Centimeter-level space debris threat approaching research and judgment method based on space-based optics

Abstract

The invention provides a centimeter-level space debris threat approaching research and judgment method based on space-based optics. The method mainly comprises the following steps: 1, calculating the angular position and luminosity of a space target optical image; 2, determining the relative angle change rate of the space target; 3, calculating a threat angular rate threshold value and primarily judging threats; 4, distance change rate inversion and threat luminosity threshold calculation; and 5, studying and judging threat approaching. According to the method, an angular position and a luminosity value of a space target are extracted from an optical image, a high-precision angular rate is fitted, a threat of space debris is preliminarily judged, relative distance change is inversed in combination with luminosity, and a threat approaching condition is quickly judged. According to the method, relative kinematics and a classical radiation theory are utilized, the obtained angular rate is high in precision, a threat threshold result is reliable, and rapid threat approaching research and judgment of centimeter-level space debris in a space-based optical observation scene can be realized.

Description

TECHNICAL FIELD

[0001] The present application provides a space target threat approaching judgment method based on space-based optics, which relates to using space-based optical images to realize rapid threat approaching judgment of centimeter-level space debris, and belongs to the field of space situation awareness. BACKGROUND

[0002] Human's increasingly frequent space exploration activities have changed the Earth space environment. The debris formed by the separation of rocket upper stages, the on-orbit spacecraft, and the space debris generated by the collision and disintegration of spacecraft form a huge space target group. The debris with a size of 1-10 cm cannot be determined its orbital distribution due to limited observation level, so it cannot be avoided in time, and there is no effective structure protection measure, which will greatly threaten the spacecraft, so it is also called "dangerous debris". A large number of unprogrammed centimeter-level space debris poses a serious safety threat to on-orbit spacecraft. The detection, positioning and threat approaching judgment of this type of debris is one of the key problems to ensure the safety of spacecraft operation.

[0003] In the traditional collision warning evaluation of space targets, the meeting process, closest approach time and position and velocity information of two space targets are obtained through orbit prediction, and the collision problem is evaluated according to these information. In order to reduce false alarm and unnecessary maneuver, a collision risk evaluation method based on collision probability is introduced to judge the collision risk of space targets. NASA stipulates that for space shuttles and international space stations, the red limit probability of taking evasive action must be 10 -4 , the yellow limit probability that the evasive action is taken without affecting the task requirements or payload is 10 -5 , and after the maneuver, the collision probability is reduced to 10 -7 , which is the effective avoidance. ESA sets the acceptable collision probability standard for its satellites to 10 -4or the proximity distance is less than 300 m. The collision probability calculation is divided into linear and nonlinear methods. There are several typical collision probability calculation methods under the assumption of linear relative motion. The calculation method of the approximate analytical expression is fast and the analytical expression is beneficial to parameter influence analysis; the two-dimensional numerical integral method in polar coordinate form simplifies the collision probability calculation process and performs numerical integral with fixed step length, but the accuracy of numerical integral is affected by the integral step length, so the calculation amount is large; one-dimensional curve integral can solve the collision probability calculation of space targets with irregular shape, and the calculation method and calculation error are more explicit. For the nonlinear collision probability calculation problem, the integral volume is no longer cylindrical, and the probability density function can change with time. In order to deal with such problems, the integral volume can be divided into multiple segments along the relative velocity direction, and the total collision probability is obtained by summing the probabilities of each segment. Among them, the one-dimensional probability along the relative velocity direction is calculated by the Mahalanobis distance of the two endpoints, and the collision probability of each segment is the product of one-dimensional and two-dimensional probabilities. In addition, the integral coordinate system can also be established to obtain the collision probability by integration, and the probability in each finite element grid can also be calculated and summed by creating a finite element grid, but this method is more complex.

[0004] In recent years, scholars have compared Mahalanobis distance, projection distance, collision probability and other indicators, and proved the feasibility and high calculation efficiency of Mahalanobis distance. Based on the 3σ rule, Huang Mengdie of Nanjing University of Aeronautics and Astronautics established a square Mahalanobis distance threshold model to realize the rapid discrimination of collision risk, but it still needs the position and velocity of the space target and the covariance, and it is not based on measurement only.

[0005] In summary, the current collision probability calculation is usually based on prior orbital information and needs a long time of orbit prediction and uncertainty propagation, and the real-time performance is low. Considering that the detectable distance of centimeter-level space debris in near-earth space is small and the collision research and judgment requires high real-time performance, the present application proposes a centimeter-level space debris threat proximity research and judgment method based on space-based optics, which is suitable for rapid response to the threat proximity of near-distance dark and weak space targets without prior information, and realizes rapid threat proximity research and judgment of centimeter-level space debris only by optical observation means. SUMMARY

[0006] (I) Invention purpose

[0007] In order to enhance the detection ability of the centimeter level space target, improve the threat approaching alarm ability, guarantee the on-orbit operation safety of the spacecraft, the application provides a centimeter level space debris threat approaching research method based on space optical observation, the angular position and luminosity value of the space target are extracted through a series of processing of the optical image, and the threat approaching research is conducted by using the angular position change and luminosity value change.

[0008] (II) Technical scheme

[0009] The application creates a centimeter level space debris threat approaching research method based on space optical observation, and aims to realize the fast threat approaching research of the near distance centimeter level dark and weak space target. The scene is that the near earth satellite carries the optical camera load to continuously observe the surrounding area of the centimeter level space debris. The limit distance of the centimeter level space debris detection is about 50-100 km. The method calculates and extracts the angular position and luminosity value of the space target through a series of image processing of the optical image in a short time. The high precision angular rate is fitted and calculated through the angular position, and the threat of the space debris is preliminarily judged according to the relative angular rate. The relative distance change rate is analyzed by combining the luminosity change of the space debris, the threat approaching judgment threshold in the dangerous distance is determined, and the fast threat approaching research of the centimeter level space debris in the space optical observation scene is realized.

[0010] The centimeter level space debris threat approaching research method based on space optical observation provided by the application is described with reference to the accompanying drawings Figure 1 The implementation steps are as follows:

[0011] Step one: angular position and luminosity calculation of the space target optical image

[0012] The extraction of the angular position and luminosity of the space target from the optical image needs to go through multiple steps, including image preprocessing, space target centroid positioning, star map identification, dark and weak space target detection, astronomical positioning, luminosity calculation and the like.

[0013] (1) the image is preprocessed through filtering and denoising, threshold segmentation, connected domain and the like, the division of all star point target regions in the image is realized.

[0014] (2) according to the connected domain extracted in the last step, the centroid positioning of the star point target is conducted by using the gray weighted centroid method, and the image coordinates of the star and the target are determined.

[0015] (3) Fast star pattern recognition is performed on the celestial object in the image, the right ascension and declination coordinates corresponding to the stars in the image are searched from the star catalog, and the coordinates are corrected to the observed epoch position.

[0016] (4) The stars in the image are removed according to the star pattern recognition result, and the suspected targets are screened out from the residual star point targets according to their relative positions in the sequence image.

[0017] (5) The centroid coordinates of the stars in the image and their corresponding observed epoch positions are input into an astronomical positioning model, the model parameter results are output through least squares iteration, the correction of the image coordinates of the stars and the targets is completed, and the attitude solution and the determination of the angular position of the space target are realized based on this.

[0018] (6) According to the star recognition result, the stars in the image close to the target luminosity value are selected, the gray value of the standard zero-magnitude star is calibrated according to the correlation between the star magnitude and the gray value, and the star magnitude corresponding to the target gray value is calculated.

[0019] Step two: determination of the relative angular change rate of the space target

[0020] In step one, the image containing the space target is photographed by the optical measurement device, and the direction of the space target relative to the optical measurement device is obtained through astronomical positioning. The direction information is represented by two angles of right ascension and declination in the ECI coordinate system, and the mathematical model is:

[0021]

[0022] where α and β are the right ascension and declination respectively, r t = [x t , y t , z t ] T is the position of the space target in the ECI coordinate system, r o = [x o , y o , z o ] T is the position of the optical measurement device in the ECI coordinate system, ρ = ||r t -r o || is the distance between the optical measurement device and the space target, w α and w β are the observation errors of the two angles, and atan2 (,) is the two-argument arctangent function, which is different from the general arctangent function in that it outputs the range between 0 and 2π according to the signs of the two input variables. The two measurement errors in the above formula mainly refer to the errors in the astronomical positioning link, which are caused by centroid positioning error, image distortion, instrument system deviation, etc.

[0023] For optical surveillance system, if a space target crosses the field of view and is visible, it forms a continuous multi-frame image. A sequence of multiple continuous angular observations in time order is obtained, and an optical measurement short arc is obtained, denoted as

[0024] {a(t0), β(t0), a(t1), β(t1),..., a(t k ), β(t k ),...} (2)

[0025] Assume that the change of angle with time is a quadratic curve, that is:

[0026]

[0027] Let

[0028]

[0029] Assume that the measurement noise level at each time in a single arc segment is equivalent, and the least square estimation is used to obtain:

[0030]

[0031] At this point, step two completes the fitting of the angular rate, and the angle and angular rate information of the measurement arc segment can be obtained.

[0032] Step three: threat angular rate threshold calculation and threat preliminary judgment

[0033] When the primary star (denoted as 1) and the debris (denoted as 2) move around the same central celestial body, their orbits are described by Kepler's law. When they are about to collide, assume that the collision occurs at time t c , at which time the positions of the primary star and the debris coincide, i.e. r1(t c ) = r2(t c ) = r c , Taylor expand the positions of the primary star and the debris near t c to the third order:

[0034]

[0035] where v 1c and v 2c are the instantaneous velocities of the primary star and the debris at the time of collision, a 1c and a 2c are the accelerations of the primary star and the debris at the time of collision caused by the gravity of the central celestial body, and are the jerk of the primary star and the debris at the time of collision caused by the gravity of the central celestial body. Then the relative position vector is:

[0036]

[0037] Because the two satellites were at the collision point r c Under the gravitational pull of the same central celestial body, the acceleration is:

[0038]

[0039] Where μ = 3.986004418 × 10 14 m 3 / kg / s 2 Since a is the Earth's gravitational constant, therefore a 2c -a 1c =0, and the jerk is:

[0040]

[0041] Where r = ||r||, thus we have

[0042]

[0043] Combining formulas (7) to (10), we can obtain

[0044]

[0045] r(t) is divided into linear terms and nonlinear terms. The linear term (v) 2c -v 1c (tt) c ) represents the principal direction of r(t), and the nonlinear term Let r(t) be the offset relative to the principal direction, then the angle can be characterized by the following formula:

[0046]

[0047] The rate of change of angle can be characterized by the following formula:

[0048]

[0049] Therefore, the magnitude of the angular velocity is related to (tt) c Related to (tt) c (tt) represents the maximum time when the debris is less than the host star's monitoring distance. The time corresponding to the 99.73% percentile is selected as (tt) based on the cumulative distribution function (CDF) of the corresponding time. c The value of ) can be used to obtain the threshold of the rate of change of angle. The current limit for detecting centimeter-level space debris with space-based optical equipment is 50–100 km; a dangerous distance of 50 km is taken as the threshold. The relationship between the relative distance between two colliding targets and time is shown in the appendix. Figure 2 The red line in the diagram represents a distance of 50km; the corresponding CDF for that time is shown in the appendix.Figure 3 .

[0050] Thus, the time corresponding to 99.73% is 80s, and the threshold of the angular change rate is:

[0051]

[0052] When the angular rate obtained in step two is greater than the threshold, it is considered that there is no threat and no collision will occur. When the angular rate is less than the threshold, there may be a threat, and it is necessary to further combine the luminosity information to determine.

[0053] Step four: distance change rate inversion and threat luminosity threshold calculation

[0054] The brightness of a space target is represented by the apparent magnitude. The apparent magnitude reflects the brightness of the target. The brighter the target, the lower the magnitude. The brightness of a 0-magnitude star is 100 times that of a 5-magnitude star. According to the Pogson formula, the apparent magnitude of a target can be expressed as:

[0055]

[0056] wherein E1 and E0 are the irradiance values corresponding to m1 and m0, respectively, and m0 and E0 represent the reference magnitude and the corresponding irradiance value.

[0057] For a space target, the target itself does not emit light, and the optical characteristics of the visible light band are mainly reflected in the reflected light of the sun. The irradiance of a space target and the relative distance follow the inverse square law, and the core formula is:

[0058]

[0059] wherein E is the irradiance value, P ⊙ is the solar constant, A is the effective cross-sectional area of the debris, p is the material albedo, r is the straight-line distance between the detector and the target, q is the phase angle (the angle between the direction of sunlight and the observation direction), and η is the system optical link efficiency.

[0060] From equation (16), it can be seen that for the same space target, the main factors affecting the brightness are the solar phase angle, the albedo of the illuminated surface and the relative distance. Under the condition of continuous shooting in a short time, the relative position of the sun is basically unchanged, and the influence of the change of the solar angle on the light intensity of the target can be ignored. The attitude change of the satellite in a short time is also small, and the change of the albedo of the illuminated surface is limited, so the influence on the light intensity of the target is small. It should be noted that the magnitude of the space target in the spinning state will also change the light intensity due to the difference of the albedo surface, but its spin is usually high speed, and the light intensity can show periodic change rule in a short time. Therefore, the large amplitude non-periodic change of the brightness of the space target in a short time can be attributed to the change of the relative distance, when the relative distance between the detector and the space target is close to one time, the observed brightness of the space target is about 4 times of the original, and the apparent magnitude is about 1.51. That is to say, in the continuous observation in a short time, the apparent magnitude value decreases by 1, and the relative distance is about 63% of the original.

[0061] According to the calculation formula of the target apparent magnitude, the apparent magnitude change rate is obtained by time differentiation:

[0062]

[0063] The irradiance is inversely proportional to the square of the distance E∝r -2 , combined with the radial velocity v r =dr / dt, the following relationship is obtained:

[0064]

[0065] Substituting equation (18) into equation (19), we have:

[0066]

[0067] In a short time, the radial velocity v r changes very small, and the light intensity change rate is basically inversely proportional to the distance. Since the relative distance information cannot be directly obtained from the optical image, it is not easy to determine a magnitude change threshold to mark that the observed target is approaching and threatening. Taking the second derivative of the apparent magnitude with respect to time, we have:

[0068]

[0069] Where a r is the radial acceleration. Take and as the conditions for threat approaching judgment together.

[0070] Reserve t c =5s as the response and avoidance decision time of threat warning, take r=-v r ·t c,but Set as the threshold for the rate of change of star magnitude Therefore, when space debris rapidly approaches, the rate of change of its observed apparent magnitude should satisfy the following condition. Meanwhile, to avoid periodic and repetitive changes in magnitude, the second derivative of magnitude with respect to time must satisfy the following condition within the dangerous distance: Threshold for second derivative of magnitude

[0071] Step 5: Threat Imminent Assessment

[0072] Based on step one, the angular position and magnitude information of space debris can be extracted from the sequence of optical images, and the rate of angular change can be calculated respectively. And magnitude change rate and its second derivative The corresponding judgment thresholds are respectively d m There are three possible scenarios.

[0073] (1) When At that time, it was considered that the relative angular velocities of the two were relatively large, and they did not have the conditions to collide with each other in the short term. It was determined that there was a very high probability that there would be no risk of collision in the short term, and this arc segment could be stored as historical data for subsequent orbit determination and cataloging of this target.

[0074] (2) When At that time, it was assumed that the relative angular velocities of the two were relatively small, and the conditions for a short-term collision were met, thus initially suggesting a certain risk of collision in the short term; and when or At that time, it was determined that its magnitude value did not decrease significantly within a short period of visibility, that is, it was determined that its relative distance to the observation platform did not decrease significantly, and it was determined that there was a high probability that there was no risk of collision in the short term. This arc segment could be stored as historical data for subsequent orbit determination and cataloging of this target.

[0075] (3) When At that time, it was assumed that the relative angular velocities of the two were relatively small, and the conditions for a short-term collision were met, thus initially suggesting a certain risk of collision in the short term; and when If the magnitude of the star decreases significantly within a short period of visibility, it is considered that the relative distance between the star and the observation platform has decreased significantly, indicating a high probability of collision risk in the short term, and a collision avoidance decision should be made as soon as possible.

[0076] In summary, the implementation steps of this invention are as follows: Figure 1The threat approaching judgment realized by the above process is a rapid risk judgment in a short-time arc segment scene, which is different from the risk judgment method of calculating collision risk according to multi-arc segment orbit cataloging. By using the angular measurement and photometric information in the optical image, the relative angular rate and star magnitude change rate are theoretically derived, and the angular rate and star magnitude change rate thresholds in the case of collision risk are given, so that the rapid threat approaching judgment of the centimeter-level space debris in the space-based optical observation scene is realized.

[0077] (III) Advantages

[0078] The threat approaching judgment method based on space-based optics provided by the application has the following advantages:

[0079] ① The threat approaching judgment method provided by the application can be applied to rapid response in the case of rapid approaching of centimeter-level dark and weak space targets at close range, and can realize rapid threat collision warning under the condition of no prior information of space debris.

[0080] ② The threat approaching judgment method provided by the application theoretically derives the fitting process of angular rate and the threat approaching threshold of angular rate, and the obtained angular rate has high accuracy and reliable threat threshold result, so that the threat approaching preliminary judgment can be rapidly realized.

[0081] ③ The threat approaching judgment method provided by the application uses the angular rate threshold for preliminary judgment, and uses photometric change for final threat judgment, fully utilizes the angular rate and photometric change information that can be extracted from the optical image, and the criterion is fully reliable, so that the confidence of threat warning is improved.

[0082] Therefore, the method of the application has great advantages in the task of threat approaching warning of space-based optical centimeter-level space debris, and can achieve high warning accuracy and fast response speed. BRIEF DESCRIPTION OF DRAWINGS

[0083] Figure 1 is the flow chart of the implementation steps of the application.

[0084] Figure 2 is a schematic diagram of the change relationship of the relative distance of two collision targets with time.

[0085] Figure 3 is a schematic diagram of the cumulative distribution function corresponding to the longest collision time.

[0086] Figure 4 is a graph of the relationship between the apparent star magnitude change rate and the relative distance under different radial relative velocities. DETAILED DESCRIPTION

[0087] In order to make the purpose, advantages and characteristics of the application clearer, the specific implementation process of the application will be further described in combination with the technical solutions and the drawings.

[0088] The application creates a centimeter-level space debris threat approaching research method based on space-based optics, aiming to realize rapid threat approaching research of centimeter-level dark and weak space targets in close proximity. The scene is set as a near-earth satellite carrying an optical camera payload for continuous observation of the surrounding area of centimeter-level space debris. With the existing space-based optical camera detection capability, the limit distance of centimeter-level space debris detection is about 50-100 km. The method calculates and extracts the angular position and luminosity value of the space target by a series of image processing on the optical image; the high-precision angular rate is fitted and calculated through the angular position, and the relative angular rate is used to preliminarily judge the threat of the space debris; on this basis, the relative distance change rate is analyzed in combination with the luminosity change of the space debris to determine the threat approaching judgment threshold in the dangerous distance, so as to realize rapid threat approaching research of centimeter-level space debris in the space-based optical observation scene.

[0089] The centimeter-level space debris threat approaching research method based on space-based optics provided by the application refers to the accompanying drawings Figure 1 , and the implementation steps are as follows:

[0090] Step one: angular position and luminosity acquisition of space target optical image

[0091] The extraction of the angular position and luminosity of the space target from the optical image needs to go through multiple steps, including image preprocessing, space target centroid positioning, star map identification, dark and weak space target detection, astronomical positioning, and luminosity calculation.

[0092] (1) The image is preprocessed through filtering and denoising, threshold segmentation, and connected domain steps to complete the division of all star point target regions in the image. The filtering process includes using Gaussian filtering, Fourier transform and its inverse transform to remove image background noise, and using median filtering to remove image salt and pepper noise.

[0093] (2) According to the connected domain extracted in the previous step, the centroid of the star point target is positioned using the gray weighted centroid method to realize the determination of the image coordinates of the stars and targets. The core formula of the gray weighted centroid method is as follows:

[0094]

[0095] Where (x c ,y c ) is the centroid coordinates of the connected domain region, (x,y) is the coordinates of each pixel point in the region, and I(x,y) is the gray value of the pixel point.

[0096] (3) The celestial targets in the image are quickly identified, the corresponding right ascension and declination coordinates of the stars in the image are found from the star catalog, and they are corrected to the observation epoch view position.

[0097] (4) According to the star map recognition result, the stars in the image are removed, and the suspected targets are screened out from the residual star point targets according to their relative positions in the sequence image.

[0098] (5) The centroid coordinates of the stars in the image and the corresponding observation epoch apparent positions are input into an astronomical positioning model, and the astronomical positioning model is shown in formula (22).

[0099]

[0100] In the formula, a ij and b ij are distortion coefficients in the horizontal and vertical directions of the image, n is the polynomial order, the higher the order, the more accurate the fitting effect, and the higher order distortion correction effect can be better, but the calculation complexity will increase exponentially, and the three-order / five-order model is widely used in astronomical positioning.

[0101] The model parameter results are output by least squares iteration, the optical image geometric distortion correction is completed, the image coordinates of the stars and the targets are corrected, and the attitude solution and the determination of the angular position of the space target are realized based on this.

[0102] (6) According to the star recognition result, the stars in the image close to the target luminosity value are selected, the standard zero-magnitude star gray value is calibrated according to the iteration of the star magnitude and gray correlation, and the star magnitude value corresponding to the target gray value is calculated. The relationship between star magnitude and gray is as follows:

[0103]

[0104] In the formula, I0 is the gray value of the zero-magnitude star, I obj is the gray value of the target, and m obj is the star magnitude value. The standard gray value of the zero-magnitude star can be calibrated by using a certain number of known star gray values and star magnitude values.

[0105] Step two: determination of the relative angular change rate of the space target

[0106] In step one, the image containing the space target is photographed by the optical measurement device, and the direction of the space target relative to the optical measurement device is obtained by astronomical positioning. The direction information is represented by the right ascension and declination in the ECI coordinate system, and the mathematical model is as follows:

[0107]

[0108] In the formula, α and β are the right ascension and declination respectively, and r t =[x t , y t , z t ] TThe position of the space target in the ECI coordinate system, r o = [x o , y o , z o ] T The position of the optical measurement device in the ECI coordinate system, p = ||r t -r o || is the distance between the optical measurement device and the space target, w α and w β are observation errors of two angles, and atan2(, ) is a two-argument arctangent function, which is different from the general arctangent function in that the output range is between 0 and 2p according to the positive and negative signs of the two input variables. The two measurement errors in the above formula mainly refer to the errors of the astronomical positioning link, which are derived from the centroid positioning error, image distortion, instrument system deviation, etc.

[0109] For an optical monitoring system, if a space target passes through the field of view and is visible, a continuous multi-frame image is formed, and a sequence of multiple continuous angle observations in time order is obtained, which is an optical measurement short arc, denoted as

[0110] {a(t0), b(t0), a(t1), b(t1),..., a(t k ), b(t k ),...} (25)

[0111] Assuming that the angle changes over time are quadratic curves, i.e.:

[0112]

[0113] Let

[0114]

[0115] Assuming that the measurement noise level at each time in a single arc segment is equivalent, the least squares estimation is used to obtain:

[0116]

[0117] Assuming that the observation sampling interval is 1 second and the angle measurement accuracy (1s) in the arc segment is 5", the angle / angle rate accuracy (1s) extracted under different arc segment lengths is shown in the following table.

[0118] Table 1 Angle / angle rate accuracy extracted under different arc segment lengths

[0119]

[0120] When the arc segment is too short or too long, the quadratic curve fitting will appear over / under fitting phenomenon, resulting in the precision is reduced or contains a large deviation, in the actual application, the order of the fitting curve can be selected adaptively, and in the case of angle fitting residual close to white noise, low order curve fitting is used as much as possible.

[0121] So far, the fitting of angular rate is completed in step two, and the angle and angular rate information of the measurement arc segment can be obtained.

[0122] Step three: threat angular rate threshold calculation and threat preliminary judgment

[0123] When the primary star (denoted as 1) and the debris (denoted as 2) move around the same central celestial body, their orbits are described by Kepler's law. When they are about to collide, it is assumed that the collision occurs at time t c , at which time the positions of the primary star and the debris coincide, i.e. r1(t c ) = r2(t c ) = r c , the positions of the primary star and the debris are Taylor expanded near t c to the third order:

[0124]

[0125] where v 1c and v 2c are the instantaneous velocities of the primary star and the debris at the time of collision, a 1c and a 2c are the accelerations of the primary star and the debris at the time of collision caused by the gravity of the central celestial body, and are the jerk of the primary star and the debris at the time of collision caused by the gravity of the central celestial body. Then the relative position vector is:

[0126]

[0127] Since the two satellites are subject to the gravity of the same central celestial body at the collision point r c , the acceleration is:

[0128]

[0129] where μ = 3.986004418 × 10 14 m 3 / kg / s 2 is the Earth's gravitational constant, so a 2c -a 1c = 0, and the jerk is:

[0130]

[0131] Where r = ||r||, thus we have

[0132]

[0133] Combining formulas (7) to (10), we can obtain

[0134]

[0135] r(t) is divided into linear terms and nonlinear terms. The linear term (v) 2c -v 1c (tt) c ) represents the principal direction of r(t), and the nonlinear term Let r(t) be the offset relative to the principal direction, then the angle can be characterized by the following formula:

[0136]

[0137] The rate of change of angle can be characterized by the following formula:

[0138]

[0139] Therefore, the magnitude of the angular velocity is related to (tt) c Related to (tt) c (tt) represents the maximum time when the debris is less than the host star's monitoring distance. The time corresponding to the 99.73% percentile is selected as (tt) based on the cumulative distribution function (CDF) of the corresponding time. c The value of ) can be used to obtain the threshold of the rate of change of angle. The current limit for detecting centimeter-level space debris with space-based optical equipment is 50–100 km; a dangerous distance of 50 km is taken as the threshold. The relationship between the relative distance between two colliding targets and time is shown in the appendix. Figure 2 The red line in the diagram represents a distance of 50km; the corresponding CDF for that time is shown in the appendix. Figure 3 .

[0140] Therefore, the time corresponding to 99.73% is 80 seconds, and the threshold for the rate of change of angle is:

[0141]

[0142] If the angular velocity obtained in step two is greater than the threshold, it is considered that there is no threat and no collision will occur. If the angular velocity is less than the threshold, there may be a threat, and further judgment needs to be made by combining photometric information.

[0143] Step 4: Distance Change Rate Inversion and Threat Photometric Threshold Calculation

[0144] The brightness of a space target is expressed by apparent magnitude, which reflects the brightness of the target. The brighter the target, the lower the magnitude. The brightness of a 0th magnitude star is 100 times that of a 5th magnitude star. According to the Pogson formula, the apparent magnitude of a target can be expressed as:

[0145]

[0146] wherein E1 and E0 are the irradiance values corresponding to m1 and m0 respectively, and m0 and E0 represent the reference magnitude and the corresponding irradiance value.

[0147] For a space target, the target itself does not emit light, and the optical characteristics of the target in the visible light band are mainly reflected in the reflected light of the sun. The irradiance of a space target and the relative distance follow the inverse square law, and the core formula is:

[0148]

[0149] wherein E is the irradiance value, P ⊙ is the solar constant, A is the effective cross-sectional area of the debris, p is the material albedo, r is the straight-line distance between the detector and the target, q is the phase angle (the angle between the direction of sunlight and the observation direction), and η is the system optical link efficiency.

[0150] For the same space target, the main factors affecting the brightness are the solar phase angle, the material albedo of the illuminated surface, and the relative distance. Under the condition of continuous shooting in a short time, the relative position of the sun is basically unchanged, and the influence of the change of the solar angle on the brightness of the target can be ignored. The attitude of the satellite also changes slightly in a short time, and the change of the albedo of the illuminated surface is limited, which has little effect on the brightness of the target. It should be noted that the magnitude of a space target in a spinning state will also change with the different albedos of the reflecting surface, but the spinning is usually high-speed, and the brightness will show periodic variation in a short time. Therefore, the large-scale non-periodic variation of the brightness of a space target in a short time can be attributed to the change of the relative distance. When the relative distance between the detector and the space target is close to one time, the observed brightness of the space target is about 4 times that of the original, and the apparent magnitude is about 1.51 less. That is, in continuous observation in a short time, the magnitude value decreases by 1, and the relative distance is about 63% of the original.

[0151] According to the calculation formula of the apparent magnitude of the target, the magnitude change rate is obtained by time differentiation:

[0152]

[0153] The irradiance is inversely proportional to the square of the distance E -2 , combined with the radial velocity v r =dr / dt, the following relationship is obtained:

[0154]

[0155] Substituting into formula (41), we have:

[0156]

[0157] In a short time, the radial velocity v r The changes are small, and the rate of change in luminosity is essentially inversely proportional to distance. Since relative distance information cannot be directly obtained from optical images, it is impossible to simply determine a threshold for magnitude change to indicate that the observed target is approaching and poses a threat. The second derivative of magnitude with respect to time is taken as follows:

[0158]

[0159] Among them, a r Let be the radial acceleration. and Together, they serve as a condition for assessing the imminent threat.

[0160] Reserve t c =5s is taken as the response and avoidance decision time for threat alarms, and r = -v in formula (42) r ·t c ,but Set as the threshold for the rate of change of star magnitude Therefore, when space debris rapidly approaches, the rate of change of its observed apparent magnitude should satisfy the following condition. See attached document Figure 4 This illustrates the trend of magnitude change rate with relative distance under different relative radial velocities, with the red line representing the magnitude change rate threshold. Furthermore, to avoid periodic and repetitive changes in magnitude, the second derivative of magnitude with respect to time must satisfy a certain condition within the critical distance. Threshold for second derivative of magnitude

[0161] Step 5: Threat Imminent Assessment

[0162] Based on step one, the angular position and magnitude information of space debris can be extracted from the sequence of optical images, and the rate of angular change can be calculated respectively. And magnitude change rate and its second derivative The corresponding judgment thresholds are respectively There are three possible scenarios.

[0163] (1) When At that time, it was considered that the relative angular velocities of the two were relatively large, and they did not have the conditions to collide with each other in the short term. It was determined that there was a very high probability that there would be no risk of collision in the short term, and this arc segment could be stored as historical data for subsequent orbit determination and cataloging of this target.

[0164] (2) When , it is considered that the relative angular velocity of the two is small, and the condition of mutual collision in a short period is met, and it is preliminarily considered that it has a certain collision risk in a short period; and when or , it is considered that the star value does not decrease significantly in a short time, that is, it is determined that the relative distance to the observation platform does not decrease significantly, and it is determined that it has no collision risk in a short period, and the arc segment can be stored as historical data for subsequent orbit determination and cataloging of the target.

[0165] (3) When , it is considered that the relative angular velocity of the two is small, and the condition of mutual collision in a short period is met, and it is preliminarily considered that it has a certain collision risk in a short period; and when , it is considered that the star value decreases significantly in a short time, that is, it is determined that the relative distance to the observation platform decreases significantly, and it is determined that it has a great probability of collision risk in a short period, and collision avoidance decision needs to be made as soon as possible.

[0166] In summary, the implementation step flow of the present application is as shown in the accompanying Figure 1 . The threat approaching research and judgment realized by the above-mentioned flow is a rapid risk research and judgment method based on the short-arc scene in a short period, which is different from the risk research and judgment method of calculating the collision risk according to the multi-arc orbit determination and cataloging. By using the angular measurement and photometric information in the optical image, the relative angular velocity and star variation rate are theoretically derived, and the angular velocity and star variation rate threshold in the case of collision risk are given, and the rapid threat approaching research and judgment of the centimeter-level space debris in the space-based optical observation scene is realized.

Claims

1. A method for assessing the approaching threat of centimeter-level space debris based on space-based optics, characterized in that, Includes the following steps: Step 1: Calculation of angular position and photometric value of optical image of space target Extracting the angular position and luminosity of a spatial target from an optical image requires multiple steps, including image preprocessing, centroid localization of the spatial target, star map recognition, detection of faint spatial targets, astronomical positioning, and luminosity calculation. (1) The image is preprocessed by filtering and denoising, thresholding and connecting domains, etc., to achieve the division of all star point target regions in the image. (2) Based on the connected domain extracted in the previous step, the centroid of the star target is located using the gray-scale weighted centroid method, thereby determining the image coordinates of the star and the target. (3) Perform rapid star map identification on celestial targets in the image, find the right ascension and declination coordinates of the stars in the image from the star catalog, and correct them to the observation epoch position. (4) Remove stars from the image based on the star map recognition results, and select suspected targets from the remaining star targets according to their relative positions in the sequence images. (5) Input the centroid coordinates of the stars in the image and their corresponding observation epochs into the astronomical positioning model, output the model parameter results through least squares iteration, complete the correction of the geometric distortion of the optical image, correct the image coordinates of the stars and the target, and realize the attitude calculation and the determination of the angular position of the space target based on this. (6) Based on the star recognition results, select stars in the image that are close to the target luminosity value, iteratively calibrate the gray value of the standard zero magnitude star according to the correlation between magnitude and gray value, and calculate the magnitude value corresponding to the target gray value accordingly. Step 2: Determining the rate of change of the relative angle of the spatial target In step one, the optical measurement equipment has already captured an image containing the space target. The orientation of the space target relative to the optical measurement equipment is obtained through astronomical positioning. This orientation information is represented by the right ascension and declination angles in the ECI coordinate system. It is assumed that the angles change over time as a quadratic curve, i.e.: make Assuming that the noise level is comparable at all times within a single arc segment, the following results can be obtained using least squares estimation: At this point, step two has completed the fitting of the angular rate, and the angle and angular rate information of the measured arc segment can be obtained. Step 3: Threat Angular Rate Threshold Calculation and Initial Threat Assessment By analyzing the relative motion of the host star and the debris under the collision scenario, the positions of the host star and the debris at time t c Perform a Taylor expansion on the vicinity, retaining the order to 3, and subtract the results to obtain the relationship between the relative position vectors: The relative position vector is divided into linear and nonlinear terms, thus obtaining a representation of the angle. Further differentiation yields the threshold of the rate of change of the angle. The representation is as follows: If the angular velocity obtained in step two is greater than the threshold, it is considered that there is no threat and no collision will occur. If the angular velocity is less than the threshold, there may be a threat, and further judgment needs to be made by combining photometric information. Step 4: Distance Change Rate Inversion and Threat Photometric Threshold Calculation For space targets, the target itself does not emit light; its optical characteristics in the visible light band are mainly manifested in the reflection of sunlight. The irradiance of a space target follows an inverse square law with respect to its relative distance, and its core formula is: Where E is the irradiance value, P ⊙ η is the solar constant, A is the effective cross-sectional area of ​​the fragment, ρ is the material albedo, r is the straight-line distance between the detector and the target, θ is the phase angle (the angle between the incident direction of sunlight and the observation direction), and η is the system optical link efficiency. As can be seen from formula (5), for the same space target, the main factors affecting brightness are the solar phase angle, the albedo of the illuminated surface, and the relative distance. Under continuous imaging conditions over a short period, the changes in solar phase angle and satellite attitude are small, and the changes in the albedo of the illuminated surface are limited, resulting in a relatively small impact on the target's brightness. Therefore, the large-scale non-periodic changes in the brightness of a space target over a short period can be attributed to changes in relative distance. Based on the formula for calculating the target's apparent magnitude, the rate of magnitude change is obtained by differentiating over time: In a short time, the radial velocity v r The changes are small, and the rate of change in luminosity is essentially inversely proportional to distance. Since relative distance information cannot be directly obtained from optical images, it is impossible to simply determine a threshold for magnitude change to indicate that the observed target is approaching and poses a threat. The second derivative of magnitude with respect to time is taken as follows: Among them, a r Let be the radial acceleration. and Together, they serve as a condition for assessing the imminent threat. Step 5: Threat Collision Assessment Based on step one, the angular position and magnitude information of space debris can be extracted from the sequence of optical images, and the rate of angular change can be calculated respectively. And magnitude change rate and its second derivative The corresponding judgment thresholds are respectively There are three possible scenarios. (1) When At that time, it was considered that the relative angular velocities of the two were relatively large, and they did not have the conditions to collide with each other in the short term. It was determined that there was a very high probability that there would be no risk of collision in the short term, and this arc segment could be stored as historical data for subsequent orbit determination and cataloging of this target. (2) When At that time, it was assumed that the relative angular velocities of the two were relatively small, and the conditions for a short-term collision were met, thus initially suggesting a certain risk of collision in the short term; and when or At that time, it was determined that its magnitude value did not decrease significantly within a short period of visibility, that is, it was determined that its relative distance to the observation platform did not decrease significantly, and it was determined that there was a high probability that there was no risk of collision in the short term. This arc segment could be stored as historical data for subsequent orbit determination and cataloging of this target. (3) When At that time, it was assumed that the relative angular velocities of the two were relatively small, and the conditions for a short-term collision were met, thus initially suggesting a certain risk of collision in the short term; and when If the magnitude of the star decreases significantly within a short period of visibility, it is considered that the relative distance between the star and the observation platform has decreased significantly, indicating a high probability of collision risk in the short term, and a collision avoidance decision should be made as soon as possible.

2. The method for assessing the approaching threat of centimeter-level space debris based on space-based optics according to claim 1, characterized in that: The specific implementation method of step three, the threat angular rate threshold calculation and initial threat assessment, is as follows: As the primary star (denoted as 1) and the debris (denoted as 2) orbit the same central object, their orbits are described by Kepler's laws. When they are about to collide, let's assume the collision occurs at time t. c At this point, the positions of the primary star and the fragment coincide, i.e., r1(t c )=r2(t c ) = r c The positions of the main star and the fragments are located at t c Perform a Taylor expansion nearby, preserving up to order 3: Where v 1c and v 2c These are the instantaneous velocities of the host star and the debris during their collision, respectively. 1c and a 2c These represent the accelerations of the primary star and the debris during the collision, respectively, caused by the gravity of the central celestial body. and Let be the jerk of the primary star and the debris during the collision, respectively, caused by the gravity of the central celestial body. Then the relative position vector is: Because the two satellites were at the collision point r c Under the gravitational pull of the same central celestial body, the acceleration is: Where μ = 3.986004418 × 10 14 m 3 / kg / s 2 Since a is the Earth's gravitational constant, therefore a 2c -a 1c =0, and the jerk is: Where r = ||r||, thus we have Combining formulas (9) to (12), we can obtain r(t) is divided into linear terms and nonlinear terms. The linear term (v) 2c -v 1c (tt) c ) represents the principal direction of r(t), and the nonlinear term Let r(t) be the offset relative to the principal direction, then the angle can be characterized by the following formula: The rate of change of angle can be characterized by the following formula: Therefore, the magnitude of the angular velocity is related to (tt) c Related to (tt) c (tt) represents the maximum time when the debris is less than the host star's monitoring distance. The time corresponding to the 99.73% percentile is selected as (tt) based on the cumulative distribution function (CDF) of the corresponding time. c The value of ) can be used to obtain the threshold of the rate of change of angle. If the angular velocity obtained in step two is greater than the threshold, it is considered that there is no threat and no collision will occur. If the angular velocity is less than the threshold, there may be a threat, and further judgment needs to be made by combining photometric information.

3. The method for assessing the approaching threat of centimeter-level space debris based on space-based optics according to claim 1, characterized in that: The specific implementation method for step four, distance change rate inversion and threat photometric threshold calculation, is as follows: The brightness of a space target is expressed using apparent magnitude. Apparent magnitude reflects the apparent brightness of the target; the brighter the target, the lower its magnitude. A 0th magnitude star is defined as 100 times brighter than a 5th magnitude star, meaning a difference of one-fold in magnitude corresponds to a difference of 2.512 in brightness. According to Posen's formula, the apparent magnitude of a target can be expressed as: Where E1 and E0 are the irradiance values ​​corresponding to m1 and m0, respectively, and m0 and E0 can represent the reference magnitude and its corresponding irradiance value. For space targets, the target itself does not emit light; its optical characteristics in the visible light band are mainly manifested in the reflection of sunlight. The irradiance of a space target follows an inverse square law with respect to its relative distance, and its core formula is: Where E is the irradiance value, P ⊙ η is the solar constant, A is the effective cross-sectional area of ​​the fragment, ρ is the material albedo, r is the straight-line distance between the detector and the target, θ is the phase angle (the angle between the incident direction of sunlight and the observation direction), and η is the system optical link efficiency. As can be seen from formula (17), for the same space target, the main factors affecting brightness are the solar phase angle, the albedo of the illuminated surface, and the relative distance. Under continuous imaging conditions over a short period of time, the relative position of the sun remains basically unchanged, and the influence of changes in the solar angle on the target's brightness can be ignored. The satellite's attitude changes are also small over a short period of time, and the changes in the albedo of the illuminated surface are limited, having little impact on the target's brightness. It should be noted that the magnitude of a space target in a spin state will also change with the different albedo surfaces, but its spin is often high-speed, and the brightness can show a periodic change pattern in a short period of time. Therefore, the large non-periodic changes in the brightness of a space target over a short period of time can be attributed to changes in relative distance. When the relative distance between the detector and the space target approaches double, the observed brightness of the space target increases to about 4 times the original value, and the apparent magnitude decreases by about 1.

51. That is to say, in continuous observation over a short period of time, for every 1 decrease in magnitude, the relative distance becomes about 63% of the original value. Based on the formula for calculating the apparent magnitude of a target, the rate of change of magnitude is obtained by differentiating over time: Irradiance is inversely proportional to the square of the distance, E∝r -2 Combined with radial velocity v r If dr / dt = dr, then the following relationship holds: Substituting into formula (19), we have: In a short time, the radial velocity v r The changes are small, and the rate of change in luminosity is essentially inversely proportional to distance. Since relative distance information cannot be directly obtained from optical images, it is impossible to simply determine a threshold for magnitude change to indicate that the observed target is approaching and poses a threat. The second derivative of magnitude with respect to time is taken as follows: in, a r Let be the radial acceleration. and Together, they serve as a condition for assessing the imminent threat. Reserve t c =5s is taken as the response and avoidance decision time for threat alarms, and r = -v in formula (20) r ·t c ,but Set as the threshold for the rate of change of star magnitude Therefore, when space debris rapidly approaches, the rate of change of its observed apparent magnitude should satisfy the following condition. Meanwhile, to avoid periodic and repetitive changes in magnitude, the second derivative of magnitude with respect to time must satisfy the following condition within the dangerous distance: Threshold for second derivative of magnitude

Images