Method for predicting visible relation and duration of satellite and ground node

Abstract

The invention provides a method for predicting the visible relation and duration of a satellite and a ground node. The method comprises the following steps: firstly, constructing a visibility function between a satellite and ground nodes according to a satellite and ground node motion model and related satellite-ground visible constraint conditions; secondly, according to a periodic rule of in-orbit movement of the satellite and related visible constraint conditions, a solution interval of all zero points is constructed for the constructed visibility function, and the zero points are solved; the starting or ending zero point of each positive interval of the constructed visibility function is the starting or ending moment of the visible interval between the satellite and the ground node, so that a visible interval set based on the set time can be quickly calculated, and the visible interval between the satellite and the ground node can be efficiently and accurately solved.

Description

Technical Field

[0001] The present invention relates to the field of satellite network technology, and in particular to a method for predicting the visible relationship and duration between a satellite and a ground node. Background Art

[0002] In recent years, with the rapid development of space communication technology, building a space-based information network based on low-orbit giant constellations has become an important direction for the development of the future Internet. However, due to the characteristics of highly dynamic topological changes, it is difficult to directly apply the existing ground IP networking and routing mechanisms to such networks. This is mainly due to the high-speed movement of satellite nodes relative to the ground, which leads to frequent switching of links established between them and ground nodes (such as gateways, terminal equipment, etc.), which seriously affects the global routing effectiveness and stability of the low-orbit giant constellation network. Therefore, how to further simplify the topological dynamics of the space-based network based on the predictability of the connection relationship between satellite and ground nodes is an important research topic, and the basic problem that needs to be solved first is how to efficiently and quickly calculate the visible time interval between the satellite and the ground node within a relatively long prediction time. At present, the more common practice is to judge the visibility of the satellite and the ground node in each time unit (for example, per second), and aggregate the results according to the changes in the connection relationship between them. Obviously, this method has a large calculation time and poor scalability in the low-orbit giant constellation network scenario with thousands or even tens of thousands of nodes. Summary of the invention

[0003] An embodiment of the present invention provides a method for predicting the visibility relationship and duration between a satellite and a ground node, so as to efficiently and accurately solve a set of visible intervals between the satellite and the ground node based on a predicted time.

[0004] In order to achieve the above object, the present invention adopts the following technical scheme.

[0005] A method for predicting the visibility relationship and duration between a satellite and a ground node, comprising:

[0006] Obtaining the motion models of the satellite and the ground node, setting the satellite-ground visibility constraint conditions according to the motion models, and constructing the visibility function between the satellite and the ground node;

[0007] The problem of determining the visible interval between the satellite and the ground node is transformed into the problem of finding the positive interval of multiple zero points of the visibility function;

[0008] According to the periodic law of the satellite's in-orbit motion and the satellite-ground visibility constraints, all zero-point solution intervals of the visibility function are constructed and the zero points are solved. The starting or ending zero point of each positive interval of the visibility function is determined as the starting or ending time of the visible interval between the satellite and the ground node, and a set of visible intervals between the satellite and the ground node is constructed.

[0009] Preferably, acquiring the motion model of the satellite and the ground node includes: determining the motion model between the satellite and the ground node, the motion model reflecting the change law of the physical motion characteristics of the satellite and the ground node over time;

[0010] Without loss of generality, assume that a satellite node has N s ∈N + (N + represents a positive integer set) kinds of motion features, then the motion model of the satellite node can be characterized as t∈R, R represents a real number, where It reflects the value of the i-th type of motion characteristics of the satellite node changing with time t, which is a continuous function or a piecewise continuous function;

[0011] Without loss of generality, assume that a ground node has N g ∈N + The motion model of the ground node can be represented as t∈R; It reflects the value of the i-th type of motion feature of the ground node changing with time t, which is a continuous function or a piecewise continuous function;

[0012] The motion characteristics include values ​​of satellite or ground node position information that change over time.

[0013] Preferably, the setting of satellite-ground visibility constraint conditions according to the motion model includes:

[0014] From satellite and ground nodes Choose any satellite node S x ,x∈{1,2,...,N x},N x ∈N + and a ground node G y ,y∈{1,2,...,N y},N y ∈N + , denoted as Build the pair of satellites and ground nodes The visibility relation expression between Defining functions Characterizing satellite and ground node pairs The logical relationship between whether it is visible at any time t∈R, where T is logically true and F is logically false. It means that at time t, the satellite and the ground node are aligned can be seen by each other; if It means that at time t, the satellite and the ground node are aligned are not visible to each other; in particular, if for a certain time point t0, if its left and right neighbors The value of is opposite, then let And call t0 The discontinuity point is used to indicate the satellite and ground node The point in time when the visibility relationship between them changes;

[0015] Assumptions is decomposed into N q ∈N + Visibility constraints at each level and These visibility constraints describe the pair of satellites and ground nodes respectively. Joint Movement Model Under the visible condition, the corresponding variable value exceeds the limit value that can be reached. These visible constraints are obtained through logical "and" operation to obtain the satellite and ground node At any time, the visibility relationship result is that if the pair of satellites and the ground node If all visible constraints are satisfied, then the satellite and the ground node are It is visible at time t, that is ∧ represents the logical “and” operation; otherwise, if at least one visibility constraint condition is not satisfied, the satellite and the ground node are not connected. It is not visible at time t, that is, ∨ represents the logical "or" operation.

[0016] Preferably, the setting of satellite-ground visibility constraint conditions according to the motion model further includes:

[0017] Consider a pair of satellites and ground nodes Joint Movement Model And the corresponding visible constraints It can be converted into a continuous function on R or a piecewise continuous function on R, and these functions are operated by continuous operators to construct the satellite and ground node pair. The visibility function between the satellite and the ground node is obtained by a related iterative method to obtain the zero point of the visibility function and the The set of visible intervals of ;

[0018] For satellite and ground node Each visible constraint Construct its discriminant function And meet the following characteristics:

[0019] (1) Satellite and ground node pairing Joint Movement Model Related, that is, there exists a mapping operator Make

[0020] (2) is continuous on R or piecewise continuous on R, that is, there exists N seg ∈N + The interval segment Continuous and bounded within each interval;

[0021] (3) At any time t∈R, and is equivalent, and and equivalence;

[0022] (4) If and only if t' is discontinuity point.

[0023] make Satellite and ground node pairing Visible constraints The set of all discriminant functions of ; and if there exists And meet and Then it is called and about Discriminant equivalence;

[0024] Satellite and ground node pair Each visible constraint To implement logical AND and OR operations between related functions, define as well as There are two types of discriminant transformation operators and they satisfy the following characteristics respectively:

[0025] Discriminant conversion operator of the first kind Meet the following characteristics:

[0026] (1) Its independent variables are (f1,f2,...,f c )∈(R R ) c ; where c∈N + , f i ∈RR,i∈{1,2,...,c}, R R is the set of all functions whose independent variables have a range of R and whose dependent variables have a range of R; (R R ) c is c R R The Cartesian product of

[0027] (2) If for any i∈{1,2,...,c}, f i is continuous on R, then continuous on R;

[0028] (3) For any t∈R, if and only if any i∈{1,2,...,c} such that f i When (t)>0, then It is positive at t;

[0029] (4) For any t∈R, if and only if there exists i∈{1,2,...,c} such that f i When (t)<0, then It is negative at t;

[0030] The second discriminant conversion operator Meet the following characteristics:

[0031] (1) Its independent variables are (f1,f2,...,f c )∈(R R ) c ; where c∈N + , f i ∈R R ,i∈{1,2,...,c}, R R is the set of all functions whose independent variables have a range of R and whose dependent variables have a range of R; (R R ) c is c R R The Cartesian product of

[0032] (2) If for any i∈{1,2,...,c}, f i is continuous on R, then continuous on R;

[0033] (3) For any t∈R, if and only if there exists i∈{1,2,...,c} such that f i When (t)>0, then It is positive at t;

[0034] (4) For any t∈R, if and only if any i∈{1,2,...,c} such that f i When (t)<0, then It is negative at t.

[0035] The first type of discriminant conversion operator implements the "and" logic of the discriminant function, that is, when the discriminant function is input into the operator, the operator result is positive for the independent variable only when all discriminant functions are positive for the independent variable; the second type of discriminant conversion operator implements the "or" logic of the discriminant function, that is, when the discriminant function is input into the operator, the operator result is positive for the independent variable only when there is a discriminant function that is positive for the independent variable.

[0036] A pair of satellites and ground nodes Visible constraints between Any discriminant function like Piecewise continuous on R, the following conversion method is used to convert Convert to a function that is continuous in R Assume that the piecewise continuous discriminant function In a continuous segment interval I k ≠R,k∈{1,2,...,N seg The function on} is h k (t):I k →R, first construct a corresponding continuous function make in I k Up and h k (t) has the same sign and is in RI k The upper limit is always negative. The specific steps are as follows:

[0037] (1) h k (t) Extended to That is, for any t∈I k , and continuous on R;

[0038] (2) Structure For any t∈R, in, The first type of discriminant conversion operator In the special case of c = 2; y(t) is any function that is continuous on R and satisfies the following conditions:

[0039] ①If I k The lower bound satisfies infI k = -∞, and the upper bound supI k =b∈R, then For any t∈(-∞,b), y(t)>0; For any t∈(b,+∞), y(t)<0;

[0040] ②If I k Satisfy the lower bound infI k=a∈R, and the upper bound supI k =b∈R, then For any t∈(a,b), y(t)>0; For any t∈(-∞,a)∪(b,+∞), y(t)<0;

[0041] ③If I k If the lower bound infI=a∈R and the upper bound supI=+∞, then For any t∈(a,+∞), y(t)>0; For any t∈(-∞,a), y(t)<0;

[0042] The continuous function constructed by the above method I k →R, which is continuous on R and satisfies (1) for any t∈R when hour, (2) When t∈I k When h k (t)>0 If h k (t)≤0

[0043] Based on the above method, the discriminant function of piecewise continuous Transformed into an equivalent discriminant function that is continuous on R Assume a piecewise continuous discriminant function With N seg ∈N + continuous segmented intervals, and its kth segmented interval I k The continuous function in is h k (t):I k →R,k∈{1,2,...,N seg}, for h k (t) Construct the above continuous function make in I k Up and h k (t) has the same positive and negative signs, in RI k The upper limit is always negative, so get about The continuous equivalent discriminant function on R, This is the second type of discriminant conversion operator When c = N seg special case, Satisfies the following characteristics, namely is continuous on R and satisfies (1) for any t∈R If and only if (2) If and only if (3) If and only if

[0044] Preferably, the step of constructing a visibility function between satellites and ground node pairs includes:

[0045] A pair of satellites and ground nodes The visibility relationship between them and all the visibility conditions between them It is an "and" logical relationship, so the first-class discriminant conversion operator is used to integrate the continuous discriminant functions corresponding to all visibility constraints to construct the visibility function about time t Its purpose is to connect a pair of satellites with a ground node The visibility interval solution problem is transformed into the visibility function independent variable t for The interval solution problem is then transformed into finding the visibility function The value of the independent variable t;

[0046] Assume that the satellite and ground node Visibility relationship between is decomposed into N q ∈N + Visible constraints Its corresponding N q The discriminant function that is continuous in R or transformed to be continuous in R is in, i∈{1,2,...,N q}; Construct visibility function satisfy:

[0047] Satellite and ground node pair The visibility function Continuous, visibility function in R Align satellites with ground nodes All visible constraints After integration, at any time t, if and only if all N q When all visible constraints are satisfied, that is, any i∈{1,2,...,N q},but If and only if any of the visible constraints is not satisfied, there exists i∈{1,2,...,N q},but If and only if any discriminant function i∈{1,2,...,N q}, and exists j∈{1,2,...,N q}, then

[0048] Preferably, according to the periodic law of the satellite's on-orbit motion and the satellite-ground visibility constraint condition, all zero-point solution intervals of the visibility function are constructed and the zero points are solved, the starting or ending zero point of each positive interval of the visibility function is determined as the starting or ending time of the visible interval between the satellite and the ground node, and the set of visible intervals between the satellite and the ground node is constructed, including:

[0049] Satellite and ground node pair The visibility function is continuous at the prediction time T p Internal visibility function The set of t constitutes the satellite and ground node pair One or more visible intervals between w∈{1,2,...,N v}, where N v ∈N + Indicates that the satellite and ground node pair at the predicted time T p The number of visible intervals within; the visible interval The left and right endpoints are The zero point of Root;

[0050] Determine the satellite and ground node pair Visibility Function The root-finding interval of each root of N r ∈N + Indicates that the satellite and ground node pair at the predicted time T p The number of root intervals in There is only one Zero point, any root interval according to the zero point theorem One end point is located between the satellite and the ground node A visible range The other endpoint falls in its adjacent invisible interval. The characteristics of each adjacent visible interval Find an endpoint in each of the invisible intervals between and construct all root-finding intervals In seeking After all the zero points are obtained, these zero points are directly used as the satellite and ground node pairs. Visible range The endpoint of

[0051] In order to Each visible interval Find a root interval in According to the periodic law of satellite motion in orbit and the related satellite-ground visibility constraints, a time interval base L is determined to convert the predicted time T p Perform continuous partitioning based on γL, where γ is a positive coefficient and satisfies each partitioned interval j∈{1,2,...,N d}, The visible interval between at most one satellite and a ground node There is an intersection; then, in each of the divided intervals Inner Seeking Maximum point And if hour, Then it is used as the root interval A potential endpoint of ; and a point in its adjacent invisible interval is used as the root-finding interval The other end point of the maximum point is used to construct all root-finding intervals Get the predicted time T p Satellite and ground node pair The visible interval between

[0052] Preferably, the above-mentioned maximum value points are used to construct all root-finding intervals. Get the predicted time T p Satellite and ground node pair The visible interval between include:

[0053] S1. Determine the time period for dividing the forecast period T p The time interval γL ensures that each divided time interval At most one satellite-to-ground node pair Visible range There is an intersection; according to the satellite and ground node Joint Movement Model And the visibility function in between To determine the time interval for dividing the forecast period (0, T p ), that is, determine the time interval in For any satellite and ground node joint motion model And the visibility function Functions that map to real numbers;

[0054] S2. Time interval Divide the entire forecast time period (0, T p ), get a set of time intervals

[0055] S3. Utilization In each Select a suitable time point t to construct the satellite and ground node pair Visible range Correlation root interval The specific steps are as follows:

[0056] S3.1. Each interval of The application of the maximum value algorithm to solve The maximum point of , get the maximum point set in ascending order N max ∈N + ;

[0057] S3.2. If for any maximum point have In Remove

[0058] S3.3. If for any two maximum points Yes |t j -t k |<γL, then Remove t j ,t k Any one of;

[0059] S3.4. Arrange to get the final The ascending set of And make satellite and ground node pairing Visible range Correlation root interval An endpoint of

[0060] S4. Utilization Satellite and ground node Determine the root-finding interval in each invisible interval The other endpoint of , and apply the iterative root-finding method to find the root, the specific steps are as follows:

[0061] S4.1. Insert each pair of adjacent time points The midpoint of Considering that for any pair of satellites and ground nodes, the length of any visible interval between them in a satellite orbit period is much shorter than its invisible interval, Established, Each pair of adjacent time points midpoint Determine the satellite and ground node pair A point in each invisible interval;

[0062] S4.2. Use the new sequence to construct satellite and ground node pairs Visibility Function The root interval set is for Any interval in It consists of three parts, namely Subintervals that are always positive or negative (t r ,t e ), Subintervals that are always negative or positive (t e ,t r' ),as well as (t e yes In the interval (t r ,t r' ) inside the root, t e ∈(t r ,t r' ));

[0063] S4.3. Consider the prediction time period (0,T p )Border situation, if or The value of is also negative, which means that the corresponding interval (0,t v1 )or There are zero points in the , which are rising zero point and falling zero point; merge them into In this way, a complete set of root-finding intervals is formed.

[0064] S4.4. In all The satellite and ground node pairs in the interval Visibility Function Find the root and get its value during the prediction time (0, T p ), that is, the ascending set of endpoints of all visible intervals Assume that the number of zero points obtained in the boundary case is N B ∈{0,1,2};

[0065] S4.5. According to The endpoint sequence constructs a set of visible intervals of the following four mutually exclusive cases:

[0066] (1) When and When N B =2, we can see that the interval set is

[0067] (2) When and When N B =1, it can be seen that the interval set is

[0068] (3) When and When N B =1, it can be seen that the interval set is

[0069] (4) When and When N B =0, it can be seen that the interval set is

[0070] according to and The value of matches one of the above four visible intervals, and the estimated visible interval between the satellite and the ground node pair is obtained.

[0071] Repeat the above method to get the set The distance between all satellites and ground nodes in the prediction time (0, T p ) within the entire visible range.

[0072] It can be seen from the technical solution provided by the above-mentioned embodiments of the present invention that the method of the present invention constructs a visibility function between a satellite and a ground node pair according to the satellite and ground node motion model and related satellite-ground visibility constraints, so as to transform the problem of solving the visible interval between the satellite and the ground node into a problem of finding a positive interval of multiple zero points of the visibility function, thereby obtaining a set of visible intervals between the satellite and the ground node, and realizing efficient and accurate solution of the visible intervals between the satellite and the ground node.

[0073] Additional aspects and advantages of the present invention will be given in part in the following description, which will become obvious from the following description, or may be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without paying creative work.

[0075] Figure 1 A processing flow chart of a method for predicting the visible relationship and duration between a satellite and a ground node provided in an embodiment of the present invention;

[0076] Figure 2 A schematic diagram of a visibility constraint condition between a satellite and a gateway provided in an embodiment of the present invention.

[0077] Figure 3 A schematic diagram of the earth occlusion relationship between a low-orbit satellite and a ground node provided in an embodiment of the present invention; DETAILED DESCRIPTION

[0078] The embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and cannot be interpreted as limiting the present invention.

[0079] It will be understood by those skilled in the art that, unless expressly stated, the singular forms "one", "said", and "the" used herein may also include plural forms. It should be further understood that the term "comprising" used in the specification of the present invention refers to the presence of the features, integers, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components and / or groups thereof. It should be understood that when we refer to an element as being "connected" or "coupled" to another element, it may be directly connected or coupled to the other element, or there may be intermediate elements. In addition, the "connection" or "coupling" used herein may include wireless connection or coupling. The term "and / or" used herein includes any unit and all combinations of one or more associated listed items.

[0080] It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as those generally understood by those skilled in the art in the art to which the present invention belongs. It should also be understood that terms such as those defined in common dictionaries should be understood to have meanings consistent with the meanings in the context of the prior art, and will not be interpreted with idealized or overly formal meanings unless defined as herein.

[0081] To facilitate understanding of the embodiments of the present invention, several specific embodiments will be further explained below with reference to the accompanying drawings, and each embodiment does not constitute a limitation on the embodiments of the present invention.

[0082] The embodiment of the present invention proposes a method for predicting the visibility relationship and duration of satellites and ground nodes. The scheme first constructs a visibility function between the two based on the motion models of satellites and ground nodes and visible constraints, and transforms the problem of determining the visible intervals of satellites and ground nodes into the problem of finding positive intervals of multiple zero points of the constructed visibility function. Afterwards, according to the periodic law of the satellite's in-orbit motion and the satellite-ground visibility constraints, all zero-point solution intervals of the visibility function are constructed and the zero points are solved; the starting or ending zero point of each positive interval is the starting or ending time of the visible interval between the satellite and the ground node, thereby constructing a set of the visible intervals.

[0083] A method for predicting the visibility relationship between a satellite and a ground node proposed in an embodiment of the present invention includes two processing steps:

[0084] 1: Satellite-to-ground visibility modeling process, the visible constraints of satellites and ground nodes are integrated and modeled as a problem of solving the positive interval of the visibility function. To this end, the motion model between the satellite and the ground node is first determined, and the relevant constraints that satisfy mutual visibility are given; then, each constraint is equivalently converted into a continuous function with time as a variable, and rewritten as a mathematical expression compared with 0; finally, a continuous satellite-to-ground visibility function is constructed, which satisfies that the visibility function takes a positive value if and only if each visibility constraint is true; in this way, the problem of determining the visible interval of the satellite and the ground node is transformed into the problem of finding the positive interval of multiple zeros of the constructed visibility function.

[0085] 2: The process of solving the positive interval of the visibility function is equivalent to finding all the zero points of the visibility function. To this end, firstly, according to the periodic law of the satellite's orbital motion and the relevant satellite-ground visibility constraints, a time interval is determined to divide a relatively long prediction time into continuous and equal intervals, and then the time point that can make the visibility function positive is found in each divided interval, and then the time point is used to construct the solution interval of the visibility function zero point. Finally, the zero point is solved in each zero point solution interval and used as the endpoint of the visible time interval.

[0086] The processing flow of a method for predicting the visibility relationship between a satellite and a ground node proposed in an embodiment of the present invention is as follows: Figure 1 As shown, the following processing steps are included:

[0087] Step S10: determine a motion model between the satellite and the ground node, where the motion model reflects how the physical motion characteristics of the satellite and the ground node change over time.

[0088] Without loss of generality, assume that a satellite node has N s ∈N + (N +represents a positive integer set) kinds of motion features, then the motion model of the satellite node can be characterized as t∈R (R represents a real number); It reflects the value of the i-th type of motion characteristics of the satellite node changing with time t, and is a continuous function or a piecewise continuous function.

[0089] Without loss of generality, assume that a ground node has N g ∈N + The motion model of the ground node can be represented as t∈R; It reflects the value of the i-th type of motion feature of the ground node changing with time t, and is a continuous function or a piecewise continuous function.

[0090] The motion characteristics may include the position, speed, sensor angle, etc. of the satellite and the ground node at any time.

[0091] Step S20: Setting visibility constraints between the satellite and the ground node according to the motion model, specifically including:

[0092] First, from the satellite and ground node collection Choose any satellite node S x ,x∈{1,2,...,N x},N x ∈N + and a ground node G y ,y∈{1,2,...,N y},N y ∈N + , denoted as After that, build the pair of satellite and ground node The visibility relation expression between Defining functions Characterizing satellite and ground node pairs The logical relationship of whether it is visible at any time t∈R, where T is logically true and F is logically false. It means that at time t, the satellite and the ground node are aligned can be seen by each other; if It means that at time t, the satellite and the ground node are aligned are not visible to each other; in particular, if for a certain time point t0, if its left and right neighbors The value of is opposite, then let And call t0 The discontinuity point is used to indicate the satellite and ground node The point in time when the visibility relationship between them changes.

[0093] Secondly, due to a pair of satellites and ground nodes The visibility relationship between them is usually the result of several related visibility constraints. Can be decomposed into N q ∈N + Visibility constraints at each level and These constraints at different levels describe the pair of satellites and ground nodes. Joint Movement Model Whether the variable value corresponding to the visible condition exceeds the limit value it can reach. Then, the visible constraints at these levels are operated by logical "AND" to obtain the relationship between the satellite and the ground node. The visibility relationship result at any time. Specifically, if all visibility constraints are satisfied, then the satellite and the ground node are It is visible at time t, that is (∧ indicates logical “AND” operation); otherwise, if at least one visibility constraint condition is not satisfied, the satellite and ground node pair It is not visible at time t, that is, (∨ represents the logical “or” operation).

[0094] Further, consider a pair of satellites and ground nodes Joint Movement Model And the corresponding visible constraints It can be converted into a continuous function on R or a piecewise continuous function on R. These functions can be “ANDed” using continuous operators to construct the satellite and ground node pair. The visibility function between the satellite and the ground node is obtained by a related iterative method to obtain the zero point of the visibility function, and then the satellite and the ground node are obtained. The set of visible intervals.

[0095] To this end, first of all, the satellite and ground node Each visible constraint Construct its discriminant function And meet the following characteristics:

[0096] (1) Satellite and ground node pairing Joint Movement Model Related, that is, there exists a mapping operator Make

[0097] (2) is continuous on R or piecewise continuous on R, that is, there exists N seg ∈N + The interval segment Continuous and bounded within each interval;

[0098] (3) At any time t∈R, and is equivalent, and and equivalence;

[0099] (4) If and only if t' is discontinuity point.

[0100] make Satellite and ground node pairing Visible constraints The set of all discriminant functions of ; and if there exists And meet and Then it is called and about Discriminant equivalence;

[0101] S2.2. Satellite and ground node pairing Each visible constraint Perform logical AND operations to include all visible constraints; further, to implement logical AND and OR operations between related functions, define as well as There are two types of discriminant transformation operators and they satisfy the following characteristics respectively.

[0102] Discriminant conversion operator of the first kind Meet the following characteristics:

[0103] (1) Its independent variables are (f1,f2,...,f c )∈(R R ) c ; where c∈N + , f i ∈R R ,i∈{1,2,...,c}, R R is the set of all functions whose independent variables have a range of R and whose dependent variables have a range of R; (R R ) c is c R R The Cartesian product of

[0104] (2) If for any i∈{1,2,...,c}, f i is continuous on R, then continuous on R;

[0105] (3) For any t∈R, if and only if any i∈{1,2,...,c} such that f i When (t)>0, then It is positive at t;

[0106] (4) For any t∈R, if and only if there exists i∈{1,2,...,c} such that f i When (t)<0, then It is negative at t.

[0107] The second discriminant conversion operator Meet the following characteristics:

[0108] (1) Its independent variables are (f1,f2,...,f c )∈(R R ) c ; where c∈N + , f i ∈R R ,i∈{1,2,...,c}, R R is the set of all functions whose independent variables have a range of R and whose dependent variables have a range of R; (R R ) c is c R R The Cartesian product of

[0109] (2) If for any i∈{1,2,...,c}, f i is continuous on R, then continuous on R;

[0110] (3) For any t∈R, if and only if there exists i∈{1,2,...,c} such that f i When (t)>0, then It is positive at t;

[0111] (4) For any t∈R, if and only if any i∈{1,2,...,c} such that f i When (t)<0, then It is negative at t.

[0112] The first type of discriminant conversion operator implements the "and" logic of the discriminant function, that is, when the discriminant function is input into the operator, the operator result is positive for the independent variable only when all discriminant functions are positive for the independent variable; the second type of discriminant conversion operator implements the "or" logic of the discriminant function, that is, when the discriminant function is input into the operator, the operator result is positive for the independent variable only when there is a discriminant function that is positive for the independent variable.

[0113] S2.3. For a pair of satellite and ground node Visible constraints Any discriminant function like It is piecewise continuous on R and can be converted to a function continuous on R by the following conversion method

[0114] S2.3.1. Assume that the discriminant function is piecewise continuous In a continuous segment interval I k ≠R,k∈{1,2,...,N seg The function on} is h k (t):I k →R; To do this, we first need to construct a corresponding continuous function Make it in I k Up and h k (t) has the same sign and is in RI k The upper limit is always negative. The specific steps are as follows:

[0115] (1) h k (t) Extended to That is, for any t∈I k , and continuous on R;

[0116] (2) Structure For any t∈R, in, The first type of discriminant conversion operator In the special case of c = 2; y(t) is any function that is continuous on R and satisfies the following conditions:

[0117] ①If I k The lower bound satisfies infI k = -∞, and the upper bound supI k =b∈R, then For any t∈(-∞,b), y(t)>0; For any t∈(b,+∞), y(t)<0;

[0118] ②If I k Satisfy the lower bound infI k =a∈R, and supI k =b∈R, then For any t∈(a,b), y(t)>0; For any t∈(-∞,a)∪(b,+∞), y(t)<0;

[0119] ③If I k If infI=a∈R and supI=+∞, then For any t∈(a,+∞), y(t)>0; For any t∈(-∞,a), y(t)<0;

[0120] The continuous function constructed by the above method It is continuous on R and satisfies (1) for any t∈R when hour, (2) When t∈I k When h k (t)>0 If h k (t)≤0

[0121] S2.3.2. Based on the above method, the discriminant function of the piecewise continuous Transformed into an equivalent discriminant function that is continuous on R Specifically, assuming a piecewise continuous discriminant function With N seg ∈N + continuous segmented intervals, and its kth segmented interval I k The continuous function in is h k (t):I k →R,k∈{1,2,...,N seg}. After that, h k (t) Construct the above continuous function make in I k Up and h k (t) has the same positive and negative signs, in RI k The upper limit is always negative; finally, let get about Continuous equivalent discriminant function on R; where, This is the second type of discriminant conversion operator When c = N seg Therefore, Satisfies the following characteristics, namely is continuous on R and satisfies (1) for any t∈R If and only if (2) If and only if (3) If and only if Thus, we can go to S2.4;

[0122] S2.4. A pair of satellites and ground nodes The visibility relationship between them and all the visibility conditions between them It is an "and" logical relationship, so the first-class discriminant conversion operator is used to integrate the continuous discriminant functions corresponding to all visibility constraints to construct the visibility function about time t Its purpose is to connect a pair of satellites with a ground node The visibility interval solution problem is transformed into the visibility function independent variable t for The interval solution problem is then transformed into finding the visibility function The value of the independent variable t;

[0123] Assume that the satellite and ground node Visibility relationship between Can be decomposed into N q ∈N + Visible constraints Its corresponding N q The discriminant function that is continuous in R or transformed to be continuous in R is in, i∈{1,2,...,N q}; Construct visibility function satisfy:

[0124] Therefore, the satellite and ground nodes The visibility function Continuous on R, which aligns the satellite with the ground node All visible constraints integrated; at any time t, if and only if all N q When all visible constraints are satisfied, that is, any but If and only if any of the visible constraints is not satisfied, there exists i∈{1,2,...,N q},but If and only if any discriminant function i∈{1,2,...,N q}, and exists j∈{1,2,...,N q}, then

[0125] Since the satellite and the ground node The visibility function is continuous and has a relatively long prediction time T p In, make its visibility function The set of t constitutes the satellite and ground node pair One or more visible intervals between w∈{1,2,...,Nv}, where N v ∈N + Indicates that the satellite and the ground node pair are in a relatively long prediction time T p The number of visible intervals within; the visible interval The left and right endpoints are The zero point of Root.

[0126] To quickly find the satellite and ground node pairs Visibility Function All roots of need to determine the root-finding interval of each root u∈{1,2,...,N r}(N r ∈N + Indicates that the satellite and the ground node pair are in a relatively long prediction time T p The number of root-finding intervals within the root-finding interval) and ensure that these root-finding intervals There is only one Zero point, and then the relevant iterative root-finding method can be used to solve it. According to the zero point theorem, any root-finding interval The characteristic is that one of its endpoints is located between the satellite and the ground node A visible range The other endpoint falls within its adjacent invisible interval. Therefore, we can use The characteristics of each adjacent visible interval Find an endpoint in each invisible interval between and construct all root-finding intervals In seeking After all the zero points are obtained, these zero points can be directly used as the satellite and ground node Visible range endpoint.

[0127] In order to Each visible interval Find a root interval in The endpoint of the satellite can be determined based on the periodic law of the satellite's orbital motion and the relevant satellite-ground visibility constraints to convert a relatively long prediction time T p Perform continuous partitioning based on γL (γ is a positive coefficient) and satisfy each partitioned interval j∈{1,2,...,N d}, The visible interval between at most one satellite and a ground node There is an intersection; then, in each of the divided intervals Inner Seeking Maximum point And if hour, Then it is used as the root interval A potential endpoint of ; and a point in its adjacent invisible interval is used as the root-finding interval Finally, use the above maximum points to construct all root-finding intervals The prediction time T can be obtained p Satellite and ground node pair The visible interval between The specific steps are as follows:

[0128] S1. Determine the time period for dividing the forecast period T p The time interval γL ensures that each divided time interval At most one satellite-to-ground node pair Visible range There is an intersection; according to the satellite and ground node Joint Movement Model And the visibility function in between To determine the time interval for dividing the forecast period (0, T p ), that is, determine the time interval in For any satellite and ground node joint motion model And the visibility function Functions that map to real numbers;

[0129] S2. Time interval Divide the entire forecast time period (0, T p ), get a set of time intervals

[0130] S3. Utilization In each Select a suitable time point t to construct the satellite and ground node pair Visible range Correlation root interval The specific steps are as follows:

[0131] S3.1. Each interval of The application of the maximum value algorithm to solve The maximum point of , get the maximum point set in ascending order N max ∈N + ;

[0132] S3.2. If for any maximum point have In Remove

[0133] S3.3. If for any two maximum points Yes |t j -t k |<γL, then Remove t j ,t k Any one of;

[0134] S3.4. Arrange to get the final The ascending set of And make satellite and ground node pairing Visible range Correlation root interval An endpoint of

[0135] S4. Utilization Satellite and ground node Determine the root-finding interval in each invisible interval The other endpoint of , and apply the iterative root-finding method to find the root. The specific steps are as follows:

[0136] S4.1. Insert each pair of adjacent time points The midpoint of Considering that for any pair of satellites and ground nodes, the length of any visible interval between them in a satellite orbit period is much shorter than its invisible interval, established; therefore, Each pair of adjacent time points midpoint Determine the satellite and ground node pair A point in each invisible interval;

[0137] S4.2. Use the new sequence to construct satellite and ground node pairs Visibility Function The root interval set is for Any interval in It consists of three parts, namely Subintervals that are always positive or negative (t r ,t e ), Subintervals that are always negative or positive (t e ,t r' ),as well as (t e yes In the interval (t r ,t r' ) inside the root, t e ∈(t r ,t r' ));

[0138] S4.3. Consider the prediction time period (0,T p )Border situation, if or The value of is also negative, which means that the corresponding interval (0,t v1 )or There are zero points in the , which are rising zero point and falling zero point; merge them into In this way, a complete set of root-finding intervals is formed.

[0139] S4.4. In all The satellite and ground node pairs in the interval Visibility Function Find the root and get its value during the prediction time (0, T p ), that is, the ascending set of endpoints of all visible intervals Assume that the number of zero points obtained in the boundary case is N B ∈{0,1,2};

[0140] S4.5. According to The endpoint sequence constructs a set of visible intervals of the following four mutually exclusive cases:

[0141] (1) When and When N B =2, we can see that the interval set is

[0142] (2) When and When N B =1, it can be seen that the interval set is

[0143] (3) When and When N B =1, it can be seen that the interval set is

[0144] (4) When and When N B =0, it can be seen that the interval set is

[0145] according to and The value of matches one of the above four visible intervals, and the estimated visible interval between the satellite and the ground node pair is obtained. Repeat the above method to get the set The distance between all satellites and ground nodes in the prediction time (0, T p ) within the entire visible range.

[0146] Embodiment 1

[0147] The embodiment of the present invention uses the low-orbit giant constellation Starlink Phase I constellation (altitude 550km, a total of 1584 satellites), and its node set is Where N y ∈N + is the number of ground gateway nodes; select a satellite node S x ,x∈{1,2,...,1584}, and the ground node selects one of its gateway nodes G y ,y∈{1,2,...,N y},; Taking a certain absolute time as the origin t = 0, predict the satellite node S during the time period from t = 0 to t = 86400s x With this ground communication gateway node G y All visible intervals between The specific steps include:

[0148] S1. Determine the satellite and the gateway station Movement Model The motion characteristics used in this embodiment include the position information under the International Terrestrial Reference Frame (ITRF), and the position information used by the satellite The motion model of the gateway is derived from the fourth generation simplified general perturbations model (SGP4) with reference time t0. is a ground-fixed model, that is is a constant; therefore, the satellite motion model satisfies at any time t The motion model of the signal gateway station meets

[0149] S2. Determine the satellite and the gateway station Visible constraints between; This embodiment assumes that the satellite has a conical field of view with a maximum half-apex angle of H max , and assuming that the gateway station field of view has a minimum elevation angle requirement, that is, E min ; Specifically use two visible constraints:

[0150] Satellite S at time t x Relative to the gateway station G y The elevation angle E(t) is greater than the gateway station G y The minimum altitude angle E min ;

[0151] t time letter station G y The half apex angle H(t) relative to the satellite field of view is less than the maximum half apex angle H of the satellite field of view max ;

[0152] Figure 2 A schematic diagram of a visible constraint condition between a satellite and a gateway provided in an embodiment of the present invention; wherein, setting E min =10°, H max =56.5°; One of the discriminant functions is Right now and E(t)-E min >0 equivalent, and E(t)-E min ≤0 equivalent.

[0153] akin, One of the discriminant functions is Right now With H max -H(t)>0 is equivalent, With H max -H(t)<0 equivalent;

[0154] From the geometric relationship, we can derive:

[0155]

[0156] From the continuity of satellite motion, we can infer changes continuously over time and can be used as Composite functions with arcsin and arccos functions, and Also continuous on R.

[0157] Based on the above two visible constraints, we need to determine the first type of conversion operator For any continuous function f i ,f j , It can be shown that it satisfies the definition of a first-class conversion operator;

[0158] S3. Utilization Will and Integrate and construct the visibility function about time t For any t∈R,

[0159] S4. Construct the time interval γL used to divide the prediction time period (0, 86400s). To this end, first analyze the visibility function For any satellite model All satellites follow the basic motion law of satellites, that is, they make approximate periodic motions with the orbit as the reference system; under the assumption that the ground node has a small range of motion, it can be considered that its relative satellite orbit only moves with the rotation of the earth. For low-orbit satellites, their orbital angular velocity is significantly higher than the rotational angular velocity of the earth.

[0160] Generally speaking, one of the necessary conditions for satellites and ground nodes to be visible is that the line between them is not blocked by the earth. Assume that the movement of ground nodes relative to the satellite orbit in a short period of time can be ignored under the high-speed orbit of low-orbit satellites; therefore, in order to meet the condition that the line between the satellite and the ground node is not blocked by the earth, the satellite needs to move above the ground plane of the ground node; based on the geometric relationship between them, the above constraints can be converted into constraints related to the geocentric angle.

[0161] Figure 3 A schematic diagram of the earth occlusion relationship between a low-orbit satellite and a ground node provided in an embodiment of the present invention requires that the geocentric angle between the satellite and the ground node is less than a certain threshold. The maximum geocentric angle range Δθ without occlusion between the satellite and the ground node is determined by the satellite altitude:

[0162]

[0163] Where R e is the radius of the earth, and h is the altitude of the satellite orbit. For circular orbit satellites, the satellite can be considered to be approximately in uniform motion. Therefore, according to Δθ, the minimum proportion of the time when the satellite and the ground node are blocked by the earth in the satellite orbit period can be obtained:

[0164]

[0165] Assuming that in each orbital period of the satellite, the ground node is stationary relative to the satellite orbit, there is at least a proportion of time α when the satellite and the ground node are blocked by the earth, thus failing to meet the visibility constraint. Therefore, using α, we can construct a time interval cardinality L, which satisfies that each interval with a length of L has at most one visible interval of the satellite and the ground node. Specifically, assuming that the satellite orbital period is T s , then L = αT sis the shortest continuous earth occlusion time between the satellite and the ground node; since any two adjacent visible intervals must experience earth occlusion, any αT s Long time intervals will not intersect with more than one visible interval. In addition, considering the rotation of the earth and the influence of various perturbations, the time interval base L is multiplied by the adjustment coefficient γ, that is, γL=γαT s , where 0<γ<1; γ needs to be appropriately selected through certain tests to ensure that any γαT s In a long time interval, there is no more than one earth-free interval between the satellite and the ground node, and thus there will be no intersection with more than one visible interval.

[0166] According to the above analysis, the time interval γL=γαT used to divide the prediction period is determined s ; For the first phase of Starlink constellation satellites, α = 87.22%, T s =5730s, select γ=0.9, then γL≈4498s;

[0167] S5. Divide the entire prediction time period (0, 86400s) into equal intervals of γL = 4498s to obtain a series of time intervals in seconds. in j∈{1,2,...,19};

[0168] S6. Utilization In each Select a suitable time point t to construct the satellite and ground node pair Visible range Correlation root interval The specific steps are as follows:

[0169] S6.1. Each interval of The application of the maximum value algorithm to solve The maximum point of , get the maximum point set in ascending order N max ∈N + ;

[0170] S6.2. If for any maximum point have In Remove

[0171] S6.3. If for any two maximum points Yes |t j -t k |<γL, then Remove t j ,t k Any one of;

[0172] S6.4. Arrange to get the final The ascending set of And make satellite and ground node pairing Visible range Correlation root interval An endpoint of

[0173] S7. Utilization Satellite and ground node Determine the root-finding interval in each invisible interval The other endpoint of , and apply the iterative root-finding method to find the root. The specific steps are as follows:

[0174] S7.1. Insert each pair of adjacent time points The midpoint of Considering that for any pair of satellites and ground nodes, the length of any visible interval between them in a satellite orbit period is much shorter than its invisible interval, established; therefore, Each pair of adjacent time points midpoint Determine the satellite and ground node pair A point in each invisible interval;

[0175] S7.2. Use the new sequence to construct satellite and ground node pairs Visibility Function The root interval set is for Any interval in It consists of three parts, namely Subintervals that are always positive or negative (t r ,t e ), Subintervals that are always negative or positive (t e ,t r' ),as well as (t e yes In the interval (t r ,t r' ) inside the root, t e ∈(t r ,t r' ));

[0176] S7.3. Consider the situation at the boundary of the prediction time period (0,86400s). If or If the value of is also negative, it means that the corresponding interval or There are zero points in the , which are rising zero point and falling zero point; merge them into In this way, a complete set of root-finding intervals is formed.

[0177] S7.4. If the value of V at t = 0 or t = 86400s is negative, the corresponding or Merge into S R In the above example, we can form a complete root-finding interval set S R ';

[0178] S7.5. In all The satellite and ground node pairs in the interval Visibility Function Find the root and get all the zero points within the prediction time period (0,86400s), that is, the ascending set of endpoints of all visible intervals Assume that the number of zero points obtained in the boundary case is N B ∈{0,1,2};

[0179] S7.6. According to The endpoint sequence constructs a set of visible intervals of the following four mutually exclusive cases:

[0180] (1) When and When N B =2, we can see that the interval set is

[0181] (2) When and When N B =1, it can be seen that the interval set is

[0182] (3) When and When N B =1, it can be seen that the interval set is

[0183] (4) When and When N B =0, it can be seen that the interval set is

[0184] according to and The value of matches one of the above four visible intervals, and the estimated visible interval between the satellite and the ground node pair is obtained.

[0185] Repeat the above method to get the set The total visible intervals between all satellite and ground node pairs in the prediction time period (0,86400s).

[0186] In summary, the embodiment of the present invention constructs a visibility function between a satellite and a ground node pair according to a satellite and ground node motion model and two satellite-ground visibility constraints, so as to transform the problem of solving the visible interval between the satellite and the ground node into a problem of finding a positive interval of multiple zero points of the visibility function; then, according to the periodic law of the satellite's in-orbit motion and relevant satellite-ground visibility constraints, all zero-point solution intervals of the visibility function are constructed and the zero points are solved, and the starting or ending zero point of each positive interval of the visibility function is determined as the starting or ending time of the visible interval between the satellite and the ground node, thereby obtaining a set of visible intervals between the satellite and the ground node.

[0187] The present invention proposes a method for predicting the visibility relationship and duration of a satellite and a ground node, that is, firstly, a visibility function between a satellite and a ground node pair is constructed according to a satellite and ground node motion model and relevant satellite-ground visibility constraints, so as to convert the problem of solving the visibility interval between the satellite and the ground node into a problem of finding a positive interval of multiple zero points of the visibility function; then, according to the periodic law of the satellite's on-orbit motion and the satellite-ground visibility constraints, all zero-point solution intervals of the visibility function are constructed and the zero points are solved, and the starting or ending zero point of each positive interval of the visibility function is determined as the starting or ending time of the visible interval between the satellite and the ground node, thereby obtaining a set of visible intervals between the satellite and the ground node, and realizing efficient and accurate solution of the visible intervals between the satellite and the ground node.

[0188] Those skilled in the art can understand that the accompanying drawings are only schematic diagrams of an embodiment, and the modules or processes in the accompanying drawings are not necessarily required to implement the present invention.

[0189] It can be known from the description of the above implementation methods that those skilled in the art can clearly understand that the present invention can be implemented by means of software plus a necessary general hardware platform. Based on such an understanding, the technical solution of the present invention is essentially or the part that contributes to the prior art can be embodied in the form of a software product, which can be stored in a storage medium such as ROM / RAM, a magnetic disk, an optical disk, etc., and includes a number of instructions for enabling a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in the various embodiments of the present invention or certain parts of the embodiments.

[0190] Each embodiment in this specification is described in a progressive manner, and the same or similar parts between the embodiments can be referred to each other, and each embodiment focuses on the differences from other embodiments. In particular, for the device or system embodiment, since it is basically similar to the method embodiment, the description is relatively simple, and the relevant parts can be referred to the partial description of the method embodiment. The device and system embodiments described above are merely schematic, wherein the units described as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they may be located in one place, or they may be distributed on multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the scheme of this embodiment. Ordinary technicians in this field can understand and implement it without paying creative labor.

[0191] The above is only a preferred specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed by the present invention should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. A method for predicting the visible relationship and duration between a satellite and a ground node, characterized in that: include: Obtaining the motion models of the satellite and the ground node, setting the satellite-ground visibility constraint conditions according to the motion models, and constructing the visibility function between the satellite and the ground node; The problem of determining the visible interval between the satellite and the ground node is transformed into the problem of finding the positive interval of multiple zero points of the visibility function; According to the periodic law of the satellite's in-orbit motion and the satellite-ground visibility constraints, all zero-point solution intervals of the visibility function are constructed and the zero points are solved. The starting or ending zero point of each positive interval of the visibility function is determined as the starting or ending time of the visible interval between the satellite and the ground node, and a set of visible intervals between the satellite and the ground node is constructed.

2. The method according to claim 1, characterized in that Acquiring the motion model of the satellite and the ground node includes: determining the motion model between the satellite and the ground node, the motion model reflecting the change law of the physical motion characteristics of the satellite and the ground node over time; Without loss of generality, assume that a satellite node has N s ∈N + (N + represents a positive integer set) kinds of motion features, then the motion model of the satellite node can be characterized as R represents a real number, where It reflects the value of the i-th type of motion characteristics of the satellite node changing with time t, which is a continuous function or a piecewise continuous function; Without loss of generality, assume that a ground node has N g ∈N + The motion model of the ground node can be represented as in It reflects the value of the i-th type of motion feature of the ground node changing with time t, which is a continuous function or a piecewise continuous function; The motion characteristics include values ​​of satellite or ground node position information that change over time.

3. The method according to claim 2, characterized in that The setting of satellite-ground visibility constraint conditions according to the motion model includes: From satellite and ground nodes Choose any satellite node S x ,x∈{1,2,...,N x },N x ∈N + and a ground node G y ,y∈{1,2,...,N y },N y ∈N + , denoted as Build the pair of satellites and ground nodes The visibility relation expression between Defining functions Characterizing satellite and ground node pairs The logical relationship between whether it is visible at any time t∈R, where T is logically true and F is logically false. It means that at time t, the satellite and the ground node are aligned can be seen by each other; if It means that at time t, the satellite and the ground node are aligned are not visible to each other; in particular, if for a certain time point t0, if its left and right neighbors The value of is opposite, then let And call t0 The discontinuity point is used to indicate the satellite and ground node The point in time when the visibility relationship between them changes; Assumptions is decomposed into N q ∈N + Visibility constraints at each level and These visibility constraints describe the pair of satellites and ground nodes respectively. Joint Movement Model Under the visible condition, the corresponding variable value exceeds the limit value that can be reached. These visible constraints are obtained through logical "and" operation for the pair of satellites and ground nodes. At any time, the visibility relationship result is that if the pair of satellites and the ground node If all visible constraints are satisfied, then the satellite and the ground node are It is visible at time t, that is ∧ indicates a logical "and" operation; otherwise, if at least one visibility constraint condition is not satisfied, the satellite and the ground node are It is not visible at time t, that is ∨ represents the logical "or" operation.

4. The method according to claim 3, characterized in that The setting of the satellite-ground visibility constraint condition according to the motion model further includes: Consider a pair of satellites and ground nodes Joint Movement Model And the corresponding visible constraints It can be converted into a continuous function on R or a piecewise continuous function on R, and these functions are operated by continuous operators to construct the satellite and ground node pair. The visibility function between the satellite and the ground node is obtained by a related iterative method to obtain the zero point of the visibility function and the The set of visible intervals of ; For satellite and ground node Each visible constraint Construct its discriminant function And meet the following characteristics: (1) Satellite and ground node pairing Joint Movement Model Related, that is, there exists a mapping operator Make (2) is continuous on R or piecewise continuous on R, that is, there exists N seg ∈N + The interval segment Continuous and bounded within each interval; (3) At any time t∈R, and is equivalent, and and equivalence; (4) If and only if t' is The discontinuity point; make Satellite and ground node pairing Visible constraints The set of all discriminant functions of ; and if there exists And meet and Then it is called and about Discriminant equivalence; Satellite and ground node pair Each visible constraint To perform logical AND operations to include all visible constraints, define as well as There are two types of discriminant transformation operators and they satisfy the following characteristics respectively: Discriminant conversion operator of the first kind Meet the following characteristics: (1) Its independent variables are (f1,f2,...,f c )∈(R R ) c ; where c∈N + , f i ∈R R ,i∈{1,2,...,c}, R R is the set of all functions whose independent variables have a range of R and whose dependent variables have a range of R; (R R ) c is c R R The Cartesian product of (2) If for any i∈{1,2,...,c}, f i is continuous on R, then continuous on R; (3) For any t∈R, if and only if any i∈{1,2,...,c} such that f i When (t)>0, then It is positive at t; (4) For any t∈R, if and only if there exists i∈{1,2,...,c} such that f i When (t)<0, then It is negative at t; The second discriminant conversion operator Meet the following characteristics: (1) Its independent variables are (f1,f2,...,f c )∈(R R ) c ; where c∈N + , f i ∈R R ,i∈{1,2,...,c}, R R is the set of all functions whose independent variables have a range of R and whose dependent variables have a range of R; (R R ) c is c R R The Cartesian product of (2) If for any i∈{1,2,...,c}, f i is continuous on R, then continuous on R; (3) For any t∈R, if and only if there exists i∈{1,2,...,c} such that f i When (t)>0, then It is positive at t; (4) For any t∈R, if and only if any i∈{1,2,...,c} such that f i When (t)<0, then It is negative at t; The first type of discriminant conversion operator implements the "and" logic of the discriminant function, that is, when the discriminant function is input into the operator, the operator result is positive for the independent variable only when all the discriminant functions are positive for the independent variable; the second type of discriminant conversion operator implements the "or" logic of the discriminant function, that is, when the discriminant function is input into the operator, the operator result is positive for the independent variable only when there is a discriminant function that is positive for the independent variable; A pair of satellites and ground nodes Visible constraints between Any discriminant function like Piecewise continuous on R, the following conversion method is used to convert Convert to a function that is continuous in R Assume that the piecewise continuous discriminant function In a continuous segment interval I k ≠R,k∈{1,2,...,N seg The function on} is h k (t):I k →R, first construct a corresponding continuous function make in I k Up and h k (t) has the same sign and is in RI k The upper limit is always negative. The specific steps are as follows: (1) h k (t) Extended to That is, for any t∈I k , and continuous on R; (2) Structure For any t∈R, in, The first type of discriminant conversion operator In the special case of c = 2; y(t) is any function that is continuous on R and satisfies the following conditions: ①If I k The lower bound satisfies infI k = -∞, and the upper bound supI k =b∈R, then For any t∈(-∞,b), y(t)>0; For any t∈(b,+∞), y(t)<0; ②If I k Satisfy the lower bound infI k =a∈R, and the upper bound supI k =b∈R, then For any t∈(a,b), y(t)>0; For any t∈(-∞,a)∪(b,+∞), y(t)<0; ③If I k If the lower bound infI=a∈R and the upper bound supI=+∞, then For any t∈(a,+∞), y(t)>0; For any t∈(-∞,a), y(t)<0; The continuous function constructed by the above method It is continuous on R and satisfies (1) for any t∈R when hour, (2) When t∈I k When h k (t)>0 If h k (t)≤0 Based on the above method, the discriminant function of piecewise continuous Transformed into an equivalent discriminant function that is continuous on R Assume a piecewise continuous discriminant function With N seg ∈N + continuous segmented intervals, and its kth segmented interval I k The continuous function in is h k (t):I k →R,k∈{1,2,...,N seg }, for h k (t) Construct the above continuous function make in I k Up and h k (t) has the same positive and negative signs, in RI k The upper limit is always negative, so get about The continuous equivalent discriminant function on R, This is the second type of discriminant conversion operator When c=N seg special case, Satisfies the following characteristics, namely is continuous on R and satisfies (1) for any t∈R If and only if (2) If and only if (3) If and only if 5. The method according to claim 4, characterized in that The construction of the visibility function between the satellite and the ground node pair includes: A pair of satellites and ground nodes The visibility relationship between them and all the visibility conditions between them It is an "and" logical relationship, so the first-class discriminant conversion operator is used to integrate the continuous discriminant functions corresponding to all visibility constraints to construct the visibility function about time t Its purpose is to connect a pair of satellites with a ground node The visibility interval solution problem is transformed into the visibility function independent variable t for The interval solution problem is then transformed into finding the visibility function The value of the independent variable t; Assume that the satellite and ground node Visibility relationship between is decomposed into N q ∈N + Visible constraints Its corresponding N q The discriminant function that is continuous in R or transformed to be continuous in R is in, Construct visibility function satisfy: Satellite and ground node pair The visibility function Continuous, visibility function in R Align satellites with ground nodes All visible constraints After integration, at any time t, if and only if all N q When all visible constraints are satisfied, that is, any but If and only if any of the visible constraints is not satisfied, there exists but If and only if any discriminant function and exists When 6. The method according to claim 5, characterized in that The method of constructing all zero-point solution intervals of the visibility function and solving the zero points according to the periodic law of the satellite's on-orbit motion and the satellite-ground visibility constraint conditions, determining the starting or ending zero point of each positive interval of the visibility function as the starting or ending time of the visible interval between the satellite and the ground node, and constructing a set of visible intervals between the satellite and the ground node includes: Satellite and ground node pair The visibility function is continuous at the prediction time T p Internal visibility function The set of t constitutes the satellite and ground node pair One or more visible intervals between Where N v ∈N + Indicates that the satellite and ground node pair at the prediction time T p The number of visible intervals within; the visible interval The left and right endpoints are The zero point of Root; Determine the satellite and ground node pair Visibility Function The root-finding interval of each root of N r ∈N + Indicates that the satellite and ground node pair at the prediction time T p The number of root intervals in There is only one Zero point, any root interval according to the zero point theorem One end point is located between the satellite and the ground node A visible range The other endpoint falls in its adjacent invisible interval. The characteristics of each adjacent visible interval Find an endpoint in each of the invisible intervals between and construct all root-finding intervals In seeking After all the zero points are obtained, these zero points are directly used as the satellite and ground node pairs. Visible range The endpoint of In order to Each visible interval Find a root interval in According to the periodic law of satellite motion in orbit and the related satellite-ground visibility constraints, a time interval base L is determined to convert the predicted time T p Perform continuous partitioning based on γL, where γ is a positive coefficient and satisfies each partitioned interval The visible interval between at most one satellite and a ground node There is an intersection; then, in each of the divided intervals Inner Seeking Maximum point And if hour, Then it is used as the root-finding interval A potential endpoint of ; and a point in its adjacent invisible interval is used as the root-finding interval The other end point of the maximum point is used to construct all root-finding intervals Get the predicted time T p Satellite and ground node pair The visible interval between 7. The method according to claim 6, characterized in that The above-mentioned maximum points are used to construct all root-finding intervals. Get the predicted time T p Satellite and ground node pair The visible interval between include: S1. Determine the time period for dividing the forecast period T p The time interval γL ensures that each divided time interval At most one satellite and ground node pair Visible range There is an intersection; according to the satellite and ground node Joint Movement Model And the visibility function in between To determine the time interval for dividing the forecast period (0, T p ), that is, determine the time interval in For any satellite and ground node joint motion model And the visibility function Functions that map to real numbers; S2. Time interval Divide the entire forecast time period (0, T p ), get a set of time intervals S3. Utilization In each Select a suitable time point t to construct the satellite and ground node pair Visible range Correlation root interval The specific steps are as follows: S3.

1. Each interval of The application of the maximum value algorithm to solve The maximum point of , get the maximum point set in ascending order S3.

2. If for any maximum point have In Remove S3.

3. If for any two maximum points Yes |t j -t k |<γL, then Remove t j ,t k Any one of; S3.

4. Arrange to get the final The ascending set of And make satellite and ground node pairing Visible range Correlation root interval An endpoint of S4. Utilization Satellite and ground node Determine the root-finding interval in each invisible interval The other endpoint of , and apply the iterative root-finding method to find the root, the specific steps are as follows: S4.

1. Insert each pair of adjacent time points The midpoint of Considering that for any pair of satellites and ground nodes, the length of any visible interval between them in a satellite orbit period is much shorter than its invisible interval, Established, Each pair of adjacent time points midpoint Determine the satellite and ground node pair A point in each invisible interval; S4.

2. Use the new sequence to construct satellite and ground node pairs Visibility Function The root interval set is for Any interval in It consists of three parts, namely Subintervals that are always positive or negative (t r ,t e ), Subintervals that are always negative or positive (t e ,t r' ),as well as (t e yes In the interval (t r ,t r' ) inside the root, t e ∈(t r ,t r' )); S4.

3. Consider the prediction time period (0,T p )Border situation, if or If the value of is also negative, it means that the corresponding interval (0,t v1 )or There are zero points in the , which are rising zero point and falling zero point; merge them into In this way, a complete set of root-finding intervals is formed. S4.

4. In all The satellite and ground node pairs in the interval Visibility Function Find the root and get its value during the prediction time (0, T p ), that is, the ascending set of endpoints of all visible intervals Assume that the number of zero points obtained in the boundary case is N B ∈{0,1,2}; S4.

5. According to The endpoint sequence constructs a set of visible intervals of the following four mutually exclusive cases: (1) When and When N B =2, we can see that the interval set is (2) When and When N B =1, it can be seen that the interval set is (3) When and When N B =1, it can be seen that the interval set is (4) When and When N B =0, it can be seen that the interval set is according to and The value of matches one of the above four visible intervals, and the estimated visible interval between the satellite and the ground node pair is obtained. Repeat the above method to get the set The distance between all satellites and ground nodes in the prediction time (0, T p ) within the entire visible range.

Images