Low-orbit multi-static radar satellite constellation coverage calculation method and system

Abstract

The invention provides a low-orbit multi-static radar satellite constellation coverage calculation method and system. The low-orbit multi-static radar satellite constellation coverage calculation method comprises the following steps: S1, calculating orbit data of all satellites under a J2000 coordinate system by adopting a J2 recursion model; s2, calculating a position vector of a target under the J2000 coordinate system; s3, for each moment, calculating and determining a satellite set sigma 1 meeting the ground elevation angle constraint; s4, calculating and determining a satellite set sigma 2 meeting the distance constraint; s5, calculating and determining a satellite set sigma3 meeting the single-satellite view field constraint; s6, solving a union set Sigma 4 of Sigma 1, Sigma 2 and Sigma 3, combining every two satellites in the Sigma 4, calculating a bistatic angle of each combination to the target, and determining a target coverage state flag FL at the moment; and S7, according to a certain time resolution, repeatedly solving the target coverage state flag FL at each moment, and calculating and determining the maximum revisit time, the average revisit time and the minimum revisit time. According to the method, the ground coverage of the low-orbit multi-static radar constellation can be quickly calculated.

Description

Technical Field

[0001] The present invention relates to the technical field of overall spacecraft design, and in particular to a method and system for calculating coverage of a low-orbit multi-base radar satellite constellation. Background Art

[0002] Low-orbit multi-base radar satellite network detection has received attention from all countries due to its outstanding advantages. Low-orbit multi-base radar satellites form a large-scale constellation through networking, which can effectively achieve short-term intermittent monitoring of the target area, or even continuous coverage throughout the day. The design of such constellation configuration and orbit involves many factors such as coverage requirements, cost, and satellite platform. Among them, coverage analysis and calculation is one of the key technologies in constellation orbit design. Multi-base radar satellite coverage of targets needs to meet certain spatial geometric structures, involving the spatial parameters of the binary satellites and the target. Traditional coverage analysis algorithms cannot solve this problem. To this end, it is necessary to study the ground coverage analysis of low-orbit multi-base radar satellite constellations and propose a coverage calculation method that meets multiple satellites and multiple constraints.

[0003] At present, people have conducted some research on constellation coverage. After searching, the main ones related to low-orbit satellites are:

[0004] The paper "Optimization Design of Homogeneous Dual-base Radar Constellation" (System Engineering and Electronic Technology, Issue 11, 2005: 1883-1888) studies the orbital characteristics of satellites, the relative motion laws between satellites in the constellation, and the ground coverage characteristics, and derives the calculation formulas for satellite-borne single-base and dual-base radar detection areas, and analyzes the relationship between the dual-base angle and the target forward scattering area and the relative position of the satellite. Based on the inherent spatial constraints of the constellation, the geometric relationship between the Doppler frequency expansion of ground clutter caused by platform motion and satellite flight is discussed. With certain simplifications, this paper converts the dual-satellite common-view coverage into a single-satellite coverage problem, so that STK can be used for simulation calculations. However, this patent focuses on multi-base radar satellites, which involve multi-satellite common-view coverage within a constellation system and cannot be converted to single-satellite coverage.

[0005] The paper "Research on Simulation Technology of Satellite-Earth Dual / Multi-base Radar Network Detection" (Beijing Institute of Technology: Song Jun, 2014) is aimed at satellite-earth dual / multi-base radar network detection. It uses target anisotropic scattering anisotropic RCS calculation, echo simulation, target detection, false alarm simulation technology and software engineering technology to develop a set of satellite-earth dual / multi-base radar network detection simulation system with comprehensive functions, simple operation and user-friendly interface. The patent mainly focuses on the simulation of detection algorithm, while this patent covers constellation calculation, which is quite different.

[0006] The invention patent with publication number CN108536964A discloses a storage medium, a satellite constellation coverage performance simulation analysis method and its system. Based on Matlab and STK joint simulation, a satellite constellation coverage analysis method is given. The patent focuses on single-satellite coverage constraints, while this patent involves multi-satellite common view constraints, and the coverage calculation is more complicated.

[0007] The invention patent with publication number CN106446333A discloses a small-scale satellite constellation configuration optimization design method, which uses the genetic algorithm toolkit in MATLAB software to iteratively optimize the configuration parameters of the constellation; during the iterative optimization process, the coverage efficiency of different constellation configurations on the target area is calculated by MATLAB calling STK. This method combines the advantages of MATLAB in numerical optimization and the advantages of STK in calculating constellation coverage efficiency to achieve fast and efficient optimization design of satellite constellation configuration. This invention helps satellite developers to quickly optimize the configuration of satellite constellations and design a better constellation configuration scheme. The patent also focuses on single-star coverage constraints, while this patent involves multi-star common view constraints, and the coverage calculation is more complicated.

[0008] The invention patent with publication number CN103870697A discloses a satellite coverage prediction method based on transcendental inequalities, and proposes a single satellite ground coverage prediction method based on transcendental inequalities. The patent focuses on the rapid solution of the coverage of a single satellite and cannot adapt to the situation of multiple satellites in common view.

[0009] In summary, people still pay insufficient attention to the research on constellation coverage analysis under the constraint of multi-satellite common view, and related research results are also relatively lacking, which is inconsistent with the important application value of multi-base radar satellite constellations. Therefore, we should further explore the constellation coverage algorithm under the constraint of multi-satellite common view and provide an effective technical approach for the orbit and constellation configuration design of multi-base radar satellite constellations. Summary of the invention

[0010] In view of the defects in the prior art, the present invention provides a method and system for calculating the coverage of a low-orbit multi-base radar satellite constellation.

[0011] According to a method and system for calculating coverage of a low-orbit multi-base radar satellite constellation provided by the present invention, the scheme is as follows:

[0012] In a first aspect, a method for calculating coverage of a low-orbit multi-base radar satellite constellation is provided, the method comprising:

[0013] Step S1: According to the constellation orbit and configuration parameters, the J2 recursive model is used to calculate the orbit data of all satellites in the J2000 coordinate system;

[0014] Step S2: Calculate the position vector of the target in the J2000 coordinate system according to the latitude, longitude and altitude of the given target;

[0015] Step S3: at each moment, calculate and determine the satellite set Σ1 that satisfies the ground elevation angle constraint, determine the satellite set Σ2 that satisfies the distance constraint, and determine the satellite set Σ3 that satisfies the single-star field of view constraint;

[0016] Step S4: Solve the union Σ4 of Σ1, Σ2, and Σ3, combine the satellites in Σ4 in pairs, and calculate the bistatic angle of each combination to the target, and determine the target coverage state flag FL at that moment;

[0017] Step S5: According to a certain time resolution, repeatedly solve the target coverage status flag FL at each moment, and calculate and determine the maximum revisit time, the average revisit time, and the minimum revisit time.

[0018] Preferably, the step S1 comprises:

[0019] Step S101: Assume that both the initial configuration and the target configuration are described by Walker constellation parameters, and define the right ascension of the ascending node of the Kth satellite in the Jth orbital plane of the initial configuration and the target configuration as Ω (J,K) , latitude argument u (J,K) , then

[0020]

[0021] In the formula, is the right ascension and latitude argument of the ascending node of the first satellite in the first orbital plane, P is the number of orbital planes, T is the total number of satellites, F is the phase factor, and S = T / P is the number of satellites per orbit;

[0022] Step S102: Assuming that the orbital semi-major axis, eccentricity, orbital inclination and perigee argument of all satellites are consistent, the six orbital numbers of all satellites are determined by combining the right ascension and latitude arguments of the ascending node in the previous step;

[0023] Step S103: Taking the number of six tracks as the initial value, the J2 model is used to recursively calculate the number of six tracks in the simulation time period, and then determine the position Rs_J2000 and the speed Vs_J2000.

[0024] Preferably, step S2 comprises:

[0025] Step S201: Calculate the position vector Rt_wgs84 in the earth fixed coordinate system according to the given longitude, latitude and altitude;

[0026] Step S202: Calculate the transformation matrix M from the WGS84 coordinate system to J2000 according to the current time;

[0027] Step S203: Calculate and determine the position vector Rt_J2000=M·Rt_wgs84 under J2000 according to the transformation matrix and the position vector under the earth fixed coordinate system.

[0028] Preferably, in step S3, calculating and determining the satellite set Σ1 satisfying the ground elevation angle constraint includes:

[0029] Step S311: Calculate the ground elevation angle C_yj=Rs_J2000·Rt_J2000 / |Rs_J2000| / |Rt_J2000| according to the satellite position Rs_J2000 and the target position vector Rt_J2000;

[0030] Step S312: judging whether the elevation angle C_yj satisfies the constraint according to the ground elevation angle threshold, and storing it if it satisfies the constraint;

[0031] Step S313: traverse and calculate the ground elevation angles and constraints of all satellites to determine the satellite set Σ1.

[0032] Preferably, in step S3, calculating and determining the satellite set Σ2 satisfying the distance constraint includes:

[0033] Step S321: Calculate the distance C_jl from the satellite to the target based on the satellite position Rs_J2000 and the target position vector Rt_J2000 = |Rs_J2000-Rt_J2000|;

[0034] Step S322: judging whether the elevation angle C_jl satisfies the constraint according to the distance threshold, and storing it if it satisfies the constraint;

[0035] Step S323: traverse and calculate the distances and constraints from all satellites to the target, and determine the satellite set Σ2.

[0036] Preferably, in step S3, calculating and determining the satellite set Σ3 satisfying the single-satellite field of view constraint comprises:

[0037] Step S331: Calculate the relative position vector rs from the satellite to the target according to the satellite position Rs_J2000 and the target position vector Rt_J2000 = Rs_J2000 - Rt_J2000;

[0038] Step S332: Calculate the target off-axis angle C_lz=-Rs_J2000·rs / |Rs_J2000| / |rs| according to the satellite position Rs_J2000 and the relative position vector rs;

[0039] Step S333: judging whether the target off-axis angle C_lz satisfies the constraint according to the single-satellite ground field of view angle threshold, and storing it if it satisfies the constraint;

[0040] Step S334: traverse and calculate the target off-axis angles and constraints of all satellites to determine the satellite set Σ3.

[0041] Preferably, step S4 comprises:

[0042] Step S401: Solve the union Σ4 of Σ1, Σ2, and Σ3, and combine the satellites in Σ4 in pairs;

[0043] Step S402: For each combination, calculate the relative position vectors rs1 and rs2 from the satellite to the target, and calculate the bistatic angle C_sjd = rs1·rs2 / |rs1| / |rs2|;

[0044] Step S403: According to the dual base angle threshold, determine whether C_sjd satisfies the constraint. If the constraint is satisfied, the target coverage status flag FL takes 1 and the calculation ends. If not, calculate the C_sjd and satisfaction of the next combination. If neither is satisfied, FL takes 0.

[0045] Preferably, step S5 comprises:

[0046] Step S501: sampling according to the time period, traversing and calculating the target coverage state flag FL at all sampling moments, and determining the target coverage state time series within the simulation time period;

[0047] Step S502: Target coverage status time series, each calculation determines the maximum revisit time, average revisit time, and minimum revisit time.

[0048] In a second aspect, a low-orbit multi-base radar satellite constellation coverage calculation system is provided, the system comprising:

[0049] Module M1: Based on the constellation orbit and configuration parameters, the J2 recursive model is used to calculate the orbital data of all satellites in the J2000 coordinate system;

[0050] Module M2: Calculate the position vector of the target in the J2000 coordinate system according to the latitude, longitude and altitude of the given target;

[0051] Module M3: For each moment, calculate and determine the satellite set Σ1 that satisfies the ground elevation angle constraint, the satellite set Σ2 that satisfies the distance constraint, and the satellite set Σ3 that satisfies the single-star field of view constraint;

[0052] Module M4: solve the union Σ4 of Σ1, Σ2, and Σ3, combine the satellites in Σ4 in pairs, and calculate the bistatic angle of each combination to the target, and determine the target coverage status flag FL at that moment;

[0053] Module M5: According to a certain time resolution, repeatedly solve the target coverage status flag FL at each moment, and calculate and determine the maximum revisit time, average revisit time, and minimum revisit time.

[0054] Preferably, the module M1 comprises:

[0055] Module M101: Assume that both the initial configuration and the target configuration are described by Walker constellation parameters, and define the right ascension of the ascending node of the Kth satellite in the Jth orbital plane of the initial configuration and the target configuration as Ω (J,K) , latitude argument u (J,K) , then

[0056]

[0057] In the formula, is the right ascension and latitude argument of the ascending node of the first satellite in the first orbital plane, P is the number of orbital planes, T is the total number of satellites, F is the phase factor, and S = T / P is the number of satellites per orbit;

[0058] Module M102: Assuming that the orbital semi-major axis, eccentricity, orbital inclination and perigee argument of all satellites are consistent, combine the right ascension and latitude argument of the ascending node in the previous module to determine the six orbital elements of all satellites;

[0059] Module M103: Taking the number of six tracks as the initial value, the J2 model is used to recursively calculate the number of six tracks in the simulation time period, and then determine the position Rs_J2000 and the speed Vs_J2000;

[0060] The module M2 comprises:

[0061] Module M201: Calculate the position vector Rt_wgs84 in the earth fixed coordinate system according to the given longitude, latitude and altitude;

[0062] Module M202: Calculate the transformation matrix M from the WGS84 coordinate system to the J2000 according to the current time;

[0063] Module M203: Calculate and determine the position vector Rt_J2000=M·Rt_wgs84 under J2000 according to the transformation matrix and the position vector under the earth fixed coordinate system;

[0064] In the module M3, calculating and determining the satellite set Σ1 that satisfies the ground elevation angle constraint includes:

[0065] Module M311: Calculate the ground elevation angle C_yj=Rs_J2000·Rt_J2000 / |Rs_J2000| / |Rt_J2000| according to the satellite position Rs_J2000 and the target position vector Rt_J2000;

[0066] Module M312: According to the ground elevation angle threshold, determine whether the elevation angle C_yj satisfies the constraint, and if so, store it;

[0067] Module M313: traverse and calculate the ground elevation angles and constraints of all satellites to determine the satellite set Σ1;

[0068] In the module M3, calculating and determining the satellite set Σ2 that satisfies the distance constraint includes:

[0069] Module M321: Calculate the distance C_jl from the satellite to the target based on the satellite position Rs_J2000 and the target position vector Rt_J2000 = |Rs_J2000-Rt_J2000|;

[0070] Module M322: judging whether the elevation angle C_jl satisfies the constraint according to the distance threshold, and storing it if it satisfies the constraint;

[0071] Module M323: traverse and calculate the distances and constraints from all satellites to the target, and determine the satellite set Σ2;

[0072] In the module M3, the calculation and determination of the satellite set Σ3 satisfying the single-satellite field of view constraint includes:

[0073] Module M331: Calculate the relative position vector rs from the satellite to the target according to the satellite position Rs_J2000 and the target position vector Rt_J2000 = Rs_J2000 - Rt_J2000;

[0074] Module M332: Calculate the target off-axis angle C_lz=-Rs_J2000·rs / |Rs_J2000| / |rs| according to the satellite position Rs_J2000 and the relative position vector rs;

[0075] Module M333: According to the single-satellite ground field of view angle threshold, determine whether the target off-axis angle C_lz meets the constraint. If it meets the constraint, store it;

[0076] Module M334: traverse and calculate the target off-axis angles and constraints of all satellites to determine the satellite set Σ3;

[0077] The module M4 comprises:

[0078] Module M401: Solve the union Σ4 of Σ1, Σ2, and Σ3, and combine the satellites in Σ4 in pairs;

[0079] Module M402: For each combination, calculate the relative position vectors rs1 and rs2 from the satellite to the target, and calculate the bistatic angle C_sjd = rs1·rs2 / |rs1| / |rs2|;

[0080] Module M403: According to the dual-base angle threshold, determine whether C_sjd satisfies the constraint. If the constraint is satisfied, the target coverage status flag FL takes 1 and the calculation ends. If not, calculate the C_sjd and satisfaction of the next combination. If neither is satisfied, FL takes 0.

[0081] The module M5 comprises:

[0082] Module M501: Sampling according to the time period, traversing and calculating the target coverage state flag FL at all sampling moments, and determining the target coverage state time series within the simulation time period;

[0083] Module M502: Target coverage status time series, each calculation determines the maximum revisit time, average revisit time, and minimum revisit time.

[0084] Compared with the prior art, the present invention has the following beneficial effects:

[0085] The method of the present invention realizes the rapid calculation of the ground coverage of the low-orbit multi-base radar constellation. By modeling the dual-ground angle constraint, elevation angle constraint, single-satellite field of view constraint and distance constraint, the constellation's revisit time parameters to the target can be accurately calculated, providing an effective technical means for constellation configuration design.

[0086] Other beneficial effects of the present invention will be explained in the specific implementation manner through the introduction of specific technical features and technical solutions. Through the introduction of these technical features and technical solutions, those skilled in the art should be able to understand the beneficial technical effects brought about by the technical features and technical solutions. BRIEF DESCRIPTION OF THE DRAWINGS

[0087] Other features, objects and advantages of the present invention will become more apparent from the detailed description of non-limiting embodiments made with reference to the following drawings:

[0088] Figure 1 is a flow chart of the method of the present invention;

[0089] Figure 2 It is the coverage status time series when the target latitude is 0 degrees in a specific implementation manner;

[0090] Figure 3 It is the coverage status time series when the target latitude is 30 degrees in a specific implementation manner;

[0091] Figure 4 is the maximum bistatic angle at each moment in the specific implementation manner. DETAILED DESCRIPTION

[0092] The present invention is described in detail below in conjunction with specific embodiments. The following embodiments will help those skilled in the art to further understand the present invention, but are not intended to limit the present invention in any form. It should be noted that, for those of ordinary skill in the art, several changes and improvements can also be made without departing from the concept of the present invention. These all belong to the protection scope of the present invention.

[0093] The embodiment of the present invention provides a method for calculating coverage of a low-orbit multi-base radar satellite constellation, referring to Figure 1 As shown, the method specifically includes the following contents:

[0094] Step S1: According to the constellation orbit and configuration parameters, the J2 recursive model is used to calculate the orbit data of all satellites in the J2000 coordinate system.

[0095] The step S1 comprises:

[0096] Step S101: Assuming that both the initial configuration and the target configuration are described by Walker constellation parameters, define the right ascension of the ascending node of the Kth satellite in the Jth orbital plane of the initial configuration and the target configuration as Ω (J,K) , latitude argument u (J,K) , then

[0097]

[0098] In the formula, is the right ascension and latitude argument of the ascending node of the first satellite in the first orbital plane, P is the number of orbital planes, T is the total number of satellites, F is the phase factor, and S = T / P is the number of satellites per orbit;

[0099] Step S102: Assuming that the orbital semi-major axis, eccentricity, orbital inclination and perigee argument of all satellites are consistent, combined with the right ascension of the ascending node and the argument of latitude in the previous step, the six orbital elements of all satellites (also called orbital elements, which are the basic parameters describing the satellite orbit. These parameters include: semi-major axis, eccentricity, orbital inclination, right ascension of the ascending node, argument of perigee, true anomaly) can be determined.

[0100] Step S103: Taking the number of six tracks as the initial value, the J2 model is used to recursively calculate the number of six tracks in the simulation time period, and then determine the position Rs_J2000 and the speed Vs_J2000.

[0101] Step S2: Calculate the position vector of the target in the J2000 coordinate system according to the latitude, longitude and altitude of the given target.

[0102] The step S2 comprises:

[0103] Step S201: Calculate the position vector Rt_wgs84 in the earth fixed coordinate system according to the given longitude, latitude and altitude;

[0104] Step S202: Calculate the transformation matrix M from the WGS84 coordinate system to J2000 according to the current time;

[0105] Step S203: Calculate and determine the position vector Rt_J2000=M·Rt_wgs84 under J2000 according to the transformation matrix and the position vector under the earth fixed coordinate system.

[0106] Step S3: at each moment, calculate and determine the satellite set Σ1 that satisfies the ground elevation angle constraint, determine the satellite set Σ2 that satisfies the distance constraint, and determine the satellite set Σ3 that satisfies the single-star field of view constraint;

[0107] In step S3, calculating and determining the satellite set Σ1 that satisfies the ground elevation angle constraint includes:

[0108] Step S311: Calculate the ground elevation angle C_yj=Rs_J2000·Rt_J2000 / |Rs_J2000| / |Rt_J2000| according to the satellite position Rs_J2000 and the target position vector Rt_J2000;

[0109] Step S312: judging whether the elevation angle C_yj satisfies the constraint according to the ground elevation angle threshold, which is generally required to be greater than 5 degrees. If the constraint is satisfied, it is stored;

[0110] Step S313: traverse and calculate the ground elevation angles and constraints of all satellites to determine the satellite set Σ1.

[0111] In this step, the calculation and determination of the satellite set Σ2 that satisfies the distance constraint includes:

[0112] Step S321: Calculate the distance C_jl from the satellite to the target based on the satellite position Rs_J2000 and the target position vector Rt_J2000 = |Rs_J2000-Rt_J2000|;

[0113] Step S322: judging whether the distance C_jl satisfies the constraint according to the distance threshold, and storing it if it satisfies the constraint;

[0114] Step S323: traverse and calculate the distances and constraints from all satellites to the target, and determine the satellite set Σ2.

[0115] In this step, the satellite set Σ3 that satisfies the single-satellite field of view constraint is calculated and determined to include:

[0116] Step S331: Calculate the relative position vector rs from the satellite to the target according to the satellite position Rs_J2000 and the target position vector Rt_J2000 = Rs_J2000 - Rt_J2000;

[0117] Step S332: Calculate the target off-axis angle C_lz=-Rs_J2000·rs / |Rs_J2000| / |rs| according to the satellite position Rs_J2000 and the relative position vector rs;

[0118] Step S333: judging whether the target off-axis angle C_lz satisfies the constraint according to the single-satellite ground field of view angle threshold, and storing it if it satisfies the constraint;

[0119] Step S334: traverse and calculate the target off-axis angles and constraints of all satellites to determine the satellite set Σ3.

[0120] Step S4: Solve for the union Σ4 of Σ1, Σ2, and Σ3, combine the satellites in Σ4 in pairs, and calculate the bistatic angle of each combination to the target, and determine the target coverage status flag FL at that moment.

[0121] The step S4 comprises:

[0122] Step S401: Solve the union Σ4 of Σ1, Σ2, and Σ3, and combine the satellites in Σ4 in pairs;

[0123] Step S402: For each combination, calculate the relative position vectors rs1 and rs2 from the satellite to the target, and calculate the bistatic angle C_sjd = rs1·rs2 / |rs1| / |rs2|;

[0124] Step S403: According to the dual base angle threshold, determine whether C_sjd satisfies the constraint. If the constraint is satisfied, the target coverage status flag FL takes 1 and the calculation ends. If not, calculate the C_sjd and satisfaction of the next combination. If neither is satisfied, FL takes 0.

[0125] Step S5: According to a certain time resolution, repeatedly solve the target coverage status flag FL at each moment, and calculate and determine the maximum revisit time, the average revisit time, and the minimum revisit time.

[0126] The step S5 comprises:

[0127] Step S501: sampling at 1 minute intervals, traversing and calculating the target coverage status flag FL at all sampling moments, and determining the target coverage status time series within the simulation time period;

[0128] Step S502: Target coverage status time series, each calculation determines the maximum revisit time, average revisit time, and minimum revisit time.

[0129] The following is a numerical simulation verification of a low-orbit multi-base radar satellite constellation coverage calculation method.

[0130] Reference Figure 2 and Figure 3 As shown in the figure, in the simulation calculation, the orbit altitude is set to 600km, the inclination is 30°, and the eccentricity is 0. The target coverage within 30 degrees north and south latitude is simulated and analyzed, where the target visibility requires that the distance between the two satellites and the target is no more than 3000km, the elevation angle is no less than 7 degrees, and the angle between the two satellites and the target line of sight is greater than 145 degrees. The total number of satellites is 150, and there are 10 orbital planes, with 15 satellites in each.

[0131] According to the above calculation conditions, numerical simulation calculation is carried out, and the results are as follows Figure 4 shown.

[0132] The present invention also provides a low-orbit multi-base radar satellite constellation coverage calculation system, which can be implemented by executing the process steps of the low-orbit multi-base radar satellite constellation coverage calculation method, that is, those skilled in the art can understand the low-orbit multi-base radar satellite constellation coverage calculation method as a preferred implementation of the low-orbit multi-base radar satellite constellation coverage calculation system. The system specifically includes the following contents:

[0133] Module M1: Based on the constellation orbit and configuration parameters, the J2 recursive model is used to calculate the orbital data of all satellites in the J2000 coordinate system.

[0134] The module M1 includes:

[0135] Module M101: Assuming that both the initial configuration and the target configuration are described by Walker constellation parameters, define the right ascension of the ascending node of the Kth satellite in the Jth orbital plane of the initial configuration and the target configuration as Ω (J,K) , latitude argument u (J,K) , then

[0136]

[0137] In the formula, is the right ascension and latitude argument of the ascending node of the first satellite in the first orbital plane, P is the number of orbital planes, T is the total number of satellites, F is the phase factor, and S = T / P is the number of satellites per orbit;

[0138] Module M102: Assuming that the orbital semi-major axis, eccentricity, orbital inclination and perigee argument of all satellites are consistent, the six orbital elements of all satellites can be determined by combining the right ascension and latitude arguments of the ascending node in the previous step.

[0139] Module M103: Taking the number of six tracks as the initial value, the J2 model is used to recursively calculate the number of six tracks within the simulation time period, and then determine the position Rs_J2000 and the speed Vs_J2000.

[0140] Module M2: Calculate the position vector of the target in the J2000 coordinate system based on the latitude, longitude and altitude of the given target.

[0141] The module M2 includes:

[0142] Module M201: Calculate the position vector Rt_wgs84 in the earth fixed coordinate system according to the given longitude, latitude and altitude;

[0143] Module M202: Calculate the transformation matrix M from the WGS84 coordinate system to the J2000 according to the current time;

[0144] Module M203: Calculate and determine the position vector Rt_J2000=M·Rt_wgs84 under J2000 based on the transformation matrix and the position vector under the earth fixed coordinate system.

[0145] Module M3: For each moment, calculate and determine the satellite set Σ1 that satisfies the ground elevation angle constraint, the satellite set Σ2 that satisfies the distance constraint, and the satellite set Σ3 that satisfies the single-star field of view constraint;

[0146] In the module M3, the satellite set Σ1 that satisfies the ground elevation angle constraint is calculated and determined to include:

[0147] Module M311: Calculate the ground elevation angle C_yj=Rs_J2000·Rt_J2000 / |Rs_J2000| / |Rt_J2000| according to the satellite position Rs_J2000 and the target position vector Rt_J2000;

[0148] Module M312: According to the ground elevation angle threshold, determine whether the elevation angle C_yj satisfies the constraint, and if so, store it;

[0149] Module M313: traverse and calculate the ground elevation angles and constraints of all satellites to determine the satellite set Σ1.

[0150] In this module, the satellite set Σ2 that satisfies the distance constraint is calculated and determined to include

[0151] Module M321: Calculate the distance C_jl from the satellite to the target based on the satellite position Rs_J2000 and the target position vector Rt_J2000 = |Rs_J2000-Rt_J2000|;

[0152] Module M322: judging whether the elevation angle C_jl satisfies the constraint according to the distance threshold, and storing it if it satisfies the constraint;

[0153] Module M323: Traverse and calculate the distances and constraints from all satellites to the target, and determine the satellite set Σ2.

[0154] In this module, the satellite set Σ3 that satisfies the single-satellite field of view constraint is calculated and determined to include:

[0155] Module M331: Calculate the relative position vector rs from the satellite to the target according to the satellite position Rs_J2000 and the target position vector Rt_J2000 = Rs_J2000 - Rt_J2000;

[0156] Module M332: Calculate the target off-axis angle C_lz=-Rs_J2000·rs / |Rs_J2000| / |rs| according to the satellite position Rs_J2000 and the relative position vector rs;

[0157] Module M333: According to the single-satellite ground field of view angle threshold, determine whether the target off-axis angle C_lz meets the constraint. If it meets the constraint, store it;

[0158] Module M334: traverse and calculate the target off-axis angles and constraints of all satellites to determine the satellite set Σ3.

[0159] Module M4: solve the union Σ4 of Σ1, Σ2, and Σ3, combine the satellites in Σ4 in pairs, and calculate the dual-base angle of each combination to the target, and determine the target coverage status flag FL at that moment.

[0160] The M4 module includes:

[0161] Module M401: Solve the union Σ4 of Σ1, Σ2, and Σ3, and combine the satellites in Σ4 in pairs;

[0162] Module M402: For each combination, calculate the relative position vectors rs1 and rs2 from the satellite to the target, and calculate the bistatic angle C_sjd = rs1·rs2 / |rs1| / |rs2|;

[0163] Module M403: According to the dual base angle threshold, determine whether C_sjd satisfies the constraint. If the constraint is satisfied, the target coverage status flag FL takes 1 and the calculation ends. If not, calculate the C_sjd and satisfaction of the next combination. If neither is satisfied, FL takes 0.

[0164] Module M5: According to a certain time resolution, repeatedly solve the target coverage status flag FL at each moment, and calculate and determine the maximum revisit time, average revisit time, and minimum revisit time.

[0165] The M5 module includes:

[0166] Module M501: Sampling at 1 minute, traversing and calculating the target coverage status flag FL at all sampling moments, and determining the target coverage status time series within the simulation time period;

[0167] Module M502: Target coverage status time series, each calculation determines the maximum revisit time, average revisit time, and minimum revisit time.

[0168] The embodiment of the present invention provides a low-orbit multi-base radar satellite constellation coverage calculation method and system, which can fully consider the dual-base angle constraints, elevation angle constraints, single-satellite field of view constraints and distance constraints according to mission requirements, and quickly calculate the revisit time of the entire constellation to the specified target, which is an effective optimization method for constellation orbit and configuration optimization.

[0169] Those skilled in the art know that, in addition to realizing the system and its various devices, modules, and units provided by the present invention in a purely computer-readable program code, it is entirely possible to realize the same functions in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers by logically programming the method steps. Therefore, the system and its various devices, modules, and units provided by the present invention can be considered as a hardware component, and the devices, modules, and units included therein for realizing various functions can also be regarded as structures within the hardware component; the devices, modules, and units for realizing various functions can also be regarded as both software modules for realizing the method and structures within the hardware component.

[0170] The above describes the specific embodiments of the present invention. It should be understood that the present invention is not limited to the above specific embodiments, and those skilled in the art can make various changes or modifications within the scope of the claims, which does not affect the essence of the present invention. In the absence of conflict, the embodiments of the present application and the features in the embodiments can be combined with each other arbitrarily.

Claims

1. A method for calculating coverage of a low-orbit multi-base radar satellite constellation, characterized in that: include: Step S1: According to the constellation orbit and configuration parameters, the orbit data of all satellites in the J2000 coordinate system are calculated using the J2 recursive model; Step S2: Calculate the position vector of the target in the J2000 coordinate system according to the latitude, longitude and altitude of the given target; Step S3: at each moment, calculate and determine the satellite set Σ1 that satisfies the ground elevation angle constraint, determine the satellite set Σ2 that satisfies the distance constraint, and determine the satellite set Σ3 that satisfies the single-star field of view constraint; Step S4: Solve the union Σ4 of Σ1, Σ2, and Σ3, combine the satellites in Σ4 in pairs, and calculate the bistatic angle of each combination to the target, and determine the target coverage state flag FL at that moment; Step S5: According to a certain time resolution, repeatedly solve the target coverage status flag FL at each moment, and calculate and determine the maximum revisit time, the average revisit time, and the minimum revisit time.

2. The low-orbit multi-base radar satellite constellation coverage calculation method according to claim 1 is characterized in that: The step S1 comprises: Step S101: Assume that both the initial configuration and the target configuration are described by Walker constellation parameters, and define the right ascension of the ascending node of the Kth satellite in the Jth orbital plane of the initial configuration and the target configuration as Ω (J,K) , latitude argument u (J,K) , then In the formula, is the right ascension and latitude argument of the ascending node of the first satellite in the first orbital plane, P is the number of orbital planes, T is the total number of satellites, F is the phase factor, and S = T / P is the number of satellites per orbit; Step S102: Assuming that the orbital semi-major axis, eccentricity, orbital inclination and perigee argument of all satellites are consistent, the six orbital numbers of all satellites are determined by combining the right ascension and latitude arguments of the ascending node in the previous step; Step S103: Taking the number of six tracks as the initial value, the J2 model is used to recursively calculate the number of six tracks in the simulation time period, and then determine the position Rs_J2000 and the speed Vs_J2000.

3. The low-orbit multi-base radar satellite constellation coverage calculation method according to claim 1 is characterized in that: The step S2 comprises: Step S201: Calculate the position vector Rt_wgs84 in the earth fixed coordinate system according to the given longitude, latitude and altitude; Step S202: Calculate the transformation matrix M from the WGS84 coordinate system to J2000 according to the current time; Step S203: Calculate and determine the position vector Rt_J2000=M·Rt_wgs84 under J2000 according to the transformation matrix and the position vector under the earth fixed coordinate system.

4. The method for calculating coverage of a low-orbit multi-base radar satellite constellation according to claim 1, characterized in that: In step S3, calculating and determining the satellite set Σ1 that satisfies the ground elevation angle constraint includes: Step S311: Calculate the ground elevation angle C_yj=Rs_J2000·Rt_J2000 / |Rs_J2000| / |Rt_J2000| according to the satellite position Rs_J2000 and the target position vector Rt_J2000; Step S312: judging whether the elevation angle C_yj satisfies the constraint according to the ground elevation angle threshold, and storing it if it satisfies the constraint; Step S313: traverse and calculate the ground elevation angles and constraints of all satellites to determine the satellite set Σ1.

5. The low-orbit multi-base radar satellite constellation coverage calculation method according to claim 1, characterized in that: In step S3, calculating and determining the satellite set Σ2 that satisfies the distance constraint includes: Step S321: Calculate the distance C_jl from the satellite to the target based on the satellite position Rs_J2000 and the target position vector Rt_J2000 = |Rs_J2000-Rt_J2000|; Step S322: judging whether the elevation angle C_jl satisfies the constraint according to the distance threshold, and storing it if it satisfies the constraint; Step S323: traverse and calculate the distances and constraints from all satellites to the target, and determine the satellite set Σ2.

6. The method for calculating coverage of a low-orbit multi-base radar satellite constellation according to claim 1, characterized in that: In step S3, calculating and determining the satellite set Σ3 that satisfies the single-satellite field of view constraint includes: Step S331: Calculate the relative position vector rs from the satellite to the target according to the satellite position Rs_J2000 and the target position vector Rt_J2000 = Rs_J2000 - Rt_J2000; Step S332: Calculate the target off-axis angle C_lz=-Rs_J2000·rs / |Rs_J2000| / |rs| according to the satellite position Rs_J2000 and the relative position vector rs; Step S333: judging whether the target off-axis angle C_lz satisfies the constraint according to the single-satellite ground field of view angle threshold, and storing it if it satisfies the constraint; Step S334: traverse and calculate the target off-axis angles and constraints of all satellites to determine the satellite set Σ3.

7. The method for calculating coverage of a low-orbit multi-base radar satellite constellation according to claim 1, characterized in that: The step S4 comprises: Step S401: Solve the union Σ4 of Σ1, Σ2, and Σ3, and combine the satellites in Σ4 in pairs; Step S402: For each combination, calculate the relative position vectors rs1 and rs2 from the satellite to the target, and calculate the bistatic angle C_sjd = rs1·rs2 / |rs1| / |rs2|; Step S403: According to the dual base angle threshold, determine whether C_sjd satisfies the constraint. If the constraint is satisfied, the target coverage status flag FL takes 1 and the calculation ends. If not, calculate the C_sjd and satisfaction of the next combination. If neither is satisfied, FL takes 0.

8. The method for calculating coverage of a low-orbit multi-base radar satellite constellation according to claim 1, characterized in that: The step S5 comprises: Step S501: sampling according to the time period, traversing and calculating the target coverage state flag FL at all sampling moments, and determining the target coverage state time series within the simulation time period; Step S502: Target coverage status time series, each calculation determines the maximum revisit time, average revisit time, and minimum revisit time.

9. A low-orbit multi-base radar satellite constellation coverage calculation system, characterized in that: include: Module M1: Based on the constellation orbit and configuration parameters, the J2 recursive model is used to calculate the orbital data of all satellites in the J2000 coordinate system; Module M2: Calculate the position vector of the target in the J2000 coordinate system according to the latitude, longitude and altitude of the given target; Module M3: For each moment, calculate and determine the satellite set Σ1 that satisfies the ground elevation angle constraint, the satellite set Σ2 that satisfies the distance constraint, and the satellite set Σ3 that satisfies the single-star field of view constraint; Module M4: solve the union Σ4 of Σ1, Σ2, and Σ3, combine the satellites in Σ4 in pairs, and calculate the bistatic angle of each combination to the target, and determine the target coverage status flag FL at that moment; Module M5: According to a certain time resolution, repeatedly solve the target coverage status flag FL at each moment, and calculate and determine the maximum revisit time, average revisit time, and minimum revisit time.

10. The low-orbit multi-base radar satellite constellation coverage calculation system according to claim 9, characterized in that: The module M1 comprises: Module M101: Assume that both the initial configuration and the target configuration are described by Walker constellation parameters, and define the right ascension of the ascending node of the Kth satellite in the Jth orbital plane of the initial configuration and the target configuration as Ω (J,K) , latitude argument u (J,K) , then In the formula, is the right ascension and latitude argument of the ascending node of the first satellite in the first orbital plane, P is the number of orbital planes, T is the total number of satellites, F is the phase factor, and S = T / P is the number of satellites per orbit; Module M102: Assuming that the orbital semi-major axis, eccentricity, orbital inclination and perigee argument of all satellites are consistent, combine the right ascension and latitude argument of the ascending node in the previous module to determine the six orbital elements of all satellites; Module M103: Taking the number of six tracks as the initial value, the J2 model is used to recursively calculate the number of six tracks in the simulation time period, and then determine the position Rs_J2000 and the speed Vs_J2000; The module M2 comprises: Module M201: Calculate the position vector Rt_wgs84 in the earth fixed coordinate system according to the given longitude, latitude and altitude; Module M202: Calculate the transformation matrix M from the WGS84 coordinate system to the J2000 according to the current time; Module M203: Calculate and determine the position vector Rt_J2000=M·Rt_wgs84 under J2000 according to the transformation matrix and the position vector under the earth fixed coordinate system; In the module M3, calculating and determining the satellite set Σ1 that satisfies the ground elevation angle constraint includes: Module M311: Calculate the ground elevation angle C_yj=Rs_J2000·Rt_J2000 / |Rs_J2000| / |Rt_J2000| according to the satellite position Rs_J2000 and the target position vector Rt_J2000; Module M312: judging whether the elevation angle C_yj satisfies the constraint according to the ground elevation angle threshold, and storing it if it satisfies the constraint; Module M313: traverse and calculate the ground elevation angles and constraints of all satellites to determine the satellite set Σ1; In the module M3, calculating and determining the satellite set Σ2 that satisfies the distance constraint includes: Module M321: Calculate the distance C_jl from the satellite to the target based on the satellite position Rs_J2000 and the target position vector Rt_J2000 = |Rs_J2000-Rt_J2000|; Module M322: judging whether the elevation angle C_jl satisfies the constraint according to the distance threshold, and storing it if it satisfies the constraint; Module M323: traverse and calculate the distances and constraints from all satellites to the target, and determine the satellite set Σ2; In the module M3, the calculation and determination of the satellite set Σ3 satisfying the single-satellite field of view constraint includes: Module M331: Calculate the relative position vector rs from the satellite to the target according to the satellite position Rs_J2000 and the target position vector Rt_J2000 = Rs_J2000 - Rt_J2000; Module M332: Calculate the target off-axis angle C_lz=-Rs_J2000·rs / |Rs_J2000| / |rs| according to the satellite position Rs_J2000 and the relative position vector rs; Module M333: According to the single-satellite ground field of view angle threshold, determine whether the target off-axis angle C_lz meets the constraint. If it meets the constraint, store it; Module M334: traverse and calculate the target off-axis angles and constraints of all satellites to determine the satellite set Σ3; The module M4 comprises: Module M401: Solve the union Σ4 of Σ1, Σ2, and Σ3, and combine the satellites in Σ4 in pairs; Module M402: For each combination, calculate the relative position vectors rs1 and rs2 from the satellite to the target, and calculate the bistatic angle C_sjd = rs1·rs2 / |rs1| / |rs2|; Module M403: According to the dual-base angle threshold, determine whether C_sjd satisfies the constraint. If the constraint is satisfied, the target coverage status flag FL takes 1 and the calculation ends. If not, calculate the C_sjd and satisfaction of the next combination. If neither is satisfied, FL takes 0. The module M5 comprises: Module M501: Sampling according to the time period, traversing and calculating the target coverage state flag FL at all sampling moments, and determining the target coverage state time series within the simulation time period; Module M502: Target coverage status time series, each calculation determines the maximum revisit time, average revisit time, and minimum revisit time.

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