An analytical model method for collision threat area prediction and collision risk assessment

Abstract

This invention provides an analytical model method for predicting collision threat areas and determining collision risks, relating to the field of space safety, particularly satellite collision early warning. The method includes: acquiring the orbital parameters and orbital angular momentum of any two spacecraft; determining a collision rendezvous scenario based on the angle between their orbital angular momentum; determining a collision scenario calculation model based on the rendezvous scenario, and determining the true anomaly angle at the rendezvous point based on the collision scenario calculation model and orbital parameters; calculating the space collision position of each spacecraft at the rendezvous point and the time required to reach the rendezvous point based on the orbital parameters, the true anomaly angle at the rendezvous point, and the orbit determination error, to perform space collision area prediction and collision risk assessment, obtaining the prediction result. This scheme can achieve collision threat area prediction and collision risk assessment through onboard autonomous real-time calculation.

Description

Technical Field

[0001] This invention relates to the field of space safety technology, particularly to the field of satellite and application industry technology, and especially to an analytical model method for predicting collision threat areas and determining collision risks. Background Technology

[0002] As orbital space becomes increasingly crowded, the risk of collisions between spacecraft and other targets is escalating, necessitating the development of spacecraft collision threat early warning technologies to predict collision zones and assess collision risks. Existing methods for orbital collision rendezvous and collision zone prediction based on high-precision orbital dynamics models, while providing relatively accurate collision rendezvous zone location information, require continuous integral recursion and iterative calculations, resulting in high computational load and long processing times. This makes it difficult to meet the requirements of autonomous real-time computing on-board systems under resource constraints, thus hindering on-board autonomous implementation. Furthermore, existing methods for orbital collision rendezvous and collision zone prediction based on the CW model, when used for orbital collision determination and collision zone prediction, are limited in application scope by linearization constraints, only suitable for scenarios with relatively short distances. Furthermore, most existing methods for spacecraft collision rendezvous determination and collision zone prediction lack consideration of the impact of systematic errors on the collision rendezvous calculation model. This leads to large prediction errors in practical applications, making it impossible to accurately determine the collision rendezvous area and time interval. This can result in either excessive avoidance maneuvers leading to high fuel consumption and potentially even mission failure, or insufficient avoidance maneuvers leaving the spacecraft's orbit still within the collision risk zone. Therefore, there is an urgent need for an analytical model method for predicting collision threat areas and determining collision risk. Summary of the Invention

[0003] This invention provides an analytical model method for predicting collision threat areas and determining collision risks. This method uses analytical calculation to predict the collision threat areas between spacecraft and targets and determine the collision risks, while meeting the requirements of autonomous real-time calculation on the satellite.

[0004] In a first aspect, the present invention provides an analytical model method for predicting collision threat areas and determining collision risks, including:

[0005] Obtain the orbital parameters and orbital angular momentum of any two spacecraft;

[0006] The collision and rendezvous scenario is determined based on the angle between the orbital angular momentum.

[0007] A collision scenario calculation model is determined based on the collision and rendezvous scenario, and the true anomaly angle at the rendezvous point is determined based on the collision scenario calculation model and the orbital parameters.

[0008] Based on the orbital parameters, the true anomaly angle at the rendezvous point, and the orbit determination error, the space collision position of each spacecraft at the rendezvous point and the time required to reach the rendezvous point are calculated to predict the space collision area and assess the collision risk, thereby obtaining the prediction results.

[0009] Secondly, the present invention also provides a device for predicting collision threat areas and determining collision risks, comprising:

[0010] The acquisition module is used to acquire the orbital parameters and orbital angular momentum of the first and second spacecraft.

[0011] The scene determination module is used to determine the collision and rendezvous scene based on the angle between the orbital angular momentum.

[0012] The prediction and judgment module is used to determine a collision scenario calculation model based on the collision and rendezvous scenario, and to determine the true anomaly angle at the rendezvous point based on the collision scenario calculation model and the orbital parameters; and to calculate the space collision position of the first spacecraft and the second spacecraft at the rendezvous point and the time required to reach the rendezvous point respectively based on the orbital parameters, the true anomaly angle at the rendezvous point and the orbit determination error, so as to perform space collision area prediction and collision risk judgment, and obtain prediction results.

[0013] Thirdly, the present invention also provides a computing device, including a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, it implements the analytical model method for collision threat area prediction and collision risk determination as described in any of the above claims.

[0014] Fourthly, the present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed in a computer, causes the computer to execute the analytical model method for collision threat area prediction and collision risk determination as described in any of the preceding claims.

[0015] Fifthly, embodiments of the present invention also provide a computer program product, including computer instructions, which, when executed by a processor, implement the steps of the method described in any of the first aspects of this specification.

[0016] This invention provides an analytical model method for predicting collision threat regions and determining collision risks. This method, considering the orbital parameters and orbital angular momentum of any two spacecraft, first determines the collision rendezvous scenario between the two spacecraft based on the angle between their orbital angular momentum. Then, it establishes analytical models for calculating the intersection points of orbital spatial collisions and temporal collisions under different collision rendezvous scenarios, thereby obtaining the spatial collision position of each spacecraft at the rendezvous point and the time required to reach the rendezvous point. Finally, it predicts the spatial collision region and determines the collision risk, obtaining the prediction results. Furthermore, this invention considers the impact of system errors, analyzing the influence of the two spacecraft's own orbit determination errors on the analytical model calculation results, and constructs the spatial and temporal boundaries of the spacecraft collision region. Finally, combining the analytical model, the spatial and temporal boundaries of the collision region, it proposes a method for predicting spacecraft orbital collision regions and a collision risk determination criterion. This overcomes the limitations of analytical model methods for spatial collision region prediction and collision risk determination based on the SGP4 / SDP4 model and the CW model, and also requires less computation, meeting the requirements for autonomous real-time computing on satellites under resource-constrained conditions. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 This is a flowchart of an analytical model method for predicting collision threat areas and determining collision risk, provided by an embodiment of the present invention;

[0019] Figure 2 This is a schematic diagram of a coplanar collision scenario provided by an embodiment of the present invention;

[0020] Figure 3 This is a schematic diagram of a non-plane collision scenario provided by an embodiment of the present invention;

[0021] Figure 4 This is a schematic diagram of the projection of spacecraft s1 and spacecraft s2 on the celestial sphere under the condition of non-plane intersection provided by an embodiment of the present invention;

[0022] Figure 5 This is a diagram showing the relationship between the true anterior angle and the argument of perigee, provided in one embodiment of the present invention.

[0023] Figure 6 This is a hardware architecture diagram of a computing device provided in an embodiment of the present invention;

[0024] Figure 7 This is a structural diagram of a collision threat area prediction and collision risk determination device provided in an embodiment of the present invention. Detailed Implementation

[0025] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are some embodiments of the present invention, but not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0026] Please refer to Figure 1 This invention provides an analytical model method for predicting collision threat areas and determining collision risks, comprising:

[0027] Step 100: Obtain the orbital parameters and orbital angular momentum of any two spacecraft;

[0028] Step 102: Determine the collision and rendezvous scenario based on the angle between the orbital angular momentum.

[0029] Step 104: Determine the collision scenario calculation model based on the collision and rendezvous scenario, and determine the true anterior angle at the rendezvous point based on the collision scenario calculation model and the orbital parameters;

[0030] Step 106: Calculate the space collision position of each spacecraft at the rendezvous point and the time required to reach the rendezvous point based on the orbital parameters, the true anomaly angle at the rendezvous point, and the orbit determination error, so as to predict the space collision area and assess the collision risk, and obtain the prediction results.

[0031] In this embodiment of the invention, for any two spacecraft's orbital parameters and orbital angular momentum, the collision rendezvous scenario between the two spacecraft is first determined based on the angle between their orbital angular momentum. Then, an analytical model for calculating the intersection points of orbital spatial collision and temporal collision under different collision rendezvous scenarios is established, thereby obtaining the spatial collision position of each spacecraft at the rendezvous point and the time required to reach the rendezvous point. Then, spatial collision region prediction and collision risk assessment are performed to obtain the prediction results. Based on this, the invention considers the influence of system errors, analyzes the impact of the two spacecraft's own orbit determination errors on the analytical model calculation results, and constructs the spatial and temporal boundaries of the spacecraft collision region. Finally, combining the analytical model, the spatial and temporal boundaries of the collision region, a spacecraft orbital collision region prediction method and collision risk assessment criteria are proposed. This overcomes the limitations of spatial collision region prediction and collision risk assessment methods based on the SGP4 / SDP4 model and the CW model, and also requires less computation, meeting the requirements for onboard autonomous real-time computing under resource-constrained conditions.

[0032] The following description Figure 1 The execution method for each step is shown.

[0033] First, in step 100, spacecraft include artificial satellites, manned spacecraft (space stations and manned spacecraft, etc.), and space probes (planetary probes and lunar probes, etc.). The orbital parameters are the six fundamental orbital parameters of the spacecraft at any given time: {a, e, Ω, i, ω, f}, including: semi-major axis a, eccentricity e, right ascension of the ascending node Ω, orbital inclination i, argument of perigee ω, and true anomaly f. The orbital angular momentum h = r × v, where r is the spacecraft's position vector in the geocentric inertial coordinate system, and v is the spacecraft's velocity vector.

[0034] In this invention, the scenarios of orbital collisions and rendezvous between two spacecraft are mainly coplanar collisions and rendezvous (hereinafter referred to as coplanar collisions) and non-coplanar collisions and rendezvous (hereinafter referred to as non-coplanar collisions). A coplanar collision refers to a collision or rendezvous that occurs when the orbits of two spacecraft are on the same orbital plane, such as... Figure 2 As shown; a non-plane collision refers to a collision or meeting that occurs when two spacecraft are orbiting in different orbital planes, such as... Figure 3 As shown. In Figure 2 and Figure 3 In this diagram, s1 and s2 represent spacecraft, o1 and o2 represent the orbits of spacecraft s1 and s2 respectively, and P1 and P2 represent the orbital rendezvous points. Because there are significant differences in characteristics between coplanar and non-coplanar collisions, it is necessary to classify and discuss these two types of collisions separately. Therefore, before predicting spacecraft collision regions and autonomously determining collision risks, it is necessary to first achieve autonomous determination of coplanar and non-coplanar collision scenarios.

[0035] In step 102, the collision scenario is determined based on the angle between the orbital angular momentum, including:

[0036] Based on the preset system error σ, the judgment conditions for collision and rendezvous scenarios are determined;

[0037] If the determination condition is that the angle between the orbital angular momentum is within (-1+σ, 1-σ), then the collision and rendezvous scenario is an off-plane collision.

[0038] If the determination condition is that the angle between the orbital angular momentum is within [-1, -1+σ] or [1-σ, 1], then the collision and rendezvous scenario is a coplanar collision.

[0039] In one specific implementation, the angle Γ between the orbital angular momentum of the two spacecraft orbital planes is determined by the following formula:

[0040]

[0041] Where h1 = r 1t ×v 1t and h2=r 2t ×v 2t Let represent the orbital angular momentum vectors of spacecraft s1 and s2 respectively, with the symbol × indicating the cross product, h1 = ||h1|| and h2 = ||h2||.

[0042] Without considering systematic errors, if Γ = ±1, then the orbital planes of spacecraft s1 and s2 are coplanar; if Γ ≠ ±1, then the orbital planes of spacecraft s1 and s2 are skew. In this invention, to improve the accuracy of the determination, systematic errors are considered, and the determination conditions for collision and rendezvous scenarios are determined as follows: Where σ > 0, and takes a very small positive number, slightly greater than 0, such as 0.0015, 0.001 or smaller, which can be set according to the specific situation.

[0043] In step 104, a collision scenario calculation model is determined based on the collision and rendezvous scenario. The true anomaly angle at the rendezvous point is then determined based on the collision scenario calculation model and orbital parameters, including the following two cases:

[0044] The first scenario: When the collision and rendezvous scenario is a coplanar collision, calculate the angle between the perigee position vectors of any two spacecraft based on the orbital parameters and the position vector of each spacecraft at perigee.

[0045] Calculate the true angle of anomaly for each spacecraft at the rendezvous point based on the position vector and orbital parameters.

[0046] Specifically, in coplanar collisions, f 1a and f 2aThe true anomalies of spacecraft s1 and s2, respectively. 1a and r 2a Let f1 and f2 be the perigee position vectors of spacecraft s1 and s2, respectively, and let f1 and f2 be the true perigee angles of spacecraft s1 and s2 at the current moment, respectively. Based on the orbital parameters of spacecraft s1 {a1, e1, Ω1, i1, ω1, f...} 1a =0} and the orbital parameters of spacecraft s2 {a2,e2,Ω2,i2,ω2,f} 2a =0} Calculate the position vector r of the perigee of spacecraft s1 and s2 in the geocentric inertial coordinate system respectively. 1a and r 2a The angle Δf between the perigee position vectors of any two spacecraft can be calculated using the following formula:

[0047] According to r 1a and r 2a Calculate Q = r 1a ×r 2a If Q(3)≥0 (Q(3) is the value of the component of Q in the third direction, which is a scalar), then f 1|P ≥f 2|P The true anomaly angle f at the orbital collision intersection point P is calculated using the following formula. 1|P and f 2|P :

[0048] f 1|P =φ±arccos(β / ncosφ),φ=arctan(m / n)

[0049] f 1|P =f 2|P +Δf,f 1|P ≥f 2|P

[0050] If Q(3) < 0, then f 1|P <f 2|P The true anomaly angle f at the orbital collision intersection point is calculated using the following formula. 1|P and f 2|P :

[0051] f 1|P =-φ±arccos(β / ncosφ),φ=arctan(m / n)

[0052] f 1|P =f 2|P -Δf,f 1|P <f 2|P

[0053] Wherein, as mentioned in the previous example, in the formula n, m, and β are intermediate quantities; h1 and h2 represent the orbital angular momentum vectors of spacecraft s1 and s2, respectively, h1 = ||h1|| and h2 = ||h2||.

[0054] The second scenario: When the collision and rendezvous scenario is an unplanned collision, the arc length from the point where the projection of each spacecraft's orbit onto the celestial sphere intersects the celestial equatorial plane to the rendezvous point is calculated based on the orbital parameters and the angle between the projections of the orbits of any two spacecraft onto the celestial sphere. The orbital parameters include the semi-major axis, eccentricity, right ascension of the ascending node, orbital inclination, and argument of perigee.

[0055] Calculate the true anomaly angle of each spacecraft's orbit at the rendezvous point based on the orbital inclination, right ascension of the ascending node, argument of perigee, and arc length.

[0056] Specifically, in non-plane collisions, such as Figure 4 As shown, the orbit o1 of spacecraft s1, the orbit o2 of spacecraft s2, and the projection of the equatorial plane onto the celestial sphere form a spherical triangle, where P1 and P2 represent the orbital intersection points (the points where the projections of the orbits onto the celestial sphere intersect). Let i1 and i2 represent the orbital inclinations of spacecraft s1 and s2, respectively. Let A and B be the ascending (descending) nodes of spacecraft s1 and s2, respectively. Arc AB represents the difference in right ascension ΔΩ between the ascending nodes of spacecraft s1 and s2. 12 (Same at the descending node), AP1 represents the arc length u1 of spacecraft s1 from its ascending node (descending node) to the intersection point P1, and BP1 represents the arc length u2 of spacecraft s2 from its ascending node (descending node) to the intersection point P1.

[0057] For the second scenario, a) the arc length from the point where the projection of each spacecraft's orbit onto the celestial sphere intersects the celestial equatorial plane to the point of intersection is determined by the following formula:

[0058]

[0059] ΔΩ 12 =|Ω1-Ω2|

[0060]

[0061] Wherein, any two spacecraft include the first spacecraft s1 and the second spacecraft s2; Let i1, Ω1, and u1 be the angle between the orbits of any two spacecraft projected onto the celestial sphere; i1, Ω1, and u1 are the orbital inclination, right ascension of the ascending node, and arc length of the first spacecraft, respectively; i2, Ω2, and u2 are the orbital inclination, right ascension of the ascending node, and arc length of the second spacecraft, respectively; u1∈(0,π / 2), u2∈(0,π / 2),

[0062] b) Based on such Figure 5 The diagram showing the relationship between true anomaly and argument of perigee illustrates that the true anomaly of each spacecraft's orbit at the rendezvous point is determined using the following formula:

[0063]

[0064] Among them, f k|P Let ω be the true anomaly angle of the orbit of the k-th spacecraft at the rendezvous point P; k u is the perigee argument of the orbit of the k-th spacecraft; k Let i be the arc length from the point where the projection of the k-th spacecraft's orbit onto the celestial sphere intersects the celestial equatorial plane to the point of intersection; k Let be the orbital inclination of the k-th spacecraft; Ω1 and Ω2 are the right ascensions of the ascending nodes of the first and second spacecraft, respectively, where k = 1 and 2; P is either P1 or P2 (e.g., ...). Figures 2 to 4 (as shown in the image).

[0065] In this invention, based on orbital parameters and the determined collision and rendezvous scenario, the true anomaly angles of each spacecraft at the rendezvous point can be analytically calculated using the aforementioned formula. This calculation does not involve numerical iteration, and the results are accurate and efficient, meeting the real-time requirements of limited onboard computing resources. Furthermore, the orbital parameters used in the formula can be directly obtained through onboard measurement and information processing, enabling autonomous onboard implementation.

[0066] For step 106, based on the orbital parameters, the true anomaly angle at the rendezvous point, and the orbit determination error, the space collision position of each spacecraft at the rendezvous point and the time required to reach the rendezvous point are calculated to predict the space collision area and assess the collision risk, yielding prediction results, including:

[0067] S1: Determine the space collision position of each spacecraft at the rendezvous point based on the orbital parameters and the true anomaly angle at the rendezvous point, as well as the time required to reach the rendezvous point;

[0068] S2: Based on the collision and rendezvous scenario and orbit determination error, use the error propagation model to calculate the position error of each spacecraft at the space collision location and the time error required to reach the rendezvous point.

[0069] S3: Determine the spatial judgment threshold based on the positional error between any two spacecraft, and determine the time judgment threshold based on the time error between any two spacecraft;

[0070] S4: Determine whether the length of the difference between the spatial collision positions of any two spacecraft is greater than the spatial determination threshold, and whether the absolute value of the difference between the time required for any two spacecraft to reach the rendezvous point is greater than the time determination threshold; if the determination results are both negative, proceed to step S5.

[0071] S5: The prediction result indicates that there is a risk of collision between the first and second spacecraft, and the collision area is a spherical region centered on the intersection point and with a spatial determination threshold as the radius.

[0072] In a preferred embodiment, step S1 determines the spatial collision location of each spacecraft at the rendezvous point using the following formula.

[0073]

[0074] Where, r k|P Let a be the spatial collision position vector of the orbit of the k-th spacecraft at the rendezvous point P; k e k Ω k 、i k ω k f k|P These are the semi-major axis, eccentricity, right ascension of the ascending node, orbital inclination, argument of perigee, and true anomaly of the orbit of the k-th spacecraft, respectively. At this time, f k|P Let be the true anomaly angle of the orbit of the k-th spacecraft at the rendezvous point P, where k = 1, 2; P is P1 or P2 (e.g., ...). Figures 2 to 4 (as shown in the image);

[0075] Step S1 uses the following formula to determine the time required for each of the spacecraft to reach the rendezvous point at the current moment:

[0076]

[0077]

[0078] In the formula, T1 represents the orbital period of spacecraft s1, and T2 represents the orbital period of spacecraft s2. k = 1, 2 represent spacecraft s1 and spacecraft s2 respectively; E1, E 1t All are intermediate variables of spacecraft s1; E2, E 2t All of these are intermediate variables for spacecraft s2, and μ is the Earth's gravitational constant.

[0079] In a preferred embodiment, following the previous example, in step S2, for any two spacecraft (including spacecraft s1 and spacecraft s2), based on the orbit determination error of spacecraft s1 {δa1,δe1,δΩ1,δi1,δω1,δf}... 1t The orbit determination errors of spacecraft s2 and spacecraft s2 are {δa2,δe2,δΩ2,δi2,δω2,δf}. 2t The position error δr is calculated using the following error propagation model, taking into account the collision and rendezvous scenarios, δf2}. k|P:

[0080]

[0081] In the formula,

[0082]

[0083] Where, δr k|P Let a be the position error of the k-th spacecraft's orbit at the rendezvous point P; k e k Ω k 、i k ω k f k|P Let f be the semi-major axis, eccentricity, right ascension of the ascending node, orbital inclination, argument of perigee, and true perigee angle of the k-th spacecraft, respectively; at this time, f k|P Let be the true anomaly angle of the orbit of the k-th spacecraft at the rendezvous point P, where k = 1, 2; P is P1 or P2 (e.g., ...). Figures 2 to 4 (as shown in the image);

[0084] (1) If it is a coplanar collision, then there exists

[0085]

[0086] Following the previous example, Δf = |f 1|P -f 2|P |;

[0087] (2) If it is a collision between opposite surfaces, then there exists

[0088]

[0089] For any two spacecraft (including spacecraft s1 and spacecraft s2), based on the orbit determination error of spacecraft s1 {δa1,δe1,δΩ1,δi1,δω1,δf} 1t ,δf1} (including semi-major axis error δa1, eccentricity error δe1, right ascension error of ascending node δΩ1, orbital inclination error δi1, perigee argument error δω1, and true perigee angle error at time t δf) 1t The true anomaly angle error at the rendezvous point δf1) and the orbit determination error of spacecraft s2 {δa2,δe2,δΩ2,δi2,δω2,δf} 2t The time error is calculated using the following error propagation model: δf2} and collision / intersection scenarios. sk :

[0090]

[0091] Where, f in the above formulak That is, f k|P f kt Let be the true anomaly angle at time t. It should be noted that the orbit determination error varies between different spacecraft, and the orbit determination error can be determined by the specific spacecraft.

[0092] In a preferred embodiment, following the previous example, step S3 determines a spatial determination threshold based on the positional error between any two spacecraft, and determines a time determination threshold based on the time error between any two spacecraft, including:

[0093] The sum of the lengths of the position errors of any two spacecraft is determined as the space determination threshold d. safe ;d safe =||δr 1|P ||+||δr 2|P ||;δr 1|P δr 2|P These are the positional errors of the orbits of spacecraft s1 and s2 at the rendezvous point P, respectively.

[0094] The sum of the absolute values ​​of the time errors between any two spacecraft is determined as the time determination threshold t. safe ;t safe =|δt s1 |+|δt s2 |;δt s1 δt s2 These represent the time errors when spacecraft s1 and spacecraft s2 arrive at the rendezvous point P, respectively.

[0095] Following the previous example, in step S4, it is determined whether the length of the difference between the spatial collision positions of any two spacecraft is greater than the spatial determination threshold, i.e., ||r 1|P -r 2|P ||>d safe ;

[0096] And whether the absolute value of the difference between the times required for any two spacecraft to reach the rendezvous point is greater than the time determination threshold, i.e., |t s1 -t s2 |>t safe ;

[0097] If both judgments are negative, then proceed to step S5.

[0098] For example, if at the intersection point P1, ||r 1|P1 -r 2|P1 ||≤d safe If so, it is determined that spacecraft s1 and spacecraft s2 have a space collision, and the space collision risk area is defined as r. 1|P1 (or r) 2|P1 With ) as the center and radius d safeWithin the spherical region, then continue with time collision detection; if |t s1 -t s2 |≤t safe If the time collision occurs, spacecraft s1 and spacecraft s2 are determined to have a time collision. Similarly, there is no spatial collision at the rendezvous point P2, but there is a time collision. Therefore, the prediction result is: spacecraft s1 and spacecraft s2 collide at the rendezvous point P1.

[0099] In this invention, through the calculations of steps S1 to S5 above, the determination result of whether there is a collision risk between any two spacecraft and the collision area prediction result under the condition of collision risk can be obtained. This information can provide effective reference input for collision threat avoidance decision-making and execution.

[0100] Compared with existing technologies, this invention has the following advantages: First, all calculations are analytical, without numerical iteration, resulting in accurate and efficient calculations that meet the real-time requirements of limited onboard computing resources. Second, all information in this invention can be directly obtained through onboard measurement and information processing, enabling autonomous implementation onboard. Third, the impact of system errors on the model is analyzed using an error propagation model based on orbit determination errors, providing a theoretical design method for spatial and temporal decision thresholds, rather than relying solely on human experience, making the design more reasonable and reliable. Fourth, the method proposed in this invention makes decisions at both spatial and temporal collision levels, improving the reliability of the decision results and reducing the false alarm rate.

[0101] like Figure 6 , Figure 7 As shown, this invention provides a device for predicting collision threat areas and determining collision risks. The device can be implemented in software, hardware, or a combination of both. From a hardware perspective, such as... Figure 6 The diagram shown is a hardware architecture diagram of a computing device containing a collision threat area prediction and collision risk assessment device provided in an embodiment of the present invention. Except for... Figure 6 In addition to the processor, memory, network interface, and non-volatile memory shown, the computing device in the embodiment may also include other hardware, such as a forwarding chip responsible for processing packets. Taking software implementation as an example, such as... Figure 7 As shown, a device in a logical sense is formed by the CPU of its computing device reading the corresponding computer program from non-volatile memory into memory and running it. This embodiment provides a collision threat area prediction and collision risk determination device, comprising:

[0102] The acquisition module 700 is used to acquire the orbital parameters and orbital angular momentum of the first and second spacecraft.

[0103] Scene determination module 702 is used to determine the collision and rendezvous scene based on the angle between the orbital angular momentum;

[0104] The prediction and judgment module 704 is used to determine the collision scenario calculation model based on the collision and rendezvous scenario, and to determine the true anomaly angle at the rendezvous point based on the collision scenario calculation model and orbital parameters; and to calculate the space collision position of the first spacecraft and the time required to reach the rendezvous point of the second spacecraft respectively based on the orbital parameters, the true anomaly angle at the rendezvous point and the orbit determination error, so as to perform space collision area prediction and collision risk judgment, and obtain prediction results.

[0105] In some specific implementations, the acquisition module 700 can be used to perform the above step 100, the scene determination module 702 can be used to perform the above step 102, and the prediction and judgment module 704 can be used to perform the above steps 104 and 106.

[0106] In some specific implementations, the scene determination module 702 is also used to perform the following operations:

[0107] Based on the preset system error σ, the judgment conditions for collision and rendezvous scenarios are determined;

[0108] If the determination condition is that the angle between the orbital angular momentum is within (-1+σ, 1-σ), then the collision and rendezvous scenario is an off-plane collision.

[0109] If the determination condition is that the angle between the orbital angular momentum is within [-1, -1+σ] or [1-σ, 1], then the collision and rendezvous scenario is a coplanar collision.

[0110] In some specific implementations, the prediction and judgment module 704 is also used to perform the following operations:

[0111] In the case of a coplanar collision, the angle between the perigee position vectors of any two spacecraft is calculated based on the orbital parameters and the position vector of each spacecraft at perigee.

[0112] Calculate the true anomaly angle of each spacecraft at the rendezvous point based on the position vector and orbital parameters;

[0113] or,

[0114] When the collision and rendezvous scenario is an uncoordinated collision, the arc length from the point where the projection of each spacecraft's orbit onto the celestial sphere intersects the celestial equatorial plane to the rendezvous point is calculated based on the orbital parameters and the angle between the projections of the orbits of any two spacecraft onto the celestial sphere. The orbital parameters include the semi-major axis, eccentricity, right ascension of the ascending node, orbital inclination, and argument of perigee.

[0115] Calculate the true anomaly angle of each spacecraft's orbit at the rendezvous point based on the orbital inclination, right ascension of the ascending node, argument of perigee, and arc length.

[0116] In some specific implementations, the prediction and judgment module 704 is also used to perform the following operations:

[0117] The arc length from the point where the projection of each spacecraft's orbit onto the celestial sphere intersects the celestial equatorial plane to the point of intersection is determined by the following formula:

[0118]

[0119] ΔΩ 12 =|Ω1-Ω2|

[0120]

[0121] Among them, any two spacecraft include the first spacecraft and the second spacecraft; Let i1, Ω1, and u1 be the angle between the orbits of any two spacecraft projected onto the celestial sphere; i1, Ω1, and u1 are the orbital inclination, right ascension of the ascending node, and arc length of the first spacecraft, respectively; i2, Ω2, and u2 are the orbital inclination, right ascension of the ascending node, and arc length of the second spacecraft, respectively.

[0122] In some specific implementations, the prediction and judgment module 704 is also used to perform the following operations:

[0123] The true anomaly of each spacecraft's orbit at the rendezvous point is determined by the following formula:

[0124]

[0125] Among them, f k|P Let ω be the true anomaly angle of the orbit of the k-th spacecraft at the rendezvous point P; k u is the perigee argument of the orbit of the k-th spacecraft; k Let i be the arc length from the point where the projection of the k-th spacecraft's orbit onto the celestial sphere intersects the celestial equatorial plane to the point of intersection; k Let Ω1 and Ω2 be the orbital inclination of the k-th spacecraft; Ω1 and Ω2 are the right ascensions of the ascending nodes of any two spacecraft.

[0126] In some specific implementations, the prediction and judgment module 704 is also used to perform the following operations:

[0127] The space collision location of each spacecraft at the rendezvous point is determined based on the orbital parameters and the true anomaly angle at the rendezvous point, as well as the time required to reach the rendezvous point;

[0128] Based on the collision and rendezvous scenario and orbit determination error, the position error of each spacecraft at the space collision location and the time error required to reach the rendezvous point are calculated using the error propagation model.

[0129] The sum of the lengths of the position errors of any two spacecraft is determined as the spatial decision threshold; the sum of the absolute values ​​of the time errors of any two spacecraft is determined as the time decision threshold.

[0130] Determine whether the length of the difference between the spatial collision locations of any two spacecraft is greater than a spatial determination threshold, and determine whether the absolute value of the difference between the time required for any two spacecraft to reach the rendezvous point is greater than a time determination threshold;

[0131] If all the judgment results are negative, the prediction result is that there is a risk of collision between the first and second spacecraft, and the collision area is a spherical area centered on the intersection point and with a spatial judgment threshold as the radius.

[0132] In some specific implementations, the prediction and judgment module 704 is also used to perform the following operations:

[0133] The positional error of the spatial collision location is determined by the following formula:

[0134]

[0135] Where, δr k|P Let a be the position error of the k-th spacecraft's orbit at the rendezvous point P; k e k Ω k 、i k ω k f k|P Let δa be the semi-major axis, eccentricity, right ascension of the ascending node, orbital inclination, argument of perigee, and true anomaly at the rendezvous point P of the k-th spacecraft. k ,δe k ,δΩ k ,δi k ,δω k ,δf k|P All of these represent the orbit determination error of the k-th spacecraft.

[0136] It is understood that the structures illustrated in the embodiments of the present invention do not constitute a specific limitation on a collision threat area prediction and collision risk assessment device. In other embodiments of the present invention, a collision threat area prediction and collision risk assessment device may include more or fewer components than illustrated, or combine some components, or split some components, or have different component arrangements. The illustrated components may be implemented in hardware, software, or a combination of software and hardware.

[0137] The information interaction and execution process between the modules in the above-mentioned device are based on the same concept as the method embodiment of the present invention, and the specific details can be found in the description in the method embodiment of the present invention, and will not be repeated here.

[0138] This invention also provides a computing device, including a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, it implements an analytical model method for predicting collision threat areas and determining collision risks according to any embodiment of this invention.

[0139] This invention also provides a computer-readable storage medium storing a computer program. When executed by a processor, the computer program causes the processor to perform an analytical model method for collision threat area prediction and collision risk determination according to any embodiment of this invention.

[0140] Embodiments of this application also provide a computer program product, which includes a computer program. A processor of a computer device reads the computer program from a computer-readable storage medium and executes the computer program, causing the computer device to perform an analytical model method for collision threat area prediction and collision risk determination as described in any of the above embodiments.

[0141] Specifically, a system or apparatus equipped with a storage medium may be provided, on which software program code implementing the functions of any of the embodiments described above is stored, and the computer (or CPU or MPU) of the system or apparatus may read and execute the program code stored in the storage medium.

[0142] In this case, the program code read from the storage medium can itself implement the function of any of the above embodiments, and therefore the program code and the storage medium storing the program code constitute part of the present invention.

[0143] Examples of storage media used to provide program code include floppy disks, hard disks, magneto-optical disks, optical disks (such as CD-ROM, CD-R, CD-RW, DVD-ROM, DVD-RAM, DVD-RW, DVD+RW), magnetic tapes, non-volatile memory cards, and ROMs. Alternatively, program code can be downloaded from a server computer via a communication network.

[0144] Furthermore, it should be clear that not only can the program code read by the computer be executed, but also the operating system or other components operating on the computer can be instructed based on the program code to perform some or all of the actual operations, thereby realizing the function of any of the embodiments described above.

[0145] Furthermore, it is understood that the program code read from the storage medium is written to the memory set in the expansion board inserted into the computer or to the memory set in the expansion module connected to the computer. Then, based on the instructions of the program code, the CPU or other components installed on the expansion board or expansion module execute some and all of the actual operations, thereby realizing the function of any of the above embodiments.

[0146] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0147] Those skilled in the art will understand that all or part of the steps of the above method embodiments can be implemented by hardware related to program instructions. The aforementioned program can be stored in a computer-readable storage medium. When the program is executed, it performs the steps of the above method embodiments. The aforementioned storage medium includes various media that can store program code, such as ROM, RAM, magnetic disk, or optical disk.

[0148] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims

1. An analytical model method for predicting collision threat areas and determining collision risk, characterized in that, include: Obtain the orbital parameters and orbital angular momentum of any two spacecraft; The collision and rendezvous scenario is determined based on the angle between the orbital angular momentum. When the collision rendezvous scenario is a coplanar collision, the angle between the perigee position vectors of any two spacecraft is calculated based on the orbital parameters and the position vector of each spacecraft at perigee. Calculate the true anomaly angle of each spacecraft at the rendezvous point based on the position vector and the orbital parameters; When the collision rendezvous scenario is an unplanar collision, the arc length from the point where the projection of the orbit of each spacecraft onto the celestial sphere intersects the celestial equatorial plane to the rendezvous point is calculated based on the orbital parameters and the angle between the projections of the orbits of any two spacecraft onto the celestial sphere. The orbital parameters include the semi-major axis, eccentricity, right ascension of the ascending node, orbital inclination, and argument of perigee. Calculate the true anomaly angle of each spacecraft's orbit at the rendezvous point based on the orbital inclination, the right ascension of the ascending node, the argument of perigee, and the arc length; The spatial collision position of each spacecraft at the rendezvous point and the time required to reach the rendezvous point are determined based on the orbital parameters and the true anomaly at the rendezvous point. Based on the collision and rendezvous scenario and the orbit determination error, the position error of each spacecraft at the space collision location and the time error required to reach the rendezvous point are calculated using the error propagation model. A spatial determination threshold is determined based on the positional error between any two spacecraft, and a time determination threshold is determined based on the time error between any two spacecraft. Determine whether the length of the difference between the spatial collision positions of any two spacecraft is greater than the spatial determination threshold, and determine whether the absolute value of the difference between the time required for any two spacecraft to reach the rendezvous point is greater than the time determination threshold; If all the judgment results are negative, the prediction result is that there is a risk of collision between the first and second spacecraft, and the collision area is a spherical area centered on the intersection point and with a spatial judgment threshold as the radius.

2. The method according to claim 1, characterized in that, Determining the collision and rendezvous scenario based on the angle between the orbital angular momentum includes: According to the preset system error σ Determine the criteria for determining collision and meeting scenarios; If the determination condition is that the angle between the orbital angular momentum is located at (-1+) σ ,1- σ If the collision scenario is within the specified range, then it is an unplanned collision. If the determination condition is that the angle between the orbital angular momentum is located in [-1, -1+], then... σ ] or [1- σ If the collision and meeting scenario is within [1], then the collision and meeting scenario is a coplanar collision.

3. The method according to claim 1, characterized in that, The arc length from the point where the projection of the orbit of each of the spacecraft onto the celestial sphere intersects the celestial equatorial plane to the point of intersection is determined by the following formula: Wherein, any two spacecraft include a first spacecraft and a second spacecraft; Let be the angle between the projections of the orbits of any two spacecraft onto the celestial sphere. , , These are the orbital inclination, right ascension of the ascending node, and arc length of the first spacecraft, respectively. , , These are the orbital inclination, right ascension of the ascending node, and arc length of the second spacecraft, respectively.

4. The method according to claim 1, characterized in that, The true anomaly of each of the spacecraft's orbits at the rendezvous point is determined by the following formula: in, For the first k The true anomaly angle of the orbits of the two spacecraft at the rendezvous point P; For the first k The perigee angle of a spacecraft's orbit; For the first k The arc length from the point where the projection of a spacecraft's orbit onto the celestial sphere intersects the celestial equatorial plane to the point of intersection; For the first k The orbital inclination of a spacecraft's orbit; , Let be the right ascension of the ascending nodes of any two spacecraft.

5. The method according to claim 1, characterized in that, The step of determining a spatial determination threshold based on the positional error between any two spacecraft and determining a temporal determination threshold based on the temporal error between any two spacecraft includes: The sum of the lengths of the position errors of any two spacecraft is determined as the spatial determination threshold; The sum of the absolute values ​​of the time errors of any two spacecraft is determined as the time determination threshold.

6. The method according to claim 1, characterized in that, The positional error of the spatial collision location is determined by the following formula: in, For the first k The positional error of the orbits of the spacecraft at the rendezvous point P; , , , , , Respectively k The semi-major axis, eccentricity, right ascension of the ascending node, orbital inclination, argument of perigee, and true anomaly at the rendezvous point P of a spacecraft; All are the first k The orbit determination error of a spacecraft.

7. A device for predicting collision threat areas and determining collision risk, used to implement the method described in any one of claims 1 to 6, characterized in that, include: The acquisition module is used to acquire the orbital parameters and orbital angular momentum of any two spacecraft. The scene determination module is used to determine the collision and rendezvous scene based on the angle between the orbital angular momentum. The prediction and judgment module is used to determine the collision scenario calculation model based on the collision rendezvous scenario, and to determine the true anomaly angle at the rendezvous point based on the collision scenario calculation model and the orbital parameters; and to calculate the space collision position of each spacecraft at the rendezvous point and the time required to reach the rendezvous point based on the orbital parameters, the true anomaly angle at the rendezvous point and the orbit determination error, so as to perform space collision area prediction and collision risk judgment, and obtain prediction results.

8. The apparatus according to claim 7, characterized in that, The scene determination module is also used to perform the following operations: According to the preset system error σ Determine the criteria for determining collision and meeting scenarios; If the determination condition is that the angle between the orbital angular momentum is located at (-1+) σ ,1- σ If the collision scenario is within the specified range, then it is an unplanned collision. If the determination condition is that the angle between the orbital angular momentum is located in [-1, -1+], then... σ ] or [1- σ If the collision and meeting scenario is within [1], then the collision and meeting scenario is a coplanar collision.

9. A computing device comprising a memory and a processor, wherein the memory stores a computer program, and the processor, when executing the computer program, implements the method as described in any one of claims 1-6.

10. A computer-readable storage medium having a computer program stored thereon, which, when executed in a computer, causes the computer to perform the method of any one of claims 1-6.

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