Method and system for quickly solving the shortest path between satellites in low-orbit satellite networks

Abstract

The present invention discloses a method and system for rapidly solving the shortest path between satellites in a low-orbit satellite network. This method requires only the input of the constellation parameters of the low-orbit satellite network and the position information of the starting and ending satellites. The method then calculates the constellation phase parameters based on the constellation parameters and constructs a mesh-like shortest path solution region based on the position information of the starting and ending satellites. The method then calculates the phase difference between the starting and ending satellites based on the constellation phase parameters and the position information of the starting and ending satellites. Finally, based on the phase difference, the phase condition of the starting and ending satellites is determined, and the shortest path with the minimum number of hops between the starting and ending satellites is solved within the shortest path solution region. This method eliminates the iterative calculation process and eliminates the need to calculate link lengths in advance. It has low computational complexity and high solution accuracy. Furthermore, the computational complexity does not increase with constellation size, while maintaining good accuracy. This method is well-suited for large constellations with a large number of satellites.

Description

Technical Field

[0001] The present invention relates to the field of satellite communication technology, and in particular to a method and system for quickly solving the shortest path between satellites in a low-orbit satellite network, an electronic device, and a computer-readable storage medium. Background Art

[0002] The shortest distance path (SDP) is widely used in communication network routing problems to achieve minimal network latency, optimal transmission cost, and maximum system efficiency. In LEO satellite networks connected by intersatellite links, the shortest path is also widely used to solve routing problems with low latency and high resource utilization. Existing methods such as the Dijkstra algorithm and the Bellman-Ford algorithm are classic algorithms for solving the shortest path. These traditional SDP algorithms are mostly graph-based iterative algorithms. They first establish a graph model of the network, calculate the connectivity relationships and edge distances of each node in the graph model, and then calculate the SDP through iterations on the graph. However, unlike other wireless networks, LEO satellite networks have unique topological characteristics. Their network topology is dynamic, while the positions of satellites in the constellation are regular. Their motion is governed by deterministic orbital dynamics, and the intersatellite link distances vary with the satellite phase. In a practical solution most similar to the present invention, the minimum hop path (MHP) from the source node to the target node is collected to form a subgraph, which can be regarded as a directed acyclic graph (DAG). A topological sorting method is used instead of the Dijkstra algorithm to solve the SDP in the DAG. Specifically, all nodes are first sorted in a linear order from the source node to the adjacent nodes to the target node. If there is a path from node u to node v, node u is ranked before node v in the vertex order. Secondly, the distance from the source node to each node is initialized to infinity. Then, when traversing each node in topological order, the distance from the source node to the node is updated until the shortest distance from the source node to the target node is obtained. However, this DAG algorithm still relies on iterative calculations and requires the link distances of all edges involved to be calculated in advance.

[0003] Therefore, existing traditional SDP algorithms rely entirely on iterative calculations. While they can achieve optimal solutions, their computational complexity increases rapidly with network size. Existing DAG-based algorithms, while reducing some of the computational complexity compared to traditional SDP algorithms, still require iterative calculations, resulting in significant computational complexity. Furthermore, they require pre-calculated link distances as input parameters, and can only produce approximate optimal solutions, leaving room for improvement in accuracy. Summary of the Invention

[0004] The present invention provides a method and system for quickly solving the shortest path between satellites in a low-orbit satellite network, an electronic device, and a computer-readable storage medium, so as to solve the technical problems of high computational complexity and poor solution accuracy in existing algorithms for solving SDP.

[0005] According to one aspect of the present invention, a method for quickly finding the shortest path between satellites in a low-orbit satellite network is provided, comprising the following steps:

[0006] Inputting constellation parameters of the low-orbit satellite network and position information of the starting and ending satellites, wherein the constellation parameters include the number of orbital planes of the low-orbit satellite network, the number of satellites evenly distributed in each orbital plane, orbital altitude, phase factor, and orbital inclination;

[0007] Based on the input constellation parameters, constellation phase parameters are calculated. The constellation phase parameters include the phase difference between satellites in the orbital plane, the right ascension difference of the ascending node between adjacent orbital planes, and the phase difference between satellites in adjacent orbits. A mesh-like shortest path solution area is constructed based on the position information of the starting and ending satellites.

[0008] The phase difference between the starting and ending satellites is calculated based on the constellation phase parameters and the position information of the starting and ending satellites;

[0009] Based on the phase difference, it is judged whether the phase situation formed by the starting and ending satellites is a single valley situation or a double valley situation. According to the phase situation judgment result, the shortest path with the minimum number of hops between the starting and ending satellites is solved in the shortest path solution area, and the distance value and the passing nodes of the shortest path are output.

[0010] Furthermore, the phase difference between the starting and ending satellites is calculated based on the following formula:

[0011] △u=u M,N -u0=(M-1)△Φ+(N-1)△f

[0012] Among them, △u represents the phase difference between the starting and ending satellites, (M, N) represents the position number of the terminal satellite in the shortest path solution area, N is the orbital plane number, M is the orbital plane number, and u M,N represents the phase of the terminal satellite, u0 represents the phase of the starting satellite, △Φ represents the phase difference between satellites in the orbital plane, and △f represents the phase difference between satellites in adjacent orbits.

[0013] Furthermore, when the phase difference between the initial and final satellites is When the phase difference between the starting and ending satellites is When , the phase situation formed by the starting and ending satellites is determined to be a double valley situation; where u0 represents the phase of the starting satellite, △f represents the phase difference between adjacent orbital satellites, and mod() represents the remainder function.

[0014] Furthermore, within the shortest path solution area, the distance calculation formula for any minimum hop path is:

[0015]

[0016] Among them, (M, N) represents the position number of the terminal satellite in the shortest path solution area, and the corresponding starting satellite position number is (1, 1). It represents the distance of the inter-satellite link on the same track, R E is the radius of the Earth, h s is the satellite's orbital height, △Φ represents the phase difference between satellites in the orbital plane, represents the distance of the i-th inter-satellite link on the minimum hop path, Θ represents the geocentric angle of the line connecting the two satellites, represents the right ascension difference of the ascending node between adjacent orbital planes, α represents the orbital inclination of the satellite, △f represents the phase difference of adjacent orbital satellites, u(v i ) represents the satellite phase at the i-th cross-orbital plane forwarding, u(v i )=u0+(v i -1)△Φ+(i-1)△f,i=1,2,...,N-1,v i Indicates the satellite number at the i-th cross-orbital plane forwarding.

[0017] Furthermore, when solving the shortest path of the minimum hop path between the starting and ending satellites in the shortest path solution area, the shortest path solution of the minimum hop path is converted into the solution of the minimum total path phase offset of all cross-orbital plane forwarding positions, where the total path phase offset is expressed as:

[0018]

[0019] represents the phase offset at the i-th cross-orbital plane forwarding, u=U s Denotes the distance function d of the inter-satellite link in different orbits H (u) is the axis of symmetry.

[0020] Furthermore, the process of solving the shortest path with the minimum number of hops between the starting and ending satellites in the single valley case is:

[0021] All cross-orbital plane forwarding in the shortest path is performed continuously. First, the satellite number v at the i-th cross-orbital plane forwarding is calculated based on the following formula: i :

[0022] v i =v1,i=1,2,...,N-1

[0023]

[0024]

[0025] Among them, u0 represents the phase of the initial satellite, Represents an intermediate variable, and Round() represents a rounding function;

[0026] Then, based on the satellite number v at the i-th cross-orbital plane forwarding i The satellite phase u(v i ), and then calculate the shortest path with the minimum number of hops between the starting and ending satellites.

[0027] Furthermore, the process of solving the shortest path with the minimum number of hops between the starting and ending satellites in the double valley situation is as follows:

[0028] The shortest path is simplified into a double-step path consisting of two consecutive cross-orbital plane forwarding segments. The forwarding number R of the first consecutive cross-orbital plane forwarding segment, the satellite number v1 at the first cross-orbital plane forwarding, and the number of consecutive forwardings △v within the orbital plane are calculated based on the following formulas:

[0029]

[0030]

[0031]

[0032] Among them, R H represents the upper limit of R, Round() represents the rounding function, u0 represents the phase of the starting satellite, mod() represents the remainder function, represents the intermediate variable, v H Indicates the upper limit of the value of v1;

[0033] Then calculate the satellite number v at the i-th cross-orbital plane forwarding based on the following formula: i and satellite phase u(v i ):

[0034]

[0035]

[0036] Then, the phase offset at the i-th cross-orbital plane forwarding is calculated based on the following formula:

[0037]

[0038] The total path phase offset is calculated based on the following formula:

[0039]

[0040] Then let △v=0, v1=v2=...=v N-1 , then traverse v1=1,2,...,N-1, and find the corresponding and And take the minimum value

[0041] Compare and The smaller of the two, R, v1 and △v, is used to calculate v i and u(v i ), and then calculate the shortest path with the minimum number of hops between the starting and ending satellites.

[0042] In addition, the present invention also provides a system for quickly solving the shortest path between satellites in a low-orbit satellite network, which uses the above-mentioned fast solution method and includes:

[0043] An input module is used to input constellation parameters of the low-orbit satellite network and position information of the starting and ending satellites, wherein the constellation parameters include the number of orbital planes of the low-orbit satellite network, the number of satellites evenly distributed in each orbital plane, orbital altitude, phase factor and orbital inclination;

[0044] A first calculation module is configured to calculate constellation phase parameters based on input constellation parameters, wherein the constellation phase parameters include the phase difference between satellites within an orbital plane, the right ascension difference of ascending nodes between adjacent orbital planes, and the phase difference between satellites in adjacent orbits, and to construct a mesh-shaped shortest path solution area based on the position information of the starting and ending satellites;

[0045] The second calculation module is used to calculate the phase difference between the starting and ending satellites based on the constellation phase parameter and the position information of the starting and ending satellites;

[0046] The output module is used to judge whether the phase situation formed by the starting and ending satellites is a single valley situation or a double valley situation based on the phase difference, and according to the phase situation judgment result, solve the shortest path with the minimum number of hops between the starting and ending satellites in the shortest path solution area, and output the distance value and the passing nodes of the shortest path.

[0047] In addition, the present invention also provides an electronic device, including a processor and a memory, wherein the memory stores a computer program, and the processor is configured to execute the steps of the above method by calling the computer program stored in the memory.

[0048] In addition, the present invention also provides a computer-readable storage medium for storing a computer program for quickly solving the shortest path between satellites in a low-orbit satellite network. When the computer program is run on a computer, the steps of the method described above are executed.

[0049] The present invention has the following effects:

[0050] The present invention provides a method for quickly solving the shortest path between satellites in a low-orbit satellite network. It only requires inputting the constellation parameters of the low-orbit satellite network and the position information of the starting and ending satellites. The constellation phase parameters can be calculated based on the constellation parameters, and a mesh-shaped shortest path solution area can be constructed based on the position information of the starting and ending satellites. The phase difference between the starting and ending satellites is then calculated based on the constellation phase parameters and the position information of the starting and ending satellites. Finally, the phase situation of the starting and ending satellites is judged based on the phase difference. The shortest path with the minimum number of hops between the starting and ending satellites is solved in the shortest path solution area according to different phase situations, and the distance value and the passed nodes of the shortest path are output. The fast solution method of this embodiment proposes a direct solution method for the shortest inter-satellite path in a low-orbit satellite network based on the topological characteristics of the satellite constellation and the distance characteristics of the inter-satellite links. This method, referred to as the EAP algorithm, eliminates the iterative calculation process and does not require the precalculation of all link lengths. It has low computational complexity and high solution accuracy. Moreover, the computational complexity does not increase with the increase in the constellation size and can maintain good accuracy. It is well suited for large constellations with a large number of satellites, such as Starlink and Kuiper.

[0051] In addition, the system for quickly solving the shortest path between satellites in a low-orbit satellite network of the present invention also has the above advantages.

[0052] In addition to the above-described objects, features and advantages, the present invention has other objects, features and advantages. The present invention will be further described in detail below with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] The accompanying drawings, which constitute part of this application, are intended to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are intended to explain the present invention and do not constitute an undue limitation of the present invention. In the accompanying drawings:

[0054] Figure 1 It is a flowchart of a method for quickly solving the shortest path between satellites in a low-orbit satellite network according to a preferred embodiment of the present invention.

[0055] Figure 2 It is a schematic diagram of the topological structure and inter-satellite link structure of the low-orbit satellite network of the preferred embodiment of the present invention.

[0056] Figure 3It is a schematic diagram of an M×N dimensional shortest path solution area constructed in a preferred embodiment of the present invention.

[0057] Figure 4 Schematic diagram of simplifying the shortest path in a double-valley situation into a double-step path including two sections of continuous forwarding across the track surface in a preferred embodiment of the present invention.

[0058] Figure 5 FIG. 4 is a bar diagram showing a comparison of time consumption results of different SDP algorithms at different constellation scales in a preferred embodiment of the present invention.

[0059] Figure 6 It is a schematic diagram of the module structure of a system for quickly solving the shortest path between satellites in a low-orbit satellite network according to another embodiment of the present invention. DETAILED DESCRIPTION

[0060] The embodiments of the present invention are described in detail below with reference to the accompanying drawings. However, the present invention can be implemented in many different ways as defined and covered below.

[0061] like Figure 1 As shown, a preferred embodiment of the present invention provides a method for quickly solving the shortest path between satellites in a low-orbit satellite network, comprising the following contents:

[0062] Step S1: Inputting constellation parameters of the low-orbit satellite network and position information of the starting and ending satellites, wherein the constellation parameters include the number of orbital planes of the low-orbit satellite network, the number of satellites evenly distributed in each orbital plane, orbital altitude, phase factor, and orbital inclination;

[0063] Step S2: Calculate constellation phase parameters based on the input constellation parameters. The constellation phase parameters include the phase difference between satellites within the orbital plane, the right ascension difference of the ascending node between adjacent orbital planes, and the phase difference between satellites in adjacent orbits. A mesh-like shortest path solution area is constructed based on the position information of the starting and ending satellites.

[0064] Step S3: Calculate the phase difference between the starting and ending satellites based on the constellation phase parameter and the position information of the starting and ending satellites;

[0065] Step S4: Based on the phase difference, determine whether the phase situation formed by the starting and ending satellites is a single valley situation or a double valley situation. According to the phase situation judgment result, solve the shortest path with the minimum number of hops between the starting and ending satellites in the shortest path solution area, and output the distance value and the passing nodes of the shortest path.

[0066] It can be understood that the method for quickly solving the shortest path between satellites in a low-orbit satellite network in this embodiment only needs to input the constellation parameters of the low-orbit satellite network and the position information of the starting and ending satellites, and can calculate the constellation phase parameters based on the constellation parameters and construct a mesh-shaped shortest path solution area based on the position information of the starting and ending satellites. Then, the phase difference between the starting and ending satellites is calculated based on the constellation phase parameters and the position information of the starting and ending satellites. Finally, the phase situation of the starting and ending satellites is judged based on the phase difference, and the shortest path with the minimum number of hops between the starting and ending satellites is solved in the shortest path solution area according to different phase situations, and the distance value and passing nodes of the shortest path are output. The fast solution method of this embodiment proposes a direct solution method for the shortest inter-satellite path in a low-orbit satellite network based on the topological characteristics of the satellite constellation and the distance characteristics of the inter-satellite links. This method, referred to as the EAP algorithm, eliminates the iterative calculation process and does not require the precalculation of all link lengths. It has low computational complexity and high solution accuracy. Moreover, the computational complexity does not increase with the increase in the constellation size and can maintain good accuracy. It is well suited for large constellations with a large number of satellites, such as Starlink and Kuiper.

[0067] It is understandable that Figure 2 As shown, the present invention is aimed at a low-orbit satellite network, namely, a LEO orbit constellation network. Most LEO orbit constellation network systems generally adopt a Walker constellation, that is, the satellites in the constellation fly in a circular orbit, and all satellites have the same orbital inclination α and altitude h. s and orbital period T s . Usually, there are N in the Walker constellation p The orbital planes are evenly distributed along the equator, and there are M p Satellites are evenly distributed, and the phase difference between satellites in the orbital plane is: The phase difference between adjacent orbital satellites F represents the phase factor. The Walker constellation specifically includes two types: Walker-delta and Walker-star constellations. The difference is that the former generally uses an inclined orbit, while the latter generally uses a near-polar orbit. The right ascension differences △Ω between the ascending nodes of adjacent orbital planes are and A bidirectional inter-satellite link (ISL) is established between each satellite and the four satellites in front, behind, and left of it. The link between two adjacent satellites in the same orbital plane is called the same-orbit ISL, and the link between two satellites in different orbital planes is called the different-orbit ISL. During the movement of the satellite, all ISLs remain connected. The Walker constellation configuration and inter-satellite links make the low-orbit satellite constellation network topology mesh-shaped, and the degree of each node is 4. The shortest path between two satellites refers to the path with the shortest total path length. Since the topology of the low-orbit satellite network is a regular mesh-shaped topology and the link distance difference is small, the shortest path passes through the least number of satellite nodes and forwarding hops. Therefore, the present invention solves the shortest path within the minimum hop path (MHP) set. When the satellite forwards along the minimum hop path, the satellite has no more than two possible forwarding directions at each passing node, all of which are towards the destination node.

[0068] It can be understood that in the steps S1 and S2, the number of orbital planes N of the low-orbit satellite network is input. p , the number of satellites M evenly distributed in each orbital plane p , track height h s , phase factor F and orbital inclination α, as well as the position information of the starting and ending satellites in the Mesh topology network and the phase of the starting satellite. Then, based on the formula: The phase difference △Φ between satellites in the orbital plane and the phase difference △f between satellites in adjacent orbits are calculated respectively. When the low-orbit satellite network adopts the Walker-delta constellation configuration, the right ascension difference △Ω between the ascending nodes of adjacent orbital planes is When the low-orbit satellite network adopts the Walker-star constellation configuration, the right ascension difference △Ω between the ascending nodes of adjacent orbital planes is Then, based on the location information of the starting and ending satellites in the Mesh topology network, an M×N dimensional shortest path solution area is constructed. Figure 3 As shown, the node number of the starting satellite is (1,1), the node number of the ending satellite is (M,N), and (v,h) represents the vth satellite on the hth orbital plane.

[0069] It can be understood that in step S3, the satellite phase of the origin node is u 1,1 =u0, u0 is the phase of the starting satellite, obtained by input, then the phase of the node (v, h) is u v,h =u0+(v-1)△Φ+(h-1)△f. Therefore, the phase difference between the starting and ending satellites is calculated based on the following formula:

[0070] △u=u M,N -u0=(M-1)△Φ+(N-1)△f

[0071] Among them, △u represents the phase difference between the starting and ending satellites, (M, N) represents the position number of the terminal satellite in the shortest path solution area, N is the orbital plane number, M is the orbital plane number, and u M,N represents the phase of the terminal satellite, u0 represents the phase of the starting satellite, △Φ represents the phase difference between satellites in the orbital plane, and △f represents the phase difference between satellites in adjacent orbits.

[0072] It can be understood that in step S4, after constructing the M×N-dimensional shortest path solution area, the number of forwarding hops between satellites in the same orbit and the number of forwarding hops between satellites in different orbits are M-1 and N-1 respectively, then the distance of any minimum hop path can be expressed as:

[0073] in, represents the distance of the i-th inter-satellite link on the minimum hop path, represents the distance of the jth co-orbital inter-satellite link. Since all co-orbital inter-satellite links have the same distance, Is a fixed value, unified as d V ,and As the satellite phase changes, the distance of any minimum hop path can be expressed as: The inter-satellite link distance on the same orbit Among them, R E is the radius of the Earth, h s is the satellite's orbital height, △Φ represents the phase difference between satellites in the orbital plane. Varies with the satellite phase u, therefore, the satellite phase at the cross-orbital plane forwarding point is used to characterize the inter-orbital link distance. Specifically, Θ represents the geocentric angle of the line connecting the two satellites, represents the satellite phase at the i-th cross-orbital plane forwarding, v i Indicates the satellite number at the i-th cross-orbital plane forwarding, that is, the node (v i , i) is forwarded across the orbital plane, where v i ∈{1, 2, ..., M}, i = 1, 2, ..., N-1, for example, Figure 3 In v1=v2=2,v3=M, as long as the set {v i} is determined, then the minimum hop path can be determined. Each intersatellite link forwarding will produce a fixed phase change, so the satellite phase u(v i ) can be expressed as: u(v i )=u0+(v i -1)△Φ+(i-1)△f,i=1,2,...,N-1.

[0074] Therefore, after calculating the satellite phase at the cross-orbital plane forwarding point, the inter-orbital forwarding link distance can be calculated, and thus the distance of any minimum hop path can be calculated.

[0075] It can be understood that the present invention uses the satellite phase at the cross-orbital plane forwarding point to characterize the distance of the inter-orbital link. It is only necessary to calculate the satellite phase at each cross-orbital plane forwarding point to calculate the distance of each inter-orbital forwarding link. The distance of the inter-orbital forwarding link is a fixed value, so the distance of any minimum hop path can be quickly calculated. The minimum hop path is the shortest distance. The entire solution process does not need to calculate the length of all links, which greatly reduces the computational complexity.

[0076] It can be understood that when solving the shortest path of the minimum hop path between the starting and ending satellites in the shortest path solution area, according to the inter-satellite link distance characteristics, the shortest path solution of the minimum hop path is converted into the solution of the minimum total path phase offset of all cross-orbital forwarding positions, that is, the solution problem Transform into a problem-solving Among them, d H (u) represents the distance function of the inter-satellite link in different orbits. Considering d H Symmetry and monotonicity of (u), d H (u) When u is far away from the axis of symmetry u=U s Time growth, Then the phase offset at the i-th cross-orbital plane forwarding is represents the phase deviation from the minimum distance position, and the total path phase offset of all cross-orbital plane forward positions can be expressed as:

[0077]

[0078] Therefore, the goal problem can be further transformed into finding satisfaction {v i}problem. It can be understood that when the phase difference between the starting and ending satellites is calculated When the phase difference between the starting and ending satellites is When , the phase situation formed by the starting and ending satellites is determined to be a double valley situation; where u0 represents the phase of the starting satellite, △f represents the phase difference between adjacent orbital satellites, and mod() represents the remainder function.

[0079] The specific process of solving the shortest path with the minimum number of hops between the starting and ending satellites in the single valley case is as follows:

[0080] All cross-orbital plane forwarding in the shortest path is performed continuously. First, the satellite number v at the i-th cross-orbital plane forwarding is calculated based on the following formula: i :

[0081] v i =v1,i=1,2,...,N-1

[0082]

[0083]

[0084] Among them, u0 represents the phase of the initial satellite, Indicates an intermediate variable, Round() indicates a rounding function, and N-1 cross-orbital plane forwarding is performed continuously in the case of a single valley.

[0085] Then, based on the satellite number v at the i-th cross-orbital plane forwarding i The satellite phase u(v i ), the calculation formula is: u(v i )=u0+(v i -1)△Φ+(i-1)△f,i=1,2,...,N-1, so the distance of the i-th inter-satellite link can be calculated Then calculate the shortest path with the minimum number of hops between the starting and ending satellites

[0086] In addition, the process of solving the shortest path with the minimum number of hops between the starting and ending satellites in the double valley situation is as follows:

[0087] First, the shortest path in the double valley case is simplified to a double-step path consisting of two consecutive forwarding segments across the track surface, such as Figure 4 As shown. The double-step path can be determined by three parameters, namely the number of forwarding times R of the first continuous cross-orbital plane forwarding, the satellite number v1 at the first cross-orbital plane forwarding, and the number of continuous forwarding times △v in the orbital plane. For example, Figure 4 In the example, starting from the source node (1,1), the first cross-orbital plane forwarding is performed at the node (v1,1), and after R consecutive cross-orbital plane forwardings, it reaches the node (v1,R+1). After △v consecutive on-orbit forwardings, it reaches the node (v1+△v,R+1), and then performs the remaining N-1-R consecutive cross-orbital plane forwardings, finally reaching the target node (M,N). Specifically, the number of forwardings R of the first continuous cross-orbital plane forwarding, the satellite number v1 at the first cross-orbital plane forwarding, and the number of consecutive forwardings within the orbital plane △v are calculated based on the following formulas:

[0088]

[0089]

[0090]

[0091] Among them, R H represents the upper limit of R, Round() represents the rounding function, u0 represents the phase of the starting satellite, mod() represents the remainder function, represents the intermediate variable, v H Indicates the upper limit of the value of v1.

[0092] Then calculate the satellite number v at the i-th cross-orbital plane forwarding based on the following formula: i and satellite phase u(v i ):

[0093]

[0094] Then, the phase offset at the i-th cross-orbital plane forwarding is calculated based on the following formula:

[0095]

[0096] The total path phase offset is then calculated based on the following formula:

[0097]

[0098] Furthermore, considering that in the double valley case, it is also possible that all cross-orbital plane forwarding in the shortest path occurs continuously, we set △v = 0, v1 = v2 = ... = v N-1 , that is, R = N-1, then traverse v1 = 1, 2, ..., N-1, and calculate the corresponding and The minimum value is taken as the total path phase offset when all inter-satellite links in different orbits are continuously forwarded.

[0099] Finally, compare and The smaller of the two, R, v1 and △v, is used to calculate v i and u(v i ), and then calculate the shortest path with the minimum number of hops between the starting and ending satellites.

[0100] It can be understood that the present invention converts the problem of solving the shortest path distance into the problem of solving the minimum total path phase deviation forwarded across the orbital plane, which greatly reduces the computational complexity and can accurately calculate the shortest distance value and the shortest path passing nodes.

[0101] It is understood that in order to further verify the advantages of the EAP algorithm of the present invention, the inventors of this application also conducted numerical simulations under various LEO constellation scenarios. In the case of a single valley, the Monte Carlo simulation method was used to randomly generate 1 million constellation networks and multiple sets of shortest paths were calculated in each constellation. The simulation results show that all shortest path distances are the same as those of the Dijkstra algorithm. Among them, the time consumption comparison results of different SDP algorithms under different constellation sizes are shown in Tables 1 and Figure 5 shown.

[0102] Table 1. Comparison of time consumption of different SDP algorithms at different constellation sizes

[0103]

[0104] From Table 1 and Figure 5 It can be seen that the EAP algorithm of the present invention can effectively reduce time consumption. Compared with the Dijkstra algorithm and the DAG algorithm, the time savings exceed 99.4% and 74.0%, respectively. Moreover, the time saving ratio increases with the increase of the constellation size. This shows that the EAP algorithm proposed in the present invention has a more significant advantage in large-scale constellations such as Starlink. This is because in large-scale constellations, M and N are large, and traditional recursive algorithms consume more time than the explicit parsing algorithm of the present invention.

[0105] The accuracy of the EAP algorithm of the present invention was also verified under a double-valley scenario, and the deviation was examined, further analyzing the SDP characteristics within the Starlink constellation. To compare the error, the inventors of this application also proposed the Rand-MHP algorithm, which randomly generates a path within the corresponding MHP region (i.e., the M×N-dimensional shortest path solution region). The accuracy analysis results of the EAP algorithm of the present invention under a double-valley scenario are shown in Table 2.

[0106] Table 2. Accuracy analysis results of the EAP algorithm in the double valley situation

[0107] Rand MHP EAP EAP (overall) Mean Relative Error 8.82％ 0.11％ 0.09％ Max Relative Error 151.39％ 7.18％ 7.32％ Optimal SDP Probability 9.67％ 77.75％ 88.38％

[0108] As shown in Table 2, the EAP algorithm of the present invention achieves an average relative error of only 0.11% in the double-valley scenario, with a maximum error as low as 7.18%. Over 77% of paths are at the same distance from the optimal solution. Furthermore, when the single-valley scenario is also included, the EAP (overall) results show that the overall performance of EAP is further improved in all cases, with an overall average relative error of less than 0.1%. Compared to the Rand-MHP algorithm, the proposed EAP algorithm is applicable and effective in both single-valley and double-valley scenarios.

[0109] In addition, if Figure 6As shown, another embodiment of the present invention further provides a system for quickly solving the shortest path between satellites in a low-orbit satellite network, preferably using the above-mentioned fast solution method, including:

[0110] An input module is used to input constellation parameters of the low-orbit satellite network and position information of the starting and ending satellites, wherein the constellation parameters include the number of orbital planes of the low-orbit satellite network, the number of satellites evenly distributed in each orbital plane, orbital altitude, phase factor and orbital inclination;

[0111] A first calculation module is configured to calculate constellation phase parameters based on input constellation parameters, wherein the constellation phase parameters include the phase difference between satellites within an orbital plane, the right ascension difference of ascending nodes between adjacent orbital planes, and the phase difference between satellites in adjacent orbits, and to construct a mesh-shaped shortest path solution area based on the position information of the starting and ending satellites;

[0112] The second calculation module is used to calculate the phase difference between the starting and ending satellites based on the constellation phase parameter and the position information of the starting and ending satellites;

[0113] The output module is used to judge whether the phase situation formed by the starting and ending satellites is a single valley situation or a double valley situation based on the phase difference, and according to the phase situation judgment result, solve the shortest path with the minimum number of hops between the starting and ending satellites in the shortest path solution area, and output the distance value and the passing nodes of the shortest path.

[0114] It can be understood that the fast solution system for the shortest path between satellites in the low-orbit satellite network of this embodiment only needs to input the constellation parameters of the low-orbit satellite network and the position information of the starting and ending satellites, and can calculate the constellation phase parameters based on the constellation parameters and construct a mesh-shaped shortest path solution area based on the position information of the starting and ending satellites. Then, based on the constellation phase parameters and the position information of the starting and ending satellites, the phase difference between the starting and ending satellites is calculated. Finally, based on the phase difference, the phase situation of the starting and ending satellites is judged, and according to different phase situations, the shortest path with the minimum number of hops between the starting and ending satellites is solved in the shortest path solution area, and the distance value and passing nodes of the shortest path are output. The fast solution system of this embodiment proposes a direct solution method for the shortest inter-satellite path in low-orbit satellite networks based on the topological characteristics of satellite constellations and the distance characteristics of inter-satellite links. This method, referred to as the EAP algorithm, eliminates the iterative calculation process and does not require the precalculation of all link lengths. It has low computational complexity and high solution accuracy. Moreover, the computational complexity does not increase with the increase in constellation size and can maintain good accuracy. It is well suited for large constellations with a large number of satellites, such as Starlink and Kuiper.

[0115] In addition, another embodiment of the present invention further provides an electronic device, including a processor and a memory, wherein the memory stores a computer program, and the processor is configured to execute the steps of the above method by calling the computer program stored in the memory.

[0116] In addition, another embodiment of the present invention further provides a computer-readable storage medium for storing a computer program for quickly solving the shortest path between satellites in a low-orbit satellite network, wherein the computer program executes the steps of the method described above when running on a computer.

[0117] Common computer-readable storage media include: floppy disks, flexible disks, hard disks, magnetic tape, any other magnetic media, CD-ROMs, any other optical media, punch cards, paper tape, any other physical medium with a pattern of holes, random access memory (RAM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), flash-erasable programmable read-only memory (FLASH-EPROM), any other memory chip or cartridge, or any other medium that can be read by a computer. Instructions can further be transmitted or received via a transmission medium. The term transmission medium includes any tangible or intangible medium that can be used to store, encode, or carry instructions for execution by a machine, and includes digital or analog communication signals or other intangible media that facilitate communication of such instructions. Transmission media include coaxial cables, copper wire, and fiber optics, including the wires of a bus used to transmit a computer data signal.

[0118] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention are intended to be within the scope of protection of the present invention.

[0119] Those skilled in the art will appreciate that the embodiments of the present application can be provided as methods, systems, or computer program products. Therefore, the application can adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the application can adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that contain computer-usable program code. The scheme in the embodiment of the present application can be implemented in various computer languages, for example, object-oriented programming language Java and literal translation scripting language JavaScript, etc.

[0120] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the steps in the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0121] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0122] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0123] Although the preferred embodiments of the present application have been described, those skilled in the art may make additional changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present application.

[0124] Obviously, those skilled in the art may make various changes and modifications to this application without departing from the spirit and scope of this application. Thus, if these modifications and variations of this application fall within the scope of the claims of this application and their equivalents, this application is intended to include these modifications and variations.

Claims

1. A method for quickly solving the shortest path between satellites in a low-orbit satellite network, characterized in that: Includes the following: Inputting constellation parameters of the low-orbit satellite network and position information of the starting and ending satellites, wherein the constellation parameters include the number of orbital planes of the low-orbit satellite network, the number of satellites evenly distributed in each orbital plane, orbital altitude, phase factor, and orbital inclination; Based on the input constellation parameters, constellation phase parameters are calculated. The constellation phase parameters include the phase difference between satellites in the orbital plane, the right ascension difference of the ascending node between adjacent orbital planes, and the phase difference between satellites in adjacent orbits. A mesh-like shortest path solution area is constructed based on the position information of the starting and ending satellites. The phase difference between the starting and ending satellites is calculated based on the constellation phase parameters and the position information of the starting and ending satellites; Based on the phase difference between the starting and ending satellites, the phase situation formed by the starting and ending satellites is judged to be a single valley situation or a double valley situation. According to the phase situation judgment result, the shortest path with the minimum number of hops between the starting and ending satellites is solved in the shortest path solution area, and the distance value and the nodes passed by the shortest path are output; When the phase difference between the initial and final satellites When the phase difference between the starting and ending satellites is When , the phase situation formed by the starting and ending satellites is determined to be a double valley situation; where u0 represents the phase of the starting satellite, Δf represents the phase difference between adjacent orbital satellites, and mod() represents the remainder function; When solving the shortest path of the minimum hop path between the starting and ending satellites in the shortest path solution area, the shortest path solution of the minimum hop path is converted into the solution of the minimum total path phase offset of all cross-orbital plane forwarding positions, where the total path phase offset is expressed as: represents the phase offset at the i-th cross-orbital plane forwarding, u=U s Denotes the distance function d of the inter-satellite link in different orbits H (u) is the symmetry axis, (M, N) represents the position number of the terminal satellite in the shortest path solution area, N is the orbital plane number, M is the orbital plane number, Indicates the total path phase offset.

2. The method for quickly solving the shortest path between satellites in a low-orbit satellite network according to claim 1, wherein: The phase difference between the starting and ending satellites is calculated based on the following formula: Δu=u M,N -u0=(M-1)ΔΦ+(N-1)Δf Among them, Δu represents the phase difference between the starting and ending satellites, (M, N) represents the position number of the terminal satellite in the shortest path solution area, N is the orbital plane number, M is the orbital plane number, and u M,N represents the phase of the terminal satellite, u0 represents the phase of the starting satellite, ΔΦ represents the phase difference between satellites in the orbital plane, and Δf represents the phase difference between satellites in adjacent orbits.

3. The method for quickly solving the shortest path between satellites in a low-orbit satellite network according to claim 1, wherein: In the shortest path solution area, the distance calculation formula for any minimum hop path is: Among them, (M, N) represents the position number of the terminal satellite in the shortest path solution area, and the corresponding starting satellite position number is (1, 1). It represents the distance of the inter-satellite link on the same orbit, R E is the radius of the Earth, h s is the orbital height of the satellite, ΔΦ represents the phase difference between satellites in the orbital plane, represents the distance of the i-th inter-satellite link on the minimum hop path, Θ represents the geocentric angle of the line connecting the two satellites, ΔΩ represents the right ascension difference of the ascending node between adjacent orbital planes, α represents the orbital inclination of the satellite, Δf represents the phase difference of the adjacent orbital satellites, u(v i ) represents the satellite phase at the i-th cross-orbital plane forwarding, u(v i )=u0+(v i -1)ΔΦ+(i-1)Δf,i=1,2,...,N-1,v i Indicates the satellite number at the i-th cross-orbital plane forwarding.

4. The method for quickly solving the shortest path between satellites in a low-orbit satellite network according to claim 1, wherein: The process of solving the shortest path with the minimum number of hops between the starting and ending satellites in the single valley case is: All cross-orbital plane forwarding in the shortest path is performed continuously. First, the satellite number v at the i-th cross-orbital plane forwarding is calculated based on the following formula: i : v i =v1,i=1,2,...,N-1 Among them, u0 represents the phase of the initial satellite, Represents an intermediate variable, and Round() represents a rounding function; Then, based on the satellite number v at the i-th cross-orbital plane forwarding i The satellite phase u(v i ), and then calculate the shortest path with the minimum number of hops between the starting and ending satellites.

5. The method for quickly solving the shortest path between satellites in a low-orbit satellite network as claimed in claim 1, wherein: The process of solving the shortest path with the minimum number of hops between the starting and ending satellites in the double valley situation is as follows: The shortest path is simplified into a double-step path consisting of two consecutive cross-orbital plane forwarding segments. The forwarding number R of the first consecutive cross-orbital plane forwarding segment, the satellite number v1 at the first cross-orbital plane forwarding, and the number of consecutive forwarding segments Δv within the orbital plane are calculated based on the following formulas: Among them, R H represents the upper limit of R, Round() represents the rounding function, u0 represents the phase of the starting satellite, mod() represents the remainder function, represents the intermediate variable, v H Indicates the upper limit of the value of v1; Then calculate the satellite number v at the i-th cross-orbital plane forwarding based on the following formula: i and satellite phase u(v i ): Then, the phase offset at the i-th cross-orbital plane forwarding is calculated based on the following formula: The total path phase offset is calculated based on the following formula: Then let Δv=0,v1=v2=...=v N-1 , then traverse v1=1,2,...,N-1, and find the corresponding and And take the minimum value Compare and The smaller of the two corresponding to R, v1 and Δv is used to calculate v i and u(v i ), and then calculate the shortest path with the minimum number of hops between the starting and ending satellites.

6. A system for rapidly solving the shortest path between satellites in a low-orbit satellite network, using the rapid solution method according to any one of claims 1 to 5, characterized in that: include: An input module is used to input constellation parameters of the low-orbit satellite network and position information of the starting and ending satellites, wherein the constellation parameters include the number of orbital planes of the low-orbit satellite network, the number of satellites evenly distributed in each orbital plane, orbital altitude, phase factor and orbital inclination; A first calculation module is configured to calculate constellation phase parameters based on input constellation parameters, wherein the constellation phase parameters include the phase difference between satellites within an orbital plane, the right ascension difference of ascending nodes between adjacent orbital planes, and the phase difference between satellites in adjacent orbits, and to construct a mesh-shaped shortest path solution area based on the position information of the starting and ending satellites; The second calculation module is used to calculate the phase difference between the starting and ending satellites based on the constellation phase parameter and the position information of the starting and ending satellites; The output module is used to judge whether the phase situation formed by the starting and ending satellites is a single valley situation or a double valley situation based on the phase difference, and according to the phase situation judgment result, solve the shortest path with the minimum number of hops between the starting and ending satellites in the shortest path solution area, and output the distance value and the passing nodes of the shortest path.

7. An electronic device, characterized in that: The method comprises a processor and a memory, wherein a computer program is stored in the memory, and the processor is configured to execute the steps of the method according to any one of claims 1 to 5 by calling the computer program stored in the memory.

8. A computer-readable storage medium for storing a computer program for rapidly solving the shortest path between satellites in a low-orbit satellite network, characterized in that: When the computer program is run on a computer, the steps of the method according to any one of claims 1 to 5 are executed.

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