Earth-Sun axis. The distance L from the end of the umbra to the center of the Earth isU Determined by the following formula:

[0143]

[0144] Substituting the values, we get the distance L between the end of the umbra and the center of the earth. U for:

[0145]

[0146] At this time, the conditions for the artificial celestial body to be in the umbra are:

[0147] d <L U and

[0148] Among them, r is the distance of the artificial celestial body from the center of the earth, that is, whether the artificial celestial body falls within the shadow cone when viewed from the center of the earth.

[0149] Step A4: Based on the coordinates of the artificial celestial body and the distance L between the end of the umbra and the center of the earth U , calculate and determine whether the artificial celestial body is in the umbra.

[0150] In this embodiment, given the geocentric rectangular coordinates (x, y, z) of the artificial celestial body, the calculation steps are as follows:

[0151] 1) Calculate the unit vector u in the Earth-Sun direction ES :

[0152]

[0153] 2) Calculate the projection d of the artificial celestial body along the Earth-Sun direction ‖ :

[0154] d ｜｜ =r·u ES

[0155] Where r = (x, y, z) is the geocentric position vector of the artificial celestial body.

[0156] 3) Calculate the shadow cone radius R shadow :

[0157]

[0158] 4) Determine whether the artificial celestial body is in the umbra:

[0159] If d ｜｜ <L U and Then the artificial celestial body is located in the umbra.

[0160] Sun / Moon avoidance constraint: To exclude artificial celestial bodies from having an angular distance from the Sun or Moon that is less than the angular distance threshold θ min The specific formula is the same as the sky light and ground shadow constraints of the ground-based platform.

[0161] In step S22, the observation priority of artificial celestial bodies includes magnitude priority and geometric configuration priority, wherein the magnitude priority means that observable targets with high brightness (low magnitude) are given priority, and the geometric configuration priority means selecting a combination of observable targets that minimizes the positioning error so that the geometric precision factor (DOP) is optimal.

[0162] Therefore, the observation priorities of artificial celestial bodies are sorted according to a fixed rule, including:

[0163] Step S221: Select the brightest m targets from the set of observable targets;

[0164] Step S222: Select n targets from the m targets and calculate the position dilution of precision (PDOP);

[0165] Step S223: select n targets with the smallest position precision dilution values ​​as the artificial celestial bodies to be observed.

[0166] When observing multiple artificial astronomical objects, geometric Dilution of Precision (DOP) is used to assess the impact of the observation geometry on positioning errors. DOP includes Geometric Dilution of Precision (GDOP), Position Dilution of Precision (PDOP), Horizontal Dilution of Precision (HDOP), Vertical Dilution of Precision (VDOP), and Time Dilution of Precision (TDOP).

[0167] The calculation of the geometric dilution of precision (DOP) is typically based on the geometric measurement matrix (Gmatrix) and involves error propagation through the observation equation. The following is a detailed method for DOP calculation.

[0168] 1) Basic principles of DOP calculation:

[0169] The DOP value is used to measure the impact of the geometric conditions of the distribution of artificial celestial bodies on the position error. The basic formula of the geometric measurement matrix G is as follows:

[0170]

[0171] Among them, (x r ,y r ,z r ) is the platform position, (xi ,y i , z i) is the position of the i-th artificial celestial body, It is the distance from the platform to the i-th artificial celestial body. The last column of the collective measurement matrix G is 1, corresponding to the clock error bias term.

[0172] Calculate the covariance matrix Q based on the geometric measurement matrix G:

[0173] Q=(G T G) -1

[0174] Extract the diagonal elements from the Q matrix and calculate different types of DOP.

[0175] 2. The calculation formula for the main DOP indicators is as follows:

[0176] The DOP value is calculated as follows:

[0177] Geometric Dilution of Precision (GDOP):

[0178]

[0179] Position precision factor (PDOP, PositionDOP):

[0180]

[0181] Horizontal Dilution of Precision (HDOP, HorizontalDOP):

[0182]

[0183] Vertical Dilution of Precision (VDOP):

[0184]

[0185] Time Dilution of Precision (TDOP, TimeDOP):

[0186]

[0187] Among them, Q ij is the element in the i-th row and j-th column of the Q matrix.

[0188] The DOP value is used to evaluate the geometric configuration of artificial celestial bodies. GDOP reflects the overall error impact, PDOP affects positioning accuracy, and HDOP and VDOP are applicable to different application scenarios. A low DOP value indicates a good geometric distribution of artificial celestial bodies, which helps improve positioning accuracy.

[0189] Therefore, the calculation steps of position dilution of precision (PDOP) are as follows:

[0190] 1) Get the coordinates of the artificial celestial body (x i ,y i ,z i ) and the platform coordinates (x r ,y r ,z r ).

[0191] Coordinates of artificial celestial bodies (x i ,y i ,z i ) is usually calculated from the ephemeris).

[0192] 2) Calculate the collective measurement matrix G.

[0193] The set measurement matrix G is calculated according to the above formula.

[0194] 3) Calculate the covariance matrix Q based on the geometric measurement matrix G:

[0195] Q=(G T G) -1

[0196] 4) Extract the position dilution of precision (PDOP) value:

[0197] PDOP is:

[0198]

[0199] Among them, Q ij is the element in the i-th row and j-th column of the Q matrix.

[0200] Step S3: Execute the observation task, that is, drive the two-dimensional turntable of the optical telescope to turn and collect observation images according to the observation task list, and use the observation images and their timestamps as observation data.

[0201] The step S3 specifically includes:

[0202] Step S31: Target pointing, that is, driving the two-dimensional turntable of the optical telescope to rotate to the direction of the artificial celestial body to be observed according to the observation task list and the current posture of the platform;

[0203] Step S32: Utilize the imaging device of the optical telescope to collect observation images.

[0204] Step S31 specifically includes:

[0205] Step S311: Obtain the current posture (φ, θ, ψ) of the platform from the initial conditions, obtain the celestial coordinates (α, δ) of the artificial celestial body to be observed from the observation task list, and convert them into the observation direction of the artificial celestial body to be observed in the platform coordinate system;

[0206] Among them, the platform coordinate system (X c ,Y c ,Z c ) Take the imaging device of the platform as the origin and the forward direction of the optical axis of the two-dimensional turntable as Z c Axis, upward direction is Y c Axis (opposite to the v axis of the image coordinate system); X c Axis and Y c Axis, X c The axes are orthogonal, usually pointing to the right (coincident with the u-axis).

[0207] The observation direction of the artificial celestial body to be observed in the platform coordinate system (x c ,y c ,z c )for:

[0208]

[0209] Among them, R φ ,R θ ,R ψ are the attitude rotation matrices of the three axes around the current attitude of the platform (φ, θ, ψ), and α and δ are the celestial coordinates of the artificial celestial body to be observed.

[0210] Step S312: Determine the pitch angle and azimuth angle of the two-dimensional turntable of the optical telescope according to the observation direction of the artificial celestial body to be observed in the platform coordinate system, and send instructions to the two-dimensional turntable of the optical telescope to drive the two-dimensional turntable of the optical telescope to turn.

[0211] The elevation angle El and azimuth angle Az of the two-dimensional turntable of the optical telescope are:

[0212] Az=arctan2(y c ,x c )

[0213] El=arcsin(z c )

[0214] Among them, (x c ,y c ,z c ) is the observation direction of the artificial celestial body to be observed in the platform coordinate system.

[0215] In step S32, a suitable image acquisition mode is selected according to the dynamic characteristics of the artificial celestial body to be observed and the platform capabilities, and the exposure parameters are adjusted to complete the observation image acquisition.

[0216] In this embodiment, the image acquisition modes include a short-exposure staring mode and a tracking shooting mode.

[0217] The short exposure staring mode is suitable for scenes where the target position is stable (i.e., scenes where the movement rate of the artificial celestial body to be observed is less than 1 pixel per second). In the short exposure staring mode, the observation image is obtained by shooting a single short exposure. The exposure time T in the exposure parameters is exp The selection must meet the following requirements:

[0218]

[0219] The unit of pixel resolution is arc seconds per pixel, and the target motion rate refers to the motion rate of the artificial celestial body to be observed, which is calculated from the ephemeris, and the unit of motion rate is arc seconds per second.

[0220] Tracking mode is suitable for scenarios where the target object's motion rate is greater than one pixel per second. In Tracking mode, the telescope uses the predicted trajectory of the target (i.e., the target object) as a reference, driving the 2D turntable for synchronous tracking. The telescope's movement rate is equal to the target object's motion rate, achieving synchronous tracking.

[0221] The predicted trajectory of the target is:

[0222]

[0223] Among them, (α0, δ0) is the current coordinate of the target, is the target's movement rate, and Δt is the exposure time, which ranges from 0.1 to 2 seconds.

[0224] Step S4: Perform astronomical positioning, that is, match the stars in the observed image with the star catalog to calculate the observed celestial coordinates of each star. The observed celestial coordinates of the star match the pixel coordinates of the observed image, including the precise right ascension α and declination δ.

[0225] The step S4 specifically includes:

[0226] Step S41: extracting the pixel coordinates (x, y) of the star in the observed image.

[0227] The star images extracted here include both stars and target artificial celestial bodies.

[0228] Step S41 may further include: after extracting the pixel coordinates (x, y) of the constellations, screening constellations with a high signal-to-noise ratio (ie, extracting constellations with a signal-to-noise ratio greater than 3).

[0229] Step S42: performing preliminary coordinate conversion; that is, establishing a preliminary mapping relationship between the observed image coordinates and the celestial coordinates according to the platform posture and imaging parameters when the observed image was collected;

[0230] The step S42 may further include: determining a search range of celestial coordinates according to a preliminary mapping relationship between image coordinates and celestial coordinates and a coordinate range of the observed image; and screening candidate stars within the search range of celestial coordinates from the star catalog.

[0231] Determining the celestial coordinate search range specifically includes: taking the observed image coordinate pixel coordinate value from (0,0) to (x 最大 ,y 最大 ) to preliminarily map the search range of the celestial coordinates (α, δ).

[0232] Step S43: performing star catalog matching; that is, matching the celestial coordinates of each candidate star with the preliminary celestial coordinates of the constellation by calculating the angular distance, wherein the preliminary celestial coordinates of the constellation are obtained based on the preliminary mapping relationship from the observed image coordinates to the celestial coordinates;

[0233] Among them, the angular distance θ between the candidate star and the constellation is:

[0234] cosθ=sinδ1sinδ2+cosδ1cosδ2cos(α1-α2),

[0235] Among them, (α1, δ1) are the preliminary celestial coordinates of the star, and (α2, δ2) are the celestial coordinates of the candidate star.

[0236] Therefore, when calculating the angular distance, it is necessary to convert the pixel coordinates (x, y) of the star image into the celestial coordinates (α1, δ1) of the star image based on the preliminary mapping relationship between the observed image coordinates and the celestial coordinates.

[0237] If the angular distance θ is less than the matching threshold (e.g., 5″), the candidate star is considered to be successfully matched with the constellation.

[0238] Step S44: performing coordinate fitting; that is, correcting the conversion parameters A0, A1, A2, B0, B1, B2 according to the matching results, and fitting to obtain a conversion formula from the coordinates of the observed image to the celestial coordinates, which serves as an accurate mapping relationship from the coordinates of the observed image to the celestial coordinates;

[0239] The conversion formula from the observed image coordinates to the celestial coordinates is obtained based on polynomial or linear model fitting. The conversion formula from the observed image coordinates to the celestial coordinates is:

[0240] α=A0+A1x+A2y+…

[0241] δ=B0+B1x+B2y+…

[0242] Among them, x and y are the pixel coordinates of the matching star, α and δ are the celestial coordinates of the matching star, A0, A1, A2 are the right ascension model fitting coefficients, and B0, B1, B2 are the declination model fitting coefficients.

[0243] Step S45: Determine the observed celestial coordinates (including right ascension α and declination δ) of all stars in the observed image based on the precise mapping relationship between the coordinates of the observed image and the celestial coordinates.

[0244] In step S42, the preliminary mapping relationship between the coordinates of the observed image and the celestial coordinates is obtained by:

[0245] The rotation matrix from the image coordinate system to the celestial coordinate system requires consideration of several key coordinate transformation steps. This transformation involves the platform coordinate system, the astronomical inertial coordinate system (ICRF), the horizontal coordinate system, and more. Generally, it can be broken down into the following key steps:

[0246] Step S421: Define the image coordinate system (u, v), the platform coordinate system (X c ,Y c ,Z c ), celestial coordinate system (α, δ);

[0247] The image coordinate system (u, v) (i.e., (x, y)) takes the center of the image as its origin, the rightward direction as the u-axis, and the downward direction as the v-axis. The focal length f determines the projection relationship from the image plane to the plane coordinate system.

[0248] Platform coordinate system (X c ,Y c ,Z c ) Take the imaging device of the platform as the origin and the forward direction of the optical axis of the two-dimensional turntable as Z c Axis, upward direction is Y c Axis (opposite to the v axis of the image coordinate system); X c Axis and Y c Axis, X c The axes are orthogonal, usually pointing to the right (coincident with the u-axis).

[0249] The celestial coordinate system (α, δ) is represented by α, which is the right ascension (RA) and δ, which is the declination (Dec). This is the final target coordinate system and is consistent with the inertial reference coordinate system.

[0250] Step S422: Obtain the pixel coordinates (u, v) of the image coordinate system to the coordinates (X c ,Y c ,Z c ) is:

[0251] X c =(u-u0)·s x

[0252] Y c =(v0-v)·s y

[0253] Z c =f

[0254] Among them, (u0, v0) is the coordinate of the center of the observed image (optical axis direction), s x ,s y is the pixel size, and f is the focal length of the imaging device.

[0255] The coordinates of the platform coordinate system (X c ,Y c ,Z c ) needs to be normalized, the normalized platform coordinate system coordinate r c for:

[0256]

[0257] Step S423: Determine the posture matrix R according to the posture of the imaging device cam , according to the posture matrix R cam Get the coordinates of the platform coordinate system (X c ,Y c ,Z c ) to the coordinates (α, δ) of the celestial coordinate system;

[0258] Specifically, according to the posture matrix R cam , first obtain the coordinates of the platform coordinate system (X c ,Y c ,Z c ) to the horizontal coordinates, and then obtain the relationship between the horizontal coordinates and the coordinates of the celestial coordinate system (α, δ).

[0259] Horizontal coordinate r hor for:

[0260] r hor =R cam ·r c

[0261] Among them, r cis the normalized platform coordinate system coordinate, R cam is the posture matrix.

[0262] Posture matrix R cam Determined by the azimuth, elevation, and roll angles of the imaging device:

[0263] R cam =R z (Az)R x (El)R z (Roll)

[0264] Among them, R z (Az) is the attitude rotation matrix around the axis of the platform's azimuth angle φ (i.e., around the Z axis), R x (El) is the attitude rotation matrix around the platform's pitch angle θ axis (i.e., around the X axis), R z (Roll) is the attitude rotation matrix around the axis of the platform's roll angle ψ (i.e., around the Z axis).

[0265]

[0266]

[0267]

[0268] Among them, Az, EL, and Roll are azimuth, pitch, and roll angles respectively.

[0269] Horizontal coordinate r hor Expressed as (Az, El), Az and El are the azimuth and elevation angles. The conversion of horizontal coordinates to celestial coordinates (α, δ) requires the use of the geographic coordinates of the observation site, including: geographic latitude LAT and local hour angle (LHA).

[0270] The local hour angle LHA is:

[0271] LHA=GST+λ-α

[0272] Where λ is longitude, GST is Greenwich Mean Sidereal Time, and α is the right ascension of the celestial coordinates.

[0273] Celestial coordinate system transformation matrix R hor2eq for:

[0274]

[0275] The unit vector r of the celestial coordinates eq for:

[0276] r eq =Rhor2eq ·r hor

[0277] Therefore, the celestial coordinates (α, δ) are:

[0278] δ=sin -1 (r eq,z )

[0279]

[0280] Among them, r eq,x 、r eq,y 、r eq,z is the unit vector r in celestial coordinates eq The x-axis, y-axis, and z-axis components of .

[0281] Step S424: Comprehensively obtain a preliminary mapping relationship between the coordinates of the observed image and the celestial coordinates.

[0282] Among them, the coordinates of the platform coordinate system (X c ,Y c ,Z c ) to the unit vector r of the celestial coordinates eq The relationship is:

[0283] r eq =R img2eq ·r c

[0284] Among them, r c is the coordinate of the normalized platform coordinate system, R img2eq is the complete rotation matrix from the platform coordinate system to the unit vector of the celestial coordinate system, r eq is the unit vector of celestial coordinates.

[0285] The complete rotation matrix R of the unit vector from the platform coordinate system to the celestial coordinate system img2eq for:

[0286] R img2eq =R hor2eq ·R cam

[0287]

[0288] This matrix is ​​used to transform the coordinates (X c ,Y c ,Z c ) is projected into the celestial coordinate system, and the celestial coordinates (α, δ) are finally calculated.

[0289] Step S5: Extract the moving target as an artificial celestial object by observing the star image changes in multiple frames, and obtain the motion trajectory of the artificial celestial object. The motion trajectory of the artificial celestial object includes the observation time t and the observed celestial coordinates (α, δ), which are used for subsequent solution.

[0290] Among them, after extracting the moving target, it also includes combining the ephemeris of the artificial celestial body to perform theoretical position verification to confirm whether it is an artificial celestial body.

[0291] The step S5 is mainly based on the following principles:

[0292] 1) The positions of stars remain basically unchanged in multiple frames of observation images.

[0293] 2) Artificial celestial bodies will show position changes in multiple frames of observation images due to orbital motion.

[0294] 3) The ephemeris of artificial celestial bodies provides the estimated trajectory of artificial celestial bodies, which can be used to verify whether the extracted moving target is an artificial celestial body.

[0295] Step S5 specifically includes:

[0296] Step S51: multi-frame correlation; that is, comparing the position changes of the stars in the multi-frame observation images to screen out the moving targets;

[0297] In step S51, the position of the constellation in the i-th frame is given as (x i ,y i ), the displacement Δ of the constellations between the i-th frame and the i+1-th frame is:

[0298]

[0299] For stars, the displacement of the star image between the i-th frame and the i+1-th frame is Δ≈0; for artificial celestial bodies, the displacement of the star image between the i-th frame and the i+1-th frame is Δ>Δ threshold , where Δ threshold is the motion determination threshold.

[0300] Step S52: Calculate the theoretical celestial coordinates (α theo ,δ theo );

[0301] Among them, according to the ephemeris data and observation time T i , interpolation is performed to obtain the theoretical celestial coordinates (α theo ,δ theo ):

[0302] (α theo ,δ theo )=f interp(ephemeris,T i )

[0303] Among them, ephemeris is the ephemeris data of artificial celestial bodies, T i is the observation time, f interp It is an interpolation calculation function that interpolates the ephemeris data to the specified observation time.

[0304] Step S53: Matching and verification; that is, matching the celestial coordinates (α, δ) of the multi-frame observation of the moving target with the theoretical celestial coordinates (α theo ,δ theo ) matches by calculating the angular distance to confirm whether it is an artificial celestial body.

[0305] The celestial coordinates (α, δ) of the multi-frame observation of the moving target are obtained based on the precise mapping relationship between the pixel coordinates of the moving target in the observation image and the coordinates of the observation image to the celestial coordinates.

[0306] The celestial coordinates (α, δ) of the multi-frame observation of the moving target and the theoretical celestial coordinates (α theo ,δ theo ) is:

[0307] cosθ=sinδsinδ theo +cosδcosδ theo cos(α-α theo )

[0308] Among them, for each frame image, the angular distance is less than the angular distance threshold (that is, θ≤θ threshold ), then the moving target is confirmed to be an artificial celestial body.

[0309] Step S6: Calculate the platform position, including: using the observed celestial coordinates (α, δ) of the artificial celestial body and the theoretical position (X i ,Y i ,Z i ) Establish an observation equation; solve the observation equation to obtain the three-dimensional position (X, Y, Z) of the platform;

[0310] The step S6 specifically includes:

[0311] Step S61: constructing the observation equation; that is, based on the observation of two or more artificial celestial bodies, using the observed celestial coordinates (α, δ) of the artificial celestial bodies and the theoretical positions (X i ,Y i ,Z i )Establish the observation equation.

[0312] In step S61, the vector r of the artificial celestial body in the platform coordinates i for:

[0313]

[0314] Among them, (X, Y, Z) is the three-dimensional position of the platform, (X i ,Y i ,Z i ) is the theoretical position of the artificial celestial body. i ,Y i ,Z i ) through the ephemeris of the artificial celestial body. It should be noted that the three-dimensional position (X, Y, Z) of the platform and the theoretical position of the artificial celestial body are both in the Earth-fixed coordinate system.

[0315] The direction cosines of the observation direction of the i-th artificial celestial body (l i ,m i ,n i )for:

[0316] l i =cosδ i cosα i ,m i =cosδ i sinα i ,n i =sinδ i

[0317] Among them, (α i ,δ i ) is the observed celestial coordinate of the i-th artificial celestial body, α i is the observed right ascension of the i-th artificial celestial body, δ i is the observed declination of the i-th artificial celestial body.

[0318] Moreover, the direction cosines of the observation direction of the i-th artificial celestial body (l i ,m i ,n i ) satisfies the normalization condition:

[0319]

[0320] Since the observation direction of the artificial celestial body is consistent with the direction from the platform to the artificial celestial body, the position relationship equation of the i-th artificial celestial body is:

[0321]

[0322] R i =||r i || Expand and get the observation equation:

[0323] X+l i R i =Xi

[0324] Y+m i R i =Y i

[0325] Z+n i R i =Z i

[0326]

[0327] Among them, R i is the distance between the ith artificial object and the platform, (X i ,Y i ,Z i ) is the theoretical position of the i-th artificial celestial body, (X, Y, Z) is the position coordinate of the platform, is the unknown quantity, (l i ,m i ,n i ) is the direction cosine of the observation direction of the i-th artificial celestial body.

[0328] Step S62: least squares solution; that is, according to the observation equation, the three-dimensional position (X, Y, Z) of the platform is obtained by least squares solution.

[0329] The core idea of ​​step S6 is to use multi-target observation to perform parallax positioning and to use the geometric distribution of multiple targets (i.e., multiple artificial celestial bodies) to improve the geometric accuracy of the observation solution.

[0330] The step S62 specifically includes:

[0331] Step S621: Obtaining the initial value of the three-dimensional position (X0, Y0, Z0) according to the initial conditions of the platform;

[0332] Step S622: Using the initial value of the three-dimensional position (X0, Y0, Z0) as the initial solution of the observation equation, the observation equation is iteratively solved until the residual vector meets the accuracy requirements. At this time, the three-dimensional position (X, Y, Z) of the platform is obtained by solution.

[0333] In the least squares method, the residual vector r is defined as:

[0334]

[0335] The goal of the least squares method is min||r|| 2 .

[0336] In this embodiment, since the three-dimensional position (X, Y, Z) of the platform is an earth-fixed coordinate system and the platform is a ground-based platform, the three-dimensional position (X, Y, Z) of the platform is constant over time.

[0337] In other embodiments, natural celestial bodies (such as planets, the moon, and the sun) with ephemeris (i.e., celestial positions that change over time) can be used instead of artificial celestial bodies with ephemeris as observation targets. Specifically, the motion of natural celestial bodies is deterministic, and observation equations can be established using the orbital data and observed positions in the ephemeris of natural celestial bodies to solve the three-dimensional position of the platform. This can also be combined with star catalogs for astronomical positioning calibration to enhance positioning accuracy.

[0338] The advantages of this approach are that natural celestial bodies are bright and easy to observe, making them suitable for use in sparse star catalogs. The disadvantages are that the number of targets is limited, which may lead to insufficient observation opportunities, and the distribution of targets is restricted to a certain area.

[0339] In other embodiments, specific reflective objects or markers fixed on the ground can be used instead of artificial celestial bodies with ephemeris as observation targets. Specifically, by placing objects with reflective or optical marking properties (such as ground reflective balls) in a specific area, navigation can be achieved by observing the relative positions of these ground targets using optical imaging equipment instead of optical telescopes.

[0340] The advantage of this approach is that it is suitable for near-Earth platforms, such as drones or ships. The disadvantage is that it is limited to a specific deployment area and cannot be applied to deep space or long-distance scenarios.

[0341] In addition, the astronomical positioning and navigation method can be further integrated with other measurement methods, such as LiDAR (Light Detection and Ranging) observations, radio signal ranging, etc., to obtain the position of the observed target, thereby reducing reliance on angular observations of stars or artificial celestial bodies. The advantage of integrating LiDAR observations is that it can provide high-precision positioning results when the target is relatively close. However, its disadvantages are its limited scope of application and the high cost of laser equipment. The advantage of integrating radio signal ranging is that it is applicable to targets with radio communication capabilities (such as orbiting satellites). However, its disadvantage is that it depends on signal quality and is easily affected by interference.

[0342] Furthermore, in resource-constrained environments (e.g., small drones), astronomical positioning and navigation methods use a simplified single observation target for observation, relying on a single artificial celestial body for rough navigation. This approach has the advantage of being suitable for small platforms and having low system complexity.

[0343] Furthermore, in the astronomical positioning and navigation system employed in the described astronomical positioning and navigation method, the optical telescope can be replaced with a catadioptric optical system instead of a refractive one, optimizing the size and imaging quality of the optical device. The astronomical positioning and navigation system can also incorporate inertial sensors (such as gyroscopes) to enhance the real-time performance and anti-interference capabilities of navigation solutions through data fusion.

[0344] The astronomical positioning and navigation method of the present invention combines astronomical positioning (orientation) of stars with observational positioning of artificial celestial bodies. Through multi-target collaborative observation, it achieves the three-dimensional position calculation of the platform, overcoming the limitation of traditional stellar navigation that can only determine orientation but not calculate position. Specifically, the astronomical positioning and navigation method of the present invention uses star catalog matching to complete the preliminary determination of the platform's attitude, and then uses the ephemeris information of artificial celestial bodies to establish observation equations to solve the platform's absolute position.

[0345] At the same time, the present invention uses autonomous timekeeping technology and optical observation to achieve fully autonomous navigation, does not require external signal support, and is adaptable to environments where GNSS signals are interfered with, deceived or denied, or where the coverage of GNSS signals is limited. It solves the problem that existing navigation technologies are difficult to operate normally and provide reliable navigation services in environments where GNSS signals are interfered with, deceived or completely denied, or where the coverage of GNSS signals is limited, such as scenarios outside the Earth's orbit or deep space exploration, military battlefields or strategic protection areas, and other special scenarios.

[0346] In addition, the present invention comprehensively utilizes the observation data of stars and artificial celestial bodies, significantly improving the adaptability of the navigation system in complex and changeable scenarios, supporting multi-scenario applications of ground-based, sea-based, air-based and space-based platforms, and meeting the needs of various complex tasks.

[0347] In addition, the present invention uses multi-frame correlation technology to separate moving targets from dynamic backgrounds and extract the star images of artificial celestial bodies; it utilizes the trajectory characteristics of the moving targets (such as angular distance changes and position correlation) to accurately distinguish between stars and artificial celestial bodies, thereby reducing the error rate.

[0348] When using star catalog matching to complete the preliminary determination of the platform's attitude, the present invention establishes a conversion model between image coordinates and celestial coordinates based on the optical characteristics of the observation equipment and the initial attitude of the platform; then, through star catalog matching, errors are corrected and the mapping relationship between the image and the celestial sphere is optimized, which greatly reduces the amount of calculation and speeds up the calculation process.

[0349] In summary, the astronomical positioning and navigation method of the present invention completes the attitude and position calculation of the platform by integrating the optical observation data of stars and artificial celestial bodies, and realizes the autonomous navigation and positioning of the platform in the absence of GNSS signals.

[0350] Among them, star observation is used to achieve astronomical positioning (attitude solution) through star catalog matching, providing a directional reference for the relative position of the platform.

[0351] Artificial celestial body observation is used to use the orbital data of known ephemeris to extract the right ascension and declination of artificial celestial bodies through optical observation, and combine the multi-target observation equation to solve the three-dimensional absolute position of the platform.

[0352] Multi-frame correlation is used to utilize the position changes of targets in multi-frame images to separate dynamic targets and improve the observation accuracy of artificial celestial bodies.

[0353] The time base is used to ensure the time synchronization of image data through autonomous timekeeping technology, providing a guarantee for high-precision position solution.

[0354] The above description is merely a preferred embodiment of the present invention and is not intended to limit the scope of the present invention. Various modifications are possible. Any simple, equivalent changes and modifications made in accordance with the claims and description of the present invention are within the scope of protection of the patent claims. Anything not fully described in this invention is conventional technology.

Claims

1. An astronomical positioning and navigation method based on optical observation, characterized in that: include: Step S1: Input the position and attitude of the platform as initial conditions to provide a high-precision reference time for the timestamp; Step S2: According to the initial conditions of the platform and the ephemeris of the observation target, the observation targets to be observed are screened and sorted according to a fixed rule to form an observation task list; Step S3: driving the two-dimensional turntable of the optical telescope to turn and collect observation images according to the observation task list, and using the observation images and their timestamps as observation data; Step S4: matching the stars in the observed image with the star catalog to calculate the observed celestial coordinates of each star; Step S5: extract the moving target as the observation target by the star image changes in the multi-frame observation image, and obtain the motion trajectory of the observation target. The motion trajectory of the observation target includes the observation time , observed celestial coordinates ; Step S6: Calculate the platform position, including: using the observed celestial coordinates of the observed target Theoretical position relative to the observed target Establish observation equations; solve the observation equations to obtain the three-dimensional position of the platform ; The step S2 specifically includes: Step S21: Determine the constraints according to the platform type, and then screen all observation targets that meet the constraints as observable targets; Step S22: determining the observation priority of the observable targets, and sorting them according to a fixed rule based on the observation priority; Step S23: generating an observation task list according to the sorting result, wherein the observation task list includes an observation window and a pointing parameter of each observation target to be observed; The step S4 specifically includes: Step S41: extracting pixel coordinates of stars in the observed image; Step S42: performing preliminary coordinate conversion; that is, establishing a preliminary mapping relationship between the observed image coordinates and the celestial coordinates according to the platform posture and imaging parameters when the observed image was collected; Step S43: matching the celestial coordinates of each candidate star with the preliminary celestial coordinates of the star image by calculating the angular distance, wherein the preliminary celestial coordinates of the star image are obtained based on the preliminary mapping relationship from the observed image coordinates to the celestial coordinates; Step S44: Correcting the conversion parameters according to the matching results, and fitting the conversion formula from the coordinates of the observed image to the celestial coordinates, which serves as the precise mapping relationship from the coordinates of the observed image to the celestial coordinates; Step S45: Determine the observed celestial coordinates of all the stars in the observed image based on the precise mapping relationship between the coordinates of the observed image and the celestial coordinates.

2. The astronomical positioning and navigation method based on optical observation according to claim 1, characterized in that: The observation targets include artificial celestial bodies, natural celestial bodies with ephemeris, or specific reflective objects or landmarks fixed on the ground.

3. The astronomical positioning and navigation method based on optical observation according to claim 1, characterized in that: In step S21, when the platform type is a ground-based platform, the constraints include a minimum elevation angle constraint and a sky light and earth shadow constraint for excluding observation targets whose angular distance from the sun is less than an angular distance threshold; when the platform type is a space-based platform, the constraints include an earth shadow constraint for excluding observation targets in the Earth's umbra and a sun / moon avoidance constraint for excluding observation targets whose angular distance from the sun or moon is less than an angular distance threshold; and / or In step S22, the observation priority of the observed target includes magnitude priority and geometric configuration priority; The observation targets are sorted according to a fixed rule based on their observation priority, including: Step S221: Select the brightest m targets from the set of observable targets; Step S222: Select n targets from the m targets and calculate the value of the position precision dilution; Step S223: select n targets with the smallest position precision factor as the targets to be observed.

4. The astronomical positioning and navigation method based on optical observation according to claim 1, characterized in that: The step S3 specifically includes: Step S31: driving the two-dimensional turntable of the optical telescope to rotate to the direction of the observation target to be observed according to the observation task list and the current posture of the platform; Step S32: Utilize the imaging device of the optical telescope to collect observation images.

5. The astronomical positioning and navigation method based on optical observation according to claim 4, characterized in that: The step S31 specifically includes: Step S311: obtaining the current attitude of the platform from the initial conditions, obtaining the celestial coordinates of the target to be observed from the observation task list, and converting them into the observation direction of the target to be observed in the platform coordinate system; Step S312: determining the pitch angle and azimuth angle of the two-dimensional turntable of the optical telescope according to the observation direction of the observation target to be observed in the platform coordinate system, and sending a command to the two-dimensional turntable of the optical telescope to drive the two-dimensional turntable of the optical telescope to turn; and / or In step S32, a suitable image acquisition mode is selected according to the dynamic characteristics of the target to be observed and the platform capabilities, and exposure parameters are adjusted to complete the observation image acquisition; the image acquisition mode includes a short exposure staring mode and a tracking shooting mode.

6. The astronomical positioning and navigation method based on optical observation according to claim 1, characterized in that: The step S4 satisfies at least one of the following: a1) Step S41 also includes: extracting the pixel coordinates of the constellation Finally, screen the stars with high signal-to-noise ratio; a2) Step S42 further includes: determining a search range for celestial coordinates based on a preliminary mapping relationship between image coordinates and celestial coordinates and a coordinate range of the observed image; and selecting candidate stars within the search range for celestial coordinates from a star catalog; a3) In step S43, the angular distance θ between the candidate star and the constellation is: ， in, is the celestial coordinate of the star, is the preliminary celestial coordinate of the candidate star; a4) in step S44, obtaining a conversion formula from the coordinates of the observed image to the celestial coordinates based on polynomial or linear model fitting; a5) In step S42, the preliminary mapping relationship between the coordinates of the observed image and the celestial coordinates is obtained by: Step S421: Define the image coordinate system , platform coordinate system , celestial coordinate system ; Step S422: Obtain pixel coordinates in the image coordinate system Coordinates to the platform coordinate system The relationship between Step S423: Determine the posture matrix based on the posture of the imaging device, and obtain the coordinates of the platform coordinate system based on the posture matrix Coordinates to the celestial coordinate system The relationship between Step S424: Comprehensively obtain a preliminary mapping relationship between the coordinates of the observed image and the celestial coordinates.

7. The astronomical positioning and navigation method based on optical observation according to claim 1, characterized in that: The step S5 specifically includes: Step S51: comparing the position changes of the stars in multiple frames of observation images to screen out moving targets; Step S52: Calculate the theoretical celestial coordinates of each frame of the observed target based on the ephemeris and observation time of the observed target. ; Step S53: The celestial coordinates of the multi-frame observation of the moving target and theoretical celestial coordinates Matching is performed by calculating the angular distance to confirm whether it is the observed target.

8. The astronomical positioning and navigation method based on optical observation according to claim 1, characterized in that: The step S6 specifically includes: Step S61: Based on the two or more observed targets, use the observed celestial coordinates of the observed targets Theoretical position relative to the observed target Establish observation equations; Step S62: According to the observation equation, the three-dimensional position of the platform is obtained by least squares solution. ; The step S62 specifically includes: Step S621: Obtain the initial value of the three-dimensional position based on the initial conditions of the platform ; Step S622: Using the initial value of the three-dimensional position is the initial solution of the observation equation, and the observation equation is solved iteratively until the residual vector meets the accuracy requirement. At this time, the three-dimensional position of the platform is obtained by solving .

Images