Satellite in-situ shielding and hiding method for ground-based radar detection

Abstract

The invention provides a satellite in-situ shielding and hiding method for ground-based radar detection. The satellite in-situ shielding and hiding method comprises the following steps: step 1, carrying out visibility modeling for ground-based comprehensive detection; and step 2, establishing a trajectory planning optimization algorithm based on three-dimensional A *. The step 1 comprises the following steps of: 1.1, establishing an in-situ shielding constraint; step 1.2, establishing an earth shielding constraint; 1.3, establishing an earth shadow constraint; in-situ shielding, earth shielding and earth shadow shielding constraints form a visibility resolving model; and step 1.4, establishing a constraint solution algorithm to solve the visibility solution model. According to the method, a novel stealth strategy can be provided, the stealth capacity of the satellite under multi-band and multi-angle radar detection is improved, and a theoretical basis is provided for satellite stealth design and on-orbit deployment.

Description

Technical Field

[0001] The present invention relates to the field of satellite on-orbit stealth, and in particular to a satellite in-situ shielding stealth method for ground-based radar detection. Background Art

[0002] The stealth capability of satellites in space confrontation scenarios has become an important means to improve their survivability. Among the existing means of detecting space targets, radar detection has become the main means due to its characteristics of all-time, all-weather, wide-area, and multi-target. Correspondingly, radar stealth has also become the primary technical means of satellite stealth. Its core indicator is the size of the radar cross section RCS (Radar Cross Section), that is, the size of the reflection cross-section of the satellite in the direction of radar illumination.

[0003] Radar RCS stealth technology uses a series of comprehensive means to reduce the RCS of spacecraft or targets in radar detection, thereby effectively reducing the probability of being detected and tracked by the radar system and improving the survivability of the target. Radar stealth technology mainly includes two means: configuration optimization and coating materials. Configuration optimization is to reduce the reflection surface of radar waves or the intensity of reflected signals by optimizing the geometric shape of the target, thereby reducing the radar reflected echo; coating materials use specific absorbing coatings or materials to absorb radar wave energy and reduce the intensity of reflected echoes.

[0004] However, while the above-mentioned appearance and material stealth achieve stealth effects, they also severely restrict the functions and performance of satellites. If a stealth appearance is adopted, the satellite's solar panels, antennas and other protrusions must be hidden or weakened, which will limit the satellite's power consumption and measurement and control. For example, SAR satellites with long antennas are not suitable for structural stealth; and materials such as metamaterials and wave absorbers covering the surface of the satellite will inevitably affect the satellite's thermal control. In addition, with the continuous improvement of space-based detection technology, optical detection methods have also begun to pose a threat to satellites. Therefore, how to achieve effective stealth in multiple frequency bands, multiple angles, and multiple detection scenarios while ensuring that its own capabilities are not limited has become an urgent problem that needs to be solved in current satellite stealth technology. Summary of the invention

[0005] Purpose of the invention: The technical problem to be solved by the present invention is to provide a satellite in-situ shielding and stealth method for ground-based radar detection in view of the deficiencies in the prior art. The method can ensure the satellite function and performance while realizing the stealth of micro-satellites within the observation arc of the ground radar base station with the help of in-situ shielding of medium and large satellites.

[0006] The method of the present invention comprises the following steps:

[0007] Step 1: Visibility modeling for ground-based integrated detection;

[0008] Step 2: Establish a trajectory planning optimization algorithm based on three-dimensional A*.

[0009] Step 1 includes:

[0010] Step 1.1, establish in-situ occlusion constraints;

[0011] Step 1.2, establish earth occlusion constraints;

[0012] Step 1.3, establish the ground shadow constraint; the in-situ occlusion, earth occlusion, and ground shadow occlusion constraints constitute the visibility solution model;

[0013] Step 1.4, establishing a constraint solving algorithm to solve the visibility solving model.

[0014] Step 1.1 includes:

[0015] In-situ occlusion is based on the relative position relationship between the own microsatellite and the target spacecraft and the ground-based detection system. By designing the microsatellite orbit, the microsatellite is always blocked by the target spacecraft during operation, blocking the direct observation of the microsatellite by the ground-based detection system, thus forming a visibility constraint on the ground. An in-situ occlusion constraint scene is built for the own microsatellite and the target spacecraft, respectively, with a 0.2m×0.2m×0.3m microsatellite and a 1.4m×2.8m×10m Starlink satellite.

[0016] In the process of geometric position relationship modeling, the target spacecraft model is first simplified, and the shape feature points of the target spacecraft are extracted according to the configuration characteristics of the target spacecraft. The target spacecraft is equivalent to a rectangle, and the ground-based detection station is regarded as a mass point in the modeling; the four vertices of the equivalent rectangle of the detection station and the target spacecraft are regarded as a quadrangular pyramid, and the inner height h is expressed as:

[0017]

[0018] Among them, P sur represents the coordinate vector of the ground-based detection station in the J2000 inertial system; P1, P2, P3 respectively represent the coordinate vectors of the three vertices of the rectangle in the J2000 inertial system;

[0019] In the in-situ occlusion constraint, the angle α formed by each vertex of the rectangle and the equivalent mass point of the microsatellite and the equivalent mass point of the detection station is i Need to be greater than the angle β between each edge of the tetrahedron and the ground i , i = 1, 2, 3, 4, and the distance between the microsatellite and the detection station is greater than the height of the tetrahedron. The in-situ occlusion constraint must meet the following conditions at the same time:

[0020]

[0021] h<||P s -P sur || (3)

[0022] Where P i represents the coordinate vectors of the vertices of the rectangle in the J2000 inertial system, P s Represents the position vector of the microsatellite in the J2000 system.

[0023] Step 1.2 includes: assuming that the earth is a perfect sphere, the earth occlusion constraint formula is obtained as follows:

[0024]

[0025] Among them, r S 、r sur They represent the position vectors of the space target and the ground detection station in the J2000 inertial system respectively; θ is the field of view angle of the detection station.

[0026] Step 1.3 includes: the shadow area of ​​the earth blocking the sun's rays is a cone, and the vertex U of the cone is set as the umbra point. The position vector r of the umbra point is calculated by the following formula: umb and cone angle θ umb :

[0027]

[0028] Where R sun is the radius of the sun, R e is the radius of the Earth, r sun is the sun position vector;

[0029] The angle between the negative direction of the umbra point position vector and the umbra point U pointing to the space target S should be greater than the umbra angle. To obtain the ground shadow constraint, the following two conditions must be met at the same time:

[0030] r umb ·r S >0 (7)

[0031]

[0032] Among them, r umb represents the position vector of the umbra point U in the J2000 inertial system, r umb2S Represents the vector pointing from the umbra point to the space target.

[0033] Step 1.4 includes: any ground-based optical or radar detection system can detect the space target only when all the constraints in steps 1.1 to 1.3 are not met; a serial algorithm is used to solve the constraints of the detection system, so that the sub-state quantity A i , i=1,2,3, when i is 1, 2, 3, Ai They represent the three sub-constraint states of the ground-based detection system: in-situ occlusion, earth occlusion, and earth shadow occlusion. When the state value is 1, it means that the constraint is satisfied, and the space target can avoid the detection of the ground-based detection system. When the state value is 0, it means that the constraint is not satisfied, and the ground-based detection system can detect the space target. Let the state quantity A represent the constraint state of a ground-based detection system. The calculation relationship between the state quantity and the sub-state quantity is A=∪A i , that is, calculate in turn whether the ground-based detection system satisfies the sub-constraint conditions. If one of the sub-constraint conditions is met, A=1, and the space target cannot be detected by this ground-based detection system. Repeat the process of step 1.4 to traverse all the set ground-based detection systems, and finally obtain the detection status of the space target to the ground at the current moment.

[0034] Step 2 includes:

[0035] Step 2.1, expand the three-dimensional space sub-node;

[0036] In the extended three-dimensional A* algorithm, construct the nth parent node (x n ,y n ,z n )'s child node (x n+1 ,y n+1 ,z n+1 ) is generated by:

[0037] (x n+1 ,y n+1 ,z n+1 )=(x n +Δx,y n +Δy,z n +Δz) (9)

[0038] Among them, Δx, Δy, Δz are the expansion steps of the child nodes, the values ​​of Δx, Δy, Δz are d, -d or 0, but not 0 at the same time, and d is the side length of the cube;

[0039] Step 2.2, define the three-dimensional cost function;

[0040] Step 2.3, construct an optimization evaluation function;

[0041] Step 2.4, establish a dynamic algorithm process.

[0042] Step 2.2 includes:

[0043] The evaluation function expression of the traditional A* algorithm in a two-dimensional plane is:

[0044] f(n)=g(n)+h(n) (10)

[0045] Where f(n) is the heuristic information strength function, g(n) is the cost function from the starting point to the current position, and h(n) is the estimated cost function from the current node to the target point. In a three-dimensional environment, the h(n) expression in the evaluation function will also be extended to three dimensions:

[0046]

[0047] Among them, (x goal ,y goal ,z goal ) is the coordinate of the target point in the three-dimensional coordinate system.

[0048] Step 2.3 includes:

[0049] The constructed optimization evaluation function f′(n) is:

[0050]

[0051] Among them, the intermediate parameter X∈[1,+∞].

[0052] Step 2.4 includes:

[0053] Step 2.4.1, input the coordinates of the starting point, target point, ground-based detection station and performance parameters (such as detection field of view, etc.);

[0054] Step 2.4.2, gradually calculating the sub-nodes of the path planning based on the set planning step size;

[0055] Step 2.4.3, convert the sub-nodes in the path planning to the geocentric inertial system;

[0056] Step 2.4.4, traversing the child nodes based on the visibility solution model;

[0057] Step 2.4.5, retain the child nodes in the detection blind area solved in step 2.4.4;

[0058] Step 2.4.6, calculate the optimal node at this moment by optimizing the evaluation function f′(n);

[0059] Step 2.4.7, plan the path to the optimal node at this moment;

[0060] Step 2.4.7, determine whether the target point has been reached. If so, output the planned path node coordinates, otherwise return to step 2.4.2.

[0061] The present invention also provides an electronic device, including a processor and a memory, wherein the memory stores program code, and when the program code is executed by the processor, the processor executes the steps of the stealth method.

[0062] The present invention also provides a storage medium storing a computer program or instruction, which executes the steps of the stealth method when the computer program or instruction is run on a computer.

[0063] The present invention also provides a verification method for verifying the stealth method of the present invention, comprising the following steps:

[0064] Step 1: Calculate the radar cross section (RCS) of satellite surface elements using the finite element method and Lambert's cosine law to obtain the RCS calculation method for complex configuration satellites;

[0065] Step 2: In the in-situ occlusion scenario, the overall RCS of the in-situ occlusion system is calculated by combining the multipath effect caused by the positional relationship between the occluding satellite and the micro-satellite;

[0066] Step 3: Analyze the in-situ shielding stealth effect based on the size and relative distance between the shielding satellite and the micro-satellite.

[0067] In step 1, the finite element method and Lambert's cosine law are used to calculate the electromagnetic wave reflection energy flux density of the satellite surface element. The formula is:

[0068]

[0069] Among them, I r Represents the energy flux density reflected to the radar detector, dI r represents the energy reflected from the satellite unit surface element to the radar detector, dp is the incident power of the radar electromagnetic wave, and ρ B represents the back reflectivity, dS is the satellite surface element, θ is the incident angle, and R represents the distance between the target and the ground-based radar detection system.

[0070] In step 1, the incident and reflected energy flux densities of the surface element are accumulated and substituted into the RCS definition formula to obtain the radar cross section RCS calculation method for complex surface satellites, where RCS is represented by the symbol σ and S triangle represents the surface area of ​​the satellite facing the radar, and the RCS calculation formula is:

[0071] σ=4πρ B cosθS triangle (14).

[0072] In step 2, the overall RCSσ of the in-situ shading system is calculated using the following formula: total :

[0073]

[0074] in, denote the scattering amplitude of the obstructing satellite and the scattering amplitude of the microsatellite, respectively, and e jφrepresents the scattering phase delay of the microsatellite, where e is the base of the natural logarithm, j is the imaginary unit, φ represents the phase angle of the scattering delay; σ multi Represents the multipath effect between two satellites.

[0075] Step 2 also includes: for the multipath effect between the two satellites, the phase and amplitude changes are calculated by the path difference, and the formula is:

[0076]

[0077] Among them, Δφ represents the delay phase angle of the multipath effect, λ represents the radar wavelength, and Δr represents the distance between the two satellites, that is, the reflection path length of the radar wave between the two satellites;

[0078] The calculation formula for the overall RCS of the in-situ shading system is:

[0079]

[0080] Here, k is a constant related to the scattering properties.

[0081] Step 3 includes: To achieve the in-situ occlusion stealth effect, formula (19) must be satisfied, where when the ratio of both sides of the formula is greater than 10 times, it is considered to satisfy the far greater than relationship:

[0082]

[0083] The distance between two satellites must satisfy the following formula (20):

[0084]

[0085] Where D blocker represents the envelope diameter of the obstructed satellite, θ radar Indicates the detection field of view of the radar;

[0086] According to formulas (19) and (20), the size and distance conditions of the micro-satellite and the obstructing satellite that meet the in-situ obstruction stealth effect are as follows. When the ratio of both sides of the formula is greater than 100 times, it is considered to meet the far greater than relationship:

[0087] σ blocker >>σ micro (twenty one)

[0088]

[0089] The beneficial effect of the present invention is that there are few studies on stealth methods for multi-band, multi-angle and multi-detection scenarios. The present invention proposes a satellite in-situ shielding stealth method for ground-based radar detection. While ensuring the function and performance of the satellite, by designing a suitable orbit and with the help of in-situ shielding of medium and large satellites, the stealth of the microsatellite within the observation arc of the ground radar base station is achieved, providing a new idea for the survival of on-orbit spacecraft. BRIEF DESCRIPTION OF THE DRAWINGS

[0090] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments, and the above and / or other advantages of the present invention will become more clear.

[0091] Figure 1 It is a schematic diagram of the present invention.

[0092] Figure 2a It is an in-situ occlusion simulation scene graph.

[0093] Figure 2b It is a schematic diagram of in-situ occlusion RCS simulation.

[0094] Figure 3a It is the RCS curve of the obstructed satellite.

[0095] Figure 3b It is the RCS curve of microsatellite.

[0096] Figure 4 It is the overall RCS curve of the in-situ shading system.

[0097] Figure 5 It is the error curve between the overall RCS of the in-situ occlusion system and the RCS of the occluding satellite itself.

[0098] Figure 6a It is a curve graph of the maximum RCS difference at different occlusion intervals.

[0099] Figure 6b It is a curve of the average RCS difference under different occlusion interval distances.

[0100] Figure 7a It is to form the RCS curve diagram under the original occlusion and unoccluded scenes.

[0101] Figure 7b It is to form the RCS difference curve under the original occlusion and unoccluded scenes.

[0102] Figure 8 It is a schematic diagram of the in-situ occlusion scene.

[0103] Fig. 9 It is a simplified schematic diagram of the target spacecraft model.

[0104] Fig.10It is a schematic diagram of relative position relationship.

[0105] Fig.11 is the Earth occlusion constraint geometry.

[0106] Fig.12 It is the geometry of the earth's shadow constraint.

[0107] Fig.13 It is the flow chart of constraint solving algorithm.

[0108] Fig.14 It is a schematic diagram of the number of child nodes that a parent node has in two-dimensional and three-dimensional environments.

[0109] Fig.15 This is a flow chart of in-situ occlusion stealth approach trajectory planning based on the optimized A* algorithm.

[0110] Fig.16 This is the trajectory diagram in the J2000 coordinate system.

[0111] Fig.17 It is the trajectory diagram of the target spacecraft in this system.

[0112] Fig.18 It is a curve diagram of the sub-satellite point trajectory of the in-situ occlusion stealth planning. DETAILED DESCRIPTION

[0113] The embodiment of the present invention proposes a satellite in-situ shielding stealth method for ground-based radar detection, the principle is as follows: Figure 1 As shown, the following steps are included:

[0114] Step 1: Visibility modeling for ground-based integrated detection;

[0115] When a space target meets certain specific position conditions, it can avoid the identification and tracking of ground-based optical and radar detection systems. In addition to the in-situ occlusion constraints proposed by the present invention, there are also constraints such as earth occlusion constraints and earth shadow constraints. When any of the above geometric constraints is met, the space target can avoid detection. The following will establish geometric constraint models for various scenarios based on the relative geometric relationship between the sun, the earth, our own microsatellites, enemy spacecraft, and ground-based detection sensors to solve the visibility constraints of space targets.

[0116] Step 1.1, in-situ occlusion constraint;

[0117] In-situ occlusion is based on the relative positional relationship between the own microsatellite and the target spacecraft and the ground-based detection system. By designing the orbit of the microsatellite, it is always blocked by the target spacecraft during its operation, blocking the direct observation of the microsatellite by the ground-based detection system, thereby forming a visibility constraint on the ground. The present invention uses a 0.2m×0.2m×0.3m microsatellite and a 1.4m×2.8m×10m Stalink satellite as the own microsatellite and the target spacecraft to build an in-situ occlusion constraint scene. The size comparison of the research object and the in-situ occlusion constraint scene are shown in the figure. Figure 2a , Figure 8 shown.

[0118] In the process of geometric position relationship modeling, in order to facilitate the search for constraint conditions, the target spacecraft model is first simplified, and its shape feature points are extracted to make it equivalent to a rectangle, such as Fig. 9 As shown in Figure 2, since the distance between the ground-based detection station and the satellite is much larger than the size of the detection station itself, the ground-based detection station is regarded as a particle in the modeling. The geometric relationship between the ground-based detection station, the target spacecraft and the micro-satellite is shown in Figure 2. Fig.10 As shown, the four vertices of the equivalent rectangle of the detection station and the target can be regarded as a tetrahedron, and its inner height h can be expressed as:

[0119]

[0120] Where P sur and P1, P2, and P3 represent the coordinate vectors of the vertices of the ground-based detection station and the target equivalent rectangle in the J2000 inertial system, respectively.

[0121] In the in-situ occlusion constraint, the angle α formed by each vertex of the Starlink equivalent rectangle and the equivalent mass point of the microsatellite and the equivalent mass point of the detection station is i Should be greater than the angle β between each edge of the quadrangular prism and the ground i , i = 1, 2, 3, 4, and the distance between the microsatellite and the detection station should be greater than the height of the tetrahedron. It can be obtained that the in-situ occlusion constraint must meet the following conditions at the same time:

[0122]

[0123] h<||P s -P sur || (3)

[0124] Step 1.2, Earth occlusion constraint;

[0125] Earth occlusion means that the ground detection station and the space target are blocked by the earth itself, thus affecting the detection visibility of the target. Fig.11The relative position relationship between the earth, ground-based detection station, and space target is given, where E represents the earth, S represents the space target, sur represents the ground detection station, and θ is the field of view of the detection station. In the modeling, it is assumed that the earth is a perfect sphere. Through geometric calculation, the angle between the two vectors of the earth center-ground detection station and the ground detection station-space target can be determined, and the angle relationship with the field of view of the detection station and its normal can be established. The earth occlusion constraint formula is as follows:

[0126]

[0127] In the formula, r S 、r sur Respectively represent the position vectors of the space target and the ground detection station in the J2000 inertial system.

[0128] Step 1.3, ground shadow constraint;

[0129] For the ground-based optical detection system, its sensor can only observe the target that can be illuminated by sunlight. That is, when the space target is in the shadow area where the sun cannot shine, it cannot be detected by the ground-based optical system. The position relationship diagram is as follows: Fig.12 As shown. The radius of the sun is larger than that of the earth. It can be seen from the figure that the shadow area of ​​the earth that blocks the sun's rays is a cone. Let the vertex U of the cone be the umbra point, and its position vector r umb and cone angle θ umb Calculated by the following formula:

[0130]

[0131] In the formula, R sun is the radius of the sun, r sun is the sun position vector.

[0132] The angle between the negative direction of the umbra point position vector and the umbra point U pointing to the space target S should be greater than the umbra angle. It can be obtained that the ground shadow constraint must simultaneously meet the following two conditions:

[0133] r umb ·r S >0 (7)

[0134]

[0135] In the formula, r umb 、r S They represent the position vectors of the umbra point U and the space target S in the J2000 inertial system, r um b2S represents the vector pointing from the umbra point to the space target.

[0136] Step 1.4, constraint solving algorithm;

[0137] Any ground-based optical or radar detection system can detect space targets only when all the above constraints are not met. The present invention adopts a serial algorithm to solve the constraints of the detection system, and the sub-state quantity A i It represents the sub-constraint state of a ground-based detection system. When the state value is 1, it means that the constraint is satisfied. When i=1, 2, 3, the space target can avoid the detection of the ground-based detection system. When the state value is 0, it means that the constraint is not satisfied, and the ground-based detection system can detect the space target. Let the state quantity A represent the constraint state of a ground-based detection system. The calculation relationship between the state quantity and the sub-state quantity is A=∪A i , that is, calculate in turn whether the ground-based detection system meets the sub-constraints. If one of the constraints is met, then A = 1, and the space target cannot be detected by the system. After traversing all the set ground-based detection systems one by one, it can be known whether the space target is visible to the ground-based integrated detection system. The algorithm flow chart is as follows Fig.13 shown.

[0138] Step 2, establish a trajectory planning optimization algorithm based on three-dimensional A*;

[0139] The traditional A* algorithm is a heuristic search algorithm that can balance the real-time performance and performance of the path and is widely used in static path planning of artificial intelligence and robots in a two-dimensional environment. According to the real-time requirement of judging the occlusion blind spot in the in-situ occlusion stealth scene, the present invention optimizes the traditional two-dimensional A* algorithm to achieve real-time planning of dynamic obstacle avoidance paths in three-dimensional space.

[0140] Step 2.1, expand the three-dimensional space sub-node;

[0141] The A* algorithm in the traditional two-dimensional environment needs to process a parent node with a maximum of 8 child nodes. In three-dimensional space, the number of child nodes owned by the parent node is expanded from 8 to 26, such as Fig.14 shown.

[0142] At the same time, the nodes of the planned path in the two-dimensional environment are the centers of the plane grid, while the nodes in the three-dimensional environment are the centers of the cubes. Therefore, in the extended three-dimensional A* algorithm, the generation function of the child nodes of the nth parent node is:

[0143] (x n+1 ,y n+1 ,z n+1 )=(x n +Δx,y n +Δy,z n +Δz) (9)

[0144] Wherein, the values ​​of Δx, Δy, and Δz are d, -d, or 0, but not all 0 at the same time, and d is the side length of the cube.

[0145] Step 2.2, define the three-dimensional cost function;

[0146] The evaluation function expression of the traditional A* algorithm in a two-dimensional plane is:

[0147] f(n)=g(n)+h(n) (10)

[0148] In the formula, f(n) is the heuristic information strength function, g(n) is the cost function from the starting point to the current position, and h(n) is the estimated cost function from the current node to the target point. In a three-dimensional environment, the h(n) expression in the evaluation function will also be extended to three dimensions:

[0149]

[0150] In the formula, (x n ,y n ,z n ) and (x goal ,y goal ,z goal ) are the coordinates of the current node and the target point in the three-dimensional coordinate system.

[0151] Step 2.3, optimize the evaluation function;

[0152] The number of child nodes increases during the expansion of the A* algorithm to three dimensions, resulting in a year-on-year increase in the number of point sets in the close list used to store the generated nodes and the open list used to store the next node, which greatly increases the workload of the A* algorithm path search planning. From formula (10), it can be seen that g(n) and h(n) determine the size of the evaluation function f(n). The concept of weight ratio introduced in the formula can balance the intensity of the heuristic information of f(n) and shorten the path finding time. The constructed optimized evaluation function is as follows:

[0153]

[0154] Where X∈[1,+∞]. By adjusting the value of X, the weight ratio of the evaluation function can be made more reasonable, the planning time can be shortened, and the planning trajectory can be optimized.

[0155] Step 2.4, dynamic algorithm flow;

[0156] In the process of planning the in-situ occlusion stealth trajectory, when planning the next path node, it is necessary to analyze the occlusion stealth status of the node, that is, the "obstacle" information needs to be globally and dynamically updated. Therefore, in the dynamic three-dimensional A* algorithm, each calculation step to the next point needs to update the relative position relationship between the earth, the sun, the occluding satellite, the microsatellite, and the ground-based sensor, and determine whether the sub-node is in the detection occlusion blind area one by one, update the global optimal path, and then continue to move forward until the target point is reached. The algorithm flow chart is as follows: Fig.15shown.

[0157] Step 3, simulation results and analysis:

[0158] Step 3.1, simulation parameter configuration;

[0159] At present, the United States has the most powerful space target detection capability in the world, which can detect targets with a diameter greater than 1 cm and an orbital altitude less than 6400 km, and track and locate targets with a diameter of more than 10 cm in the orbital altitude. The setting of the ground-based integrated detection system in the simulation of the present invention refers to the U.S. Space Detection and Tracking System (SPADATS), and its typical space detection full-time observation equipment includes Space Fence, phased array radar AN / FPS-85 and Ground-based Electro-Optical Deep Space Surveillance (GEODSS). The specific information of the ground-based integrated detection system set in the simulation is shown in Table 1.

[0160] Table 1

[0161]

[0162] The Starlink plan proposed by the American company SpaceX deploys a hybrid low-orbit satellite constellation at different orbital altitudes and with different orbital inclinations in space. It has the characteristics of large-scale deployment and multiple coverage, and provides multi-angle shielding conditions for the stealth method proposed in the present invention. The present invention takes the Starlink satellite as the target spacecraft, and designs the micro-satellite approach trajectory to achieve a stealth approach to the Starlink satellite. Since the approach process is usually described under the target spacecraft system, the initial and final conditions of the approach trajectory simulation set by the present invention under the target spacecraft system are shown in Table 2. The orbits of the two satellites are approximated as circular orbits. According to the orbital deployment information of Starlink and the relative positions of the two satellites, their orbital parameters and size envelopes are shown in Table 3, where due to the characteristics of the circular orbit, the perigee angle ω and the true anomaly angle in the orbit description are Merged into latitude argument μ.

[0163] Table 2

[0164] Initial location (km) Initial speed (km / s) Target location (km) Target speed (km / s) (6，8，10) (0.02，0.02，0.04) (0.1，0.3，0.5) (0，0，0)

[0165] Table 3

[0166]

[0167]

[0168] Step 3.2, simulation results and analysis;

[0169] The simulation process in the J2000 coordinate system and the target spacecraft system is as follows: Fig.16 , Fig.17 As shown in the figure, the coordinate axes are the three-axis directions defined by the J2000 coordinate system and the target spacecraft system. It can be seen that under the optimization of the A* algorithm evaluation function, the microsatellite moves in a straight line in the direction of the target spacecraft from the initial position in the target spacecraft system, actively avoids the detected path point when encountering it, and continues to plan the optimal path to the target point after avoiding it, and repeats the optimization and obstacle avoidance process until it finally reaches the target point.

[0170] The sub-satellite point trajectory corresponding to the micro-satellite approach trajectory and the ground station layout are as follows: Fig.18 As shown in the figure, the red part of the entire approach trajectory indicates that when facing multiple ground-based detection systems, if the small satellite does not approach the target spacecraft sufficiently, it may not be able to avoid all ground detection stations. At this time, the small satellite chooses to move in a straight line along the direction of the target spacecraft to approach the target in the shortest time.

[0171] The approach time and detection time are shown in Table 4 below. Only 24% of the entire path with in-situ occlusion can be detected. The planned path with in-situ occlusion is compared with the time-optimal path based on continuous small thrust for ground-based detection visibility. After optimizing the trajectory stealth by in-situ occlusion, the total time of approaching the target is extended by 20%, but the proportion of obscured stealth in the path increases by 42%. This shows that when microsatellites are facing ground-based comprehensive detection, the use of in-situ occlusion for trajectory planning can effectively improve the stealth performance of orbital maneuvers.

[0172] Table 4

[0173] Approach Path Total time of approach(s) Detection duration(s) In-situ occlusion based path 5390 1307 Time-optimal path based on continuous small thrust 4324 2851

[0174] The embodiment of the present invention also provides a verification method for verifying the principle of the stealth method. Figure 2a , Figure 2b As shown, it provides a new idea for the survival of spacecraft on orbit. The specific process of the verification method includes:

[0175] 1. The finite element method and Lambert's cosine law are used to calculate the electromagnetic wave reflection energy flux density of the satellite surface element, as shown in formula (13):

[0176]

[0177] Among them, I rrepresents the energy flux density reflected on the radar detector, dp is the incident power of the radar electromagnetic wave, and ρ B represents the back reflectivity, dS is the satellite surface element, θ is the incident angle, and R represents the distance between the target and the ground-based radar detection system.

[0178] By accumulating the incident and reflected energy flux densities of the surface element and substituting them into the RCS definition formula, we can obtain the RCS calculation method for complex surface satellites, as shown in formula (14):

[0179] σ=4πρ B cosθS triangle (14)

[0180] In this embodiment, the blocking satellite is a flat-panel satellite of 10m×2.8m×1.4m, and the microsatellite is a 12U small satellite of 0.2m×0.2m×0.3m. The RCS calculation results of the two satellites are as follows: Figure 3a , Figure 3b shown.

[0181] 2. In the in-situ occlusion scene, under the influence of multipath effect, the overall RCSσ of the in-situ occlusion system total There are three sources of contributions:

[0182] (1) RCSσ of the obstructing satellite blocker ;

[0183] (2) RCSσ of microsatellites micro ,Due to occlusion, its scattering path will be affected to a certain extent;

[0184] (3) Multipath effect σ between two satellites multi , such as the reflection of radar waves between the two.

[0185] The total RCS of the in-situ shading system can be expressed by the following formula (15):

[0186]

[0187] in, is the scattering amplitude of the obstructing satellite and microsatellite, e jφ represents the scattering phase delay of the microsatellite, which depends on the radar wave propagation path. The multipath effect between two satellites can be calculated by the path difference to calculate its phase and amplitude changes, as shown in formulas (16) and (17):

[0188]

[0189] Among them, Δr represents the distance between the two satellites, that is, the reflection path length of the radar wave between the two satellites. Then the overall RCS calculation formula (18) of the in-situ shielding system can be obtained as follows:

[0190]

[0191] Here, k is a constant related to the scattering properties.

[0192] In this embodiment, the overall RCS calculation result of the in-situ shielding system composed of shielding satellites and micro-satellites is as follows: Figure 4 shown.

[0193] 3. To achieve the stealth effect of in-situ shielding, the RCS of the two satellites should meet the following conditions:

[0194] (1) Blocking satellite σ blocker For σ total The greatest contribution;

[0195] (2) Microsatellite σ micro For σ total The contribution of

[0196] (3) Multipath effect σ multi minimize the impact as much as possible.

[0197] According to the above formula, the following relationship (19) should be established:

[0198]

[0199] At the same time, in order for the blocking satellite to effectively block the radar waves, it is necessary to ensure that the physical size of the blocking satellite is large enough within the radar detection field of view, so as to completely block the micro-satellite. The distance between the two satellites must satisfy the following formula (20):

[0200]

[0201] According to formulas (19) and (20), the size and distance conditions between the microsatellite and the obstructing satellite that meet the in-situ obstruction stealth effect are as follows:

[0202] σ blocker >>σ micro (twenty one)

[0203]

[0204] In this embodiment, the size diagram of the shielding satellite and the micro-satellite is as follows: Figure 2a As shown in the figure, the horizontal axis is the incident angle of radar detection, and the vertical axis is the RCS size in dBsm. According to formula (14), the RCS is 17.714m 2 With 0.012m 2, satisfying the conditions of formula (21). At different distances satisfying the in-situ shielding stealth interval constraint, the curves of the overall RCS of the in-situ shielding system and its difference with the RCS of the shielding satellite are as follows: Figure 4 , Figure 5 From all the calculated data, the maximum and average values ​​of the difference between the in-situ occlusion overall RCS and the occluding satellite body RCS within the detection field of view at different distances are extracted separately for research, and a curve is drawn as shown in Figure 6a , Figure 6b As shown in the figure, it can be seen that at different distances, the RCS difference between the in-situ shielding system and the shielding satellite is only 0.36dBsm, which is much smaller than the RCS of the shielding satellite, proving the effectiveness of in-situ shielding stealth. When the detection distance is moved outside the constraint, the difference curve is as follows: Figure 7a , Figure 7b As shown, it can be seen that the peak difference between the RCS of the in-situ shielding system and the shielding satellite body has reached 10.35dBsm, which can no longer be ignored relative to the shielding satellite. The above research proves that in the present invention, when the micro-satellite is facing the ground-based detection, by changing the relative position to the detection blind area generated by the shielding satellite, the radar can effectively reduce the detection of its own RCS characteristics, thereby achieving the effect of in-situ shielding stealth.

[0205] Those skilled in the art can clearly understand that the technical solution in the embodiment of the present invention provides a new satellite stealth method, which mainly uses the shielding of other satellites to achieve the stealth effect of micro-satellites against ground-based radar detection. Based on this understanding, the technical solution in the embodiment of the present invention can effectively shield the electromagnetic wave propagation path between the satellite and the ground-based radar through means such as physical structure design, material selection and optimization algorithm, combined with the satellite's orbit and attitude control, to reduce the reflection and scattering of radar detection signals, and achieve the purpose of stealth. This method has a significant stealth effect and strong adaptability, can enhance the survivability of satellites in complex environments, and has important military and civilian application value.

[0206] The present invention provides a satellite in-situ shielding stealth method for ground-based radar detection. There are many methods and ways to implement the technical solution. The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, without departing from the principle of the present invention, several improvements and modifications can be made, and these improvements and modifications should also be regarded as the protection scope of the present invention. All components not specified in this embodiment can be implemented by existing technologies.

Claims

1. A satellite in-situ shielding stealth method for ground-based radar detection, characterized in that: The following steps are involved: Step 1: Visibility modeling for ground-based integrated detection; Step 2: Establish a trajectory planning optimization algorithm based on three-dimensional A*.

2. The method according to claim 1, characterized in that Step 1 includes: Step 1.1, establish in-situ occlusion constraints; Step 1.2, establish earth occlusion constraints; Step 1.3, establish the ground shadow constraint; the in-situ occlusion, earth occlusion, and ground shadow occlusion constraints constitute the visibility solution model; Step 1.4, establishing a constraint solving algorithm to solve the visibility solving model.

3. The method according to claim 2, characterized in that Step 1.1 includes: In-situ occlusion is based on the relative position relationship between the own microsatellite and the target spacecraft and the ground-based detection system. By designing the microsatellite orbit, the microsatellite is always blocked by the target spacecraft during operation, blocking the direct observation of the microsatellite by the ground-based detection system, thus forming a visibility constraint on the ground. An in-situ occlusion constraint scene is built for the own microsatellite and the target spacecraft, respectively, with a 0.2m×0.2m×0.3m microsatellite and a 1.4m×2.8m×10m Starlink satellite. In the process of geometric position relationship modeling, the target spacecraft model is first simplified, and the shape feature points of the target spacecraft are extracted according to the configuration characteristics of the target spacecraft. The target spacecraft is equivalent to a rectangle, and the ground-based detection station is regarded as a mass point in the modeling; the four vertices of the equivalent rectangle of the detection station and the target spacecraft are regarded as a quadrangular pyramid, and the inner height h is expressed as: Among them, P sur represents the coordinate vector of the ground-based detection station in the J2000 inertial system; P1, P2, P3 respectively represent the coordinate vectors of the three vertices of the rectangle in the J2000 inertial system; In the in-situ occlusion constraint, the angle α formed by each vertex of the rectangle and the equivalent mass point of the microsatellite and the equivalent mass point of the detection station is i Need to be greater than the angle β between each edge of the tetrahedron and the ground i , i = 1, 2, 3, 4, and the distance between the microsatellite and the detection station is greater than the height of the tetrahedron. The in-situ occlusion constraint must meet the following conditions at the same time: h<||P s -P sur || (3) Where P i represents the coordinate vectors of the vertices of the rectangle in the J2000 inertial system, P s Represents the position vector of the microsatellite in the J2000 system.

4. The method according to claim 3, characterized in that Step 1.2 includes: assuming that the earth is a perfect sphere, the earth occlusion constraint formula is obtained as follows: Among them, r S 、r sur They represent the position vectors of the space target and the ground detection station in the J2000 inertial system respectively; θ is the field of view angle of the detection station.

5. The method according to claim 4, characterized in that Step 1.3 includes: the shadow area of ​​the earth blocking the sun's rays is a cone, and the vertex U of the cone is set as the umbra point. The position vector r of the umbra point is calculated by the following formula: umb and cone angle θ umb : Where R sun is the radius of the sun, R e is the radius of the Earth, r sun is the sun position vector; The angle between the negative direction of the umbra point position vector and the umbra point U pointing to the space target S should be greater than the umbra angle. To obtain the ground shadow constraint, the following two conditions must be met at the same time: r umb ·r S >0 (7) Among them, r umb represents the position vector of the umbra point U in the J2000 inertial system, r umb2S Represents the vector pointing from the umbra point to the space target.

6. The method according to claim 5, characterized in that Step 1.4 includes: any ground-based optical or radar detection system can detect the space target only when all the constraints in steps 1.1 to 1.3 are not met; a serial algorithm is used to solve the constraints of the detection system, so that the sub-state quantity A i , i=1,2,3, when i is 1, 2, 3, A i They represent the three sub-constraint states of the ground-based detection system: in-situ occlusion, earth occlusion, and earth shadow occlusion. When the state value is 1, it means that the constraint is satisfied, and the space target can avoid the detection of the ground-based detection system. When the state value is 0, it means that the constraint is not satisfied, and the ground-based detection system can detect the space target. Let the state quantity A represent the constraint state of a ground-based detection system. The calculation relationship between the state quantity and the sub-state quantity is A=∪A i , that is, calculate in turn whether the ground-based detection system satisfies the sub-constraint conditions. If one of the sub-constraint conditions is met, A=1, and the space target cannot be detected by this ground-based detection system. Repeat the process of step 1.4 to traverse all the set ground-based detection systems, and finally obtain the detection status of the space target to the ground at the current moment.

7. The method according to claim 6, characterized in that Step 2 includes: Step 2.1, expand the three-dimensional space sub-node; In the extended three-dimensional A* algorithm, construct the nth parent node (x n ,y n ,z n )'s child node (x n+1 ,y n+1 ,z n+1 ) is: (x n+1 ,y n+1 ,z n+1 )=(x n +Δx,y n +Δy,z n +Δz) (9) Among them, Δx, Δy, Δz are the expansion steps of the child nodes, the values ​​of Δx, Δy, Δz are d, -d or 0, but not 0 at the same time, and d is the side length of the cube; Step 2.2, define the three-dimensional cost function; Step 2.3, construct an optimization evaluation function; Step 2.4, establish a dynamic algorithm process.

8. The method according to claim 7, characterized in that Step 2.2 includes: The evaluation function expression of the traditional A* algorithm in a two-dimensional plane is: f(n)=g(n)+h(n) (10) Where f(n) is the heuristic information strength function, g(n) is the cost function from the starting point to the current position, and h(n) is the estimated cost function from the current node to the target point. In a three-dimensional environment, the h(n) expression in the evaluation function will also be extended to three dimensions: Among them, (x goal ,y goal ,z goal ) is the coordinate of the target point in the three-dimensional coordinate system.

9. The method according to claim 8, characterized in that Step 2.3 includes: The constructed optimization evaluation function f′(n) is: Among them, the intermediate parameter X∈[1,+∞].

10. The method according to claim 9, characterized in that Step 2.4 includes: Step 2.4.1, input the coordinates of the starting point, target point, ground-based detection station and performance parameters (such as detection field of view, etc.); Step 2.4.2, gradually calculating the sub-nodes of the path planning based on the set planning step size; Step 2.4.3, convert the sub-nodes in the path planning to the geocentric inertial system; Step 2.4.4, traversing the child nodes based on the visibility solution model; Step 2.4.5, retain the child nodes in the detection blind area solved in step 2.4.4; Step 2.4.6, calculate the optimal node at this moment by optimizing the evaluation function f′(n); Step 2.4.7, plan the path to the optimal node at this moment; Step 2.4.7, determine whether the target point has been reached. If so, output the planned path node coordinates, otherwise return to step 2.4.2.

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