A method for predicting and avoiding space debris trajectories

Abstract

This invention relates to the field of spacecraft orbit control and space safety technology, and discloses a method for space debris orbit prediction and avoidance. The method includes: a ground-based computing center screening candidate targets and generating enhanced data packets; an onboard computer performing geometric feature screening based on real-time navigation data to generate an immediate list of high-risk targets; controlling star sensors to perform optical observations, and using shift superposition and Kalman filtering to calculate the relative orbital state of the optical measurements; selecting a high-confidence or conservative probability threshold based on the acquired optical measurement state, and generating an avoidance command when the collision probability exceeds the limit; the propulsion system responding to the command to execute the avoidance, verifying the effect by confirming the change in the semi-major axis, and performing orbit restoration as appropriate. This invention employs ground-space collaborative screening and shift superposition enhancement technology, solving the problems of high false alarm rate due to low-precision ephemeris and insufficient detection capability of onboard sensors for faint targets, thus improving the accuracy of avoidance decisions and the reliability of execution.

Description

Technical Field

[0001] This invention relates to the field of spacecraft orbit control and space safety technology, specifically a method for predicting and avoiding space debris orbits. Background Technology

[0002] Implementing proactive collision avoidance maneuvers has become a means of ensuring the survivability of spacecraft. Current space collision early warning systems mainly rely on space target cataloging data provided by ground-based surveillance networks. Ground computing centers perform orbit extrapolation and collision probability calculations on all targets and send early warning information to spacecraft when risks are detected.

[0003] However, relying solely on ground-based telemetry and control systems for collision warning has limitations. Due to limited ground-based observation resources and the vast number of space targets, the cataloging data is updated infrequently, and long-term prediction models based on biplane orbital elements accumulate significant errors over time. This uncertainty in orbital prediction can lead to deviations in collision probability calculations, easily resulting in high false alarm rates. This can cause spacecraft to perform unnecessary evasive maneuvers, consuming onboard fuel and disrupting routine missions.

[0004] To reduce reliance on ground-based data and improve early warning accuracy, autonomous observation using onboard sensors is becoming a development trend for spacecraft. However, space debris is typically small and lacks active light emission, resulting in weak reflections of sunlight. Existing onboard optical sensors (such as star sensors) primarily target the attitude of bright stars, but their limited aperture and sensitivity make it difficult to separate faint debris signals from background noise in a single frame image. Furthermore, the high-speed motion of targets relative to spacecraft produces a trailing effect in the image, reducing the signal-to-noise ratio and making it difficult for conventional optical detection methods to effectively capture small debris.

[0005] At the avoidance decision-making and execution level, existing methods typically use fixed probability thresholds to trigger maneuvers, failing to fully consider the impact of input data quality on probability calculation results. When the data error covariance is large, the probability density function distribution is sparse, leading to an underestimation of the calculated collision probability, thus ignoring the actual collision risk. Furthermore, existing avoidance strategies mostly employ open-loop control, meaning that after ground-based commands are sent, the spacecraft lacks a real-time autonomous verification mechanism for the maneuver's effectiveness. This makes it difficult to promptly correct the trajectory in case of thruster performance fluctuations or execution anomalies, and also hinders the accurate restoration to the nominal mission orbit after avoidance, impacting the long-term operational stability of the spacecraft. Summary of the Invention

[0006] To address the shortcomings of existing space debris monitoring and early warning systems, such as high false alarm rates due to outdated and inaccurate ground-based radar cataloging data, and the limitation of spacecraft-based resources making independent, all-weather monitoring of small and faint debris difficult, this invention provides a method for space debris trajectory prediction and avoidance. This method utilizes ground-based computing power to perform large-scale coarse screening and generate enhanced data containing physical characteristics. Combined with onboard real-time navigation and optical precision measurement technologies, it performs orbit determination and graded avoidance of high-risk targets, solving the false alarm problem under low-precision ephemeris data and the insufficient detection capability of onboard sensors for faint targets.

[0007] To achieve the above objectives, the present invention provides the following technical solution:

[0008] A method for predicting and avoiding space debris trajectories includes the following steps: A ground-based computing center selects candidate targets whose nominal rendezvous distance is less than a first-level distance threshold and whose collision probability density integral is non-zero, generates an enhanced data package containing the candidate targets' orbital data and covariance matrix, and uploads it; An onboard computer, in conjunction with real-time navigation data, performs geometric feature screening on the targets in the enhanced data package, eliminating targets whose minimum orbital intersection distance is greater than a physical safety threshold, whose radial envelopes are mutually exclusive, or whose time phase difference exceeds a dynamic window, generating an immediate high-risk target list; The onboard computer controls a star sensor to perform optical observations on the targets in the immediate high-risk target list, and outputs the photometric relative orbital state using shift superposition and Kalman filtering; The onboard computer selects a high-confidence probability threshold or a conservative probability threshold based on whether the photometric relative orbital state is obtained, and generates a maneuvering avoidance command when the calculated collision probability exceeds the determined probability threshold; The propulsion system responds to the maneuvering avoidance command to execute avoidance, verifies the effect by confirming the semi-major axis change, and performs orbit recovery as appropriate.

[0009] Preferably, the specific process of generating the enhanced data package containing orbital data and covariance matrix of candidate targets includes: the ground computing center uses the Earth orientation parameters provided by the International Earth Rotation Service to uniformly convert the orbital status of the accessed full-volume space target catalog data to a unified spatiotemporal reference based on the J2000 coordinate system; targets are classified according to their radar cross section size and orbital altitude distribution, and the corresponding empirical initial covariance matrix is ​​matched based on the residual statistical characteristics of historical observation data under the unified spatiotemporal reference; targets with nominal rendezvous distances less than the first-level distance threshold are retained, and the predicted covariance matrix of the spacecraft platform is combined with the empirical initial covariance matrix to form a merged covariance matrix; the collision probability density integral corresponding to the merged covariance matrix is ​​calculated using the probability density integral method, and targets with non-zero results and greater than the screening lower limit are judged as candidate targets to construct the enhanced data package; wherein, the screening lower limit is determined based on the preset minimum effective collision probability density integral value; the first-level distance threshold is determined based on the maximum error envelope of the SGP4 model within the prediction duration.

[0010] Preferably, the specific process of generating the immediate high-risk target list includes: converting real-time navigation data to the J2000 coordinate system by combining the current Greenwich Mean Time (GMT), and converting the Cartesian state vector of the spacecraft platform into instantaneous occult orbital elements; using the orbital elements of candidate targets in the enhanced data package and the instantaneous occult orbital elements, calculating the minimum orbital intersection distance using the orbital geometric distance minimization formula; if the minimum orbital intersection distance is less than the physical safety threshold, then verifying the perigee radius and apogee radius of the spacecraft platform and the candidate targets respectively by combining the radial safety margin, and determining the radial envelope relationship; for targets that satisfy the radial envelope relationship, calculating the time difference between its arrival at the closest point in space to the spacecraft platform as the time phase difference; if the absolute value of the time phase difference is less than the dynamic window determined by the dynamic time window calculation formula, then including the target in the immediate high-risk target list; wherein, the physical safety threshold is determined based on the sum of the upper limit of the positioning error of the global navigation satellite system receiver and the maximum lateral position error of the candidate target's double-row orbital element data.

[0011] Preferably, the specific process of controlling the star sensor to perform optical observation of targets in the immediate high-risk target list includes: calculating the solar phase angle and the angle between the target's line-of-sight vector and the Earth's edge to determine if the illumination background is acceptable; if the illumination background is acceptable, calculating the Earth's shadow state using a cylindrical projection model to exclude targets within the Earth's umbra; calculating the estimated apparent magnitude using the radar cross section estimate in the enhanced data packet, and determining whether the targets screened by the Earth's shadow state meet the physical observation conditions; if the physical observation conditions are met, generating an attitude maneuver command; and using the attitude maneuver command to control the star sensor's optical axis to align with the estimated target azimuth.

[0012] Preferably, in the process of calculating the relative orbital state of the optical sensor using shift superposition, a digital image shift superposition formula is used to generate a synthetic enhanced image. Specifically, this includes: controlling a star sensor to continuously acquire a set of original grayscale image sequences at a fixed frame rate; determining the shift amount based on the estimated angular velocity in the instantaneous high-risk target list; processing the original grayscale image sequences using the digital image shift superposition formula to generate a synthetic enhanced image; extracting the target centroid coordinates with a signal-to-noise ratio exceeding a detection threshold from the synthetic enhanced image, and converting them into azimuth and pitch angles in the inertial frame using the star sensor's inertial attitude data; wherein, the detection threshold is determined based on the minimum signal-to-noise ratio required to distinguish the target centroid from background noise.

[0013] Preferably, the specific process of using Kalman filtering to calculate and output the optical relative orbital state includes: using the relative orbital dynamics equation as the state transition equation, and constructing a measurement update equation using the azimuth and elevation angles; solving the measurement update equation by processing data from multiple epochs using an extended Kalman filter, updating the state covariance, and calculating the relative distance and relative velocity; when the state covariance converges to a preset accuracy range, outputting the optical relative orbital state of the target relative to the spacecraft platform based on the relative distance and relative velocity; wherein, the preset accuracy range is determined based on the position error convergence limit required to generate maneuver avoidance commands.

[0014] Preferably, the specific process of selecting a high-confidence probability threshold or a conservative probability threshold based on whether the optical relative orbital state is obtained includes: if the acquisition is successful, reading the optical relative orbital state and the precision covariance matrix and setting a high-confidence probability threshold; if the acquisition fails, reading the data in the enhanced data packet and setting a conservative probability threshold, and determining the calculation input data; using the calculation input data to extrapolate the orbital state to the nearest rendezvous time and establish a B-plane; projecting the position error covariance onto the B-plane and superimposing it to construct a combined covariance ellipse, while simultaneously calculating the B-plane miss vector of the target relative to the spacecraft platform; wherein, the high-confidence probability threshold is set as the upper limit of the probability to avoid frequent maneuvers; the conservative probability threshold is set as the lower limit of the probability, which is lower than the high-confidence probability threshold and is used to ensure a safety baseline.

[0015] Preferably, the specific process of generating a maneuver avoidance command when the calculated collision probability exceeds a predetermined probability threshold includes: using the combined covariance ellipse and the B-plane miss vector, calculating the collision probability using the collision probability density integral formula; if the collision probability exceeds the currently set high confidence probability threshold or conservative probability threshold, calculating the B-plane phase angle of the B-plane miss vector in the B-plane coordinate system; searching a preset strategy library according to the quadrant where the B-plane phase angle is located, determining along-track acceleration or along-track deceleration as the thrust direction; and combining a preset maneuver lead and the thrust direction to generate a maneuver avoidance command including ignition time, duration, and thrust direction.

[0016] Preferably, the specific process of verifying the effect by confirming the semi-major axis change includes: the propulsion system responding to the maneuvering avoidance command to generate thrust; the onboard computer using real-time data to calculate the instantaneous close orbital elements and calculate the actually observed semi-major axis change; the onboard computer using the semi-major axis change prediction formula to calculate the predicted semi-major axis change based on the thrust model; comparing the difference between the actually observed semi-major axis change and the predicted semi-major axis change based on the thrust model, and if the relative error is less than the execution monitoring threshold, the maneuver is determined to be successful; wherein, the execution monitoring threshold is determined based on the calibration error of the propulsion system and the navigation calculation residual.

[0017] Preferably, the specific process of selectively performing orbit recovery includes: monitoring the relative distance after completing the maneuver; generating an orbit recovery operation command when it is confirmed that the rendezvous point has been passed and the relative distance has increased; responding to the orbit recovery operation command, selecting the first perigee or apogee after passing the rendezvous point as the orbit recovery maneuver point; and performing a recovery maneuver of the same amplitude but in the opposite direction to the original thrust direction at the orbit recovery maneuver point according to the thrust direction determined when the maneuver evasion command was generated.

[0018] This invention provides a method for predicting and avoiding space debris trajectories. It has the following beneficial effects:

[0019] 1. This invention utilizes the collaborative processing of a ground computing center and an onboard computer to deploy the initial screening of all targets on the ground. High-performance ground computing power is used to complete the coarse screening based on covariance, and only high-risk candidate targets are uploaded to the spacecraft. The onboard computer uses real-time navigation data to calculate the minimum orbital intersection distance with geometric invariance and the dynamic time window, and immediately eliminates false alarm targets caused by the lag in ground ephemeris updates. This hierarchical screening architecture not only solves the problem of high false alarm rate caused by insufficient ground data accuracy, but also effectively reduces the occupancy rate of onboard computing resources.

[0020] 2. This invention utilizes a star sensor to acquire image sequences and combines them with a shift-overlay algorithm. It uses the velocity information of the target relative to background stars to perform pixel-level energy accumulation, extracting weak signals submerged in background noise. This method improves the signal-to-noise ratio through data processing without altering the star sensor's hardware structure, solving the problem of spacecraft struggling to effectively detect small, faint space debris using limited-aperture sensors in orbit, and enhancing the ability to detect non-cooperative, small targets.

[0021] 3. This invention establishes a hierarchical avoidance decision-making and execution closed-loop mechanism based on data source quality. It sets two probability thresholds, one high confidence and one conservative, for the success or failure of optical measurement. This reduces unnecessary maneuvers caused by data errors while ensuring that high-risk targets are not missed. At the same time, it verifies the maneuver execution effect by monitoring the semi-major axis change that is sensitive to the thrust along the track, and performs recovery operations in combination with the principle of orbital symmetry. This solves the problem of uncontrollable risks caused by relying solely on open-loop command execution for avoidance, and ensures the stability of the spacecraft mission orbit. Attached Figure Description

[0022] Figure 1 This is a schematic diagram of the system architecture and data flow for space debris trajectory prediction and avoidance according to an embodiment of the present invention;

[0023] Figure 2 This is a schematic diagram of a space debris trajectory prediction and avoidance method according to an embodiment of the present invention;

[0024] Figure 3 This is a comparison chart of simulation verification data in a typical intersection scenario according to an embodiment of the present invention.

[0025] Among them, 100 is the ground computing center; 101 is the telemetry, tracking and command communication link; 200 is the spacecraft platform; 201 is the onboard computer; 202 is the global navigation satellite system receiver; 203 is the star sensor; 204 is the propulsion system; 301 is the ground screening module; 302 is the geometric verification module; 303 is the optical precision measurement module; and 304 is the avoidance decision module. Detailed Implementation

[0026] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0027] See attached document Figure 1 This invention provides a method for predicting and avoiding space debris trajectories, which is executed by a collaborative processing system consisting of a ground computing center 100, a telemetry and control communication link 101, and a spacecraft platform 200.

[0028] Ground computing center 100 is equipped with a high-performance server cluster for accessing full-volume space target cataloging data and establishing a unified spatiotemporal reference based on the J2000 coordinate system. Spacecraft platform 200 carries an onboard computer 201, a global navigation satellite system receiver 202, a star sensor 203, and a propulsion system 204. The onboard computer 201 serves as the core processing unit, performing orbit calculations, image processing, and strategy generation. The global navigation satellite system receiver 202 provides real-time position and velocity data for spacecraft platform 200.

[0029] Star sensor 203 is an open optical sensor with a raw image data readout interface and programmable exposure control. In addition to outputting attitude data, star sensor 203 is configured to output a full-frame or windowed sequence of raw grayscale images in response to exposure control commands, for detecting weak signals from non-stellar targets. Propulsion system 204 is configured to generate thrust vectors in response to maneuver commands; its type may include chemical thrusters or electric propulsion systems.

[0030] The collaborative processing system includes a ground screening module 301 running at the ground computing center 100, and a geometry verification module 302, an optical precision measurement module 303, and an avoidance decision module 304 running within the onboard computer 201. The ground screening module 301 performs long-period orbit extrapolation and initial collision probability screening. The geometry verification module 302 uses real-time onboard data to screen for geometric invariant characteristics of the target. The optical precision measurement module 303 controls the star sensor 203 to perform target acquisition and precise orbit determination when physical observation conditions are met. The avoidance decision module 304 generates tiered avoidance strategies based on orbital data with different confidence levels.

[0031] See attached document Figure 2 This invention provides a method for predicting and avoiding space debris trajectories, comprising the following steps:

[0032] S1, the ground computing center 100 accesses the full amount of space target cataloging data through the ground screening module 301, uses the orbit prediction model to extrapolate the target orbit state to a preset future time window, calculates the nominal rendezvous distance and collision probability density integral between the target and the spacecraft platform 200, screens out candidate targets whose nominal rendezvous distance is less than the first-level distance threshold and whose collision probability density integral is non-zero, and generates an enhanced data package containing the candidate target's orbital elements, radar cross section estimate and initial covariance matrix;

[0033] S2, the onboard computer 201 receives the enhanced data packet and drives the geometry verification module 302 to combine the real-time position and velocity data provided by the global navigation satellite system receiver 202 to calculate the minimum orbital intersection distance, radial envelope relationship and time phase difference of arrival at the orbital intersection point between the spacecraft platform 200 and the candidate target. Targets with a minimum orbital intersection distance greater than the physical safety threshold, mutually exclusive radial envelopes or time phase difference exceeding the dynamic window are eliminated, and an immediate high-risk target list is generated.

[0034] S3, the optical precision measurement module 303 judges the solar phase angle, shadow state and estimated angular velocity of the targets in the real-time high-risk target list. When the physical observation conditions are met, it controls the star sensor 203 to perform attitude pointing and multi-frame image acquisition. It uses the shift superposition algorithm based on prior velocity guidance and the extended Kalman filter algorithm to calculate the state of the target relative to the spacecraft platform 200 and outputs the optical relative orbit state.

[0035] S4, the avoidance decision module 304 performs a graded judgment based on whether the relative orbital state of the optical measurement is obtained. When the acquisition is successful, a high confidence probability threshold is used. When the acquisition fails or is unobservable, the prior information in the enhanced data packet is used to calculate the minimum collision probability and a conservative probability threshold is used. When the collision probability exceeds the corresponding threshold, the preset strategy library is retrieved to generate a maneuver avoidance command that includes the ignition time, duration and thrust direction.

[0036] S5, the propulsion system 204 responds to the maneuver avoidance command to generate a thrust vector to avoid the risk of collision, and after the flyby rendezvous moment, verifies the avoidance effect by confirming the change in the semi-major axis, and performs the orbit recovery operation when the opportunity arises.

[0037] The technical implementation of each step will be explained in detail below, combining specific computational models and logical judgment conditions.

[0038] The initial screening and data generation steps for candidate targets based on ground-air collaboration are executed by the ground computing center 100. This step utilizes the high computing power resources of the ground to complete a coarse screening of all targets, providing concise prior data for the spacecraft platform 200. Specifically, it includes the following sub-steps:

[0039] S101, full cataloging data access and spatiotemporal benchmark unification. Ground computing center 100 connects to the Space-Track.org website (the authoritative source of the full cataloging database of space objects) via a network communication interface through its ground screening module 301 to download and obtain the two-line element set (TLE) of the on-orbit objects.

[0040] TLE is a common orbital data format in the aerospace field and the core data product of the Space-Track.org platform. Its standard format includes a header line and two data lines. Taking a single data entry from this website as an example:

[0041] "ISS (ZARYA)"

[0042] 1 25544U 98067A 25345.12345678 .00000023 00000-0 12345-4 0 9999

[0043] 2 25544 51.6400 320.0000 0006700 80.0000 280.0000 15.48999999234567”

[0044] The header row records the target name; the first data row contains the satellite number, launch number, epoch time, and atmospheric drag coefficient (used for subsequent SGP4 model calculations of atmospheric perturbation effects on the orbit); the second data row contains key orbital elements such as orbital inclination, right ascension of the ascending node, eccentricity, argument of perigee, mean perigee, and mean motion (number of orbits per day). Given the differences between different data sources (especially the true equatorial mean vernal equinox coordinate system defaulted to TLE) and the system's internal coordinate system, the ground screening module 301 utilizes Earth orientation parameters provided by the International Earth Rotation and Reference Systems Service (IERS) to uniformly convert the orbital status of all targets to a unified spatiotemporal reference based on the J2000 coordinate system, thereby eliminating systematic positional errors caused by different coordinate definitions.

[0045] S102, Long-Period Orbit Extrapolation and Covariance Preprocessing. The ground screening module 301 uses the SGP4 orbit prediction model or a high-precision numerical integration model to extrapolate the orbital states of all targets to a preset future warning time window. Addressing the issue of insufficient covariance information in cataloged data, this invention employs a covariance reconstruction method based on target physical characteristics: the ground screening module 301 classifies targets into large satellites, rocket bodies, or debris based on their radar cross section (RCS) size and orbital altitude distribution, and matches a corresponding empirical initial covariance matrix for each type of target based on the residual statistical characteristics of historical observation data. The empirical initial covariance matrix reflects the increasing trend of positional uncertainty for that type of target during the prediction process.

[0046] S103, Initial collision probability screening based on covariance truncation. Ground screening module 301 calculates the relative motion trajectories of all targets and spacecraft platform 200 within the warning time window and performs two-level screening:

[0047] First, a geometric distance screening is performed: the nominal intersection distance between the target and spacecraft platform 200 in three-dimensional space is calculated. The nominal intersection distance is the minimum Euclidean distance between two nominal position vectors without considering covariance. Targets with nominal intersection distances less than the first-level distance threshold are retained. The value of the first-level distance threshold is determined based on the maximum error envelope of the SGP4 model within the prediction time, typically ranging from 30km to 100km.

[0048] Subsequently, a probability integral re-screening is performed: the predicted covariance matrix of the spacecraft platform and the empirical initial covariance matrix of the target are synthesized and merged into a single covariance matrix. The probability density integral method is used to calculate the probability of a collision between the two covariance ellipsoids in three-dimensional space. The calculation principle is to merge the two position error ellipsoids and calculate the volume integral of the relative position error probability density function within a spherical space with a radius equal to the sum of the radii of the spacecraft platform (200) and the target's hard body. When the calculated collision probability density integral result is non-zero and greater than the ground-preset screening lower limit (e.g., 10), the collision probability is considered a valid collision probability. −6 When ), the target is determined to be a candidate target.

[0049] S104, Enhanced Data Package Construction and Uploading. The ground screening module 301 extracts key feature parameters of candidate targets to construct enhanced data packages. The data fields of the enhanced data packages include: the identifier of the candidate target, the latest double-row orbital elements, the radar cross section estimate, and the empirical initial covariance matrix at the warning time. Among them, the radar cross section estimate is used by the subsequent onboard optical precision measurement module 303 to predict the apparent magnitude of the target and adjust the exposure time; the empirical initial covariance matrix serves as prior information for the subsequent initialization of the onboard Kalman filter and the determination of the field of view search range. The ground computing center 100 sends the generated enhanced data packages to the onboard computer 201 of the spacecraft platform 200 for storage via the telemetry, tracking, and command (TT&C) communication link 101.

[0050] The onboard secondary verification step based on real-time geometric invariants is executed by the geometric verification module 302 running inside the onboard computer 201. This step utilizes real-time high-precision navigation data acquired onboard to rapidly clean the candidate targets in the augmentation data packets injected from the ground at the geometric level. Due to errors in ground forecasts and limited onboard computing resources, this step aims to quickly eliminate false alarm targets and generate an immediate list of high-risk targets by calculating geometric invariants that do not change rapidly with orbital phase and large-scale envelope relationships. Specifically, it includes the following sub-steps:

[0051] S201, Real-time Status Acquisition and Orbital Element Conversion. The geometry verification module 302 reads the current real-time position and velocity vectors of the spacecraft platform 200 from the Global Navigation Satellite System receiver 202 via the internal bus. The geometry verification module 302 first combines the current Greenwich Mean Time (GMT) to transform the GNSS data from a geocentric-fixed coordinate system to a unified spatiotemporal reference based on the J2000 coordinate system, consistent with the enhanced data packet. Subsequently, using the Kepler orbital transformation algorithm, the Cartesian state vector of the spacecraft platform 200 is converted into instantaneous oscillatory elements, which at least include the semi-major axis, eccentricity, orbital inclination, right ascension of the ascending node, argument of perigee, and true anomaly.

[0052] S202, Minimum Orbit Intersection Distance (MOID) analytical screening. The geometric verification module 302 uses the orbital elements of the candidate target and the instantaneous climactonic orbital elements of the spacecraft platform 200 to calculate the minimum geometric distance between the two orbits in three-dimensional space, i.e., the minimum orbital intersection distance. This metric characterizes the closest distance in terms of the geometric shape of two elliptical orbits in space, and is independent of the spacecraft's current position, exhibiting geometric invariance.

[0053] The minimum orbital intersection distance is calculated using the formula for minimizing orbital geometric distance. The formula for minimizing the orbital geometric distance is:

[0054] ;

[0055] in, This represents the minimum intersection distance between two orbits in three-dimensional space geometry. This indicates the operation of finding the minimum value of the function; The true anomaly angle is an independent variable representing the spacecraft platform 200 within its own orbital plane. The true anomaly angle is an independent variable representing the candidate target's orbital plane. The range of values ​​for the true anterior angle is: arrive radian; This indicates that the spacecraft platform 200 corresponds to the true anomaly angle. The geocentric position vector; This indicates that the candidate target corresponds to the true anterior angle. The geocentric position vector; The Euclidean norm (i.e., the modulus) of a vector.

[0056] In practical implementation, those skilled in the art can use algebraic polynomial root-finding methods or numerical optimization algorithms to solve the above minimization problem. The minimum orbital intersection distance is then calculated. Then, the geometry verification module 302 compares it with a preset physical safety threshold. The physical safety threshold is typically set between 3km and 10km, and this value is determined based on the sum of the upper limit of the positioning error of the Global Navigation Satellite System receiver 202 and the maximum lateral position error of the candidate target's TLE data. If the distance exceeds the physical safety threshold, the two orbits are determined to be geometrically separated, and the candidate target is directly eliminated.

[0057] S203, Altitude-level safety verification based on radial envelope mutual exclusion. For targets that pass the MOID screening, further checks are performed to see if their orbital radial altitude range intersects with that of the spacecraft platform 200. The geometric verification module 302 calculates the perigee radius (semi-major axis multiplied by one minus eccentricity) and apogee radius (semi-major axis multiplied by one plus eccentricity) of the spacecraft platform 200 and the candidate target, respectively. If the perigee radius of the spacecraft platform 200 minus the radial safety margin is still greater than the apogee radius of the candidate target, or the apogee radius of the spacecraft platform 200 plus the radial safety margin is still less than the perigee radius of the candidate target, then the two orbits are determined to be mutually exclusive at the altitude level. The radial safety margin is used to cover altitude attenuation and control errors caused by atmospheric drag, and is generally taken as 1km to 2km. Candidate targets that meet the mutual exclusion condition will be directly eliminated, and targets that pass the above verification are recorded as targets that pass the radial safety verification.

[0058] S204, Dynamic Time Window Phase Synchronization Screening Based on Ephemeral Aging. For targets with a risk of crossing orbital geometric paths, it is necessary to further verify the time synchronization of their arrival at the intersection point. The geometric verification module 302 calculates the time difference between the spacecraft platform 200 and the candidate target reaching the closest point in space, denoted as the time phase difference. Considering that the TLE data in the enhanced data packet will significantly increase its prediction error along the track direction over time, this invention does not use a fixed threshold, but instead adopts a dynamic window that adaptively adjusts according to the degree of accumulation of prediction error.

[0059] The dynamic window is determined using the dynamic time window calculation formula. The formula for calculating the dynamic time window is:

[0060] ;

[0061] in, This represents the dynamic window, i.e., the maximum allowed time deviation threshold. This represents the base time threshold, which corresponds to the minimum uncertainty time window when the TLE data is first generated (typically 2 to 5 seconds). This represents the aging coefficient, used to quantify the rate of divergence of forecast errors over time (typically taken as a value based on the statistical characteristics of the trace error in the SGP4 model). to ); This indicates the current system time of the onboard computer 201; Indicates the epoch time of the generation of candidate target TLE data in the enhanced data packet; The overall meaning indicates the aging time of the data.

[0062] If the absolute value of the calculated time phase difference is greater than the dynamic window This indicates that although the orbits intersect geometrically, neither will arrive at the area at the same time, and there is no risk of collision, so they are eliminated. Finally, all targets that pass the above checks form an immediate high-risk target list, which is then passed to the optical precision measurement module 303 for further processing.

[0063] The relative orbit determination step, based on physical visibility assessment and signal enhancement, is executed by the optical precision measurement module 303 running within the onboard computer 201. Upon receiving an immediate list of high-risk targets, this step first assesses the optical observability of the targets. If conditions are met, it activates the star sensor 203 to bypass conventional attitude measurement functions, utilizing image signal processing algorithms to extract weak space target signals and calculate a high-precision optical relative orbit state. Specifically, it includes the following sub-steps:

[0064] S301, Physical Visibility Prediction and Observation Mission Planning. The optical precision measurement module 303, based on the coarse orbital information of targets in the immediate high-risk target list and the real-time position of the spacecraft platform 200, comprehensively calculates three key physical constraint parameters: solar phase angle, Earth shadow state, and estimated angular velocity, to determine whether the target meets the optical observation conditions.

[0065] The optical precision measurement module 303 calculates the solar phase angle, which is the angle between the solar vector and the target line-of-sight vector. The illumination background is deemed acceptable only if this angle is greater than the solar shading angle of the star sensor 203 (the stray light suppression limit determined by the physical structure of the shading shield, typically 30 to 45 degrees) and the angle between the target line-of-sight vector and the Earth's edge is greater than the Earth's infrared avoidance angle (to avoid Earth's albedo interference, typically 10 to 20 degrees). Simultaneously, the optical precision measurement module 303 calculates the Earth's shadow state using a cylindrical projection model. If the target is within the Earth's umbra, it cannot be detected by the passive optical sensor due to lack of solar illumination and is therefore deemed unobservable. Furthermore, the optical precision measurement module 303 combines the radar cross section estimate from the enhanced data packet and the target distance estimate to predict the apparent magnitude. If the predicted apparent magnitude is within the dynamic detection range of the star sensor 203 and the predicted angular velocity is less than the maximum tracking angular velocity of the star sensor 203 (limited by readout noise and trailing effects), the physical observation conditions are deemed met. Targets that meet all the above conditions are included in the observation queue, and the optical precision measurement module 303 generates attitude maneuver commands to control the optical axis of the star sensor 203 to align with the target and estimate the azimuth.

[0066] S302, Image Enhancement Based on Prior Velocity-Guided Shift-Stacking. Since space debris targets are typically faint and move relative to background stars, direct single-frame imaging often fails to separate them from background noise. The optical precision measurement module 303 controls the star sensor 203 to continuously acquire a sequence of raw grayscale images at a fixed frame rate and executes a shift-stacking algorithm. This algorithm utilizes the relative velocity information implicit in the immediate high-risk target list as prior guidance, shifting the image sequence in the opposite direction of the target's motion to compensate for the shift. This allows the target signal to achieve coherent accumulation in phase across multiple frames, while the background noise is incoherently discretized.

[0067] The digital image shifting and overlay formula is used to calculate the pixel coordinates of the synthesized enhanced image. grayscale value at The formula for digital image shifting and superposition is:

[0068] ;

[0069] in, Indicates the pixel coordinates of the synthesized enhanced image. The grayscale value at that location; This represents the summation operation; This indicates the total number of frames in the acquired image sequence; Indicates the first The original grayscale image of the frame; Indicates the first The amount of horizontal pixel shift of a frame relative to a reference frame; Indicates the first The amount of displacement of a frame relative to a reference frame in the vertical pixel direction.

[0070] No. The amount of horizontal pixel shift of a frame relative to a reference frame and the The amount of shift of a frame relative to a reference frame in the vertical pixel direction The optical precision measurement module 303 calculates the angular velocity based on the estimated angular velocity from the real-time high-risk target list, as well as the focal length and pixel size parameters of the star sensor 203. Through this algorithm, the optical precision measurement module 303 synthesizes the enhanced image at pixel coordinates... grayscale value at The centroid coordinates of targets with a signal-to-noise ratio exceeding the detection threshold (e.g., signal-to-noise ratio greater than 5) are extracted from the constructed image matrix and combined with the inertial attitude data of star sensor 203 to convert them into high-precision angle observation data in the inertial frame, namely azimuth and pitch angles.

[0071] S303, Extended Kalman Filter State Solution Based on Angle-Only Data. The optical precision measurement module 303 initializes the extended Kalman filter, setting the state vector as the target's relative position and relative velocity vectors relative to the spacecraft platform 200. The filter uses relative orbital dynamics equations (such as the Clohessy-Wiltshire equations or nonlinear relative motion equations considering J2 perturbations) as state transition equations, and constructs measurement update equations using the azimuth and elevation angles output from S302.

[0072] Although a single angle observation cannot directly determine the distance, the optical precision measurement module 303, by processing the angle change rate at multiple epochs, can progressively calculate the relative distance and relative velocity, eliminating the uncertainty in state estimation, because the target and spacecraft platform 200 follow predetermined orbital dynamics constraints. When the state covariance of the filter converges to a preset accuracy range (e.g., position error less than 100m), the optical precision measurement module 303 outputs the final optical relative orbital state to the avoidance decision module 304. If the filter fails to converge or the target is lost within a specified time, the system will mark the target as unmeasurable and instruct subsequent steps to use the prior information in the enhanced data packet as backup data.

[0073] The confidence-weighted hierarchical avoidance decision-making step is executed by the avoidance decision-making module 304 running inside the onboard computer 201. This step aims to resolve the dilemma in avoidance decision-making caused by the large differences in the accuracy of orbital data of non-cooperative targets in space, namely, the contradiction between false alarms caused by the low accuracy of ground data and the high accuracy but low availability of onboard precision measurement data. This step adopts a two-branch decision logic, dynamically adjusts the decision threshold according to the source and quality of the input data, and generates the optimal maneuver strategy based on a lookup table of rendezvous geometric features. Specifically, it includes the following sub-steps:

[0074] S401, Data source validity determination and projection plane construction. The avoidance decision module 304 first checks the output status flag of the optical precision measurement module 303. If the flag displays "Precision measurement successful," the system enters "Precision measurement mode," and the avoidance decision module 304 reads the relative orbital state of the optical measurement and its corresponding precision measurement covariance matrix as calculation input. If the flag displays "Precision measurement failed" or "Unobservable," the system automatically switches to "safety mode," and the avoidance decision module 304 backtracks to read the candidate target orbital elements and initial covariance matrix from the enhancement data packet as calculation input.

[0075] After determining the input data, the avoidance decision module 304 uses an orbital dynamics extrapolation algorithm to propagate the orbital states and covariance matrices of the spacecraft platform 200 and the target to the Time of Closest Approach (TCA). Subsequently, a B-plane is established, which is an imaginary plane passing through the target's center and perpendicular to the relative velocity vectors of both. On this plane, the three-dimensional rendezvous problem is reduced to a two-dimensional problem. The avoidance decision module 304 projects the position error covariances of both targets onto this plane and superimposes them to construct a combined covariance ellipse. Simultaneously, it calculates the target's B-plane miss vector relative to the spacecraft platform 200.

[0076] S402, Dual-branch collision probability calculation and threshold screening. The avoidance decision module 304 calculates the collision probability using the constructed combined covariance ellipse and the B-plane miss vector. Regardless of the mode, its mathematical essence is to calculate the integral volume of the two-dimensional Gaussian probability density function within the hard-body collision region.

[0077] The collision probability density integral formula is used to calculate the collision probability between spacecraft platform 200 and the candidate target at the future rendezvous moment. The integral formula for the collision probability density is:

[0078] ;

[0079] in, This indicates the probability of a collision between spacecraft platform 200 and the candidate target at a future rendezvous point; Pi is a constant. This represents double integral operations; This represents an exponential function with the natural constant e as its base. This represents the horizontal coordinate variable in the B-plane coordinate system; This represents the vertical coordinate variable in the B-plane coordinate system; This represents the standard deviation of the combined covariance ellipse on the horizontal coordinate axis of the B-plane. This represents the standard deviation of the combined covariance ellipse on the longitudinal coordinate axis of the B-plane; This represents the correlation coefficient of the combined covariance ellipse in the B-plane coordinate system; This represents the component of the B-plane miss vector on the horizontal coordinate axis of the B-plane; This represents the component of the B-plane miss vector on the longitudinal coordinate axis of the B-plane; The integration region is a circular area defined by the combined hardware radius of the spacecraft platform 200 and the candidate target.

[0080] The collision probability between spacecraft platform 200 and the candidate target at the future rendezvous moment was calculated. Then, the avoidance decision module 304 performs a graded threshold determination.

[0081] In "precision measurement mode," due to the high data accuracy and small area of ​​the error ellipse, the calculated probability value truly reflects the risk level. Therefore, a high-confidence probability threshold (typically set to...) is adopted. This is to avoid frequent maneuvers due to excessive sensitivity.

[0082] In the "safety net" mode, due to large data errors, the huge covariance ellipse can cause a "probability dilution" phenomenon. Even if the actual risk is high, the probability value obtained by integration is actually very small because the probability density is distributed over a very large area. Therefore, this mode employs a more sensitive conservative probability threshold (typically set to...). This is to ensure that a safety baseline is maintained even when data quality is poor. If the threshold corresponding to the current mode is exceeded, an avoidance request will be generated.

[0083] S403, a lookup-based maneuver strategy is generated based on rendezvous geometry features. Once an evasion request is triggered, the evasion decision module 304 needs to generate specific maneuver evasion instructions. To avoid complex on-board orbit optimization iterations, this invention employs a lookup-based method based on geometric features. The evasion decision module 304 calculates the B-plane phase angle of the B-plane miss vector in the B-plane coordinate system. .

[0084] The avoidance decision module 304 retrieves a pre-set strategy library stored in the onboard computer 201. This library is based on the principle of relative orbital dynamics, and its logic is: to most effectively change the time to reach the rendezvous point by increasing the velocity along the track direction, thereby increasing the radial or normal distance. The specific mapping rules are as follows:

[0085] If the phase angle of plane B If the target is located in the first quadrant (0 to 90 degrees) or the fourth quadrant (270 to 360 degrees), it indicates that the target is located in the right region of the B plane relative to the spacecraft platform 200, and the strategy library outputs "acceleration along the track" as the thrust direction;

[0086] If the phase angle of plane B If the target is located in the second quadrant (90 to 180 degrees) or the third quadrant (180 to 270 degrees), it indicates that the target is located in the left region, and the strategy library outputs "decelerate along the track" as the thrust direction.

[0087] The avoidance decision module 304, in conjunction with the preset maneuver lead (usually 0.5 orbital cycles before the rendezvous point), generates a maneuver avoidance command that includes the ignition time, duration and thrust direction, and sends it to the propulsion system 204 for execution.

[0088] The evasion maneuver execution and orbit recovery step is the final step of the entire method, jointly executed by the onboard computer 201, the propulsion system 204, and the global navigation satellite system receiver 202 on the spacecraft platform 200. This step is responsible for translating the strategy generated by the evasion decision module 304 into actual orbital control forces, confirming the maneuver effect through real-time on-orbit monitoring, and ultimately restoring the spacecraft to its nominal mission orbit after avoiding the risk. Specifically, it includes the following sub-steps:

[0089] S501, Thrust vector execution and maneuver confirmation based on semi-major axis change. The propulsion system 204 receives maneuver avoidance commands generated by the avoidance decision module 304, and analyzes the ignition time, duration, and thrust direction parameters contained therein. When the system time reaches the ignition time, the propulsion system 204 drives the thrusters according to the commands, generating a precise thrust vector in the specified thrust direction. Since the strategy generated by this invention is mainly acceleration or deceleration along the track direction, according to the Gaussian perturbation equation, the thrust along the track direction will directly change the spacecraft's orbital energy, thus causing a significant change in the semi-major axis. The change in the semi-major axis will lead to a change in the orbital period, and through the cumulative effect over time, a phase deviation will be generated at the rendezvous point, thereby achieving avoidance.

[0090] During and after the maneuver, the onboard computer 201 uses the real-time position and velocity data output by the global navigation satellite system receiver 202 to calculate the instantaneous climactogenic elements in real time. To verify whether the evasive maneuver achieves the expected effect, this invention uses the change in the semi-major axis, which is sensitive to thrust and has geometric invariance, as the core monitoring indicator. The onboard computer 201 calculates the actual observed change in the semi-major axis and compares it with the theoretical prediction value based on the thrust model.

[0091] The predicted change in semi-major axis calculated based on the thrust model is calculated using the semi-major axis change prediction formula. The formula for predicting the semi-major axis change is:

[0092] ;

[0093] in, This represents the predicted change in the semi-major axis calculated based on the thrust model. Indicates the instantaneous semi-major axis of spacecraft platform 200 at the moment of maneuver; This indicates the instantaneous velocity of spacecraft platform 200 at the moment of maneuver; Represents the Earth's gravitational constant (with a value of approximately...). ); This indicates the thrust amplitude applied by the propulsion system 204 in the thrust direction; Indicates the duration specified in the maneuver evasion command; This indicates the current total mass of the spacecraft platform 200.

[0094] The onboard computer 201 will compare the semi-major axis change calculated by actual measurements with the predicted semi-major axis change calculated based on the thrust model. A difference comparison is performed. If the relative error between the two is less than the preset execution monitoring threshold (typically 5%, determined based on the combined error of the propulsion system calibration and the navigation calculation residual), the maneuver is deemed successful, confirming that spacecraft platform 200 has entered the expected avoidance trajectory; if the error exceeds the execution monitoring threshold, the anomaly handling logic is triggered, the current attitude is maintained, and the spacecraft awaits ground telemetry and control commands.

[0095] S502, Orbit Recovery and Maintenance Strategy After Passing the Rendezvous Point. After completing the maneuver, the onboard computer 201 monitors the relative distance between the spacecraft platform 200 and the target based on the extrapolated orbit. When the current time exceeds the predicted closest rendezvous time and the relative distance shows an increasing trend, it is determined that the rendezvous point has been safely passed. At this point, in order to eliminate the long-term effects of the avoidance maneuver on the orbital period and semi-major axis and to ensure the normal operation of subsequent missions, orbit recovery needs to be performed.

[0096] The onboard computer 201 generates orbit recovery operation commands. This operation is based on the principles of orbital energy conservation and symmetry: by applying a velocity increment equal in magnitude but opposite in direction to the evasive maneuver, the orbit's semi-major axis is restored to its nominal value. To minimize fuel consumption, the onboard computer 201 selects the first orbital cycle return point after the flyby rendezvous point (i.e., a position 360 degrees out of phase with the evasive maneuver point) to execute the recovery maneuver. If "track acceleration" was performed in step S4, the recovery strategy is to perform "track deceleration" of the same magnitude; if "track deceleration" was performed, the recovery strategy is to perform "track acceleration" of the same magnitude.

[0097] After recovery, the orbital semi-major axis and eccentricity of spacecraft platform 200 returned to the nominal range, achieving long-term stability of the mission orbit while ensuring space safety.

[0098] Specific application examples and experimental verification:

[0099] To verify the effectiveness of the space debris orbit prediction and avoidance method proposed in this invention, a typical low Earth orbit application scenario was constructed for simulation verification.

[0100] Scenario preset:

[0101] The spacecraft platform (Sat-X) is configured to operate in a sun-synchronous orbit at an altitude of 700 km and an inclination of 98°, with a mass of... The propulsion system is configured as thrust. The Hall thruster. The encountered space debris target (Obj-D) is set to have a radar cross section (RCS) of 0.05. Non-cooperative small debris. Time reference: January 18, 2026, 12:00:00. Ground catalog data predicts that the two will meet at close range at the future TCA (Time of Closest Encounter), with a nominal encounter distance of 0.8 km, posing a risk of collision.

[0102] Detailed explanation of the execution process:

[0103] S1, Ground-based initial screening and data uploading

[0104] The ground-based computing center extrapolated using the SGP4 model and calculated the nominal rendezvous distance to be 800m (less than the first-level distance threshold of 30km). Combining this with the empirical covariance matrix of debris RCS feature matching, the collision probability was calculated to be 2.5 × 10⁻⁶. −5 (greater than the lower limit of 10) −6 The ground generates an enhanced data packet containing the target orbital elements and covariance, which is then uploaded to Sat-X via the telemetry, tracking, and command link.

[0105] S2, On-board Geometric Verification

[0106] After receiving the data, the onboard computer verifies it using real-time GNSS data (position error <5m). The minimum orbital intersection distance (MOID) is calculated using the formula for minimizing orbital geometric distance. The calculation results show... (Less than the physical safety threshold of 3km) indicates a dangerous approach to the orbital geometry. The calculated time phase difference is 1.2s. Based on the dynamic time window formula, the following settings are made: aging coefficient Data aging time: 10 hours (36000s); calculation window: A phase difference of 1.2 seconds is within the window, indicating an immediate high-risk target.

[0107] S3, Optical Precision Measurement and Condition Resolution

[0108] Ten minutes before TCA, the target satisfies the solar phase angle (50° > 45°) and Earth shadow constraint. The star sensor acquires images at a frequency of 10 Hz.

[0109] At this point, the target signal-to-noise ratio in a single frame image is only 1.8, submerged in noise. The optical precision measurement module utilizes a shift-and-stacking algorithm, setting the number of stacked frames. .

[0110] After superposition processing, the target signal energy is accumulated, and the signal-to-noise ratio is improved to 5.6 (detection threshold 5.0), and the centroid is successfully extracted.

[0111] Extended Kalman filtering uses angle data to update the state. After 20 epochs of iteration, the relative position covariance converges from the initial 2km (ground data accuracy) to 80m.

[0112] S4, the hierarchical avoidance decision-making system enters "precision testing mode".

[0113] The avoidance decision module constructs the B-plane using the converged optical orbital state and a covariance of 80m. The collision probability is then calculated. Substituting into the integral formula for collision probability density, the result is: .because Greater than the high confidence threshold This triggers an evasion request. The phase angle in the B-plane is calculated. (First quadrant), the lookup table strategy outputs "acceleration along the track". Based on the warning time window, the ignition time is set to t=1000s (approximately 1 / 4 orbital period from the TCA point), and the duration is... .

[0114] S5, the evasion and recovery propulsion system, ignites at a predetermined time, with thrust directed along the velocity vector. The onboard computer monitors the semi-major axis variation in real time. Based on the semi-major axis variation prediction formula, it is known... , , Substitute numerical values ​​into the predicted change calculation:

[0115] ;

[0116] The actual GNSS measurement results showed a semi-major axis change of 110.5m with a relative error of 2.3% (<5%), confirming that the maneuver was performed normally.

[0117] After passing the TCA, the relative distance was continuously increased. During the subsequent safe flight phase (t=3000s in this embodiment), the propulsion system performed a 300s deceleration along the track to restore the semi-major axis to the nominal value, completing the closed loop.

[0118] See attached document Figure 3 , Figure 3 Subfigure (a) shows a comparison of the signal grayscale distribution before and after on-board image processing. The dashed line in the figure represents the pixel grayscale value of the original single-frame image, which fluctuates randomly between 0 and 50. The target signal feature located at the 50th pixel is submerged in the background noise and cannot be identified. The solid line represents the shifted and superimposed enhanced image after processing by step S302 of this invention. The background noise variance is reduced, and a clear peak with a grayscale value of about 60 is shown near the 50th pixel. Figure 3 Subplot (b) shows the evolution of the calculated collision probability over observation time. The dashed line in the figure represents the probability calculation result based on ground-based TLE data, with values ​​ranging from 10... −5The magnitude of fluctuations remains below the high confidence threshold; the solid line represents the fusion probability based on on-board optical measurement data, which increases logarithmically with time and exceeds 10 at approximately t=450s. −4 The high confidence threshold. Figure 3 Subplot (c) shows the monitoring curves of semi-major axis deviation changes throughout the evasive maneuver and track recovery process. The curves show that the semi-major axis deviation begins to increase linearly at t=1000s (evasive ignition), stabilizes at about 113 meters around t=1300s, then begins to decrease linearly at t=3000s (recovery ignition), and finally returns to the zero deviation baseline.

[0119] in conclusion:

[0120] Combined with appendix Figure 3 Based on the simulation data and the above-described embodiments, the technical effectiveness analysis of the space debris trajectory prediction and avoidance method proposed in this invention is as follows:

[0121] In terms of detecting faint targets Figure 3 The data pattern in sub-image (a) verifies the physical gain effect of the shift-and-stacking algorithm on the signal-to-noise ratio (SNR). Comparing the waveforms of the dashed and solid lines shows that the system successfully transforms hidden signals with an SNR below 2 in a single frame into effective signal peaks with an SNR greater than 5. This processing, without changing the hardware sensitivity of the optical sensor, substantially improves the system's performance for an RCS of 0.05m through multi-frame coherent accumulation. 2 The ability to independently detect minute debris solves the technical problem that traditional spaceborne sensors are limited by readout noise and thus have difficulty detecting non-cooperative, faint targets.

[0122] Regarding the accuracy of early warning decisions, Figure 3 Subgraph (b) reveals the decisive impact of different data source precision on collision probability calculation. Calculations relying solely on ground data (dashed line) suffer from excessive initial covariance, leading to over-dispersion of the probability density function in spatial distribution and a "probability dilution" phenomenon. This results in the calculated probability of actual high-risk rendezvous events remaining consistently below the alarm threshold, posing a risk of missed detection. In contrast, this invention utilizes precise on-board measurement data (solid line) to rapidly converge the state estimation covariance, ensuring that the collision probability value accurately reflects the physical collision risk. Furthermore, it correctly triggers the high-confidence threshold approximately 150 seconds before rendezvous (at t=450s), transforming ambiguous ground warnings into definitive avoidance instructions and effectively eliminating false safe zones.

[0123] In terms of the precision of circumventing control, Figure 3Subgraph (c) in the figure verifies the effectiveness of the closed-loop control mechanism based on semi-major axis variation. The curves show that after the propulsion system responded to the avoidance command at t=1000s, the semi-major axis accurately rose by approximately 113 meters. The deviation of this change from the theoretical model prediction was controlled within 2.3%, achieving a quantitative assessment of the maneuver effect. More importantly, after passing the rendezvous point, the symmetric recovery maneuver performed by the system at t=3000s successfully restored the orbital semi-major axis to its nominal state (deviation returned to zero). This demonstrates that the method can ensure the safe avoidance of collisions for space assets while maintaining the long-term stability of the mission orbit through precise energy management, avoiding the accumulation of orbital drift caused by open-loop maneuvers.

Claims

1. A method for predicting and avoiding space debris trajectories, characterized in that, Includes the following steps: The ground computing center (100) filters out candidate targets whose nominal rendezvous distance is less than the first-level distance threshold and whose collision probability density integral is non-zero, generates an enhanced data package containing the orbital data and covariance matrix of the candidate targets, and uploads it. The onboard computer (201) combines real-time navigation data to perform geometric feature screening on candidate targets in the enhanced data packet, and removes candidate targets whose minimum orbital intersection distance is greater than the physical safety threshold, whose radial envelopes are mutually exclusive, or whose time phase difference exceeds the dynamic window, and uses the remaining candidate targets to generate an instant high-risk target list. The onboard computer (201) controls the star sensor (203) to perform optical observations on the instantaneous high-risk targets in the instantaneous high-risk target list, and outputs the optical relative orbital state by using shift superposition and Kalman filtering to solve the problem; The onboard computer (201) selects a high-confidence probability threshold or a conservative probability threshold based on whether the optical relative orbital state is obtained, and generates a maneuver avoidance command when the calculated collision probability exceeds the determined probability threshold. The propulsion system (204) responds to the maneuvering avoidance command to perform avoidance, verifies the effect by confirming the semi-major axis change, and performs track restoration when appropriate.

2. The method for predicting and avoiding space debris trajectories according to claim 1, characterized in that, The specific process of generating the enhanced data packet containing candidate target orbit data and covariance matrix includes: The ground computing center (100) uses the Earth orientation parameters provided by the International Earth Rotation Service to uniformly convert the orbital status of the full amount of spatial target cataloging data to a unified spatiotemporal reference based on the J2000 coordinate system. Targets are classified according to their radar cross-section size and orbital altitude distribution, and corresponding empirical initial covariance matrices are matched based on the residual statistical characteristics of historical observation data under the unified spatiotemporal reference. Targets whose nominal rendezvous distance is less than the first-level distance threshold are retained, and the predicted covariance matrix of the spacecraft platform is combined with the empirical initial covariance matrix to form a merged covariance matrix; The collision probability density integral corresponding to the merged covariance matrix is ​​calculated using the probability density integral method. Targets with non-zero results and greater than the screening lower limit are identified as candidate targets to construct an enhanced data packet. The lower limit of the screening is determined based on the preset minimum effective collision probability density integral value, and the first-level distance threshold is determined based on the maximum error envelope of the SGP4 model within the prediction time.

3. The method for predicting and avoiding space debris trajectories according to claim 1, characterized in that, The specific process for generating the real-time high-risk target list includes: Combine the current Greenwich Mean Time to convert the real-time navigation data to the J2000 coordinate system, and convert the Cartesian state vector of the spacecraft platform (200) into instantaneous climactonic elements; Using the orbital elements of the candidate targets in the enhanced data packet and the instantaneous closely spaced orbital elements, the minimum orbital intersection distance is calculated using the orbital geometric distance minimization formula; If the minimum orbital intersection distance is less than the physical safety threshold, the perigee radius and apogee radius of the spacecraft platform (200) and the candidate target are checked respectively in combination with the radial safety margin to determine the radial envelope relationship; For a candidate target that satisfies the radial envelope relationship, the time difference between its arrival at the closest point in space and that of the spacecraft platform (200) is calculated as the time phase difference; If the absolute value of the time phase difference is less than the dynamic window determined by the dynamic time window calculation formula, then the candidate target is included in the list of immediate high-risk targets as an immediate high-risk target. The physical security threshold is determined based on the sum of the upper limit of the positioning error of the global navigation satellite system receiver and the maximum lateral position error of the candidate target's dual orbital element data.

4. The method for predicting and avoiding space debris trajectories according to claim 1, characterized in that, The specific process by which the control star sensor (203) performs optical observations of the instantaneous high-risk targets in the instantaneous high-risk target list includes: Calculate the solar phase angle of the instantaneous high-risk targets in the instantaneous high-risk target list and the angle between the line-of-sight vector of the instantaneous high-risk targets and the edge of the Earth; If the solar phase angle is greater than the solar shading angle of the star sensor (203) and the angle between the instantaneous high-risk target line-of-sight vector and the edge of the earth is greater than the earth's infrared avoidance angle, then the illumination background is deemed qualified. Under the condition that the lighting background is qualified, the state of the ground shadow is calculated using a cylindrical projection model to exclude high-risk targets that are located in the Earth's umbra. The estimated apparent magnitude is calculated by combining the radar cross section estimate in the enhanced data packet, and the estimated angular velocity is determined based on the data in the real-time high-risk target list; If the estimated apparent magnitude is within the dynamic detection range of the star sensor (203) and the estimated angular velocity is less than the maximum tracking angular velocity of the star sensor (203), then the physical observation conditions are met. When the physical observation conditions are determined to be met, attitude maneuver commands are generated; The attitude maneuver command is used to control the optical axis of the star sensor (203) to align with the estimated bearing of an immediate high-risk target.

5. The method for predicting and avoiding space debris trajectories according to claim 1, characterized in that, In the process of calculating the relative orbital state of the optical measurement using shift superposition and Kalman filtering, the process of generating a synthetic enhanced image using the digital image shift superposition formula specifically includes: The star sensor (203) is controlled to continuously acquire a sequence of original grayscale images at a fixed frame rate; The displacement is determined based on the estimated angular velocity in the instant high-risk target list, and the original grayscale image sequence is processed by the digital image shifting and superposition formula to generate a synthetic enhanced image; The target centroid coordinates with a signal-to-noise ratio exceeding the detection threshold are extracted from the synthetic enhanced image and converted into azimuth and pitch angles in the inertial frame by combining the inertial attitude data of the star sensor (203). The detection threshold is determined based on the minimum signal-to-noise ratio required to distinguish the target centroid from background noise.

6. The method for predicting and avoiding space debris trajectories according to claim 5, characterized in that, In the process of calculating the output optical relative orbit state using shift superposition and Kalman filtering, the specific process of calculating the output optical relative orbit state using Kalman filtering includes: The relative orbital dynamics equations are used as the state transition equations, and the azimuth and pitch angles are used to construct the measurement update equations. The measurement update equation is solved by processing data from multiple epochs using an extended Kalman filter, updating the state covariance, and calculating the relative distance and relative velocity. When the state covariance converges to a preset accuracy range, the optical relative orbital state of the target relative to the spacecraft platform (200) is output based on the relative distance and relative velocity; The preset accuracy range is determined based on the position error convergence limit required to generate the maneuver evasion command.

7. The method for predicting and avoiding space debris trajectories according to claim 1, characterized in that, The specific process of selecting a high-confidence probability threshold or a conservative probability threshold based on whether the optical relative orbital state is obtained includes: If the acquisition is successful, the optical relative orbital state and the precision covariance matrix are read and a high confidence probability threshold is set. If the acquisition fails, the data in the enhanced data packet is read and a conservative probability threshold is set to determine the calculation input data. The orbital state is extrapolated to the nearest rendezvous time using the calculated input data, and a B-plane is established. The position error covariance is projected onto the B plane and superimposed to construct a combined covariance ellipse, while the B plane miss vector of the target relative to the spacecraft platform (200) is calculated. The high confidence probability threshold is set as the upper limit of probability to avoid frequent maneuvers, and the conservative probability threshold is set as the lower limit of probability to ensure a safety baseline, which is lower than the high confidence probability threshold.

8. The method for predicting and avoiding space debris trajectories according to claim 7, characterized in that, The specific process of generating a maneuver avoidance command when the calculated collision probability exceeds a determined probability threshold includes: The collision probability is calculated using the combined covariance ellipse and the B-plane target-avoidance vector, and the collision probability density integral formula is used. If the collision probability exceeds the currently set high confidence probability threshold or conservative probability threshold, then calculate the B-plane phase angle of the B-plane miss vector in the B-plane coordinate system. Based on the quadrant where the phase angle of the B plane is located, a preset strategy library is retrieved to determine whether to accelerate or decelerate along the track as the thrust direction. Combining the preset maneuver lead and the thrust direction, the maneuver evasion command, which includes the ignition time, duration, and thrust direction, is generated.

9. The method for predicting and avoiding space debris trajectories according to claim 1, characterized in that, The specific process of verifying the effect by confirming the change in the semi-major axis includes: The propulsion system (204) generates thrust in response to the maneuvering evasion command, and the onboard computer (201) uses real-time data to calculate the instantaneous close orbital elements and calculate the actual observed semi-major axis change. The onboard computer (201) uses the semi-major axis change prediction formula to calculate the predicted semi-major axis change based on the thrust model; The difference between the actual observed change in the semi-major axis and the predicted change in the semi-major axis calculated based on the thrust model is compared. If the relative error is less than the execution monitoring threshold, the maneuver is determined to be successful. The execution monitoring threshold is determined based on the combined calibration error of the propulsion system and the navigation calculation residual.

10. The method for predicting and avoiding space debris trajectories according to claim 1, characterized in that, The specific process of performing track restoration at an opportune time includes: After completing the maneuver, monitor the relative distance. When it is confirmed that the rendezvous point has been passed and the relative distance has increased, generate an orbit recovery operation command. In response to the orbit recovery operation command, the first perigee or apogee after the rendezvous point is selected as the orbit recovery maneuver point; Based on the thrust direction determined when the maneuver evasion command is generated, a recovery maneuver with the same amplitude but in the opposite direction to the original thrust direction is performed at the track recovery maneuver point.

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