WO2021203575A1 - Satellite-terrestrial information network unified routing method based on hyperbolic geometry - Google Patents

Abstract

Provided is a satellite-terrestrial information network unified routing method based on hyperbolic geometry. The method comprises: S1, mapping nodes in a satellite-terrestrial information network in a three-dimensional geographic space to a three-dimensional hypersphere by means of stereographic projection; S2, performing hyperbolic radius component setting on points mapped to the three-dimensional hypersphere, and finally mapping coordinates of the nodes in the three-dimensional geographic space to a four-dimensional hyperbolic space to obtain hyperbolic coordinates; S3, calculating an included angle between two nodes in the four-dimensional hyperbolic space by using the acquired hyperbolic coordinates; S4, when routing is performed in the satellite-terrestrial information network, calculating a hyperbolic distance between the two nodes by using the acquired hyperbolic coordinates of the nodes and the included angle between the two nodes in the four-dimensional hyperbolic space; and S5, completing greedy routing forwarding according to the calculated hyperbolic distance between the two nodes. The satellite-terrestrial information network routing does not depend on a global link state and the distributed and centralized scheduling of router node information, a large amount of routing table storage overheads can be saved, and expandability is achieved.

Description

A unified routing method for sky-ground information network based on hyperbolic geometry Technical field

The invention belongs to the field of communication technology, and in particular relates to a unified routing method for a sky-ground information network based on hyperbolic geometry.

Background technique

After the third industrial revolution, mankind has entered the information age, and information has become the core driving force of current social and economic development. Cosmic space has become the fourth territory of all countries after land, sea, and air. China’s security interests in ocean, space and other fields, as well as the rapid development of space science exploration missions, have also proposed real-time transmission and timely sharing of cross-regional and cross-airspace information. Higher requirements. Traditional terrestrial information facilities and transmission systems have been unable to fully meet the needs of the information society and national defense information wide-area coverage and the integration and sharing of multiple types of information. It is necessary to use the advantages of high-level spatial transmission and processing of information. Satellite communication technology has been greatly developed in the last few decades. At present, the function of satellites is mainly as a signal relay, providing curved-tube signal forwarding. Space satellite networks have advantages in information transmission in terms of coverage area, access speed, efficiency, real-time performance, accuracy, and networking flexibility. However, due to the limitations of historical conditions, most satellite groups are often “tailor-made” and mutual Irrelevant. At the same time, China's current ground stations are not enough to cover the world, and cannot meet the needs of information and space resource sharing. After long-term development, the ground communication network has the advantages of mature technology and rich resources. The integration of space satellite networks and ground networks is conducive to maximizing the advantages of each network, achieving complementary advantages, improving resource utilization, and achieving more variety. The support of a richer and larger number of businesses breaks the status quo of foreign technology monopoly.

The future information network needs wide-area coverage that does not rely solely on ground station networking. Therefore, based on the preliminarily available space conditions and in order to meet the increasingly complex information needs, it is urgent to build an integrated space, space, and ground information network. However, building an integrated sky-ground information network faces many challenges, including reasonable network architecture design, constellation orbit design, networking technology, transmission technology, network management and security technology, etc. Networking technology is the basis for realizing the heterogeneous interconnection between the satellite network in the space-based part and the terrestrial Internet, and the routing problem is one of the key challenges facing the construction of an effective integrated information network.

The integrated sky-ground information network consists of three layers: a space-based network containing various satellite nodes, a space-based network containing various types of flight probes, and a ground-based network containing various ground nodes. The routing problem is one of the key problems to realize the heterogeneous interconnection of all layers of the sky-ground information network.

From the perspective of the different characteristics of each layer of the sky, the air, and the ground, the existing Internet routing technology cannot comprehensively adapt to the characteristics of each layer in the sky-ground information network during the interactive information transmission between the layers. Different from the ground-based Internet, the space-based satellite network is mainly composed of geostationary orbit (GEO) satellites, medium orbit (MEO) satellites, and low orbit (LEO) satellites. Some nodes in the satellite network, such as low-orbit satellite nodes, move at high speeds relative to the ground. The distribution of nodes is determined by physical characteristics such as satellite orbits. The topology is highly dynamic, and the energy consumption, volume, and weight of space router nodes are limited by the satellite carrying capacity. The performance is low. At the same time, due to the extremely long transmission distance of space communication, the transmission loss, time delay, bit error rate, transmission rate and other performance are closely related to the transmission distance. As the distance between the communication terminals increases, the transmission loss and transmission The time delay will increase significantly. The terrestrial Internet topology is relatively stable, router nodes are distributed in areas where users are concentrated, and the nodes are not restricted by factors such as energy consumption, volume, and weight, and have high performance. In contrast, the space link structure of the satellite network is more complicated and the communication requirements are higher. If the traditional routing method is directly applied to the satellite network of the space-based part, the sky-ground information network formed by it will face the change of the link state. Frequent notifications, high routing recalculation overhead, slow routing convergence, and difficulty in meeting the requirements for the quality of service provided by the path. Therefore, the traditional routing method alone cannot fully cater to the different characteristics of the sky, the air, and the ground, and cannot meet the requirements for the realization of heterogeneous interconnection routing at each layer with different topological structures in the sky-to-ground network.

On the whole, the integrated sky-ground information network is a large-scale, nonlinear, dynamic and changeable complex system. There are many types of services in the network and the dynamic change of the network environment, which further increases the routing path calculation in the process of information transmission. Deal with complexity and overhead. In order to route information to a given destination in the network, all nodes must jointly discover the best path to each possible destination based on the current state of the global network topology. With the rapid growth of the number of destinations, the huge amount of information that must be maintained in each node's routing table will cause serious scalability problems and endanger the performance and stability of the sky-ground integrated information network. To make matters worse, the integrated information network of the sky is not static. Due to the failure of existing links and nodes or the emergence of new links and nodes, and the dynamics determined by the physical characteristics of upper space nodes such as satellites and drones, the network topology will continue to change. If every time such a change occurs anywhere on the network, the information about this event must be diffused to all nodes, and then quickly processed by the nodes to recalculate the new optimal route, then the network continues to increase in scale and dynamics Uncertainty will lead to huge and rapidly increasing routing overhead. The network lacks self-adaptability and cannot respond adaptively to changes in the network environment, which will result in fragile information transmission capabilities. The integrated, heterogeneous and interconnected sky-ground information network must be able to accurately and stably complete the task of information transmission to meet the needs of society and militarization. Therefore, a robust and effective routing strategy is an important foundation for the sky-to-ground information network to play the role of information transmission.

In summary, one of the urgent problems to be solved in the current construction of the sky-to-ground information network is to study a method that can facilitate the comprehensive and uniform expression of the topological characteristics between the nodes of each layer, so as to deal with the interactive information transmission between the layers. The existing routing problems also make the routing based on this expression method have good stability and scalability, and can actively adapt to the high dynamics brought about by the transformation of the sky-ground information network topology.

Different from the European geometry proposed by the ancient Greek mathematician Euclid, the hyperbolic geometry is Lobachevsky's geometry, that is, Roche's geometry. Euclidean geometry is based on a plane with a curvature of 0; Rogowski geometry is based on a hyperboloid, with a curvature less than 0, which is a negative number. Network mapping is a method of using a coordinate system in geometric space and then adding a certain method to express the distribution of network nodes in the real world, which is conducive to the realization of simple and efficient network routing. The routing on the network mapping model based on hyperbolic geometry can be called hyperbolic routing.

Greedy routing strategy has good routing performance in large-scale networks. Each node in the network is given a space coordinate. Based on the coordinates, the distance between any two points can be calculated. After the network is established, each node only needs to know the space coordinate information of itself and its immediate neighbor nodes to be greedily based on the distance. By forwarding the message, the size of the routing table can be compressed to a minimum, which can save the node's data storage and routing lookup overhead. Hyperbolic routing is a kind of geometric greedy routing, and the corresponding geometric space is hyperbolic geometric space, which is suitable for scale-free networks, that is, nodes in the network obey power distribution. Hyperbolic space has significant advantages when used to deal with large-scale network topologies. Hyperbolic coordinates can provide a higher routing success rate for greedy routing. Kleinberg et al. proposed the earliest mapping algorithm for hyperbolic routing in 2007. In this paper, by constructing the minimum spanning tree of the network, any network can be mapped into the hyperbolic space, and the greedy routing based on this mapping has extremely high The success rate. In the article "Sustaining the Internet with hyperbolic mapping" in 2010, Krioukov et al. proposed the use of statistical inference techniques to find the coordinates in the hyperbolic space under the Internet. Under the guidance of inferred coordinates, greedy forwarding in the Internet achieves efficiency and robustness. In 2010, it was proved that greedy forwarding is indeed effective in an Internet-like synthetic network embedded in a geometric space. It is constructed based on hyperbolic geometry to maximize efficiency.

An important prerequisite for hyperbolic routing is to have a good coordinate mapping algorithm. Hyperbolic routing takes the degree of centralization of the node as a coordinate component, and the central node is more likely to attract packets to be forwarded, so that it can achieve a near-optimal path selection while ensuring a certain success rate of routing. All in all, hyperbolic routing can use geographic coordinates for routing without knowing the global topology. You only need to know the coordinates to complete the forwarding. It can adapt to the dynamic changes of the network topology, and the expansion of the network has almost no impact on the routing. Therefore, a more scalable and dynamic routing solution is provided.

At the same time, hyperbolic space has the nature of exponential expansion, which is consistent with the large-scale and complex structure of the integrated information network of space, space and earth. It can be seen that the combination of hyperbolic geometry related knowledge and sky-ground information network technology is a brand-new and valuable research direction. Nowadays, related routing research based on hyperbolic geometry applied to traditional terrestrial networks has gradually developed. However, the integrated sky-ground information network is different from traditional terrestrial networks, and its network nodes have strong three-dimensional spatial characteristics. The common hyperbolic routing algorithm is based on the completion of the coordinate mapping of the ground network nodes on the two-dimensional plane. For example, in 2019, a multi-mode identification network addressing method based on coordinate mapping was proposed, which will The scaled multi-mode identification network is mapped to a three-dimensional hyperbolic space, that is, each node is assigned a three-dimensional spherical coordinate, and then the hyperbolic distance between two points can be calculated based on the coordinate to effectively address and route forwarding . This kind of hyperbolic routing algorithm specially designed for two-dimensional ground network is not applicable in the sky-ground information network space. It is suitable for the coordinate mapping strategy of the three-dimensional cosmic coordinate space of the sky-ground information network and the hyperbolic design based on it. The routing algorithm is worth studying. Therefore, the technology of the present invention is oriented to the information network of the sky. Aiming at the difficulty of using a comprehensive and unified routing strategy caused by the different characteristics of each layer of nodes, a new network mapping strategy based on hyperbolic geometry is proposed, which can complete the processing. The network mapping from the sky-ground information network in the three-dimensional space to the four-dimensional hyperbolic space, thus giving each layer node in the sky-ground information network a unified expression based on the hyperbolic coordinates, making the network as a whole highly scalable and adaptable The highly dynamic transformation of the network topology will help solve the routing problem of addressing during interactive information transmission between nodes at various layers, and at the same time, routing on its basis will help save routing table storage overhead.

In terms of military affairs, war under modern high-tech conditions is a system-to-system confrontation and a contest of the overall combat capability of the weapon equipment system. Weapon systems, between various subsystems in the weapon system, and between individual equipment must work closely with each other to form an organic whole to function. The integrated sky-ground information network can organically connect early warning detection, information processing, command and control, and weapon platforms, and real-time and stable information transmission is an important guarantee for its excellent overall effectiveness. The routing strategy based on the hyperbolic geometry of the space, space, and ground integrated information network has robustness and effectiveness in a dynamically changing network environment, which helps the space, space, and ground integrated information network to form an integrated “aggregation” The "multiplier" and the "multiplier" that improve the overall combat effectiveness have exerted their due effect.

In terms of social benefits, as the key to network information transmission, a robust and effective routing strategy is also an important guarantee for the sky-to-ground information network to exert social service effects. The Beidou satellite navigation system (hereinafter referred to as the Beidou system) has an important position in the construction of China's space, air, and ground integrated information network. It is China's self-constructed and independently operated satellite navigation system focusing on the needs of national security and economic and social development. It is an important national space infrastructure that provides all-weather, all-time, high-precision positioning, navigation and timing services for global users. With the development of Beidou system construction and service capabilities, related products have been widely used in transportation, marine fishery, hydrological monitoring, weather forecasting, surveying and mapping geographic information, forest fire prevention, communication timing, power dispatch, disaster relief and mitigation, emergency search and rescue and other fields , Gradually penetrate into all aspects of human social production and people’s lives, and inject new vitality into global economic and social development. The routing strategy of the sky-to-ground information network based on hyperbolic geometry guarantees the success rate of routing while adapting to the dynamics of the network, provides good scalability, and helps support the sky-to-ground information network including the Beidou system to provide society Robust information service. At the same time, the geographic location service provided by the Beidou navigation and positioning system provides solid technical support for obtaining the three-dimensional geographic spatial coordinates of nodes in the hyperbolic geometry-based sky-ground information network routing strategy.

Therefore, the technology of the present invention combines the actual conditions of each layer of the sky-ground network to do specific analysis work, and proposes a network mapping strategy based on hyperbolic geometry, which can complete the sky-ground information network in the three-dimensional space to the network of the four-dimensional hyperbolic space. Mapping gives each layer of nodes with different characteristics in the sky-ground information network a unified expression based on hyperbolic coordinates. It is not only conducive to solving the dilemma that the sky-ground information network is difficult to use a comprehensive and unified routing strategy, but also has important application significance. And realize value.

In 2015, Huangguke put forward a unified air-space-ground integrated addressing scheme based on the analysis of the existing network routing protocol problems. The quad-tree is used to uniformly address the nodes in the network, which reduces the storage overhead. The quadtree is a very commonly used data mining structure, which is widely used in the fields of image processing and geometry. This method can effectively characterize the geographical location information of entities distributed in space with the least number of bits. Its basic usage is to cover the area of interest with a square, and then iteratively divide this area into smaller domains until each area contains only one node. Suppose the original undivided large square area is represented by S, and the set of nodes in this area is V. Repeat the division of S into four smaller squares, until each small square contains only one node, and stop continuing the division for the empty square area without nodes. The efficiency of the quadtree lies in the area query.

The idea of Huang Guke's quadtree addressing scheme is to use the hierarchical structure of all the squares generated after the quadtree divides the network topology to perform hierarchical routing. First, assign representatives to each square, and then connect all the representatives according to the quad-tree hierarchical structure to form a network topology. In a compound quadtree network, a node can represent one or more squares in which it is located, and each square can also have one or more representatives. In this plan, the entire air-space-ground integrated network is finally represented by the entire model of a compound quadtree. During routing, the node forwards the information to the neighboring node that is closest to the destination node in the composite quad-tree hierarchical network topology. The composite quadtree network structure has the following characteristics:

(1) Long links and short links coexist. In the compound quad-tree structure, there are both communication links between short-distance nodes and communication links between long-distance nodes. The parent node of a long link generally has a large communication range. For example, the link between a satellite node and a ground station or a ground mobile node is a long link. The communication range of the parent node of the short link is generally very small, and mostly exists between the internal nodes of the ground mobile network. Although a long link represents a large communication range, and a short link represents a small communication range, the corresponding communication delay of the long link is large and the communication delay of the short link is small. The coexistence of long links and short links can make the nodes in the network find the optimal path with the least communication overhead.

(2) Compared with the quadtree, the redundancy is increased. Each non-root node in the quadtree has only one parent node, and each non-root node in the compound quadtree may have multiple parent nodes, thus increasing the redundancy of the tree structure. Increasing redundancy is of great benefit to the routing of nodes. If an intermediate node in the quadtree fails, then the connectivity between the parent node and the child node connected to it will be lost. It is precisely because of the redundancy in the compound quadtree structure that if an intermediate node fails, the parent node and child node connected to it may have another link connection, which will not destroy the entire quadtree network. The impact of sex.

(3) The higher the node, the higher the stability. It can be seen from the compound quadtree structure that the nodes in the upper area have long links and can communicate with nodes with a large coverage area. Even if the upper node moves from a block area to another block area, the node is in The newly formed composite quadtree structure may still be at the upper node, so it has high stability. The stability of the node at the bottom is very low. If the node is moved from the current block area to another block area, its parent node will change, it is no longer the original parent node, and may be on another branch. .

The main advantages of this method are that, first, it uses a quadtree-based method to uniformly address each node in the air-space-ground integrated network, reducing storage overhead; second, it uses a network defined by a compound quadtree It has good load balancing and stability.

The above method also has certain shortcomings. First of all, if the object is unevenly distributed in the spatial region, too much concentrated in a certain part of the region while other parts are less or not distributed, then the left and right branches of the generated quadtree will be unbalanced, which will lead to a sharp decline. Query efficiency. Secondly, the solution needs to calculate the position of the satellite in advance, and periodically divide the quadtree to construct a composite quadtree structure. When the node moves fast, it needs to perform quadtree division and addressing twice frequently. , Resulting in greater computational overhead.

In 2017, Yang's team proposed an addressing and routing design with IPv6 technology as the core, using a 128-bit IPv6 address as an interface on a space-based router to assign a globally unique aggregated unicast address. Among them, the first 64 bits identify the routing prefix and subnet identifier of this address, and the last 64 bits are the network interface identifier, which is consistent with the EUI-64 address specified by the IEEE 802 series. The low-medium orbit satellite nodes in the space-ground integrated information network are highly dynamic, and this feature brings two possible addressing schemes.

The first solution is to perform addressing based on the satellite's position relative to a certain reference system, such as the latitude and longitude coordinates of the satellite's projection on the earth's surface. This scheme divides the space into several regions according to the latitude and longitude of the space, and uses a part of the subnet ID field in the IPv6 address to number the regions. The remaining bits in the subnet ID field are used to distinguish the satellite node. Different interfaces. For example, when longitude and latitude are each identified by 8bit, 256×256 areas can be supported, and the maximum side length of each area is only about 156km. Essentially, this solution is to completely hand over the dynamics of the satellite to the network layer to keep the user's transmission layer and application layer simple, but it does not conform to the Internet's design principles of "complex edges and simple core".

The second solution is based on the logical position of the satellite for addressing. The satellite number or the orbit of the satellite and its position in the orbit are embedded in the first few bits of the IPv6 address subnet ID field, so that the satellite no matter where it moves. Everywhere has a permanent address. With the movement of satellites, for communication that lasts for a long time and does not want to be interrupted, such as real-time audio or video transmission, the IPv6 protocol supports mobility to achieve address switching.

The main advantage of the first solution is that users who access via satellite can automatically obtain an IPv6 access address based on their geographic location, combined with the routing prefix. Even if the satellite accessed by the user changes, the user does not need to change the address. (The bits in the subnet ID except for the longitude ID and latitude ID can use fixed values reserved for the access network).

The main advantages of the second scheme are that, firstly, the control plane is simpler and more stable, and the ground station can easily access the target satellite without knowing its current coordinates; secondly, it can also easily perform address aggregation, and the data is grouped between the satellites. When forwarding, you only need to use the satellite number in the target address to find the next hop route instead of using a complete IPv6 address. This can greatly reduce the storage, calculation, and bandwidth consumption of the control plane, and realize a lightweight routing protocol.

In the first scheme, first, satellite nodes need to dynamically update addresses and routes frequently, which brings greater overhead and instability to the control plane, especially when the number of divided areas is large. Secondly, some boundary conditions need to be dealt with, such as ensuring that there cannot be multiple satellites in an area.

In the second solution, with the high-speed movement of low-medium orbit satellites, users may need to change their addresses as they access satellites, which is accompanied by a certain communication overhead.

Summary of the invention

The purpose of the present invention is to provide a unified routing method for sky-ground information network based on hyperbolic geometry, which aims to solve the above-mentioned technical problems.

The present invention is realized in this way, a sky-ground information network unified routing method based on hyperbolic geometry, the sky-ground information network unified routing method includes the following steps:

S1. Using spherical polar projection to map the nodes in the sky-ground information network in the three-dimensional geographic space to the three-dimensional hypersphere, the mapping relationship is:

S2. Set the hyperbolic radius component of the points mapped to the three-dimensional hypersphere, and map the node coordinates in the three-dimensional geographic space to the four-dimensional hyperbolic hypersphere space according to the hyperbolic radius component identification node, so that the hyperbolic radius component identifies the node to The distance of the four-dimensional hyperbolic hypersphere center constitutes the hyperbolic coordinates;

S3. Calculate the angle between two nodes in the four-dimensional hyperbolic hypersphere space by using the obtained hyperbolic coordinates;

S4. When routing in the sky-ground information network, use the obtained hyperbolic coordinates of the node and the angle between the two nodes in the four-dimensional hyperbolic space to calculate the hyperbolic distance between the two nodes;

S5. Complete greedy routing and forwarding according to the calculated hyperbolic distance between the two nodes;

Among them, r _A is the radial quantity coordinate of point A, and R is the maximum distance of a node in space from the center of the earth's sphere.

A further technical solution of the present invention is that the step S1 further includes the following steps:

S11. Establish a spherical polar coordinate system in the three-dimensional geographic space where the universe is located in the space covered by the sky-ground information network with the center of the earth as the origin;

S12. Map the point set with spherical polar coordinates in the three-dimensional geographic space to the three-dimensional hypersphere.

The further technical solution of the present invention is: the step S2 further includes the following steps:

S21, rank the nodes according to the communication radius from high to low;

S22. Bring the scale coefficient into k _n =log ₂ (ε+rank _n ·scale _sur ) to calculate the hyperbolic radius of each level node respectively;

S23. The hyperbolic coordinates are formed by assigning hyperbolic radius components to the nodes mapped to the three-dimensional hypersphere to identify the distance from the node to the center of the four-dimensional hyperbolic hypersphere;

Among them, k _n represents the hyperbolic radius component value corresponding to level n, ε represents the value increment of the hyperbolic radius component; rank _n represents the scale factor of the node level division; scale _sur is the scale of the near-surface node, that is, the total number.

The further technical solution of the present invention is: the step S3 further includes the following steps:

S31. For the sphere in the three-dimensional space that contains the earth and the outer circle of the earth, a spherical polar coordinate system is established with the earth sphere center O as the origin, A and B are any two points on the surface of the sphere, and the earth sphere center O is the center of the equatorial plane. , O ₁ is the center of the circle parallel to the equatorial plane where point A is located, O ₂ is the center of the circle parallel to the equatorial plane where point A is located, and R is the sphere space containing the earth and the outer space of the earth. The spatial radius of the range,

Is the azimuth angle of point A, that is, the angle between the projection line of the line from point A to point O on the xy plane and the positive x-axis, the value range is [0,2π],

Is the azimuth angle of point B, that is, the angle between the projection line of the line connecting point B to point O on the xy plane and the positive x axis, and the value range is

θ ₁ is the elevation angle of point A, that is, the angle between the line from point A to point O and the positive z axis, and the value range is [0,π], θ ₂ is the elevation angle of point B, that is, the angle from point B to point O The angle between the line and the positive z axis, the value range is [0,π]; according to the law of cosines

Calculate the straight-line distance AB between A and B, the formula:

AB ² ＝AO ² +BO ² -2AO·BOcosτ

＝2R ² -2R ² cosτ

＝2R ² (1-cosτ); at the same time, according to the formula between two points on a straight line on a different plane

Calculate the straight-line distance AB between A and B; since AB ² =AB ² , the relational formula for calculating the angle τ between two points in three-dimensional space can be obtained

S32. Calculate the value of the included angle ρ between the two points A" and B" corresponding to the two points A and B in the four-dimensional hyperbolic hypersphere space using an iterative method according to the relational formula for calculating the included angle in the three-dimensional space,

Where ψ ₁ represents the mapping angle component of the corresponding mapping point obtained after the point A is mapped to the four-dimensional hyperbolic hypersphere space, and ψ ₂ represents the coordinate of the corresponding mapping point obtained after the point B is mapped to the four-dimensional hyperbolic hypersphere space The mapped angular component.

The further technical solution of the present invention is: according to the hyperbolic cosine theorem in the step S4, A" and B" are the corresponding mapping points obtained after any two points A and B in the three-dimensional space are mapped to the four-dimensional hyperbolic hypersphere. Calculate the hyperbolic distance h between two points A" and B" in the four-dimensional hyperbolic hypersphere space, and set the coordinates of A" as

The B'coordinate is

The hyperbolic distance h between them is related to the hyperbolic components k ₁ , k ₂ and the angle ρ between two points; the hyperbolic distance h between any two points in the four-dimensional hyperbolic hypersphere space satisfies the formula:

h=arccosh[cosh(k ₁ )cosh(k ₂ )-sinh(k ₁ )sinh(k ₂ )cosρ].

The further technical solution of the present invention is: the step S12 further includes the following steps:

S121: Perform mapping transformation according to the radial quantity of point A;

S122, according to θ _A ,

ψ _A determines the specific position of A′ in the three-dimensional hypersphere;

Among them, θ _A is the elevation coordinate component of point A′;

Is the azimuth coordinate component of point A'; ψ _A is the mapping angle coordinate component of point A'.

The further technical solution of the present invention is: in the step S23, the mapping node

The hyperbolic coordinate component is assigned to identify the distance between the node and the center of the four-dimensional sphere, and it is formally mapped from the three-dimensional hypersphere to the four-dimensional hyperbolic space. The hyperbolic coordinate component is denoted by k, and the hyperbolic component of the corresponding node A is denoted as k _A.

The further technical solution of the present invention is that in the step S23, the mapping sphere corresponding to each node of the sky-ground information network under the original three-dimensional geographic space on the three-dimensional hypersphere will complete the respective mapping expansion and contraction according to the respective hyperbolic coordinate component values. The expansion and contraction will not change the angle, and finally the nodes in the sky-ground information network in the original three-dimensional geographic space can obtain the mapping expression in the four-dimensional hyperbolic hypersphere space

Among them, θ is the elevation coordinate component;

Is the azimuth coordinate component; ψ is the mapping angle coordinate component.

The beneficial effect of the present invention is that the method completes the network mapping from the sky-ground information network in the three-dimensional space to the four-dimensional hyperbolic space, and based on the hyperbolic geometry, it gives a basis for each layer of the sky-ground information network with different characteristics. The unified expression of geographic coordinates helps to quickly identify and locate nodes in the network, which will greatly simplify subsequent routing tasks; make the sky-to-ground network routing independent of global information distribution and scheduling, and topological changes have an impact on mapping Not big, it can adapt well to the dynamic environment. The space constructed by hyperbolic geometry has the nature of exponential expansion, which is consistent with the huge scale and complex structure of the heterogeneous integrated sky-ground information network. At the same time, hyperbolic coordinates can provide a higher routing success rate for greedy routing. The greedy routing strategy based on hyperbolic geometry has good routing performance in large-scale networks. It can use geographic coordinates for routing without knowing the global topology. The expansion of the network has almost no impact on routing; because each node in the network Both are given hyperbolic coordinates, and the distance between any two points can be calculated based on the coordinates. After the network is established, each node only needs to know the spatial coordinate information of itself and its immediate neighbor nodes to greedily forward the message based on the distance Therefore, the scale of the routing table can be compressed to the minimum, which can save the node's data storage and routing lookup overhead. At the same time, by setting the hyperbolic component in the hyperbolic coordinates to adjust the tendency of routing to select the next hop, the routing strategy can be inclined to select nodes with better properties, which can further optimize the routing effect.

Description of the drawings

FIG. 1 is a unified routing method for a sky-ground information network based on hyperbolic geometry provided by an embodiment of the present invention;

Fig. 2 is a schematic diagram showing that the spherical polar projection method provided by an embodiment of the present invention can complete the projection from a two-dimensional plane to a three-dimensional spherical surface.

FIG. 3 is a schematic diagram of the distance between the satellite and the ground node provided by the embodiment of the present invention is much larger than the distance between the ground node.

FIG. 4 is a schematic diagram of using the spherical polar projective idea to reduce the influence of excessive distance provided by an embodiment of the present invention.

Fig. 5 is a schematic diagram of establishing a spherical polar coordinate system with the center of the earth as the origin O provided by an embodiment of the present invention.

Fig. 6 is a schematic diagram of a mapping point A′ on a three-dimensional hypersphere provided by an embodiment of the present invention.

Fig. 7 is a flowchart of a hyperbolic coordinate mapping algorithm in a three-dimensional geographic space provided by an embodiment of the present invention.

Fig. 8 is a schematic diagram of a cosine triangle provided by an embodiment of the present invention.

Fig. 9 is a schematic diagram of the distance between any two points on two straight lines of different planes provided by an embodiment of the present invention.

FIG. 10 is a schematic diagram of calculating the angle between two points A and B on a spherical surface provided by an embodiment of the present invention.

Detailed ways

As shown in Fig. 1, the method for unified routing of sky-ground information network based on hyperbolic geometry provided by the present invention is detailed as follows:

The Sky-Ground Information Network is a dynamic heterogeneous large-scale network, which contains three layers of sky, air and ground with different characteristics. The highly dynamic characteristics require nodes to be able to dynamically access, fast handover, etc. At the same time, due to the highly dynamic changes of nodes , The topological structure of the entire network will change rapidly, forming a dynamic network topology. What's more serious is that due to the long information transmission distance between the sky and the earth and the limited link quality, the time delay, transmission loss, and bit error rate that increase significantly in proportion to the increase in the distance will also be faced when the information is exchanged and transmitted. These all pose great challenges to network routing. For information loss and congestion caused by high bit error rate and high delay, the direct use of the traditional TCP/IP protocol will significantly reduce the data throughput. The original Internet routing technology also It cannot comprehensively adapt to the characteristics of each level in the integrated information network of space, space and ground. And with the rapid growth of the network scale in the future, the huge amount of information that must be maintained in each node's routing table will bring serious scalability problems and endanger the performance and stability of the sky-to-ground integrated information network.

At the same time, the various levels of the sky, the air, and the ground have different characteristics, and the lack of a unified network protocol specification makes it difficult for the heterogeneous layers of the sky-ground network to effectively implement heterogeneous interconnection routing, and it is difficult to realize the sharing of resources and information, and the utilization efficiency is low. Therefore, one of the urgent problems to be solved in the current construction of the sky-to-ground information network is to study a method that can facilitate the comprehensive and uniform expression of the topological characteristics between the nodes of each layer, so as to deal with the routing that exists when the interactive information transmission is carried out between the layers. The problem is that the routing based on this expression method has good stability and scalability, and can actively adapt to the high dynamics brought by the transformation of the sky-to-ground information network topology, thereby ensuring an integrated sky-to-ground information network It can accurately and stably complete the task of information transmission to meet the needs of society and militarized applications.

The technology of the present invention is a hyperbolic geometry-based sky-ground information network routing method, and a hyperbolic geometry-based network mapping strategy for an integrated sky-ground information network is proposed, which can complete the sky-ground information in a three-dimensional space. The network mapping from the information network to the four-dimensional hyperbolic space, based on the hyperbolic geometry, gives each layer of the sky-ground information network a unified expression based on geographic coordinates, which helps to quickly identify and locate the nodes in the network, so that the network as a whole has High scalability and adaptability to highly dynamic network topology environment, the node coordinates with the closest hyperbolic distance can be used for routing during routing, which is beneficial to solve the routing problem of addressing when interactive information transmission between nodes of different layers. Will greatly save the routing table storage overhead.

The main task of the present invention is to think about how to use the hyperbolic space network mapping technology to express the distribution of nodes in the three-dimensional geographic space where the integrated sky-ground information network is located, and specifically propose a four-dimensional hyperbolic space applicable to the sky-ground information network Network coordinate mapping algorithm. The specific implementation methods are described in the following subsections.

Spherical projection

In mathematical concepts, an n-dimensional sphere has an n-1 dimensional sphere. It can be understood through such a phenomenon: Our ground is part of the spherical surface in three-dimensional space, but the spherical surface is too large that the ground looks like a two-dimensional plane. Now, we push this phenomenon up one dimension. Relative to the extremely large four-dimensional space, near-Earth space looks three-dimensional. Therefore, for two points in space, we can assume that the near-Earth space (three-dimensional space) is a part of the spherical surface in a larger four-dimensional space. Therefore, in this part of the research, the scheme adopted by the patent of the present invention is to learn from the idea of spherical projection and map the three-dimensional space to the three-dimensional hypersphere (3-sphere).

Spherical projection refers to drawing rays from the apex of the sphere, passing through the sphere from the inside, and intersecting the plane. It can project nodes in a two-dimensional plane onto a three-dimensional sphere, as shown in Figure 2. The patent of the present invention applies this projection idea to the problem of raising one dimension. The resulting three-dimensional hypersphere is the surface of the four-dimensional hyperbolic space.

Drawing on the idea of spherical projection can not only complete the processing of high-dimensional problems, but also have certain benefits for the subsequent routing of the sky-to-ground information network based on hyperbolic geometry. The main idea of routing based on hyperbolic geometry is the greedy strategy based on spatial distance. Under normal circumstances, when the ground network between two ground nodes is not interoperable, it is necessary to rely on sky and sky nodes as relays to complete information transmission. As shown in Figure 3, the actual H is much larger than d, and the traditional greedy strategy based on spatial distance is difficult to use aerospace nodes. Using the method of spherical polar projection, the key sky and sky nodes can be given higher weights (that is, shorter hyperbolic distances) while reducing the impact of the distance of high-altitude nodes, so that the sky and sky nodes can be considered in the hyperbolic greedy strategy. Category, as shown in Figure 4, for the three points A, B, and C on the graph, suppose point C is a satellite node, and A', B', and C'are the corresponding points obtained after mapping A, B, and C, respectively. In the original geographic space, the distance between BC is much larger than the distance between AB, and in the image obtained after spherical projection, the distance between B'C' and the gap between A'B' and A'B' are reduced when viewed from the top.

Algorithm process of hyperbolic coordinate mapping in three-dimensional geographic space

The specific process is as follows.

In the first step, assume that the earth is a hollow sphere, and establish a spherical polar coordinate system in space with the center of the earth as the origin O. The spherical polar coordinate system, also known as the spatial polar coordinate, is a kind of three-dimensional coordinate system, which is extended from the two-dimensional polar coordinate system to determine the position of points, lines, surfaces and bodies in the three-dimensional space. It takes the origin of the coordinates as The reference point is composed of azimuth, elevation and distance. The spherical polar coordinate system is widely used in geography and astronomy.

The coordinate expression form of any point in space in the spherical polar coordinate system is

Among them, r represents the radial distance between the origin O and the target point. It is assumed that the nodes in the space are within the range of R from the center of the earth's sphere, that is, r∈(0,R]; θ represents the elevation angle, that is, O and The angle between the line to the target point and the positive z axis, where the value range is [0,π];

Represents the azimuth angle, that is, the angle between the projection line OM of the line connecting O to the target point on the xy plane and the positive x axis, where the value range is [0,2π]. As shown in Figure 5, taking a node A in space as an example, the coordinates of A are

The second step is to map the point set in the three-dimensional geographic space to the three-dimensional hypersphere. As can be seen from the previous section of the article, mathematically, an n-dimensional sphere has an n-1 dimensional sphere, so the surface of the four-dimensional hyperbolic space required by the patent of the present invention has three-dimensional characteristics, which can be abstracted as consisting of multiple three-dimensional spheres. It is a three-dimensional hypersphere (3-sphere). The patent of the present invention accomplishes this step by using the method of spherical polar projection, that is, each node in the three-dimensional geographic space under the spherical polar coordinate system is allocated a spherical polar projective reference sphere separately and the spherical projection is used on it. For example, for a node

The corresponding reference sphere sphere sphere center electrode projection labeled P _A, as shown in FIG.

In Fig. 6, the sphere enclosed by the dashed outer layer represents a three-dimensional hypersphere. Because it is assumed above that the nodes in the space are within the range of R from the center of the earth's sphere O, that is, r≤R, in order to ensure complete mapping, the patent of the present invention also sets the radius of the sphere abstracted by the three-dimensional hypersphere as R , The center of the sphere abstracted by the three-dimensional hypersphere is set to H.

First, the mapping transformation is performed according to the radial quantity of the point A. Align the spherical polar projective reference sphere P _A with the bottom center P _A ′ of the earth sphere center O, and use P _A ′ as a tangent to find point A, and perform subsequent mapping calculations according to the radial amount of point A, that is, when mapping P _A 'A=OA=r _A. In the center of the sphere in its three-dimensional hypersphere H in place stereographic projection apex sphere of reference P _A, node A is mapped to sphere reference stereographic projection of point P _A A ', while the stereographic projection P _A is the reference sphere mapping The small ball becomes one of the components of the three-dimensional hypersphere, that is, the mapping result A'of node A is in the three-dimensional hypersphere. The specific mapping relationship calculation method is as follows. Referring stereographic projection of a sphere of radius P _A R ', shown in FIG. 6, R' and R have a relationship as equation (2.1), while the ratio of the component map ψ having a relationship as shown in equation _A (2.2), thus Its specific value can be calculated by formula (2.3),

R=2R' (2.1)

∴

Then, according to θ _A ,

ψ _A determines the specific position of A'in the three-dimensional hypersphere. As shown in Figure 6. It is known that the surface of the four-dimensional hyperbolic hypersphere space is a three-dimensional hypersphere, which contains many small spheres. In Figure 6, we plot the three-dimensional projection when the four-dimensional hyperbolic hypersphere space is compressed to retain only the three-dimensional hypersphere. At this moment, the center H of the three-dimensional hypersphere described above is the four-dimensional hyperbolic hypersphere space. Ball heart. A four-dimensional space coordinate system of x-axis, y-axis, z-axis, and w-axis is constructed with H as the origin of the four-dimensional space, and each coordinate axis is perpendicular to each other. Using the mapping angle offset w-axis ψ _A as the direction, locate the position _{of the spherical polar projective reference sphere with P A} as the center of the sphere and R′ as the radius in the three-dimensional hypersphere. _{The patent of the present invention does not compare the angular position θ A} of point A in three-dimensional space when mapping with the aid of spherical projection.

Make changes, so the orientation of the mapping point A′ in the three-dimensional hypersphere in the xyz space under the four-dimensional coordinate system is still θ _A ,

So far, through the above-mentioned method of borrowing from the spherical polar projection, the patent of the present invention takes a point in the three-dimensional geographic space

Mapped to a point on the 3D hypersphere

In the same way, the general mapping calculation relationship obtained according to formula (2.3)

The other nodes in the three-dimensional geographic space are mapped one by one according to the above-mentioned method. For example, in Figure 6, another node B completes the mapping and is mapped to a point B'on the three-dimensional hyperplane. Assuming that there are N original nodes in the three-dimensional geographic space, the mapped three-dimensional hypersphere finally contains N mapping spheres, and each mapping sphere contains a corresponding mapping node.

Through the above-mentioned method of drawing on the spherical polar projection, the patent of the present invention can convert the spherical polar coordinate form in the three-dimensional geographic space

The point set of is mapped to the point set in the three-dimensional hypersphere

The third step is to formally map the node to the final correct position in the four-dimensional hyperbolic hypersphere space. The three-dimensional hypersphere is the surface composition of the four-dimensional hyperbolic space. Continue to take point A as an example, the node after completing the mapping with the spherical polar projection

At present, it is only on the surface part of the entire four-dimensional hyperbolic hypersphere. We need to map the node

The hyperbolic coordinate component is assigned to identify the distance between the node and the center of the four-dimensional sphere, and formally map it from the surface to the four-dimensional hyperbolic space. The hyperbolic coordinate component is denoted by k, and the hyperbolic component of the corresponding node A is denoted as k _A. In the subsequent research on hyperbolic routing, the hyperbolic coordinate component k will affect the forwarding tendency of routing. The closer the node is to the center, that is, the smaller the k, the higher the forwarding tendency. After the corresponding hyperbolic coordinate component value k _A completes the expansion and contraction relative to the center of the four-dimensional hyperbolic space, the node A in the original three-dimensional geographic space is considered to be officially successfully mapped. Since the radial expansion does not change the angle, finally node A can obtain the mapping expression in the four-dimensional hyperbolic hypersphere space

The mapping spheres corresponding to each node in the original three-dimensional geographic space will complete their mapping and expansion according to their respective hyperbolic coordinate component values, forming a four-dimensional hyperbolic hypersphere space. Taking the mapping nodes A′ and B′ on the three-dimensional hypersphere as an example, the results of points A” and B” are obtained after the radial expansion and contraction are completed according to the respective hyperbolic radius components. The four-dimensional hyperbolic hypersphere space that retains the three-dimensional hypersphere is similar to the point A″. The coordinate of the point B″ after the point B′ is stretched is

Finally, after the mapping is officially completed, the general expression form of the coordinates of the node in the four-dimensional hyperbolic hypersphere space is

In short, the hyperbolic coordinate mapping algorithm in three-dimensional geographic space can be summarized into three steps, and the flow of the algorithm is shown in Figure 7.

Through the above method, all the nodes of the sky-ground information network in the three-dimensional geographic space can be mapped to the four-dimensional hyperbolic hypersphere space.

Hyperbolic radius component setting

In fact, the value of the hyperbolic radius component k should be adapted to the actual network, and it is meaningful to discuss it in the actual scene. The patent of the present invention optimizes the value of the hyperbolic radius through the simulation experiment results and provides a relatively preliminary method for the value of the hyperbolic radius. In future research, continuous improvement can be made on this basis.

In our simulation experiments, the air nodes and ground base station nodes that are below the stratosphere and have a very low altitude relative to the satellite nodes are uniformly classified as near-surface nodes, and the number of experimental settings is 2000. In the experiment, the hyperbolic radii of near-surface nodes and satellite nodes are obtained according to different methods.

The method of setting the hyperbolic radius of the near-surface node is as follows. First, the nodes are arranged from high to low according to the communication radius, and are divided into five levels. Define the scale factor rank _n ∈[0,1], and multiply the number of nodes by the scale factor rank _{n to} calculate the division of nodes at each level. The node rank is divided according to: the node rank of the scale coefficient rank _n ∈ (rank _n-1 ,rank _n ] is rank _n , where n ∈ {12,3,4,5} is used to distinguish different ranks. Used for node rank The specific settings of the divided scale coefficients are as follows: rank ₁ =0.0625, rank ₂ =0.125, rank ₃ =0.25, rank ₄ =0.5, rank ₅ = 1, as shown in the following table.

Secondly, the scale coefficient rank _{n is} substituted into the formula (2.4) to calculate the hyperbolic radius k of each level node, where k _n is specifically used to represent the value corresponding to the node level n. Theoretically, the hyperbolic radius should obey the power-law distribution, that is, if the true number of the log function (independent variable ε+rank _n ·scale _sur ) in formula (2.4) is uniformly distributed, then its logarithm obeys the power-law distribution . Where ε represents the incremental range of the hyperbolic radius. Scale _sur is the scale of near-surface nodes, that is, the total number, which is 10,000 in our experiment. For example, in the experiment of the present invention, the hyperbolic radius value increment range ε=30 is set. At this time, rank ₁ = 0.0625, rank ₂ = 0.125, rank ₃ = 0.25, rank ₄ = 0.5, rank ₅ = 1 respectively. Substituting formula (2.4) into the formula (2.4), keeping the calculation result to two decimal places, then the hyperbolic distances corresponding to the five levels of near-surface nodes are calculated as k ₁ =9.36, k ₂ =10.32, k ₃ =11.30, k ₄ =12.30, k ₅ = 13.29.

k _n =log(ε+rank _n ·scale _sur ) (2.4)

In the current experiment, the hyperbolic radius of the satellite node is set as follows, the hyperbolic radius of the low-orbit satellite k _LEO = 5.00, the hyperbolic radius of the medium-orbit satellite k _MEO = 4.90, and the dual-radius of the synchronous orbit satellite in the high orbit. The radius of curvature k _GEO =4.20.

Among them, the scale factor used for node level division of the near-surface node and the setting value of the hyperbolic radius of the satellite node are obtained through continuous testing and adjustment based on the results of simulation experiments.

We select different multi-layer satellite network structures to test the routing method proposed in this patent. The multi-layer satellite network integrates the advantages of satellites in different orbits, such as low/medium orbit satellites with small transmission delay and large coverage area of synchronous satellites, so that different types of satellites have formed a good complementary advantage. Based on the network structure of classic satellite systems such as Iridium, GlobalStar, and ICO, researchers in many countries have further integrated the advantages of various orbiting satellites, and have proposed many good multi-layer satellite network design schemes, among which are more representative networks. The structure and specific structural parameters are shown in Table 2.1 below. When researching the patent of the present invention, the three heterogeneous satellite node configuration parameters in Table 2.1 are used as reference.

Table 2.1 Multi-layer satellite communication network structure

Calculation of the angle between two points after mapping

First of all, there are two mathematical theorems.

Mathematical theorem 1, the law of cosines: As shown in Figure 8, the three internal angles of △ABC are ∠A, ∠B, and ∠C, and the three sides are a, b, and c. Then they have a relationship as shown in formula (2.5) Shown.

Mathematical theorem 2: The distance between any two points on two different plane straight lines: As shown in Figure 9, it is known that the angle formed by two different plane straight lines a and b is γ, and the length of their common perpendicular line segment DD′ is d , Take the points E and F on the straight lines a and b respectively, set D'E=m, DF=n, and find EF. Then the calculation method of EF is shown in formula (2.6).

EF ² =m ² +n ² +d ² -2mn cosγ (2.6)

Therefore, for a sphere with a radius of R existing in the three-dimensional space, a spherical polar coordinate system is constructed with the sphere center O as the origin, and A and B are two points on the surface of the sphere, and the coordinates of point A are

The coordinates of point B are

make

Suppose the angle between AO and BO is τ, that is, the center angle of the sphere between A and B, as shown in Figure 10. When both A and B are on the same side of the "equatorial plane" with point O as the center of the sphere, the angle τ can be calculated according to the following process.

First, suppose the circular surface parallel to the "equatorial plane O" where A and B are located are circular surface O ₁ , circular surface O ₂ , and the center of the sphere is O. Then O ₁ , O ₂ , and O are collinear, and OO ₁ ⊥AO ₁ , OO ₂ ⊥BO ₂ . Since the radius of the sphere is R, AO=BO=R, then AO ₁ =R sinθ ₁ , BO ₂ =R sinθ ₂ , OO ₁ =R cosθ ₁ , and OO ₂ =R cosθ ₂ . Then O ₁ O ₂ can be calculated by formula (2.7).

O ₁ O ₂ =OO ₁ -OO ₂ =R cosθ ₁ -R cosθ ₂ (2.7)

Then, the straight-line distance AB between A and B can be calculated according to the formula (2.5) of the law of cosines mentioned above, as shown in formula (2.8).

AB ² ＝AO ² +BO ² -2AO·BOcosτ

＝2R ² -2R ² cosτ

= 2R ² (1-cosτ) (2.8)

At the same time, we can use another method to calculate AB according to the above-mentioned formula (2.6) for the distance between two points on a straight line on a different plane.

It is the angle between the plane perpendicular to the "equatorial plane" where the line AO _{1 is located and the plane perpendicular to the "equatorial plane" where the line BO 2} is located. The specific calculation process is shown in formula (2.9).

Finally, since AB ² =AB ² , combining equation (2.8) and equation (2.9), the relational equation about the included angle τ can be obtained, as shown in equation (2.10).

∴

Suppose the coordinates of the two points A" and B" in the four-dimensional hyperbolic space after the mapping is completed are

with

And the angle between ρ. Then, iterative method can be used to calculate the specific value of ρ according to the formula (2.10) for calculating the included angle in the three-dimensional space.

If the coordinates are

The azimuth space formed by and ψ is named ω, then ω ₁ represents

In the azimuth space, ω ₂ represents

The azimuth space in which it is located. As in formula (2.10)

On behalf of the two points containing A", B"

The angle between the azimuth planes of the measurement, (ω ₂ -ω ₁ ) is the relative

The angle between the azimuth space formed by and ψ. And k ₁ , k ₂ are the hyperbolic radius components, which represent the radial distance between the node and the center of the four-dimensional hyperbolic space. The specific value of the length will not change the angle ρ between the two nodes. Therefore, for (θ ₁ ,ω ₁ ,k ₁ ) and (θ ₂ ,ω ₂ ,k ₂ ), the relevant formula for calculating the included angle ρ is shown in (2.11).

cosρ=cosθ ₁ cosθ ₂ +sinθ ₁ sinθ ₂ cos(ω ₂ -ω ₁ ) (2.11)

And according to the specific

with

You can further refer to the formula (2.11) to calculate the position difference between the two nodes.

The angle between and the azimuth space formed by ψ is shown in formula (2.12).

Substituting (2.12) into (2.11), you can finally get two points in the four-dimensional hyperbolic space

with

The complete formula for the included angle ρ between (2.13).

∴

So far, the patent of the present invention provides two points in a four-dimensional hyperbolic space after calculating the mapping.

with

The method of the included angle ρ provides an important guarantee for calculating the hyperbolic distance between two points based on the included angle ρ and routing and forwarding according to the hyperbolic coordinates.

Calculation of hyperbolic distance

The coordinate mapping algorithm proposed by the patent of the present invention is applicable to all levels of the sky-ground information network, and can provide a decision basis for the distance calculation in the sky-ground information network routing strategy based on hyperbolic geometry. Calculate the distance between nodes during forwarding, and select the neighboring node with the smallest hyperbolic distance as the forwarding object. For the node coordinates after the transformation to the four-dimensional hyperbolic space mapping is completed through the coordinate mapping algorithm proposed by the patent of the present invention, the specific calculation method of the hyperbolic distance between two nodes in the network is as follows.

In the classic algorithm for mapping the scale-free network to the hyperbolic space, the hyperbolic space model usually used is the extended Poincaré disk. Under the extended Poincaré disk, the polar coordinates of any two points are (r, θ), (r′, θ′), and the hyperbolic distance between them is x. The formula is as follows:

coshx=cosh(r)cosh(r′)-sinh(r)sin(r′)cos(Δθ) (2.15)

Among them, Δθ is the difference in angular distance between two points. It can be further derived that the hyperbolic distance x of any two points satisfies the formula (2.16). It can be seen that the hyperbolic distance between two points is only related to their hyperbolic radii r and r′ and the angle Δθ between the two points. .

x=arccosh[cosh(r)cosh(r′)-sinh(r)sin(r′)cos(Δθ)] (2.16)

Since the mapping in the hyperbolic space is an equidistant transformation, that is, the distance-preserving mapping in the hyperbolic space does not change the distance between two points, it is only related to the hyperbolic radii and Δθ of the two points. Therefore, we can infer that in polar coordinates, the hyperbolic distance between two points in a four-dimensional hyperbolic space is only related to the respective hyperbolic radius components and Δθ. The geometric meaning of Δθ at this time is the center of the sphere between the two points. Horn.

Then, when performing hyperbolic routing according to the coordinate mapping algorithm proposed in the patent of the present invention, the coordinates of any two points in the four-dimensional hyperbolic space are

with

The hyperbolic distance h between them is related to its hyperbolic components k ₁ , k ₂ and the angle ρ between the two points. Substituting the hyperbolic coordinate components and included angles of two points into equation (2.16), the hyperbolic distance h of any two points in the four-dimensional hyperbolic space can be derived to satisfy equation (2.17):

h=arccosh[cosh(k ₁ )cosh(k ₂ )-sinh(k ₁ )sinh(k ₂ )cosρ] (2.17)

Among them, the specific calculation method of the angle ρ between two points, please refer to the calculation of the angle between two points after mapping.

The technology of the present invention proposes a hyperbolic geometry-based network mapping strategy for an integrated sky-ground information network, which can complete the network mapping from the sky-ground information network in the three-dimensional space to the four-dimensional hyperbolic space, based on the hyperbolic geometry. A unified expression based on geographic coordinates for each layer of nodes with different characteristics in the air-ground information network is helpful to quickly identify and locate the nodes in the network, which will greatly simplify subsequent routing tasks.

Based on the technology of the present invention, the sky network routing does not depend on global information distribution and scheduling, and topological changes have little effect on mapping, and can be well adapted to dynamic environments. The space constructed by hyperbolic geometry has the nature of exponential expansion, which is consistent with the large-scale and complex structure of the integrated information network of space, space and earth. At the same time, hyperbolic coordinates can provide a higher routing success rate for greedy routing. The greedy routing strategy based on hyperbolic geometry has good routing performance in large-scale networks. It can use geographic coordinates for routing without knowing the global topology. The expansion of the network has almost no impact on the optimality of the routing path, so it provides A more scalable routing solution is proposed.

In addition, since each node in the network is given hyperbolic coordinates, the distance between any two points can be calculated based on the coordinates. After the network is established, each node only needs to know the spatial coordinate information of itself and its immediate neighbor nodes. The message is greedily forwarded based on the distance, so the scale of the routing table can be compressed to the minimum, which can save the node's data storage and routing lookup overhead. At the same time, by setting the hyperbolic component in the hyperbolic coordinates to adjust the tendency of routing to select the next hop, the routing strategy can be inclined to select nodes with better properties, which can be used to further optimize the routing effect.

The technology of the present invention revolves around an integrated sky-ground information network, draws on the idea of spherical projection, and proposes a method of mapping three-dimensional geographic space to four-dimensional hyperbolic space, combining the idea of hyperbolic space network mapping with the actual situation of the sky-ground information network , To map and transform the three-dimensional geographic space containing the sky-ground information network, and realize that based on the hyperbolic geometry, each layer of the air-ground information network with different characteristics is given a unified expression based on geographic coordinates, which is helpful for rapid identification and positioning Nodes in the network.

The technology of the present invention comprehensively and uniformly expresses the topological characteristics between the nodes of each layer through a network mapping algorithm based on hyperbolic geometry, so as to deal with the routing problem existing in the interactive information transmission between the layers, so that it is based on this expression method. The routing on the network has good stability and scalability. Using hyperbolic coordinates, routing can be performed without knowing the global topology. The expansion of the network has almost no impact on routing. It can actively adapt to the high dynamics brought by the transformation of the sky-to-ground information network topology, thereby ensuring integrated sky-to-ground information. The network can accurately and stably complete the task of information transmission and meet the needs of social and militarized applications.

The technology of the present invention assigns hyperbolic coordinates to each node in the sky-ground information network. Based on the coordinates, the distance between any two points can be calculated. After the network model is established, each node only needs to know the space between itself and its immediate neighbor nodes. The coordinate information can greedily forward the message based on the distance, so the scale of the routing table can be compressed to the minimum, which can save the node's data storage and routing lookup overhead.

In order to reduce the influence of the distance of high-altitude nodes, the patent of the present invention uses the method of spherical polar projection to give the key sky and sky nodes a higher weight (ie shorter hyperbolic distance), so as to incorporate the sky and sky nodes into the hyperbolic greedy strategy. Consider the purpose of the category.

Under the three application scenarios in Table 2.1, the patent of the present invention provides a set of configuration parameters that can guarantee a 90% routing success rate. The specific settings of the scale coefficient used for the level division of the near-surface nodes are as follows: rank ₁ = 0.0625, rank ₂ = 0.125, rank ₃ = 0.25, rank ₄ = 0.5, rank ₅ = 1, when the hyperbolic radius is set, the value increases The quantity range ε=30. At this time, replace rank ₁ =0.0625, rank ₂ =0.125, rank ₃ =0.25, rank ₄ =0.5, rank ₅ = 1 into formula (2.4), and keep the calculation result to two decimal places, then The hyperbolic distances corresponding to the five levels of near-surface nodes are calculated as k ₁ =9.36, k ₂ =10.32, k ₃ =11.30, k ₄ =12.30, k ₅ =13.29; the hyperbolic radius setting value for satellite nodes As follows, the hyperbolic radius of a low-orbit satellite k _LEO = 5.00, the hyperbolic radius of a medium-orbit satellite k _MEO = 4.90, and the hyperbolic radius of a synchronous orbit satellite in high orbit k _GEO = 4.20.

The above descriptions are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modification, equivalent replacement and improvement made within the spirit and principle of the present invention shall be included in the protection of the present invention. Within range.

Claims (8)

1. A unified routing method for a sky-ground information network based on hyperbolic geometry, characterized in that the sky-ground information network unified routing method includes the following steps:

   S1. Use the spherical polar projection to map the nodes in the sky-ground information network in the three-dimensional geographic space to the three-dimensional hypersphere. The mapping relationship is:

   

   S2. Set the hyperbolic radius component of the points mapped to the three-dimensional hypersphere, and finally realize the mapping of the node coordinates in the three-dimensional geographic space to the four-dimensional hyperbolic hypersphere space to obtain the hyperbolic coordinates;

   S3. Calculate the angle between two nodes in the four-dimensional hyperbolic hypersphere space by using the obtained hyperbolic coordinates;

   S4. When routing in the sky-ground information network, use the obtained hyperbolic coordinates of the node and the angle between the two nodes in the four-dimensional hyperbolic hypersphere space to calculate the hyperbolic distance between the two nodes;

   S5. Complete greedy routing and forwarding according to the calculated hyperbolic distance between the two nodes;

   Among them, r _A is the radial quantity coordinate of point A, and R is the maximum distance of a node in space from the center of the earth's sphere.
2. The method for unified routing of a sky-ground information network based on hyperbolic geometry according to claim 1, wherein said step S1 further comprises the following steps:

   S11. Establish a spherical polar coordinate system in the three-dimensional geographic space where the universe is located in the space covered by the sky-ground information network with the center of the earth as the origin;

   S12. Map the point set with spherical polar coordinates in the three-dimensional geographic space to the three-dimensional hypersphere.
3. The method for unified routing of a sky-ground information network based on hyperbolic geometry according to claim 2, wherein said step S2 further comprises the following steps:

   S21, rank the nodes according to the communication radius from high to low;

   S22. Bring the scale coefficient into k _n =log ₂ (ε+rank _n ·scale _sur ) to calculate the hyperbolic radius of each level node respectively;

   S23. The hyperbolic coordinates are formed by assigning hyperbolic radius components to the nodes mapped to the three-dimensional hypersphere to identify the distance from the node to the center of the four-dimensional hyperbolic hypersphere;

   Among them, k _n represents the hyperbolic radius component value corresponding to level n, ε represents the value increment of the hyperbolic radius component; rank _n represents the scale factor of the node level division; scale _sur is the scale of the near-surface node, that is, the total number.
4. The unified routing method of the sky-ground information network based on hyperbolic geometry according to claim 3, wherein said step S3 further comprises the following steps:

   S31. For the sphere in the three-dimensional space that contains the earth and the outer circle of the earth, a spherical polar coordinate system is established with the earth sphere center O as the origin, A and B are any two points on the surface of the sphere, and the earth sphere center O is the center of the equatorial plane. , O ₁ is the center of the circle parallel to the equatorial plane where point A is located, O ₂ is the center of the circle parallel to the equatorial plane where point A is located, and R is the sphere space containing the earth and the outer space of the earth. The spatial radius of the range,

   

   Is the azimuth angle of point A, that is, the angle between the projection line of the line from point A to point O on the xy plane and the positive x-axis, and the value range is [0, 2π],

   

   Is the azimuth angle of point B, that is, the angle between the projection line of the line connecting point B to point O on the xy plane and the positive x axis, and the value range is

   

   θ ₁ is the elevation angle of point A, that is, the angle between the line from point A to point O and the positive z axis, and the value range is [0, π], θ ₂ is the elevation angle of point B, that is, the angle from point B to point O The angle between the line and the positive z axis, the value range is [0, π]; according to the law of cosines

   

   Calculate the straight-line distance AB between A and B, the formula:

   AB ² ＝AO ² +BO ² -2AO·BO cosτ

   ＝2R ² -2R ² cosτ

   ＝2R ² (1-cosτ); at the same time, according to the formula between two points on a straight line on a different plane

   

   

   Calculate the straight-line distance AB between A and B; since AB ² =AB ² , the relational formula for calculating the angle τ between two points in three-dimensional space can be obtained

   

   S32. Calculate the value of the included angle ρ between the two points A" and B" corresponding to the two points A and B in the four-dimensional hyperbolic hypersphere space using an iterative method according to the relational formula for calculating the included angle in the three-dimensional space,

   

   Where ψ ₁ represents the mapping angle component of the corresponding mapping point obtained after the point A is mapped to the four-dimensional hyperbolic hypersphere space, and ψ ₂ represents the coordinate of the corresponding mapping point obtained after the point B is mapped to the four-dimensional hyperbolic hypersphere space The mapped angular component.
5. The sky-ground information network unified routing method based on hyperbolic geometry according to claim 4, characterized in that in step S4, according to the hyperbolic cosine theorem, A" and B" are any two of A and B in a three-dimensional space. The corresponding mapping point obtained after the point is mapped to the four-dimensional hyperbolic hypersphere space, the hyperbolic distance h between two points A" and B" in the four-dimensional hyperbolic hypersphere space is calculated, and the coordinate of A" is

   

   The B'coordinate is

   

   The hyperbolic distance h between them is related to the hyperbolic components k ₁ , k ₂ and the angle ρ between two points; the hyperbolic distance h between any two points in the four-dimensional hyperbolic hypersphere space satisfies the formula:

   h=arccosh(cosh(k ₁ )cosh(k ₂ )-sinh(k ₁ )sinh(k ₂ )cosρ].
6. The sky-ground information network unified routing method based on hyperbolic geometry according to claim 5, wherein said step S12 further comprises the following steps:

   S121: Perform mapping transformation according to the radial quantity of point A;

   S122, according to θ _A ,

   

   ψ _A determines the specific position of A′ in the three-dimensional hypersphere;

   Among them, θ _A is the elevation coordinate component of point A′;

   

   Is the azimuth coordinate component of point A'; ψ _A is the mapping angle coordinate component of point A'.
7. The sky-ground information network unified routing method based on hyperbolic geometry according to claim 6, characterized in that, in the step S23, the mapping node A'

   

   The hyperbolic coordinate component is assigned to identify the distance between the node and the center of the four-dimensional sphere, and it is formally mapped from the three-dimensional hypersphere to the four-dimensional hyperbolic hypersphere space. The hyperbolic coordinate component is denoted by k, and the hyperbolic component of the corresponding node A is denoted Is k _A.
8. The sky-ground information network unified routing method based on hyperbolic geometry according to claim 7, characterized in that, in the step S23, the mapping ball corresponding to each node of the sky-ground information network under the original three-dimensional geographic space on the three-dimensional hypersphere The respective mapping expansion will be completed according to the respective hyperbolic coordinate component values, and the radial expansion will not change the angle. Finally, the nodes in the sky-ground information network in the original three-dimensional geographic space can obtain the mapping expression in the four-dimensional hyperbolic hypersphere space.

   

   Among them, θ is the elevation coordinate component;

   

   Is the azimuth coordinate component; ψ is the mapping angle coordinate component.

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