Constellation satellite improved space flux fast collision warning method

Abstract

The application discloses a constellation satellite improved space flux fast collision warning method and belongs to the satellite collision warning field.The application realizes the method as follows: a related coordinate system and a dynamics model are established, and an error propagation calculation model is given.Two methods of near / apogee screening and orbit plane intersection distance screening are used respectively to screen out evaluation objects with too large orbit characteristic difference.Space density on the orbits of the rest of stars is calculated, an improved space flux expression is used to clearly define dangerous areas on the orbit of a target star, and a time screening method and minimum relative distance calculation are used to determine subsequent evaluation objects.Based on the screening process of the improved space flux, information is provided for task planning and warning decision-making, and the collision risk degree of each section of the orbit of the target star and the satellite constellation is directly displayed.Individual threat targets are determined from the satellite constellation with high efficiency, the reserved evaluation objects enter a risk evaluation link, collision threats are clearly defined through a collision probability criterion, and the collision warning precision and efficiency of the satellite constellation are improved.

Description

Technical Field

[0001] This invention relates to a collision warning method, belonging to the field of satellite collision warning. Background Technology

[0002] In recent years, constellation satellites, with their advantages of flexible launch and low cost, have developed rapidly and been deployed in large numbers. However, due to the large number of constellation satellites, their operation in orbit has brought about problems such as the strain on orbital resources. Among the related problems, the increasing risk of collisions poses a significant threat to both satellites inside and outside the constellation. In the face of the increasing risk of collisions, it has become particularly important to develop early warning measures for a specific satellite constellation.

[0003] The core of collision warning methods is risk assessment, which can be broadly categorized into the Box area method and the collision probability method. The Box area method was applied earlier, has strong applicability, and a large assessment range, but is prone to false alarms. The collision probability method has higher accuracy and is currently more widely used, but its calculations are more complex. Besides the inherent reliability limitations of each risk assessment method, the assessment process typically consumes a significant amount of time. In particular, the Monte Carlo algorithm is currently the most stable method for accuracy verification, while the collision probability threshold is on the order of magnitude lower than... The collision probability calculation for lower-risk scenarios is much smaller, requiring verification algorithms to use massive samples and consuming significant computation time. Therefore, including the entire constellation of satellites in the assessment process leads to excessively long assessment times, potentially missing optimal avoidance opportunities and further increasing subsequent avoidance maneuver fuel consumption and failing to achieve the expected collision risk reduction. Therefore, this paper proposes a rapid early warning method that clearly defines the threat level of each segment of the orbit, applying different warning intensities to different regions to narrow the assessment scope and effectively shorten the time required for the early warning process. Summary of the Invention

[0004] To address the collision risk posed by constellation satellites deployed at target spacecraft altitudes, the main objective of this invention is to provide a rapid collision warning method for constellation satellites with improved space flux. This method determines the degree of collision risk for each orbital segment of the constellation satellites based on the improved space flux, thereby improving the accuracy and efficiency of collision warning for constellation satellites.

[0005] The objective of this invention is achieved through the following technical solution.

[0006] This invention discloses a rapid collision warning method for constellation satellites using improved space flux. It establishes a relevant coordinate system and dynamic model, and provides an error propagation calculation model. Two methods are used: perigee / apogee screening and orbital plane intersection distance screening, to eliminate assessment targets with excessively different orbital characteristics, reducing computational load in subsequent processes. The space density on the remaining satellite orbits is calculated, and the improved space flux expression is further used to identify hazardous areas on the target satellite orbit. Time-based screening and minimum relative distance calculation are then used to determine subsequent assessment targets. The improved space flux-based screening process serves as a core step, providing effective information for mission planning and early warning decisions, and visually displaying the collision risk level between each segment of the target satellite orbit and the satellite constellation, thus visualizing the collision threat. This method efficiently identifies individual threatening targets from an operational satellite constellation, significantly shortening the collision warning process for satellite constellations and reducing computation time. The retained assessment targets enter the risk assessment stage, where collision probability criteria are used to clarify their collision threat, improving the accuracy and efficiency of constellation satellite collision warnings.

[0007] This invention discloses a rapid collision warning method for improving space flux of constellation satellites, comprising the following steps:

[0008] Step 1: Define the RSW coordinate system for satellite orbits and establish a relative orbital dynamic model for constellation satellites. The dynamic model is used to provide orbital prediction information for close encounters, including position and velocity information. Establish an error propagation calculation model based on the dynamic model to provide prior information for calculating the collision probability in risk assessment. Establish an encounter coordinate system and, through coordinate transformation methods, convert the position and velocity information obtained from the dynamic model and the error information obtained from the error propagation model into position and error information in the encounter coordinate system used for collision probability calculation.

[0009] Define the RSW coordinate system, origin. At the target spacecraft's center of mass, the R-axis points towards the spacecraft along the Earth's center, the S-axis lies in the orbital plane and is perpendicular to the R-axis, pointing in the direction of the spacecraft's velocity, and the W-axis forms a right-handed coordinate system with the two. This coordinate system can be used to more intuitively represent the relative motion of the two spacecraft.

[0010] Within the RSW system, the relative orbital dynamics model of constellation satellites is expressed as:

[0011]

[0012] in, These are the position measurements on the R-axis, S-axis, and W-axis, respectively. express Regarding time Find the second derivative. and Similarly. These represent the perturbation accelerations on the R-axis, S-axis, and W-axis, respectively. ω is the Earth's gravitational constant; if the orbit is circular, then the angular velocity is... For constant values, its rate of change Target vector Equation (1) can be written as a state transition matrix. The form is as follows

[0013]

[0014] Equation (2) represents the known initial state. ,use It can be calculated state of time ; The analytical solution is

[0015]

[0016] Given the relative distance vector of the spacecraft The relationship between the absolute derivative and the relative derivative is:

[0017]

[0018] According to equation (4), the transition matrix for transferring absolute quantities to relative quantities is as follows:

[0019]

[0020] The updated state transition matrix is ​​then obtained. expression

[0021]

[0022] in, Indicates will Find the inverse. According to equation (6), use the initial error covariance matrix. The error propagation calculation model is derived.

[0023]

[0024] for The covariance matrix at time t.

[0025] Define the meeting coordinate system, with the origin at... Defined at the center of mass of the target spacecraft, Axis pointing relative distance vector direction, Axis pointing relative velocity vector direction, The axis forms a right-handed coordinate system with this axis. This coordinate system utilizes the relative distance vector at the closest moment. With relative velocity vector The vertical property reduces the three-dimensional spatial relationship between the target spacecraft and the evaluation object when they meet at close range to the relationship of motion in the same plane, simplifying the calculation of collision probability.

[0026] The method for transforming position and error information from the RSW coordinate system to the meeting coordinate system is as follows:

[0027]

[0028]

[0029] in In the meeting coordinate system shaft and The position of the axis; In the meeting coordinate system shaft and The joint error between the on-axis target spacecraft and the evaluation object; Let the error of the target spacecraft on the R-axis, S-axis, and W-axis in the RSW frame be represented. To evaluate the error of the object on the R-axis, S-axis, and W-axis in the RSW system, The velocity angle between the target spacecraft and the object being evaluated.

[0030] Step 1 is mainly used to obtain the position, velocity and error information of the target star and the threat star during the encounter process, so as to provide data support for risk assessment based on collision probability calculation.

[0031] Step 2: Using all constellation satellites as the evaluation object, conduct preliminary screening based on the characteristics of the orbit itself, and eliminate evaluation objects with excessive orbital differences.

[0032] Perform near / far location screening using the semi-major axis of the evaluation object. and eccentricity Calculate screening indicators Semi-major axis and eccentricity are both readily available basic operating parameters, making near / far-point selection very convenient and feasible. Selection Criteria The calculation formula is as follows:

[0033]

[0034] in and The perigee and apogee radii of the target spacecraft; given the allowable orbital clearance value. For each evaluation object, the calculation process of equation (10) is performed, and the result is... If the track gap is too large, the screening condition is met, and the evaluation object will not be considered in subsequent steps.

[0035] For the remaining evaluation targets, a selection process based on the distance between their orbital plane intersections is performed. The orbits of the target spacecraft and the evaluation targets are projected onto the celestial sphere. If a collision occurs, their projections on the celestial sphere will overlap; therefore, the intersection point of the orbital projections on the celestial sphere is the primary evaluation criterion. The orbital projection intersection point corresponds to the orbital plane intersection line; therefore, the distance between the orbital plane intersection lines is used as the selection criterion. .

[0036] Obtain the remaining orbital elements of the evaluation object. : Indicates the orbital inclination angle. Indicates the argument of perigee. Indicates the right ascension of the ascending node. Represent the true anomaly angle. Express the orbital plane normal vector of the target spacecraft using orbital elements. Normal vector of the orbital plane of the evaluation object

[0037]

[0038] The calculation result of equation (11) represents the orientation of the spacecraft's orbital plane; the vector of the orbital plane intersection line passing through the Earth's center. Further expressed as

[0039]

[0040] Perigee direction vector of the target spacecraft Represented as

[0041]

[0042] According to the intersection vector of the orbital plane Perigee direction vector of the target spacecraft List the true perimeter angle of the target spacecraft at this time. The calculation expression

[0043]

[0044] The true perimeter angle of the target spacecraft Substituting into the two-body motion equations, the lengths of the lines of intersection at both ends of the target spacecraft's orbital plane are obtained.

[0045]

[0046] The perigee direction vector of the evaluation object True near point angle Length of intersection with both ends of the track surface The calculation method is the same as in formula (13). Equation (15); Finally, the screening indicators will be used. Represented as

[0047]

[0048] Given This is the allowable clearance value for the intersection of the track surfaces. This will eliminate the assessment target. Step 2 initially eliminates some assessment targets, which helps to shorten the collision warning process for satellite constellations and improve warning efficiency.

[0049] Step 3: Using the target spacecraft's true perimeter angle Using space flux as the variable, calculate the space density at various points in the target spacecraft's orbit; repeat this calculation for the remaining evaluation objects. Calculate the space flux at various points in the target star's orbit using an improved space flux method. During the calculation process, quantities involving distance units and time units are dimensionless.

[0050] Known spacecraft speed

[0051]

[0052] The volume element is defined as the cross-section of the spacecraft's main area. , length is The cylindrical space region, in which The true near point angle has changed. The corresponding arc length, volume element for

[0053]

[0054] Spacecraft Cycle Represented as

[0055]

[0056] This applies to spatial density with arbitrary orbital characteristics. The expression is as follows

[0057]

[0058] spatial density It is the ratio of the time taken by any volume element to its orbital period, representing the frequency of encounters with the spacecraft at any point in its orbit. Space density. The only variable is the true anterior angle. The value is Define spatial flux. Let the number density of the target spacecraft and the evaluation object simultaneously appearing in any region within a unit of time, satisfying the weighted relationship, be expressed as the spatial density of any point on the target spacecraft's orbit. The evaluation object calculates the spatial density over one orbital period using a certain step size. For the first of them The value is obtained; the space flux at any point on the target spacecraft's orbit is calculated. as follows

[0059]

[0060] Different true near point angles The values ​​correspond to different orbital positions, therefore each true perimeter angle of the target spacecraft Each value corresponds to a spatial flux. value, These are the weight parameters.

[0061] Weight parameters The expression is designed as an exponential function similar to the collision probability calculation formula, which represents the relative distance vector. Place the square of the modulus in the exponent position and add a gain parameter. , Therefore, the greater the distance, the better. The smaller the calculated impact, the lower the value, and when it exceeds the evaluation range, the lower the value is set to 0. Weighting parameters. The expression is as follows

[0062]

[0063] in The natural constant is the relative distance vector. , The target spacecraft's radius vector relative to the geocenter; To evaluate the relative geocentric radius of the object. Calculate using the following formula

[0064]

[0065] The calculation is the same as formula (23). Calculate all the target star's... After determining the corresponding total flux, the risk level of each segment of the target star's orbit is presented using a visualization method. Another advantage of this process is that the parameters used for calculation only require the most basic classical orbital elements. The visualization methods include line graphs and scatter plots.

[0066] Using the target spacecraft's fixed parameters, namely its semi-major axis and orbital period, as dimensionless units, the space flux is... The calculations involving distance units (km) and time units (s) were treated as dimensionless.

[0067]

[0068] Dimensionless processing addresses the issue of excessively large differences in the magnitude of individual parameters. Using the original units for calculation leads to loss of precision, and the large magnitude of the calculated results makes it difficult to reflect the impact of parameters that can only change slightly. Dimensionless processing makes the comparison of data more intuitive. Step 3 provides intuitive information on the collision risk level of each track segment, aiding in the identification of dangerous encounter zones.

[0069] Step 4: Calculate the relative threat level The dangerous encounter segment is identified, and a time-based screening method is used to eliminate assessment objects that will not encounter the target spacecraft during the dangerous encounter segment, for both the target spacecraft and the remaining assessment objects. Through orbital prediction, the minimum relative distance between the remaining assessment objects and the target spacecraft during the dangerous encounter segment is calculated. ,like If the value is less than the safety value, it will be determined as the final evaluation target.

[0070] Using the space flux F of each segment of the target spacecraft's orbit obtained in step 3, the relative threat level is calculated.

[0071]

[0072] in, and These represent the minimum and maximum spatial flux values ​​over a single period. Given a threat level threshold. When a certain segment of the track When this orbital segment is recorded as a dangerous encounter segment, orbital prediction is performed using a dynamic model over the next period of time to observe whether the time periods during which the target spacecraft and the assessment object pass through this encounter segment overlap; if there is no overlap, the assessment object is eliminated.

[0073] The remaining assessment targets use position information generated from orbital predictions to calculate the minimum relative distance to the target spacecraft within the overlapping time period. ,like If the value is less than the safety value, it will be determined as the final evaluation target.

[0074] Step 5: Calculate the maximum collision probability using uncertainty, and then compare the maximum collision probability with the collision probability threshold. By comparing the results, the collision probability is used to determine the level of risk, and the Monte Carlo algorithm is used to verify the risk assessment results to ensure the credibility of the assessment.

[0075] When the uncertainty is known, the position and error information of the closest point in the encounter coordinate system are obtained through the dynamic model and the error propagation calculation model. At this time, the collision probability expression is taken as...

[0076]

[0077] in, Let be the radius of the collision domain.

[0078] When the uncertainty is unknown, solving for the collision probability is transformed into a two-dimensional extremum problem. and Treat it as an unknown and solve for the collision probability. Maximum point

[0079]

[0080] The expression for the maximum collision probability is derived.

[0081]

[0082] If the calculated collision probability is less than the given collision probability threshold If so, a safety signal will be output directly.

[0083] Conversely, if the initial covariance matrix is ​​not found, the Monte Carlo test is performed, using the initial covariance matrix. Error information in Generated at location Each sample is placed into a dynamic model for trajectory prediction; if a sample is in the prediction process... Descending to The following is counted as one collision, based on the total number of collisions. To obtain the Monte Carlo collision probability

[0084]

[0085] The calculation results using equation (29) replace or , and the collision probability threshold In comparison, if at this time there are still It outputs a danger signal when it is in danger and a safety signal when it is not.

[0086] This step involves accuracy verification, which requires a large sample size and is time-consuming. Therefore, Monte Carlo algorithm verification is only performed in dangerous situations where the calculated collision probability value exceeds the collision probability threshold. By verifying accuracy, the number of false alarms is reduced.

[0087] Beneficial effects:

[0088] 1. The present invention discloses a rapid collision warning method for improving space flux of constellation satellites. Taking constellation satellites as the main evaluation object, when dealing with the collision risk brought by a large number of constellation satellites, it effectively and accurately screens and determines targets with relatively higher threat levels. The risk assessment part, which accounts for the most time, is precisely applied to individual targets, thereby shortening the time of the entire warning process and improving the efficiency of collision warning.

[0089] 2. The present invention discloses a rapid collision warning method for constellation satellites with improved space flux. It improves the flux concept in the field of space debris and extends its application to the field of satellite collision warning to determine the collision risk at each space location. It uses the relatively easy-to-obtain classical orbital elements to represent the degree of collision risk of each segment of the target satellite's orbit, reducing the dependence on the accuracy of measurement data and calculation time, and improving the efficiency of collision warning.

[0090] 3. The present invention discloses a rapid collision warning method for constellation satellites with improved space flux. It uses the calculated space flux to represent the collision risk level of each segment of the target satellite's orbit. While providing effective criteria for screening, it also provides intuitive visualization information, thereby enabling targeted high-intensity warnings for some orbital segments, correspondingly reducing the warning intensity for low-threat segments, improving the efficiency of collision warnings, and providing assistance and support for subsequent mission planning and decision-making. Attached Figure Description

[0091] Figure 1 A flowchart of a rapid early warning method for constellation satellites based on improved space flux;

[0092] Figure 2 This diagram illustrates the geocentric inertial coordinate system, the target spacecraft's orbital coordinate system, and the encounter coordinate system.

[0093] Figure 3 Calculation results for near / far location screening indicators;

[0094] Figure 4The results of the calculation of the selection index for the distance between the track surface intersection lines;

[0095] Figure 5 The results of space flux calculations and the relative threat curve;

[0096] Figure 6 The results of the time-based screening method are evaluated.

[0097] Figure 7 This is a schematic diagram showing the spatial position of the target star and the overall evaluation object. Detailed Implementation

[0098] To better illustrate the objectives and beneficial effects of this invention, the following description, in conjunction with an embodiment and accompanying drawings, further explains the invention.

[0099] like Figure 1 As shown in the figure, this embodiment discloses a rapid collision warning method for improving space flux of constellation satellites. The specific implementation steps are as follows:

[0100] Step 1: Define the RSW coordinate system for satellite orbits and establish a relative orbital dynamic model for constellation satellites. The dynamic model provides orbital prediction information for close encounters, including position and velocity information. An error propagation calculation model is established using the dynamic model to provide prior information for calculating collision probability in risk assessment. Subsequently, an encounter coordinate system is established, and the position and velocity information obtained from the dynamic model and the error information obtained from the error propagation model are converted into position and error information in the encounter coordinate system used for collision probability calculation through coordinate transformation.

[0101] First, define the RSW coordinate system, with the origin at... At the target spacecraft's center of mass, the R-axis points towards the spacecraft along the Earth's center, the S-axis lies in the orbital plane and is perpendicular to the R-axis, pointing in the direction of the spacecraft's velocity, and the W-axis forms a right-handed coordinate system with the two. This coordinate system can be used to more intuitively represent the relative motion of the two spacecraft.

[0102] Within the RSW system, the relative orbital dynamics model of constellation satellites is expressed as:

[0103]

[0104] in, These are the position measurements on the R-axis, S-axis, and W-axis, respectively. express Regarding time Find the second derivative. and Similarly. These represent the perturbation accelerations on the R-axis, S-axis, and W-axis, respectively. ω is the Earth's gravitational constant; if the orbit is circular, then the angular velocity is... For constant values, its rate of change Target vector Equation (1) can be written as a state transition matrix. The form is as follows

[0105]

[0106] Equation (2) represents the known initial state. ,use It can be calculated state of time ; The analytical solution is

[0107]

[0108] Given the relative distance vector of the spacecraft The relationship between the absolute derivative and the relative derivative is:

[0109]

[0110] According to equation (4), the transition matrix for transferring absolute quantities to relative quantities is as follows:

[0111]

[0112] The updated state transition matrix is ​​then obtained. expression

[0113]

[0114] in, Indicates will Find the inverse. According to equation (6), use the initial error covariance matrix. The error propagation calculation model is derived.

[0115]

[0116] for The covariance matrix at time t.

[0117] Define the meeting coordinate system, with the origin at... Defined at the center of mass of the target spacecraft, Axis pointing relative distance vector direction, Axis pointing relative velocity vector direction, The axis forms a right-handed coordinate system with this axis. This coordinate system utilizes the relative distance vector at the closest moment. With relative velocity vector The perpendicularity property reduces the three-dimensional spatial relationship between the target spacecraft and the evaluation object during a close encounter to a relationship of motion within the same plane, simplifying the calculation of the collision probability. A schematic diagram of the orbital coordinate system, encounter coordinate system, and geocentric inertial coordinate system defined in this paper is shown below. Figure 2 As shown.

[0118] The method for transforming position and error information from the RSW coordinate system to the meeting coordinate system is as follows:

[0119]

[0120]

[0121] in In the meeting coordinate system shaft and The position of the axis; In the meeting coordinate system shaft and The joint error between the on-axis target spacecraft and the evaluation object; Let the error of the target spacecraft on the R-axis, S-axis, and W-axis in the RSW frame be represented. To evaluate the error of the object on the R-axis, S-axis, and W-axis in the RSW system, The velocity angle between the target spacecraft and the object being evaluated.

[0122] Step 1 is mainly used to obtain the position, velocity and error information of the target star and the threat star during the encounter process, providing data support for risk assessment based on collision probability calculation.

[0123] Step 2: Using all constellation satellites as the evaluation object, conduct preliminary screening based on the characteristics of the orbit itself, and eliminate evaluation objects with excessive orbital differences.

[0124] The assessment covers all satellites in the BeiDou satellite constellation, with an initial time of 4:00 am Apr 20. th In 2023, the simplified Julian Days were... The target star's orbital elements are currently...

[0125]

[0126] in Indicates the semi-major axis. Indicates the eccentricity. Indicates the orbital inclination angle. Indicates the argument of perigee. Indicates the right ascension of the ascending node. Indicates the true nearest point angle.

[0127] Perform near / far location screening using the semi-major axis of the evaluation object. and eccentricity Calculate screening indicators Semi-major axis and eccentricity are both readily available basic operating parameters, making near / far-point screening very convenient and feasible. Screening Indicators The calculation formula is as follows:

[0128]

[0129] in and The perigee and apogee radii of the target spacecraft; given the allowable orbital clearance value. For each evaluation object, the calculation process of equation (10) is performed, and the result is... If the track gap is too large, the screening condition is met, and this evaluation object will not be considered in subsequent steps. The result obtained by equation (40) is as follows: Figure 3 As shown, all evaluation subjects were retained in this round of screening.

[0130] For the remaining evaluation targets, a selection process based on the distance between their orbital plane intersections is performed. The orbits of the target spacecraft and the evaluation targets are projected onto the celestial sphere. If a collision occurs, their projections on the celestial sphere will overlap; therefore, the intersection point of the orbital projections on the celestial sphere is the primary evaluation criterion. The orbital projection intersection point corresponds to the orbital plane intersection line; therefore, the distance between the orbital plane intersection lines is used as the selection criterion. .

[0131] Obtain the remaining orbital elements of the evaluation object. The orbital normal vector of the target spacecraft is expressed using orbital elements. Normal vector of the orbital plane of the evaluation object

[0132]

[0133] The calculation result of equation (11) represents the orientation of the spacecraft's orbital plane; the vector of the orbital plane intersection line passing through the Earth's center. Further expressed as

[0134]

[0135] Meanwhile, the perigee direction vector of the target spacecraft Represented as

[0136]

[0137] According to the intersection vector of the orbital plane Perigee direction vector of the target spacecraft List the true perimeter angle of the target spacecraft at this time. The calculation expression

[0138]

[0139] The true perimeter angle of the target spacecraft Substituting into the two-body motion equations, the lengths of the lines of intersection at both ends of the target spacecraft's orbital plane are obtained.

[0140]

[0141] The perigee direction vector of the evaluation object True near point angle Length of intersection with both ends of the track surface The calculation method is the same as in formula (13). Equation (15); Finally, the screening indicators will be used. Represented as

[0142]

[0143] Given This is the allowable clearance value for the intersection of the track surfaces. The evaluation subject will be excluded. The result obtained by equation (46) is as follows: Figure 4 As shown. Step 2 initially screened out some assessment targets, facilitating the subsequent early warning process.

[0144] Step 3: Using the target spacecraft's true perimeter angle Using space flux as a variable, the spatial density at various points in the target spacecraft's orbit is calculated, and this calculation is repeated for the remaining evaluation objects; subsequently, the spatial flux at various points in the target star's orbit is calculated using an improved space flux method. During the calculation, quantities involving distance units and time units were dimensionless.

[0145] Known spacecraft speed

[0146]

[0147] The volume element is defined as the cross-section of the spacecraft's main area. , length is The cylindrical space region, in which The true near point angle has changed. The corresponding arc length, volume element for

[0148]

[0149] Spacecraft Cycle Represented as

[0150]

[0151] This applies to spatial density with arbitrary orbital characteristics. The expression is as follows

[0152]

[0153] spatial density It is the ratio of the time taken by any volume element to its orbital period, representing the frequency of encounters with the spacecraft at any point in its orbit. Space density. The only variable is the true anterior angle. The value is Define spatial flux. Let the number density of the target spacecraft and the evaluation object simultaneously appearing in any region within a unit of time, satisfying the weighted relationship, be expressed as the spatial density of any point on the target spacecraft's orbit. The evaluation object calculates the spatial density over one orbital period using a certain step size. For the first of them The value is obtained; the space flux at any point on the target spacecraft's orbit is calculated. as follows

[0154]

[0155] Different true near point angles The values ​​correspond to different orbital positions, therefore each true perimeter angle of the target spacecraft Each value corresponds to a spatial flux. value. The design concept for the weight parameters is as follows:

[0156] The weighting parameter expression is designed as an exponential function similar to the collision probability calculation formula, and the relative distance vector is used. The square of the modulus is placed in the exponent position, and the gain parameter is added last. , Therefore, the greater the distance, the better. The smaller the calculated impact, the lower the value, and when it exceeds the evaluation range, the lower the value is set to 0. The weight parameter expression is as follows:

[0157]

[0158] in The natural constant is the relative distance vector. , The target spacecraft's radius vector relative to the geocenter; To evaluate the relative geocentric radius of the object. Calculate using the following formula

[0159]

[0160] The calculation is the same as in formula (23).

[0161] Calculate all of the target star After determining the corresponding total flux, the risk level of each segment of the target star's orbit can be presented using visualization methods such as line graphs and scatter plots. Another advantage of this process is that the parameters used for calculation only require the most basic classical orbital elements.

[0162] Using the target spacecraft's fixed parameters, namely its semi-major axis and orbital period, as dimensionless units, the space flux is... The calculations involving distance units (km) and time units (s) were treated as dimensionless.

[0163]

[0164] Dimensionless processing primarily addresses the issue of significant differences in the magnitude of individual parameters. Using the original units for calculations would lead to loss of precision, and the large magnitude of the calculated results would obscure the impact of parameters that only change slightly. Dimensionless processing makes data comparisons more intuitive. Step 3 provides a clear picture of the collision risk level for each track segment, aiding in the identification of potentially dangerous encounter zones.

[0165] Step 4: Calculate the relative threat level The dangerous encounter zone was identified, and a time-based screening method was used to eliminate a batch of assessment objects that would not encounter the target spacecraft during the dangerous encounter zone. Through orbital prediction, the minimum relative distance between the remaining assessment objects and the target spacecraft during the dangerous encounter zone was calculated. ,like If the value is less than the safety value, it will be determined as the final evaluation target.

[0166] Using the space flux F of each segment of the target spacecraft's orbit obtained in step 3, the relative threat level is calculated.

[0167]

[0168] in, and These represent the minimum and maximum spatial flux values ​​over a single period. Given a threat level threshold. When a certain segment of the track When this orbital segment is recorded as a dangerous encounter segment, orbital prediction is performed using a dynamic model over the next period of time to observe whether the time periods during which the target spacecraft and the assessment object pass through this encounter segment overlap; if there is no overlap, the assessment object is eliminated.

[0169] Space flux calculation results and relative threat curves are as follows: Figure 4 As shown, this map can help identify key prevention areas and provide mission planning information for ground personnel. If the dangerous encounter period is defined as 10:00 am to 2:00 am on the same day, and the orbital forecast period covers 2:00 am, then the time selection results are as follows: Figure 6 As shown, unmarked evaluation objects on the timeline indicate that they did not pass through the danger zone during that time period.

[0170] The remaining assessment targets use position data generated from orbital predictions to calculate the minimum relative distance to the target spacecraft during the overlapping time period. ,like If the value is less than the safety value, it will be determined as the final evaluation target.

[0171] Calculations show that G-2's closest approach time is 11:59:59 am, with a closest distance of 0.07 km; BD-11's closest approach time is 12:45:43 am, with a closest distance of 982.42 km; and BD-16's closest approach time is 11:51:04 am, with a closest distance of 855.92 km. Taking an empirical value of 10 km as the safe relative distance, only G-2 will be retained for subsequent risk assessment.

[0172] Step 5: Determine the risk level using collision probability; calculate the maximum collision probability using uncertainty, and finally compare it with the collision probability threshold. The comparison was performed, and the Monte Carlo algorithm was used for verification to ensure the credibility of the evaluation.

[0173] When the uncertainty is known, the position and error information of the closest point in the encounter coordinate system are obtained through the dynamic model and the error propagation calculation model. At this time, the collision probability expression is taken as...

[0174]

[0175] in, Let be the radius of the collision domain. Assume the initial uncertainty of the satellite's position on each axis is 100m, the velocity uncertainty is 0.1m / s, and the radius of the collision domain is 5m. Calculations show that at the moment when the target spacecraft and the object under evaluation are closest, = m. The collision probability is calculated from the simplified expression as: Higher than the collision probability threshold .

[0176] When the uncertainty is unknown, solving for the collision probability is transformed into a two-dimensional extremum problem. and Treat it as an unknown and solve for the collision probability. Maximum point

[0177]

[0178] The expression for the maximum collision probability is derived.

[0179]

[0180] If the calculated collision probability is less than the given collision probability threshold If so, a safety signal will be output directly.

[0181] Conversely, if the initial covariance matrix is ​​not found, the Monte Carlo test is performed, using the initial covariance matrix. Error information in Generated at location Each sample is placed into a dynamic model for trajectory prediction; if a sample is in the prediction process... Descending to The following is counted as one collision, based on the total number of collisions. To obtain the Monte Carlo collision probability

[0182]

[0183] The calculation results using equation (29) replace or , and the collision probability threshold In comparison, if at this time there are still It outputs a danger signal when it is in danger and a safety signal when it is not.

[0184] This step involves accuracy verification, which is time-consuming due to the large sample size. Therefore, it is only performed in dangerous situations where the calculated collision probability exceeds the collision probability threshold. Performing accuracy verification in such cases will effectively reduce the number of false alarms. The sample size is set here to [size missing]. The collision probability is obtained by the Monte Carlo algorithm. The accuracy of the collision probability calculation model was verified. The initial calculation took 0.1026 seconds, and the verification process took 27.0659 seconds. Setting the verification process to only activate when the probability is higher than the threshold demonstrates the rationality of the process arrangement and significantly reduces the time when the calculation result is lower than the threshold.

[0185] Figure 7 This invention discloses a rapid early warning method for constellation satellites as the primary assessment target. By improving space flux and using the true perihelion angle of the target satellite as a variable, it intuitively and effectively presents the collision risk level of each segment of the target spacecraft's orbit when dealing with a large number of satellites with complex orbital intersections. This information can be used for ground-based test simulations and orbit design, as well as for on-orbit mission planning, and can be applied in many situations. With this step as the core, targeted high-intensity early warnings can be implemented for certain orbital segments, correspondingly reducing the warning intensity for low-threat orbital segments. This allows for rational resource allocation, improving safety while also increasing the efficiency and lifespan of the onboard computer. It quickly identifies the risk assessment target, effectively streamlining the early warning process.

[0186] The above detailed description further illustrates the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A rapid collision early warning method for improving space flux of constellation satellites, characterized in that: Includes the following steps, Step 1: Define the RSW coordinate system for satellite orbits and establish a relative orbital dynamic model for constellation satellites. The dynamic model is used to provide orbital prediction information when they meet at close range. The orbital prediction information includes position information and velocity information. Establish an error propagation calculation model through the dynamic model to provide prior information for calculating the collision probability in risk assessment. Establish an encounter coordinate system, and use coordinate transformation methods to convert the position and velocity information obtained from the dynamic model and the error information obtained from the error propagation model into position and error information in the encounter coordinate system for collision probability calculation. Step 2: Using all constellation satellites as the evaluation object, conduct preliminary screening based on the characteristics of their orbits, and eliminate evaluation objects with excessively large orbital differences; Step 3: Using the target spacecraft's true perimeter angle Using space flux as the variable, calculate the space density at various points in the target spacecraft's orbit; repeat this calculation for the remaining evaluation objects. Calculate the space flux at various points in the target star's orbit using an improved space flux method. During the calculation process, quantities involving distance units and time units are dimensionless. Step 3 is implemented as follows: Known spacecraft speed in The gravitational constant of Earth, Indicates the semi-major axis. The eccentricity is represented; the volume element is defined as the cross-section of the spacecraft's main area. , length is The cylindrical space region, in which The true near point angle has changed. The corresponding arc length, volume element for Spacecraft Cycle Represented as This applies to spatial density with arbitrary orbital characteristics. The expression is as follows spatial density It is the ratio of the time taken by any volume element to its orbital period, representing the frequency of encounters with the spacecraft at any point in its orbit; spatial density. The only variable is the true anterior angle. The value is Define spatial flux Let the number density of the target spacecraft and the evaluation object simultaneously appearing in any region within a unit of time, satisfying the weighted relationship, be expressed as the spatial density of any point on the target spacecraft's orbit. The evaluation object calculates the spatial density over one orbital period using a certain step size. For the first of them The value is obtained; the space flux at any point on the target spacecraft's orbit is calculated. as follows Different true near point angles The values ​​correspond to different orbital positions, therefore each true perimeter angle of the target spacecraft Each value corresponds to a spatial flux. value, These are weight parameters; Weight parameters The expression is designed as an exponential function similar to the collision probability calculation formula, which represents the relative distance vector. Place the square of the modulus in the exponent position and add a gain parameter. , Therefore, the greater the distance, the better. The smaller the calculated impact, the lower the value, and when it exceeds the evaluation range, the lower the value is set to 0; weight parameters The expression is as follows in The natural constant is the relative distance vector. , The radius vector of the target spacecraft relative to the geocenter; To evaluate the relative geocentric radius of the object; Calculate using the following formula in Indicates the orbital inclination angle. Indicates the argument of perigee; The calculation is the same as formula (23); calculate all the target star After determining the total flux corresponding to the value, the degree of risk to each segment of the target star's orbit is presented in a visual representation. Using the target spacecraft's fixed parameters, namely its semi-major axis and orbital period, as dimensionless units, the space flux is... The calculations involving distance units (km) and time units (s) were treated as dimensionless. ； Step 4: Calculate the relative threat level The dangerous encounter segment is identified, and a time-based screening method is used to eliminate assessment objects that will not encounter the target spacecraft during the dangerous encounter segment, for both the target spacecraft and the remaining assessment objects. Through orbital prediction, the minimum relative distance between the remaining assessment objects and the target spacecraft during the dangerous encounter segment is calculated. ,like If the value is less than the safety value, it will be determined as the final evaluation target; Step 4 is implemented as follows: Using the space flux F of each segment of the target spacecraft's orbit obtained in step 3, the relative threat level is calculated. in, and These represent the minimum and maximum spatial flux over a single period; given a threat level threshold. When a certain segment of the track When this orbital segment is recorded as a dangerous encounter segment, orbital prediction is performed using a dynamic model over the next period of time to observe whether the time periods of the target spacecraft and the evaluation object passing through this encounter segment overlap; if there is no overlap, the evaluation object is eliminated. The remaining assessment targets use position information generated from orbital predictions to calculate the minimum relative distance to the target spacecraft within the overlapping time period. ,like If the value is less than the safety value, it will be determined as the final evaluation target; Step 5: Calculate the maximum collision probability using uncertainty, and then compare the maximum collision probability with the collision probability threshold. The risk level is determined by comparing the collision probabilities and then using the Monte Carlo algorithm to verify the risk level assessment results.

2. The rapid collision warning method for improving space flux of constellation satellites as described in claim 1, characterized in that: Step 1 is implemented as follows: Define the RSW coordinate system, origin. At the target spacecraft's center of mass, the R-axis points along the Earth's center towards the spacecraft, the S-axis lies in the orbital plane and is perpendicular to the R-axis, pointing towards the spacecraft's velocity direction, and the W-axis forms a right-handed frame with the two axes. Within the RSW system, the relative orbital dynamics model of constellation satellites is expressed as: in, These are the position measurements on the R-axis, S-axis, and W-axis, respectively. express Regarding time Find the second derivative. and Similarly; These represent the perturbation accelerations on the R-axis, S-axis, and W-axis, respectively. ω is the Earth's gravitational constant; if the orbit is circular, then the angular velocity is... For constant values, its rate of change Target vector Equation (1) can be written as a state transition matrix. The form is as follows Equation (2) represents the known initial state. ,use It can be calculated state of time ; The analytical solution is Given the relative distance vector of the spacecraft The relationship between the absolute derivative and the relative derivative is: According to equation (4), the transition matrix for transferring absolute quantities to relative quantities is as follows: The updated state transition matrix is ​​then obtained. expression in, Indicates will Find the inverse; according to equation (6), use the initial error covariance matrix The error propagation calculation model is derived. for The covariance matrix at time t; Define the meeting coordinate system, with the origin at... Defined at the center of mass of the target spacecraft, Axis pointing relative distance vector direction, Axis pointing relative velocity vector direction, The axis forms a right-handed coordinate system with it; this coordinate system utilizes the relative distance vector at the closest moment. With relative velocity vector The vertical property reduces the three-dimensional spatial relationship between the target spacecraft and the evaluation object when they meet at close range to the relationship of motion in the same plane, simplifying the calculation of collision probability; The method for transforming position and error information from the RSW coordinate system to the meeting coordinate system is as follows: in In the meeting coordinate system shaft and The position of the axis; In the meeting coordinate system shaft and The joint error between the on-axis target spacecraft and the evaluation object; Let the error of the target spacecraft on the R-axis, S-axis, and W-axis in the RSW frame be represented. To evaluate the error of the object on the R-axis, S-axis, and W-axis in the RSW system, The velocity angle between the target spacecraft and the object being evaluated.

3. The rapid collision warning method for improving space flux of constellation satellites as described in claim 2, characterized in that: Step 2 is implemented as follows: Perform near / far location screening using the semi-major axis of the evaluation object. and eccentricity Calculate screening indicators Screening Indicators The calculation formula is as follows: in and The perigee and apogee radii of the target spacecraft; Given track clearance value For each evaluation object, the calculation process of equation (10) is performed, and the result is... If the track gap is too large, the screening condition is met, and this evaluation object will not be considered in subsequent steps. For the remaining evaluation targets, a selection process based on the distance between their orbital plane intersections is performed. The orbits of the target spacecraft and the evaluation targets are projected onto the celestial sphere. If a collision occurs, their projections on the celestial sphere will overlap. Therefore, the intersection point of the orbital projections on the celestial sphere is the primary focus. Since the orbital projection intersection point corresponds to the orbital plane intersection line, the distance between the orbital plane intersection lines is used as the selection criterion. ; Obtain the remaining orbital elements of the evaluation object. : Indicates the orbital inclination angle. Indicates the argument of perigee. Indicates the right ascension of the ascending node. Indicates the true nearest point angle; Express the orbital plane normal vector of the target spacecraft using orbital elements. Normal vector of the orbital plane of the evaluation object The calculation result of equation (11) represents the orientation of the spacecraft's orbital plane; the vector of the orbital plane intersection line passing through the Earth's center. Further expressed as Perigee direction vector of the target spacecraft Represented as According to the intersection vector of the orbital plane Perigee direction vector of the target spacecraft List the true perimeter angle of the target spacecraft at this time. The calculation expression The true perimeter angle of the target spacecraft Substituting into the two-body motion equations, the lengths of the lines of intersection at both ends of the target spacecraft's orbital plane are obtained. The perigee direction vector of the evaluation object True near point angle Length of intersection with both ends of the track surface The calculation method is the same as in formula (13). Equation (15); Finally, the screening indicators will be used. Represented as Given This is the allowable clearance value for the intersection of the track surfaces. The candidate being evaluated will be excluded.

4. The rapid collision warning method for improving space flux of constellation satellites as described in claim 3, characterized in that: Step 5 is implemented as follows: When the uncertainty is known, the position and error information of the closest point in the encounter coordinate system are obtained through the dynamic model and the error propagation calculation model. At this time, the collision probability expression is taken as... in, The radius of the collision domain; When the uncertainty is unknown, solving for the collision probability is transformed into a two-dimensional extremum problem. and Treat it as an unknown and solve for the collision probability. Maximum point The expression for the maximum collision probability is derived. If the calculated collision probability is less than the given collision probability threshold If so, a safety signal will be output directly; Conversely, if the initial covariance matrix is ​​not found, the Monte Carlo test is performed, using the initial covariance matrix. Error information in Generated at location Each sample is placed into a dynamic model for trajectory prediction; if a sample is in the prediction process... Descending to The following is counted as one collision, based on the total number of collisions. To obtain the Monte Carlo collision probability The calculation results using equation (29) replace or , and the collision probability threshold In comparison, if at this time there are still If it outputs a danger signal, it will output a safety signal; otherwise, it will output a safety signal. Monte Carlo algorithm verification is only performed in dangerous situations where the calculated collision probability is greater than the collision probability threshold.

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