Integrated design approach for the configuration, deployment, and maintenance of heterogeneous constellations for ground coverage

Abstract

This invention discloses an integrated design method for the configuration, deployment, and maintenance of heterogeneous constellations for Earth coverage. The method includes: conducting mission and resource analysis to determine direct constraints, calculating indirect constraints, and constructing a candidate satellite pool; employing a genetic algorithm, with the optimization objective of minimizing the total constellation cost, and combining direct and indirect constraints, to solve for the optimal number of sub-constellations and their configuration parameters hierarchically and stepwise, obtaining the optimal number of sub-constellations and their configuration parameters; configuration parameters include inclination angle, semi-major axis, number of orbital planes, right ascension set of ascending nodes, number of satellites per orbit, and satellite selection; for each sub-constellation, determining the deployment scheme for each orbital plane; and for each sub-constellation, determining the maintenance scheme for each orbital plane. This invention's method encompasses configuration design, deployment scheme design, and maintenance scheme design, realizing the full-process design and comprehensive performance optimization of heterogeneous constellations for Earth coverage.

Description

Technical Field

[0001] This invention relates to a design method for heterogeneous constellations, and more particularly to an integrated design method for the configuration, deployment, and maintenance of heterogeneous constellations covering the Earth. Background Technology

[0002] Heterogeneous constellations employ a network of satellites with different functions, orbital types, and payloads, achieving a multiplier effect in functionality and efficiency through inter-satellite, inter-group, and inter-subconstellation collaboration. Compared to traditional homogeneous constellations, the differences in the windward surface-to-mass ratio and sensor coverage range of individual satellites in heterogeneous constellations are the main factors influencing constellation configuration design and control schemes. The core capabilities of heterogeneous constellations for Earth coverage depend on Earth coverage efficiency, constellation stability, and overall constellation cost control. Regarding Earth coverage efficiency, the different coverage ranges of heterogeneous satellites render the traditional approaches of uniformity, homogenization, and linear superposition in constellation coverage analysis and configuration design ineffective. In terms of stability, the drift characteristics caused by differences in orbital type and surface-to-mass ratio among heterogeneous satellites lead to drift in inter-satellite configuration, coverage characteristics, and coverage indicators. Traditional design and control methods for homogeneous constellations would increase the number of satellites and control costs. Therefore, in terms of overall cost, it is necessary to seek a constellation with the lowest overall cost while meeting coverage indicators, relatively low control costs, and achievable fuel consumption expectations.

[0003] In multifunctional heterogeneous constellation and hybrid constellation architectures, configuration optimization methods based on intelligent optimization algorithms are often employed. For example, patent 202410995614 addresses the constellation configuration determination problem for mega-constellations in low Earth orbit (LEO), defining boundary constraints for continuous dual coverage, constructing and solving the constellation configuration objective function to minimize the number of LEO satellites required while achieving continuous dual Earth coverage. However, existing configuration optimization methods do not consider the constellation design problem under the simultaneous influence of heterogeneous payloads and heterogeneous mass ratios, and have not yet overcome the optimization bottleneck of coverage performance and overall cost under nonlinear superposition of coverage capabilities, drift trajectory differences, and complex constraints in heterogeneous constellations. For instance, patent 202410105592 provides a method and system for optimizing the design of LEO heterogeneous satellite constellations. Based on the Walker-δ configuration, it establishes a multi-objective optimization model for constellation design with observation performance indicators and long-term operation and control cost indicators, and uses an improved non-dominated genetic algorithm to solve for the optimal strategy. Although observation indicators and operation and control costs are considered, the operation and control costs only refer to the right ascension drift relative to the ascending node, the constellation orbital altitude, and the total duration of inter-satellite link connectivity. The differences in control schemes caused by the drift of heterogeneous satellites and the differences in burn-out are not taken into account. Using the six orbital elements as optimization variables will also lead to excessive computational load, which is not conducive to the large-scale application of constellations.

[0004] Regarding heterogeneous constellation control, patent 202310708655.3 proposes a constellation relative configuration maintenance strategy based on a baseline configuration, aiming to reduce the number of satellite maintenance operations. Patents 202111386240.6 and 202111386227.0 propose specific procedures for the deployment and maintenance of heterogeneous constellations, aiming to improve control accuracy and frequency, and can be used as methods for implementing the control process. However, these methods cannot optimize the overall performance of the constellation, nor do they achieve integrated design across the entire process.

[0005] Furthermore, existing methods decouple configuration design from control schemes, but in reality, configuration design variables are deeply coupled with track control and there are complex inconsistencies. Existing methods lead to the isolation of each link and fail to achieve optimal global efficiency, thus restricting the efficiency of resource coordination and overall process planning. Summary of the Invention

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

[0007] Step 1: Through task and resource analysis, determine the direct constraints, calculate the indirect constraints, and construct a pool of candidate satellites.

[0008] In step 1, the direct constraints include one or more combinations of the following constraints:

[0009] a) Target deployment duration, target maintenance duration, target maintenance cycle, and target design life;

[0010] b) The highest and lowest target latitudes;

[0011] c) Ideal revisit time;

[0012] d) Highest optical image resolution;

[0013] e) Multiple alternative satellites and their total manufacturing cost, total mass, windward surface-to-mass ratio, total fuel, payload focal length to probe size ratio, and payload coverage half-angle;

[0014] In step 1, the indirect constraints include one or more combinations of the following constraints:

[0015] a) Semi-major axis constraint interval;

[0016] b) Inclination constraint range: the maximum inclination value corresponds to the highest target latitude, and the minimum inclination value corresponds to the lowest target latitude.

[0017] The pool of candidate satellites includes the total manufacturing cost, total fuel, total mass, payload focal length to probe size ratio, payload coverage half-angle, semi-major axis attenuation parameter set, and fuel requirement estimate set for satellites with different surface-to-mass ratios; the fuel requirement estimate set includes fuel requirement estimates under different characteristic semi-major axes.

[0018] Step 2: Using a genetic algorithm, with the goal of minimizing the total cost of the constellation, and combining direct and indirect constraints, the number of sub-constellations and the configuration parameters of each sub-constellation are solved hierarchically to obtain the optimal number of sub-constellations and the configuration parameters of each sub-constellation. The configuration parameters include inclination angle, semi-major axis, number of orbital planes, set of right ascension of ascending nodes, number of satellites per orbit, and satellite selection.

[0019] In step 2, each individual mainly consists of the number of sub-constellations, the tilt angle of each sub-constellation, and the semi-major axis of the sub-constellation with the largest tilt angle. The tilt angle of the sub-constellation with the largest tilt angle is set as the highest target latitude. The reciprocal of the fitness value of each individual is the total cost of the constellation.

[0020] In step 2, the hierarchical stepwise solution means: stepwise solving other configuration parameters and the total constellation cost based on the configuration parameter values ​​of the individual, and using the reciprocal of the total constellation cost as the fitness value, with the individual with the higher fitness value being the better individual.

[0021] Specifically, the hierarchical step-by-step solution process is as follows:

[0022] Calculate the semi-major axes of the remaining sub-constellations based on the semi-major axis of the sub-constellation with the largest tilt angle;

[0023] Based on the semi-major axis of the sub-constellation, select all satellites that meet the imaging resolution constraints from the candidate satellite pool to form an optional satellite pool; determine the latitude of the two observation points based on the optional satellite pool of the sub-constellation;

[0024] For each sub-constellation, the number of satellites per orbit and the satellite type are determined through star selection;

[0025] For the sub-constellation with the largest inclination angle, the sub-constellation configuration is designed according to the independent covering method, and the number of orbital planes and the set of right ascension of the ascending nodes of the sub-constellation with the largest inclination angle are obtained;

[0026] For the sub-constellations other than the one with the largest inclination, the sub-constellation configuration is designed in sequence according to the combination coverage method, with the goal of maintaining the ideal revisit time for ground targets at lower latitudes and arbitrary longitudes within the cycle. This results in the number of orbital planes and the set of right ascension of ascending nodes for each sub-constellation.

[0027] The inclination, semi-major axis, number of orbital planes, set of right ascension of ascending nodes, number of satellites per orbit, and satellite selection of each sub-constellation constitute the configuration parameters of the sub-constellation;

[0028] The manufacturing and launch costs are determined based on the configuration parameters of each sub-constellation. The manufacturing and launch costs of all sub-constellations are then tallied to obtain the total cost of the constellation.

[0029] The process of obtaining satellite selection through star selection is specifically as follows:

[0030] First, the total fuel and fuel requirement estimates for each optional satellite are selected from the pool of optional satellites for the sub-constellation;

[0031] Subsequently, optional satellites that do not meet the following criteria are removed, resulting in an updated pool of optional satellites:

[0032] △v j ≤(△v per j / β)

[0033] In the formula, △v j Δv represents the total fuel of the j-th optional satellite. per j β represents the estimated fuel requirement of the j-th optional satellite, and β represents the preset fuel coefficient.

[0034] Finally, from the updated pool of available satellites, select a satellite using either method:

[0035] a) Select the satellite with the lowest total manufacturing cost; when manufacturing costs are the same, select the satellite with the larger total fuel; when both total manufacturing cost and total fuel are the same, select the satellite with the larger ratio of payload focal length to probe size.

[0036] b) Select a combination of multiple satellites to form an orbit based on actual needs or preferences.

[0037] The process of obtaining the number of satellites per orbit through satellite selection is as follows: First, arbitrary longitudes are selected at the latitudes of two observation points to form the first and second ground targets; then, the number of satellites per orbit is obtained based on the revisit time threshold of each sub-constellation for the first and second ground targets; finally, the number of satellites per orbit of the sub-constellation with the largest inclination angle is iteratively corrected using simulation methods until the revisit time of any orbit of the sub-constellation with the largest inclination angle for the first and second ground targets is less than the corresponding revisit time threshold.

[0038] During the iterative correction process, under the conditions of the semi-major axis, inclination, randomly generated right ascension (RAAN) of the ascending node of the sub-constellation with the largest inclination angle, the current number of satellites per orbit, satellite selection, and uniform phase distribution of each satellite, the revisit time of each orbit facing the first and second ground targets in the sub-constellation with the largest inclination angle is obtained through simulation. If both revisit times are less than the corresponding revisit time threshold, the current number of satellites per orbit is used as the corrected number of satellites per orbit, and the correction ends; otherwise, the number of satellites per orbit of the sub-constellation with the largest inclination angle is increased by a preset step size, the satellite selection is re-acquired, and the simulation and comparison process is repeated. Re-acquiring satellite selection refers to selecting new satellites to obtain their corresponding satellite models.

[0039] Step 3: For each sub-constellation, determine the deployment plan for each orbital plane.

[0040] Specifically, the deployment scheme for an orbital plane consists of the deployment schemes for all satellites on that orbital plane. The deployment schemes for all orbital planes within the constellation are identical. The specific deployment scheme for each satellite on an orbital plane is as follows: At the start of deployment, the satellite performs its first orbital maneuver from its entry point, adjusting its semi-major axis to the initial deployment semi-major axis, which is equal to the semi-major axis of the sub-constellation. After the satellite has been freely orbiting the target deployment for a considerable period, the difference between its relative AoL (Aspect-Oriented Least) and the entry point becomes the target AoL. At this point, a second orbital maneuver is performed, adjusting the semi-major axis to the target deployment semi-major axis, thus completing the satellite deployment.

[0041] Specifically, the deployment scheme includes the target AoL of each satellite on the orbital plane, the initial semi-major axis of deployment, and the target deployment semi-major axis.

[0042] In step 3, the deployment scheme of satellites on each orbital plane in the sub-constellation is determined through the following process:

[0043] First, for each satellite in the orbital plane, the total fuel and fuel requirement estimates of the satellites are selected from the pool of candidate satellites, and the ratio of total fuel to fuel requirement estimates is obtained as the fuel adequacy value; based on the number of satellites per orbit of the sub-constellation, the standard AoL for each target deployment location is calculated;

[0044] Subsequently, the satellites are arranged in ascending order of fuel adequacy, and the target deployment locations are arranged in ascending order of standard AoL absolute value. The satellites and target deployment locations are then deployed in sequence one by one.

[0045] Subsequently, the half-major axis attenuation parameters of the satellites within the target deployment duration are selected from the candidate satellite pool, and then the target deployment half-major axis of the satellites is calculated. Based on the target deployment half-major axis, the maximum AoL offset of the satellites within the target maintenance period is calculated.

[0046] Finally, based on the satellite's standard AoL and maximum AoL offset, the target AoL, initial semi-major axis of deployment, and fuel consumption required for deployment orbital maneuvers are calculated using the following formulas:

[0047] u mai q =u1 q +△u max,q / 2

[0048] △v dep q =(n i ·|a i -a dep q |) / 2+[n i ·|(a dep q +k1 d q ·T d 2 +k2 d q T d )-a mai q,0 |] / 2

[0049] a dep q =a i -(2a i u mai q ) / [(7λ'+3n i )T d ]-(k1 d q ·T d 2 ) / 3-(k2 d q ·T d ) / 2

[0050] In the formula, u mai q u1 q , △u max,q Let Δv represent the target AoL, standard AoL, and maximum AoL offsets of satellite q, respectively. dep q a represents the fuel consumption required for the deployment orbital maneuver of satellite q. dep q n represents the initial semi-major axis of satellite q during deployment; i a represents the orbital angular velocity corresponding to the semi-major axis of the sub-constellation to which satellite q belongs. i k1 represents the semi-major axis of the sub-constellation to which satellite q belongs. dq k2 d q Let a represent the second-order semi-major axis attenuation coefficient and the first-order semi-major axis attenuation coefficient of satellite q during the deployment phase, respectively. mai q,0 The initial working semi-major axis represents the first sustaining period of satellite q, || denotes taking the absolute value, u mai q Let AoL represent the target angle of satellite q, λ' represent the long-term rate of change of the mean anomaly angle, and T represent the target angle of satellite q. d Indicates the target deployment time.

[0051] Step 4: For each sub-constellation, determine the maintenance plan for each orbital plane.

[0052] Specifically, the maintenance schemes for each orbital plane are consistent, and all are implemented during each target maintenance period T. mp Maintenance should be carried out at the end.

[0053] Specifically, the maintenance plan for each satellite is as follows: perform orbital maneuvers to adjust the satellite's semi-major axis from the working semi-major axis before maintenance to the working semi-major axis after maintenance, and achieve automatic correction of AoL through the adjustment of the semi-major axis.

[0054] Specifically, the maintenance scheme includes the working semi-major axis of each satellite after maintenance.

[0055] In step 4, the maintenance scheme for satellites on each orbital plane in the sub-constellation is determined through the following process:

[0056] 4.1 For each satellite, based on the satellite's current remaining available fuel and the current number of sustaining operations, obtain the expected fuel consumption value for the current sustaining operation;

[0057] 4.2 For each satellite, based on the current expected burnup and the working semi-major axis and angular velocity before the current maintenance, combined with the imaging resolution constraint, determine the working semi-major axis range after the current maintenance, and then obtain the nominal semi-major axis range based on the working semi-major axis range after the current maintenance and the semi-major axis attenuation parameters of the satellite during the target deployment period.

[0058] 4.3. Determine a common nominal semi-major axis based on the nominal semi-major axis range of all satellites on the orbital plane, and then combine the semi-major axis attenuation parameters of each satellite during the target deployment period to obtain the current working semi-major axis after maintenance.

[0059] 4.4 For each satellite, calculate the sustainment burnup during the current sustainment period and update the current remaining available fuel, then return to step 4.1;

[0060] 4.5 Repeat steps 4.1 to 4.4 until the target number of maintenance cycles is reached.

[0061] Furthermore, step 4 also includes step 4.6:

[0062] 4.6.1 Perform a full-process simulation of the complete heterogeneous constellation, including all orbits, and check whether the direct constraints within the maintenance duration are met. If they are met, the full-process design of the constellation is completed. If the mission phase and duration are not met, proceed to step 4.6.2. If the revisit time constraint is not met, proceed to step 4.6.3.

[0063] 4.6.2. Identify satellites with insufficient fuel, and reselect satellites for the sub-constellation to obtain the number of satellites per orbit and satellite type for the sub-constellation. Return to step 4.6.1.

[0064] 4.6.3. Locate the location of the coverage hole. If the coverage hole appears on adjacent satellites in the same orbital plane, increase the number of satellites per orbit of the orbital plane and complete the satellite selection. If the coverage hole appears on adjacent orbital planes, increase the number of orbital planes in the sub-constellation of the orbital plane, and re-select satellites and redesign the sub-constellation configuration. Update the number of orbital planes in the sub-constellation of the orbital plane and return to step 4.6.1.

[0065] 4.6.4 Execute steps 4.6.1 to 4.6.3 until all direct constraints are met, update the constellation's configuration design, deployment plan, and maintenance plan, calculate the total cost of the constellation, and the entire constellation design process is complete.

[0066] The beneficial effects of this invention are:

[0067] 1. The method of the present invention includes configuration design, deployment scheme design and maintenance scheme design, realizing the whole process design and comprehensive performance optimization of heterogeneous constellations for ground coverage.

[0068] 2. The method of this invention realizes the integrated design of the entire process of a circular Earth-covering heterogeneous constellation in low and medium orbits, and achieves comprehensive performance optimization based on manufacturing costs, control costs and complex constraints, avoiding the waste of resources and repeated manual iterations caused by the decoupling of traditional configuration design and control scheme design. Attached Figure Description

[0069] Figure 1 This is a schematic flowchart of the method of the present invention;

[0070] Figure 2 This is a flowchart illustrating step 1 of the method of the present invention;

[0071] Figure 3 This is a flowchart illustrating step 2 of the method of the present invention;

[0072] Figure 4 This is a flowchart illustrating step 3 of the method of the present invention;

[0073] Figure 5 This is a flowchart illustrating step 4 of the method of the present invention;

[0074] Figure 6 A schematic diagram of multi-tilt sub-constellation collaborative coverage;

[0075] Figure 7 This is a schematic diagram of the relative change trajectory of the satellite's semi-major axis - AoL;

[0076] Figure 8 This is a schematic diagram showing the trajectory of the satellite's nadir and the coverage of ground stations. Detailed Implementation

[0077] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0078] This invention provides an integrated design method for the configuration, deployment, and maintenance of heterogeneous constellations for ground coverage.

[0079] The method of the present invention specifically includes the following steps:

[0080] Step 1: Through task and resource analysis, determine the direct constraints, calculate the indirect constraints, and construct a pool of candidate satellites.

[0081] Specifically, direct constraints include one or more combinations of the following constraints:

[0082] a) Target deployment duration, target maintenance duration, target maintenance cycle, and target design life, where the target design life is the sum of the target deployment duration and the target maintenance duration;

[0083] b) The highest and lowest target latitudes;

[0084] c) Ideal revisit time for the observed target by heterogeneous Earth-covering constellations;

[0085] d) Minimum optical image resolution;

[0086] e) Multiple alternative satellites and their respective total manufacturing cost, total mass, windward surface-to-mass ratio, total fuel, payload focal length to detector size ratio, and payload coverage half-angle;

[0087] In step 1, the indirect constraints include one or more combinations of the following constraints:

[0088] a) Semi-major axis constraint interval a min ≤a≤a max ;

[0089] The maximum value of the semi-major axis, a, is set according to the following formula based on the lowest optical image resolution. max :

[0090] a max =δ·(f / p max )+R e

[0091] In the formula, a max The semi-major axis represents the maximum value, δ represents the minimum optical image resolution, f / p max R represents the maximum value of the ratio of the load focal length to the element size. e This represents the Earth's radius.

[0092] Minimum value of semi-major axis a min Typically greater than 300km;

[0093] b) Inclination constraint range: the maximum inclination value corresponds to the highest target latitude, and the minimum inclination value corresponds to the lowest target latitude.

[0094] Specifically, the candidate satellite pool includes the total manufacturing cost, total fuel, total mass, payload focal length to detector size ratio, payload coverage half-angle, semi-major axis attenuation parameter set, and fuel requirement estimate set for satellites with different areal-to-mass ratios. The fuel requirement estimate set includes fuel requirement estimates under different characteristic semi-major axes. The semi-major axis attenuation parameter set includes: semi-major axis attenuation parameters during the target deployment duration and semi-major axis attenuation parameters during the target maintenance period under different characteristic semi-major axes; the semi-major axis attenuation parameters include second-order and first-order semi-major axis attenuation coefficients.

[0095] Step 2, Heterogeneous constellation configuration design: Using a genetic algorithm, with the goal of minimizing the total cost of the constellation, and combining direct and indirect constraints, the number of sub-constellations and the configuration parameters of each sub-constellation are solved hierarchically to obtain the optimal number of sub-constellations and the configuration parameters of each sub-constellation. The configuration parameters include inclination angle, semi-major axis, number of orbital planes, set of right ascension of ascending nodes, number of satellites per orbit, and satellite selection.

[0096] Specifically, each individual is mainly composed of the number of sub-constellations, the tilt angle of each sub-constellation, and the semi-major axis of the sub-constellation with the largest tilt angle. The tilt angle of the sub-constellation with the largest tilt angle is set as the highest target latitude. The fitness value of each individual is the reciprocal of the total cost of the constellation, and individuals with higher fitness values ​​are considered better individuals.

[0097] Furthermore, the initial solution generation process is as follows: The number of sub-constellations is randomly generated from a range of positive integers. When the number of sub-constellations in an individual is one, the inclination angle of the sub-constellation is set to the highest target latitude; when the number of sub-constellations in an individual is greater than one, the inclination angle of the sub-constellation with the largest inclination angle is set to the highest target latitude, and the inclination angles of the remaining sub-constellations are randomly generated from the inclination angle constraint interval. The semi-major axis of the sub-constellation with the largest inclination angle is randomly generated from the semi-major axis constraint interval.

[0098] Furthermore, in each iteration, after generating a new population, it is determined whether each individual in the population satisfies the constraints. If all individuals in the population satisfy the constraints, the fitness value of each individual is calculated; otherwise, the population is updated again.

[0099] Specifically, the process of determining whether an individual meets the constraints is as follows: when the number of sub-constellations in an individual is greater than one, determine whether the sub-constellations meet the semi-major axis constraint interval and imaging resolution constraints.

[0100] The process of determining whether a sub-constellation satisfies the semi-major axis constraint range and imaging resolution constraint is as follows:

[0101] The rate of change of RAAN is calculated based on the semi-major axis of the sub-constellation with the largest tilt angle;

[0102] Calculate the semi-major axis of each of the remaining sub-constellations based on the RAAN change rate of the sub-constellation with the largest tilt angle;

[0103] Under the semi-major axis of each sub-constellation, determine whether there is a selectable payload focal length to detector size ratio in the satellite pool such that the imaging resolution value of the sub-constellation is less than or equal to the minimum optical image resolution.

[0104] If the semi-major axis of all sub-constellations in an individual falls within the semi-major axis constraint range, and the ratio of available payload focal length to detector size in the candidate satellite inventory makes the imaging resolution of all sub-constellations less than or equal to the minimum optical image resolution, then the individual is deemed to meet the constraint conditions; otherwise, the individual is deemed not to meet the constraint conditions.

[0105] Specifically, hierarchical stepwise solution means: solving other configuration parameters and the total constellation cost stepwise based on the configuration parameter values ​​of an individual, and using the reciprocal of the total constellation cost as the fitness value.

[0106] Specifically, the step-by-step solution process is as follows:

[0107] Calculate the semi-major axes of the remaining sub-constellations based on the semi-major axis of the sub-constellation with the largest tilt angle;

[0108] For each subconstellation, based on the semi-major axis of the subconstellation, select all satellites that meet the imaging resolution constraints from the candidate satellite pool to form an optional satellite pool;

[0109] The latitudes of the two observation points are determined based on the optional satellite library of the sub-constellation;

[0110] For each sub-constellation, the number of satellites per orbit and the satellite type are determined through star selection;

[0111] For the sub-constellation with the largest inclination angle, the sub-constellation configuration is designed according to the independent covering method, and the number of orbital planes and the set of right ascension of the ascending nodes of the sub-constellation with the largest inclination angle are obtained;

[0112] For the sub-constellations other than the one with the largest inclination, the sub-constellation configuration is designed in sequence according to the combination coverage method, with the goal of maintaining the ideal revisit time for ground targets at lower latitudes and arbitrary longitudes within the cycle. This results in the number of orbital planes and the set of right ascension of ascending nodes for each sub-constellation.

[0113] The inclination, semi-major axis, number of orbital planes, set of right ascension of ascending nodes, number of satellites per orbit, and satellite selection of each sub-constellation constitute the configuration parameters of the sub-constellation; among which, the set of right ascension of ascending nodes of a sub-constellation is composed of the right ascension of ascending nodes of all orbital planes of the sub-constellation;

[0114] The manufacturing and launch costs are determined based on the configuration parameters of each sub-constellation. The manufacturing and launch costs of all sub-constellations are then tallied to obtain the total cost of the constellation.

[0115] Specifically, the process of determining the latitude of two observation points based on the subconstellation's optional satellite library is as follows: The equivalent coverage geocentric angle is calculated based on the average coverage half-angle of all satellites in the subconstellation's optional satellite library; the latitude of the two observation points is then determined based on this equivalent coverage geocentric angle.

[0116] When the number of sub-constellations I>1, for the sub-constellation with the largest tilt angle (a1, inc1), the latitude of the observation point is φ. H and inc2+θ2; for the sub-constellation with the smallest tilt angle (a I ,inc I The latitude of the observation point is inc. I +θ I and φ L Other sub-constellations (a i ,inc i The latitude of the observation point is inc i +θ i and inc i+1 +θ i+1 ;

[0117] When I=1, there is only one constellation (a1, inc1), and the latitude of the observation point is φ. H and φ L .

[0118] Specifically, the process of selecting satellites through star selection is as follows:

[0119] First, the total fuel and fuel requirement estimates for each optional satellite are selected from the pool of optional satellites for the sub-constellation;

[0120] Subsequently, optional satellites that do not meet the following criteria are removed from the optional satellite pool of the subconstellation, resulting in an updated optional satellite pool:

[0121] △v j ≤(△v per j / β)

[0122] In the formula, △v j Δv represents the total fuel of the j-th optional satellite. per j β represents the estimated fuel requirement of the j-th optional satellite, and β represents the preset fuel coefficient.

[0123] Finally, from the updated pool of available satellites, select a satellite using either method:

[0124] a) Select the satellite with the lowest total manufacturing cost; when manufacturing costs are the same, select the satellite with the larger total fuel; when both total manufacturing cost and total fuel are the same, select the satellite with the larger ratio of payload focal length to probe size.

[0125] b) Select a combination of multiple satellites to form an orbit based on actual needs or preferences.

[0126] Specifically, the process of obtaining the number of satellites per orbit through satellite selection is as follows: First, take arbitrary longitudes at the latitudes of the two observation points to form two ground targets; then, obtain the number of satellites per orbit based on the revisit time threshold of each sub-constellation for the two ground targets; finally, iteratively correct the number of satellites per orbit of the sub-constellation with the largest inclination angle using simulation methods until the revisit time of any orbit of the sub-constellation with the largest inclination angle for the two ground targets is less than its corresponding revisit time threshold.

[0127] Specifically, during the iterative correction process, under the conditions of the semi-major axis, inclination, randomly generated right ascension (RAAN) of the ascending node of the sub-constellation with the largest inclination, the current number of satellites per orbit, satellite selection, and uniform phase distribution of each satellite, the revisit time of each orbit facing the first and second ground targets in the sub-constellation with the largest inclination is obtained through simulation. If both revisit times are less than the corresponding revisit time threshold, the current number of satellites per orbit is taken as the corrected number of satellites per orbit, and the correction ends; otherwise, the number of satellites per orbit of the sub-constellation with the largest inclination is increased according to the preset step size, the satellite selection is obtained again, and the simulation and comparison process is executed again.

[0128] Specifically, re-acquiring satellite selection means selecting new satellites to obtain their corresponding models.

[0129] Specifically, the process of obtaining the manufacturing cost based on the configuration parameters of each sub-constellation is as follows:

[0130] Based on the satellite selection, the manufacturing cost of each satellite is selected from the pool of candidate satellites; based on the manufacturing cost of all satellites, the number of orbital planes of the sub-constellation, and the number of satellites per orbit, the manufacturing cost of the sub-constellation is obtained.

[0131] Specifically, the launch method adopted in this invention is as follows: each sub-constellation adopts a multi-satellite launch method, and planes with different inclination angles must be launched separately. Since planes with the same inclination angle can help with RAAN deployment by utilizing the drift caused by the differential semi-major axis, some planes with the same inclination angle but different RAANs can be launched together. For all satellites on each orbital plane, the minimum RAAN adjustment amount is obtained as the RAAN adjustment capability value of the orbital plane. If the RAAN interval between adjacent orbital planes is less than or equal to the RAAN adjustment capability value of either orbital plane, the two orbital planes are launched together.

[0132] Specifically, the process of obtaining the launch cost based on the configuration parameters of each sub-constellation is as follows:

[0133] First, based on the satellite selection, the total fuel for each satellite is selected from the pool of candidate satellites;

[0134] Next, determine the orbital planes that can be merged for launch, and then obtain the number of launches for the sub-constellation;

[0135] Finally, the launch cost of the sub-constellation is calculated using the following formula:

[0136] Clau i =∑ G g+1 (w1inc i +w2a i +w3Mass+ε g )

[0137] In the formula, Clau i Let ε represent the launch cost of the i-th sub-constellation. g Let G represent the base cost of the g-th launch, G represent the number of launches for the i-th sub-constellation, and a represent the base cost of the g-th launch. i 、inc i Let w1, w2, and w3 represent the semi-major axis and inclination angle of the i-th sub-constellation, respectively, and let Mass represent the total weight of the satellites in the i-th sub-constellation. Let w1, w2, and w3 represent the first, second, and third weight parameters, respectively.

[0138] Specifically, the process of determining the orbital plane suitable for combined launches is as follows: For each satellite, based on its total fuel and the configuration parameters of its subconstellation, the RAAN adjustment amount is obtained using the following formula:

[0139] △Ω i,mi,q =(21n i ·J2·R e 2 ·T d ·cos(inc i )·△a i,mi,q ) / (4ai 3 ), m i ∈[1,M i ],q∈[1,N i ]

[0140] △a i,mi,q =(2△v d_exp i,mi,q ) / n i m i ∈[1,M i ],q∈[1,N i ]

[0141] △v d_exp i,mi,q =(T d / T L )△v i,mi,q

[0142] In the formula, △Ω i,mi,q , △a i,mi,q , △v d_exp i,mi,q , △v i,mi,q Let a represent the RAAN adjustment amount, the semi-major axis adjustment amount used for RAAN adjustment, the estimated deployment fuel, and the total fuel, respectively, for the q-th satellite in the mi-th orbital plane of the i-th sub-constellation; i n i 、inc i M i N i Let J1 represent the semi-major axis, angular velocity, inclination, number of orbital planes, and number of satellites per orbit for the i-th sub-constellation, respectively; let I represent the number of sub-constellations; J2 represent the second-order band harmonic coefficients; and R... e T represents the Earth's radius. d T represents the target deployment duration. L Indicates the target design life;

[0143] Subsequently, the minimum RAAN adjustment amount of the satellite in this orbital plane is obtained as the RAAN adjustment capability value of the orbital plane. If the RAAN interval between any two orbital planes is less than or equal to the RAAN adjustment capability value of either orbital plane, the satellites in the two orbital planes are launched together.

[0144] Step 3: Design of Heterogeneous Constellation Deployment Scheme: For each sub-constellation, determine the deployment scheme for each orbital plane.

[0145] Specifically, the deployment plan for each satellite is as follows:

[0146] At the start of deployment, the satellite performs its first orbital maneuver from its entry point, adjusting its semi-major axis to the initial deployment semi-major axis a. dep qThe semi-major axis of the entry point is equal to the semi-major axis of the sub-constellation;

[0147] Satellite free-operation target deployment time T d After a certain time, the difference between the relative AoL and the orbital insertion point is the target AoL u. mai q At this point, a second orbital maneuver is performed to adjust the semi-major axis to the target deployment semi-major axis a. mai q,0 The satellite deployment is now complete.

[0148] Specifically, the deployment plan includes the target AoL of each satellite on the orbital plane, the initial half-major axis of deployment, and the target deployment half-major axis.

[0149] Specifically, for each subconstellation, the deployment plan for satellites on each orbital plane within the subconstellation is determined through the following process:

[0150] First, for each satellite in the orbital plane, based on the semi-major axis of the sub-constellation and the type of satellite, the total fuel and fuel requirement estimates of the satellites are selected from the pool of candidate satellites, and the ratio of the total fuel to the fuel requirement estimates is obtained as the fuel adequacy value; based on the number of satellites per orbit of the sub-constellation, the standard AoL of each target deployment location is calculated;

[0151] Subsequently, the satellites are arranged in ascending order of fuel adequacy, and the target deployment locations are arranged in ascending order of standard AoL absolute value. The satellites and target deployment locations are then deployed in sequence one by one.

[0152] Subsequently, based on the semi-major axis of the sub-constellation and the type of satellite, the semi-major axis attenuation parameters of the satellite within the target deployment period are selected from the candidate satellite library. Then, the target deployment semi-major axis of the satellite is calculated based on the semi-major axis of the sub-constellation and the semi-major axis attenuation parameters. Based on the target deployment semi-major axis, the maximum AoL offset of the satellite within the target maintenance period is calculated.

[0153] Finally, based on the satellite's standard AoL and maximum AoL offset, the target AoL, initial semi-major axis of deployment, and fuel consumption required for deployment orbital maneuvers are calculated using the following formulas:

[0154] u mai q =u1 q +△u max,q / 2

[0155] △v dep q =(n i ·|a i -a dep q |) / 2+[n i ·|(a depq +k1 d q ·T d 2 +k2 d q T d )-a mai q,0 |] / 2

[0156] a dep q =a i -(2a i u mai q ) / [(7λ'+3n i )T d ]-(k1 d q ·T d 2 ) / 3-(k2 d q ·T d ) / 2

[0157] In the formula, u mai q u1 q , △u max,q Let Δv represent the target AoL, standard AoL, and maximum AoL offsets of satellite q, respectively. dep q a represents the fuel consumption required for the deployment orbital maneuver of satellite q. dep q n represents the initial semi-major axis of satellite q during deployment; i a represents the orbital angular velocity corresponding to the semi-major axis of the sub-constellation to which satellite q belongs. i k1 represents the semi-major axis of the sub-constellation to which satellite q belongs. d q k2 d q Let a represent the second-order semi-major axis attenuation coefficient and the first-order semi-major axis attenuation coefficient of satellite q during the deployment phase, respectively. mai q,0 The initial working semi-major axis of satellite q during its first maintenance period is represented by || (calculated in step 3.2.2 of this embodiment), where || represents taking the absolute value, u mai q Let AoL represent the target angle of satellite q, λ' represent the long-term rate of change of the mean anomaly angle, and T represent the target angle of satellite q. d Indicates the target deployment time.

[0158] Step 4: Design of Heterogeneous Constellation Maintenance Scheme: For each sub-constellation, determine the maintenance scheme for each orbital plane.

[0159] Specifically, the maintenance schemes for each orbital plane are consistent, and all are implemented during each target maintenance period T. mp Maintenance should be carried out at the end.

[0160] Specifically, the maintenance plan for each satellite is as follows: the execution time for satellite q in the h-th maintenance is hT. mp The orbital maneuver will change the semi-major axis of satellite q from the working semi-major axis a before the h-th maintenance. beg q,h Adjusted to the working semi-major axis a after the h-th hold mai q,h Automatic correction of AoL is achieved by adjusting the semi-major axis.

[0161] Specifically, the maintenance scheme includes the working semi-major axis a of satellite q after the h-th maintenance. mai q,h .

[0162] Specifically, for each subconstellation, the maintenance scheme for satellites on each orbital plane within the subconstellation is determined through the following process:

[0163] 4.1 For each satellite, based on the satellite's current remaining available fuel and the current number of sustaining operations, obtain the expected fuel consumption value for the current sustaining operation;

[0164] 4.2 For each satellite, based on the current expected burnup and the working semi-major axis and angular velocity before the current maintenance, combined with the imaging resolution constraint, determine the working semi-major axis range after the current maintenance, and then obtain the nominal semi-major axis range based on the working semi-major axis range after the current maintenance and the semi-major axis attenuation parameters of the satellite during the target deployment period.

[0165] 4.3. Determine a common nominal semi-major axis based on the nominal semi-major axis range of all satellites on the orbital plane, and then combine the semi-major axis attenuation parameters of each satellite during the target deployment period to obtain the current working semi-major axis after maintenance.

[0166] 4.4 For each satellite, calculate the sustainment burnup during the current sustainment period and update the current remaining available fuel, then return to step 4.1;

[0167] 4.5 Repeat steps 4.1 to 4.4 until the target number of maintenances is reached. The target number of maintenances is obtained by rounding down the ratio of the target maintenance duration to the target maintenance cycle.

[0168] Furthermore, step 4 also includes step 4.6:

[0169] 4.6.1. Conduct a full - process simulation on the complete heterogeneous constellation including all orbits, and review whether all direct constraints within the maintenance duration are met; if met, the full - process design of the constellation ends. If the mission phase and duration are not met, proceed to step 4.6.2. If the revisit time constraint is not met, proceed to step 4.6.3;

[0170] 4.6.2. Identify the satellites with insufficient fuel, re - select satellites for the sub - constellation where the satellites are located, obtain the number of satellites per orbit and satellite selection for the sub - constellation where the satellites are located, and return to step 4.6.1;

[0171] 4.6.3. Identify the locations where coverage holes occur. If the coverage holes occur in adjacent satellites within the same orbital plane, increase the number of satellites per orbit of the orbital plane and complete satellite selection; if the coverage holes occur in adjacent orbital planes, increase the number of orbital planes of the sub - constellation where the orbital plane is located, re - conduct satellite selection and sub - constellation configuration design, update the number of orbital planes of the sub - constellation where the orbital plane is located, and return to step 4.6.1;

[0172] 4.6.4. Execute steps 4.6.1 to 4.6.3 until all direct constraints are met, update the configuration design plan, deployment plan, and maintenance plan of the constellation, calculate the total cost of the constellation, and the full - process design of the constellation ends.

[0173] The specific embodiments of the present invention are as follows:

[0174] Embodiment

[0175] This embodiment uses a geometric solution method for the circular orbit non - continuous coverage problem to calculate the range of the right ascension of the ascending node of satellites that meet the satellite - to - ground visibility conditions. The summary and description of this geometric solution method are as follows:

[0176] For a target ground station M(λ, φ) with geocentric longitude and latitude of λ and φ respectively, coverage can be achieved when the sub - satellite point trajectory passes through a circular area centered at M with a radius of θ. When inc - θ < φ < inc + θ, the sub - satellite point trajectory with the inflection point within the coverage circle can achieve coverage, as shown in Figure 8 , where inc is the orbital inclination. In the figure, L2 is the longest trajectory, L1 and L3 are the trajectories tangent to the coverage circle, and the tangent points S A , S D are named boundary points. △L is the range that the right ascension of the ascending node must satisfy when the satellite is visible to the ground station M. Only the satellites within this range have the opportunity to be visible. <00012​​​​​​​​​​-arctan[tan(u SA )·cos(inc)]

[0179] Ω SD =λ+G-△λ MS -arctan[tan(u SD )·cos(inc)]-π

[0180] In the formula, Ω SA S represents A The point corresponds to RAAN and Ω in the orbit. SD S represents D The point corresponds to RAAN in the orbit, λ represents the geocentric longitude of the target ground station M, G represents the Greenwich sidereal hour angle, and Δλ MS This indicates the target ground station M and its southern boundary point S. A or S D The difference in longitude (if they are equal), u SA Represents boundary point S A In the orbit, the corresponding AoL, u SD Represents boundary point S D In the orbit, AoL and inc represent the orbital inclination angle.

[0181] Considering Earth's rotation, the actual RAAN coverage area △L that can be achieved is:

[0182] △L=2(△λ MS -△λ S )+π-(w e T d / 2π)|u SD -u SA |

[0183] In the formula, △λ MS Indicates the target ground station and boundary point S A or S D The difference in longitude (the two are equal), △λ S This indicates the longitude span of a satellite traveling along its orbit from the equator to the boundary point. w e T represents the angular velocity of Earth's rotation. d Indicates the orbital period.

[0184] The calculation methods for each parameter are as follows:

[0185] u SA =arcsin[sinφ S / sin(inc)],u SD =π-u SA

[0186] △λMS =arccos[(cosθ-sinφ S ·sinφ) / (cosφ S ·cosφ ) ]

[0187] △λ S =arcsin[cot(inc)·sinφ S / cosφs]

[0188] sinφ S =sinφ·cosθ-sinθ·cos(inc)

[0189] cosφ S =(1-sin 2 φs) 1 / 2

[0190] In the formula, φ S Represents boundary point S A or S D The latitude (the two are equal).

[0191] This embodiment specifically includes the following steps:

[0192] Step 1: Task and Resource Analysis

[0193] The main function of this step is to clarify the constellation's primary functions, mission requirements, and available resources, and to convert the missions into numerical indicators. This step involves mission and resource analysis to determine direct and indirect constraints, identify satellite orbital attenuation parameters, estimate the constellation's fuel requirements, and establish lookup tables.

[0194] Step 1.1: Determine direct constraints

[0195] Direct constraints include:

[0196] (1) Task Phases and Duration: The task phases include the deployment phase and the maintenance phase. The duration of the deployment phase is determined and denoted as the target deployment duration T. d Determine the duration of the maintenance phase and express it as the target maintenance duration T. m Determine the period of each orbit control operation during the maintenance phase and express it as the target maintenance period T. mp Determine the design life of the constellation and express it as the target design life T. L =T d +T m .

[0197] The actual deployment time t achieved after design d Duration t m Maintenance period t mp and design life tL It should satisfy: t d ≤T d , t m ≥T m , t mp ≥T mp , t L ≥T L .

[0198] It is important to note that during the deployment phase, each satellite uses orbital control to move from its insertion point to its target position. During the maintenance phase, each satellite employs periodic orbital control to maintain the constellation's basic configuration without significant deviation from its nominal configuration; this is the main phase in which the constellation performs its mission.

[0199] (2) Observation target: The observation target is a set of points or regions. The latitude of the highest target is represented by φ. H The lowest target latitude is represented by φ. L .

[0200] (3) Coverage index: Ideal revisit time Δt for constellations to ground targets tar This characterizes the temporal resolution of constellation observations, and the ideal revisit time constraints for each observation target can differ.

[0201] (4) Imaging resolution: Determine the minimum optical image resolution δ, which is used to characterize the spatial resolution of constellation observations.

[0202] (5) Satellite platform and functional payload selection: The satellite platform and functional payload must be selected from the existing products. The two can be freely combined to form a candidate satellite. Record the total manufacturing cost, total mass, windward surface mass ratio, total fuel, payload focal length to probe size ratio, and payload coverage half angle of all candidate satellites.

[0203] (6) Other: Including other constraints specified by the user, such as the allowable design range of the semi-major axis of the constellation [a min a max ]wait.

[0204] 1.2 Calculation of indirect constraints

[0205] Indirect constraints include:

[0206] (1) Semi-major axis

[0207] The semi-major axis should meet the following constraints:

[0208] a min ≤a≤a max

[0209] In the formula, a min Let a represent the minimum value of the semi-major axis, and let a represent the semi-major axis.max This represents the maximum value of the semi-major axis.

[0210] Specifically, to meet the imaging resolution constraint, the maximum value of the semi-major axis is:

[0211] a max =δ·(f / p max )+R e

[0212] In the formula, a max The semi-major axis represents the maximum value, δ represents the minimum optical image resolution, f / p max R represents the maximum ratio of the load focal length to the detector element size among the candidate loads. e R is the Earth's radius. e =6378.139km.

[0213] Specifically, when the semi-major axis of a constellation is too small, atmospheric drag has a significant impact, which is unfavorable for orbital maintenance; the minimum value of the semi-major axis is 'a'. min Usually above 300km.

[0214] (2) Inclination angle

[0215] To ensure that all observation targets can be observed without wasting observation capacity, the tilt angle constraint is as follows:

[0216] φ L ≤inc≤φ H

[0217] In the formula, φ L Indicates the minimum target latitude, inc represents the inclination angle, and φ H Indicates the highest target latitude.

[0218] 1.3 Calculate satellite orbital attenuation parameters

[0219] 1.3.1 Sampling of characteristic semi-major axis

[0220] Within the allowable adjustment range of the constellation's semi-major axis [a] min a max Within [a], several semi-major axis values ​​are selected at equal intervals as the characteristic semi-major axis a. r Suppose we take X characteristic semi-major axes, denoted as a. r,x , x∈[1,X].

[0221] 1.3.2 Simulation of Track Parameter Variation

[0222] The surface-to-mass ratio of the windward side of each satellite in the dummy equipment selection satellite is S / m z , z∈[1,Z], where Z is the total number of candidate satellites.

[0223] Iterate through x∈[1,X], z∈[1,Z] and perform the following operations:

[0224] 1.3.2.1 Simulate the deployment time T using simulation methods. d Inside, located on the characteristic semi-major axis a r,x Above, and the surface-to-mass ratio is S / m z The satellite's trajectory is recorded, along with data on the change in its semi-major axis.

[0225] 1.3.2.2 Simulation method to simulate the maintenance period T mp Inside, located on the characteristic semi-major axis a r,x Above, and the surface-to-mass ratio is S / m z The satellite's trajectory is recorded, along with data on the change in its semi-major axis.

[0226] 1.3.3. Fitting of semi-major axis attenuation

[0227] Iterate through x∈[1,X], z∈[1,Z] and perform the following operations:

[0228] 1.3.3.1. Using a quadratic fitting method, the deployment time T is... d The data for the variation of the semi-major axis within the range are fitted using the following formula:

[0229] a d x,z (t)=a r,x +k1 d x,z ·t 2 +k2 d x,z ·t, t∈[1,T d x∈[1,X], z∈[1,Z]

[0230] In the formula, a d x,z (t) represents the characteristic semi-major axis a r,x The mass ratio above is S / m z The semi-major axis of the satellite at time t, a r,x Indicates the characteristic semi-major axis, k1 d x,z Indicates the characteristic semi-major axis a r,x The mass ratio above is S / m z The second-order semi-major axis attenuation coefficient, k2, of the satellite during the deployment phase. d x,z Indicates the characteristic semi-major axis a r,x The mass ratio above is S / m z The first-order semi-major axis attenuation coefficient of the satellite during the deployment phase, k2 d x,z <k1 d x,z <0.

[0231] 1.3.3.2. Using a quadratic fitting method, the maintenance period T is... mp The data for the variation of the semi-major axis within the range are fitted using the following formula:

[0232] a mp x,z (t)=a r,x +k1 mp x,z ·t 2 +k2 mp x,z ·t, t∈[1,T mp x∈[1,X], z∈[1,Z]

[0233] In the formula, a mp x,z (t) represents the characteristic semi-major axis a r,x The mass ratio above is S / m z The semi-major axis of the satellite at time t, a r,x Indicates the characteristic semi-major axis, k1 mp x,z Indicates the characteristic semi-major axis a r,x The mass ratio above is S / m z The second-order semi-major axis attenuation coefficient of the satellite during its maintenance period, k2 mp x,z Indicates the characteristic semi-major axis a r,x The mass ratio above is S / m z The first-order semi-major axis attenuation coefficient of the satellite during its maintenance period, k2 mp x,z <k1 d x,z <0.

[0234] The reason for using a quadratic fitting method to fit the satellite's semi-major axis decay data is that, under the influence of atmospheric drag, the decay of the semi-major axis of a low-Earth orbit satellite is approximately linear in the short term, but the decay rate increases over a longer period. Quadratic fitting can better simulate the medium- to long-term decay of the semi-major axis. After fitting, the semi-major axis during the mission period can be described by the semi-major axis decay parameters and the initial semi-major axis, avoiding the introduction of empirical or exponential models and facilitating subsequent numerical calculations.

[0235] 1.4. Estimated constellation fuel demand

[0236] The constellation's fuel consumption is related to its maintenance method. The maintenance method used for fuel prediction is: starting from the initial moment, each time the target maintenance period T is reached... mp At that time, the satellite will be raised to its initial orbit. If the total fuel of the satellite is greater than the fuel required by this method, it indicates that the fuel is sufficient.

[0237] Iterate through x∈[1,X], z∈[1,Z], and calculate the estimated fuel demand:

[0238] △v per x,z =[(n x ·|a r,x -a mp x,z |) / 2]·floor(T L / T mp )

[0239] In the formula, △v per x,z n represents the estimated fuel demand. x Indicates the characteristic semi-major axis a r,x The satellite's angular velocity, floor() represents rounding down, a mp x,z Indicates the target maintenance period T mp The semi-major axis of the satellite after time T is obtained from step 1.3.2.2. L T represents the target design life. mp Indicates the target maintenance period.

[0240] 1.5. Create a query table

[0241] Create the alternative satellite library SatLib shown in Table 1 as a lookup table.

[0242]

[0243] The reason for creating a lookup table is that the data in the lookup table is data that the algorithm needs to use frequently in subsequent steps, and pre-calculation can save resources and time in subsequent calculations.

[0244] Step 2: Design heterogeneous constellation configuration

[0245] This invention employs multiple sub-constellations with different tilt angles to achieve coordinated coverage. For ease of understanding, Figure 6 Three examples of sub-constellation combinations with tilt angles inc1, inc2, and inc3 are illustrated, where the target region latitudes, from low to high, are φ4, φ3, φ2, and φ1. In the figures, the black curve represents the nadir point trajectory, and the gray area represents the region swept by the sensor's half-angle. This invention employs both independent and combined coverage methods, as follows:

[0246] (1) Independent coverage mode: refers to the coverage mode in which sub-constellations with different tilt angles independently complete the coverage of their respective areas and meet the coverage indicators. For example, the sub-constellation with tilt angle inc1 is only responsible for the coverage of area one, the sub-constellation with tilt angle inc2 is only responsible for the coverage of area two, and the sub-constellation with tilt angle inc3 is only responsible for the coverage of area three.

[0247] (2) Combined coverage method: refers to the coverage method in which sub-constellations work together to complete the coverage of the target area and meet the coverage index through parameter design and coordination. That is, area 1 is covered by a sub-constellation with an inclination angle of inc1, area 2 is covered by a sub-constellation with an inclination angle of inc2 and a sub-constellation with an inclination angle of inc1, and area 3 is covered by a sub-constellation with an inclination angle of inc1, an inclination angle of inc2 and an inclination angle of inc3.

[0248] Assume a constellation has I sub-constellations, where i∈[1,I] is the sub-constellation index. The constellation configuration design method used in this invention is as follows: minimizing the total cost of the constellation is the optimization objective, with coverage indicators and other constraints as constraints. A genetic algorithm is used to solve for the number of sub-constellations I and the tilt angle inc of each sub-constellation in a hierarchical manner. i i∈[1,I], nominal semi-major axis a i i∈[1,I], number of orbital surfaces M i , i∈[1,I], nominal RAAN value Ω of each orbital i,m , i∈[1,I], m∈[1,M] i [and the star selection scheme for each orbit.]

[0249] Step 2 involves generating a solution, verifying its feasibility, pre-calculating parameters, selecting stars for each orbital plane of the sub-constellation, designing parameters for the sub-constellation with the largest inclination angle according to an independent coverage method, making condition judgments, designing parameters for the sub-constellation with the largest inclination angle based on a combined coverage method, and calculating costs. The fitness value of the current solution is then used in a genetic algorithm for iterative optimization of the solution. Finally, a heterogeneous constellation configuration with the lowest cost that meets coverage criteria, has acceptable control costs, and meets expected fuel consumption is obtained.

[0250] Step 2 is as follows:

[0251] 2.1 Solution Generation

[0252] During the initialization of the optimization algorithm, an initial solution is generated, and subsequent solutions are automatically generated by the genetic algorithm.

[0253] The initial solutions include:

[0254] (1) Number of sub-constellations: Generate one sub-constellation I within the range of positive integers. To accelerate convergence, the value of I should not be too large. It should be noted that the launch cost of the orbital plane is usually much greater than the manufacturing cost of a single star, and planes with different inclinations must be launched separately. Therefore, to reduce the overall cost, the constellation configuration design should minimize the number of planes, especially those with different inclinations.

[0255] (2) Generate the tilt angle: Let the tilt angle inc1 = φ H When I>1, within the tilt angle constraint interval φ L ≤inc≤φ HInternally generate I-1 tilt angle values ​​inc i , i∈[2,I].

[0256] (3) Generate the nominal semi-major axis: in [a min a max The range generates a semi-major axis value a.

[0257] 2.2 Feasibility Verification of the Solution

[0258] 2.2.1 If I=1, proceed to step 2.3; otherwise, proceed to step 2.2.2.

[0259] 2.2.2, Set the inclination angle inc1=φ H Let the nominal semi-major axis of the orbit of the sub-constellation with the largest inclination be named a1. Let a1 = a, and calculate the corresponding RAAN rate of change:

[0260] Ω'=-[(3n1J2R e 2 ) / (2a1 2 )]·cos(inc1)

[0261] In the formula, Ω' represents the RAAN rate of change of the sub-constellation with the largest tilt angle, n1 represents the angular velocity on the orbit with the nominal semi-major axis a1, a1 represents the nominal semi-major axis of the sub-constellation with the largest tilt angle, inc1 represents the tilt angle of the sub-constellation with the largest tilt angle, J2 represents the second-order zonal harmonic coefficient, J2=0.00108263, R e This represents the Earth's radius.

[0262] 2.2.3 For i∈[2,I], calculate the tilt angle inc for each i. i The semi-major axis a corresponding to the orbit i :

[0263] a i =-{[(3n i J2R e 2 ) / (2Ω')]·cos(inc i )} 1 / 2

[0264] Among them, a i Let n represent the semi-major axis of the i-th sub-constellation. i Indicates that the nominal semi-major axis is a i angular velocity on the orbit, inc i Let J2 represent the tilt angle of the i-th sub-constellation, and R represent the second-order band harmonic coefficients. e This represents the Earth's radius.

[0265] 2.2.4 For i∈[2,I], determine the semi-major axis a one by one. iDoes it satisfy the semi-major axis constraint interval: a min ≤a i ≤a max If yes, proceed to step 2.2.5; otherwise, proceed to step 2.1.

[0266] 2.2.5 For i∈[2,I], determine one by one whether it falls on the semi-major axis a. i Does the SatLib library contain any available payloads that allow for satisfactory imaging resolution?

[0267] (a i -R e )·(p / f)≤δ

[0268] In the formula, p / f represents the ratio of the load focal length to the detector element size. If yes, proceed to step 2.3; otherwise, proceed to step 2.1.

[0269] 2.3 Parameter Pre-calculation

[0270] 2.3.1 Sort the I sub-constellations in descending order of their tilt angles, as follows: inc=[φ H inc2, inc3, ..., inc I ] 1×I The corresponding semi-major axis is a = [a1, a2, a3, ..., a...]. I ] 1×I .

[0271] 2.3.2 For i∈[1,I], calculate the sub-constellations (a) one by one. i ,inc i The equivalent coverage angle of the geocentric angle is:

[0272] 2.3.2.1 In the candidate satellite library SatLib, according to the formula in step 2.2.5 (a i -R e If (p / f) ≤ δ, choose a as the semi-major axis. i At that time, payloads and corresponding satellites that meet the imaging resolution constraints form the SatLib library of optional satellites for the current subconstellation. i , i∈[1,I].

[0273] 2.3.2.2 Calculate the optional satellite library SatLib for the current subconstellation i The average coverage half-angle of all satellite payloads is named α. i Solve the following equation to calculate the equivalent geocentric angle θ. i .

[0274] α i =(R e ·sinθ i ) / tanαi +R e ·cosθ i

[0275] 2.3.3 For i∈[1,I], calculate the sub-constellations (a) one by one. i ,inc i The latitude of the observation point:

[0276] When I>1, for the sub-constellation with the largest tilt angle (a1, inc1), the latitude of the observation point is φ. H and inc2+θ2; for the sub-constellation with the smallest tilt angle (a I ,inc I The latitude of the observation point is inc. I +θ I and φ L Other sub-constellations (a i ,inc i The latitude of the observation point is inc i +θ i and inc i+1 +θ i+1 .

[0277] When I=1, there is only one constellation (a1, inc1), and the latitude of the observation point is φ. H and φ L .

[0278] The reason for setting up sub-constellation observation points is that constellations have continuous coverage effectiveness over continuous latitude zones. Therefore, it is only necessary to observe the latitude boundary points of each sub-region, that is, the highest and lowest latitude points, while the coverage effectiveness of other latitudes is between the two.

[0279] 2.4. Selecting stars for each orbital plane of a sub-constellation

[0280] For i∈[1,I], calculate the number of satellites per orbit and the satellite type for each sub-constellation:

[0281] 2.4.1 Satellite Type Selection

[0282] Assuming the satellite library SatLib i There are J types of satellites to choose from. Iterate through j∈[1,J] and perform the following operations:

[0283] 2.4.1.1 In SatLib i In the fuel demand estimate column, select the characteristic semi-major axis value 'a'. r With respect to the nominal semi-major axis a of the current sub-constellation i The closest row records the estimated fuel demand Δv per j In SatLib iIn the middle, the total fuel Δv of satellite j is recorded. j .

[0284] 2.4.1.2, If △v j ≤(△v per j / β), from SatLib i Satellite j is excluded. The value of β is determined by the designer's experience. For example, setting β=2 excludes satellites whose fuel cannot sustain half of their design life.

[0285] The reason for this design is that satellites with more total fuel can have more margin for their own control, thereby reducing the overall fuel pressure on the constellation. When Δv j >△v per j This indicates that the satellite has relatively sufficient fuel. It can use its own fuel to correct its orbital descent and simultaneously adjust its phase angle. And Δv j <△v per While a satellite may not be able to fully correct its orbital drift using its own fuel, it may be able to compensate for the constellation's configuration drift through the orbit control of other satellites with sufficient fuel. However, if a satellite carries too little fuel, meaning it cannot sustain orbit control throughout its lifespan on its own fuel, and it is also difficult to maintain its configuration through coordinated orbit changes with other satellites, then the coverage gaps caused by this satellite are difficult to correct. This could reduce the overall lifespan of the constellation or require the addition of additional satellites. Therefore, such satellites should be excluded.

[0286] 2.4.1.3 In the updated SatLib i In the updated SatLib, the satellite with the lowest total manufacturing cost is selected; when manufacturing costs are the same, the satellite with the larger total fuel consumption is selected; when both total manufacturing cost and total fuel consumption are the same, the satellite with the larger payload focal length / detector size is selected; or, based on actual needs or preferences, the satellite with the largest payload focal length / detector size is selected. i Multiple satellites are selected and combined to form an orbit.

[0287] 2.4.2 Calculation of the number of satellites

[0288] 2.4.2.1. Calculate the latitude (two points) of the observation points for sub-constellation i according to step 2.3.3. Use arbitrary longitudes to form two ground target coordinates, named point1 and point2. Assume the revisit time threshold for point1 and point2 is Δt. tar,1 , △t tar,2 .

[0289] 2.4.2.2 Calculate the number of satellites N per orbit for sub-constellation i. i :

[0290] N i =(2ai 3 / 2 π) / [2a i 3 / 2 θ i +μ 1 / 2 max(△t tar,1 ,△t tar,2 )]

[0291] In the formula, μ represents the Earth's gravitational constant, μ = 398600.44 km 3 / s 2 , △t tar,1 Δt represents the revisit time threshold for point1. tar,2 This represents the revisit time threshold for point2.

[0292] 2.4.2.3 When I=1, proceed to step 2.4.2.4; otherwise, proceed to step 2.5.

[0293] 2.4.2.4 Corrected number of satellites N1: Take any orbital plane P of sub-constellation 1 1,m Its semi-major axis is a1, inclination is inc1, RAAN is any value within [0, 2π], the number of satellites is N1, the satellite selection scheme is determined according to step 2.4.1, and the phases of each satellite are uniformly distributed. The orbital plane P is calculated using simulation methods. 1,m When passing through point 1 and point 2, the orbital plane P 1,m The revisit times Δt1 and Δt2 for all satellites for the two ground targets point1 and point2.

[0294] 2.4.2.5. If △t1≤△t tar,1 And △t2≤△t tar,2 Proceed to step 2.5; otherwise, let N i =N i +1, and execute steps 2.4.1, 2.4.2.4, and 2.4.2.5 in sequence.

[0295] Step 2.4.1 refers to selecting the type of the newly added satellite after the number of satellites is increased by one, i.e., selecting the type of the newly added satellite.

[0296] The reason why sub-constellation 1 needs satellite number correction is that sub-constellation 1 has the largest inclination angle and needs to independently cover the area between point 1 and point 2, so the number of satellites must be sufficient. Other constellations with smaller inclination angles can rely on the large-inclination constellations to assist in covering their respective areas, so the number of satellites can be minimized.

[0297] 2.5 Design of Parameters for Subconstellations with Maximum Tilt Angle Based on Independent Coverage Mode

[0298] The tilt angle of the sub-constellation Con1 with the largest current tilt angle is inc1=φ H The nominal semi-major axis is a1, and the latitude of the observation point is lat1=φ. H lat2=inc2+θ2 (when I>1) or φ L (When I=1). Perform the following steps:

[0299] 2.5.1 The estimated number of orbital surfaces that meet the coverage index at lat1 is:

[0300] M1=ceil[(2π-△L) / (w e △t tar,1 )]

[0301] In the formula, ceil() represents rounding up, and Δt tar,1 For φ H The revisit time constraint is given, where △L is the RAAN range that this orbit can cover, calculated based on the equivalent coverage geocentric angle of this orbital plane. The calculation method is described in the aforementioned geometric solution method.

[0302] 2.5.2 The optimal distribution of the tracks at lat2 is uniform distribution, with M1 track surfaces evenly arranged within the range [0, 2π]. Let m1 be the sequence number of each track, and the RAAN of each track is:

[0303] Ω 1,m1 =[(m1-1)π] / M1, m1∈[1,M1]

[0304] In the formula, Ω 1,m1 RAAN represents the m1th orbit of the sub-constellation with the largest inclination, where M1 represents the orbital plane number of the sub-constellation with the largest inclination.

[0305] 2.5.3 Calculation of the number of track surfaces that meet the coverage requirements at lat2:

[0306] The current sub-constellation Con1 has a total of M1 orbital planes. The right ascension of the ascending node of each orbit has been calculated according to step 2.5.2. The number of satellites per orbit and the satellite type have been calculated according to step 2.4. The phases of each satellite are evenly distributed.

[0307] 2.5.3.1 At lat2, a ground target of arbitrary longitude is named point2. The maintenance period T is solved using simulation and other methods. mp Within, the revisit time Δt2 of sub-constellation Con1 for point2.

[0308] 2.5.3.2 If the revisit time Δt2 reaches the expected value of the latitude, proceed to step 2.5.3.3; otherwise, let M1 = M1 + 1 and proceed to step 2.5.2.

[0309] 2.5.3.3 Record the configuration parameters of the sub-constellation Con1 with the largest tilt angle, including the nominal semi-major axis a1 and the tilt angle inc1=φ. H The number of orbital planes M1, the set of right ascension of ascending nodes Ω1, the number of satellites per orbit N1, and the satellite selection, as well as the average phase distribution of each satellite.

[0310] 2.6 Conditional Judgment

[0311] If the number of designed constellations is I, proceed to step 2.8; otherwise, sort the currently undesigned sub-constellations according to their tilt angles and proceed to step 2.7.

[0312] 2.7 Design of Parameters for Subconstellations with Maximum Tilt Angle Based on Combined Coverage Method

[0313] The sub-constellation currently under design will be named Coni, with an inclination angle of inc. i The nominal semi-major axis is a i Number of orbital planes M i =0, the latitudes of the observation points are lat1 and lat2. Calculate according to step 2.3.3, and the latitude of lat1 is higher than that of lat2. Perform the following steps:

[0314] 2.7.1 At lat2, name a ground target of arbitrary longitude as point2.

[0315] 2.7.2 Calculate the target maintenance period T using simulation and other methods. mp Within, the designed constellation and the set of constellations Coni, the revisit time △t2 of point2 for the constellation Con.

[0316] 2.7.3 If the revisit time Δt2 reaches the constraint Δt at that latitude. tar,2 If yes, proceed to step 2.7.6; otherwise, proceed to step 2.7.4.

[0317] 2.7.4. In the constellation Coni, which has been designed, arrange the RAANs of all orbital planes in order of size. Calculate the interval of the RAANs of adjacent orbital planes one by one, and find the maximum value of the RAAN interval. If there are multiple maximum values ​​for the RAAN interval, take any one of them. Assume orbital plane P... i,1 and P i,2 The RAAN interval is the largest, and the RAAN of the two are Ω respectively. i,1 Ω i,2 , and Ω i,1 <Ω i,2 , let Ω new =Ω i,2 +1 / 2(Ω i,2 -Ω i,1 ).

[0318] 2.7.5. Add an inclination angle of inc to the sub-constellation Coni. i The nominal semi-major axis is a i The RAAN value is Ω new The orbital planes, the number of satellites per orbit, and the satellite types have been calculated according to step 2.4, with the phases of each satellite evenly distributed. Let M be the number of orbital planes for the sub-constellation Coni. i =M i +1, proceed to step 2.7.2.

[0319] 2.7.6 Record the configuration parameters of the sub-constellation Coni. If M i ≠0, record the nominal semi-major axis a i Inclination angle i Number of orbital planes M i Right ascension of ascending node Ω i The RAAN value of the completed constellation is compared with the Ω value added in step 2.7.4. new The set of values, the number of satellites per orbit N i And satellite selection, the phase of each satellite is evenly distributed; if M i =0, record the right ascension of the ascending node Ω i Empty, number of satellites per orbit N i =0, satellite selection is empty.

[0320] 2.8 Cost Calculation

[0321] 2.8.1 Manufacturing Costs

[0322] Query the "Total Manufacturing Cost" column of the candidate satellite library (SatLib) in step 1.5. Based on the satellite selection scheme for each sub-constellation, record the total manufacturing cost (Pricei) of the selected satellites for each sub-constellation. The manufacturing cost (Cman) of all satellites within the constellation is:

[0323] Cman=∑ I i=1 (M i ·N i Price i )

[0324] 2.8.2 Launch Costs

[0325] Using a multi-satellite launch method, satellites with different inclination angles must be launched separately. Satellites with the same inclination angle can utilize the drift caused by the differential semi-major axis to assist in RAAN deployment. Therefore, some satellites with the same inclination angle but different RAANs can be launched together. However, whether a combined launch is possible is constrained by the deployment cycle and satellite fuel.

[0326] For i∈[1,I], execute steps 2.8.2.1 to 2.8.2.5 to calculate the launch cost of each sub-constellation:

[0327] 2.8.2.1, Sub-constellation Coni contains M i There are N orbitals, each containing N. i One satellite. For m i ∈[1,M i ],q∈[1,N i ], calculate the orbital plane m one by one i Estimated deployment fuel demand for each satellite in China Δv d_exp i,mi,q :

[0328] △v d_exp i,mi,q =(T d / T L )△v i,mi,q

[0329] In the formula, T d T represents the target deployment duration. L Δv represents the target design life, q represents the satellite serial number, and Δv represents the satellite's design life. i,mi,q This represents the satellite's total fuel, obtained by querying SatLib.

[0330] 2.8.2.2, For m i ∈[1,M i ],q∈[1,N i ], calculate the orbital plane m one by one i Each satellite in China utilizes △v d _exp i,mi,q Adjustable semi-major axis value △a i,mi,q :

[0331] △a i,mi,q =(2△v d_exp i,mi,q ) / n i m i ∈[1,M i ],q∈[1,N i ]

[0332] In the formula, n i Represents the semi-major axis a of the sub-constellation Coni i The corresponding angular velocity.

[0333] 2.8.2.3 Calculate using J2 perturbation and Δa i,mi,q During deployment time T d Within, the RAAN adjustment amount ΔΩ achievable by each orbit of the sub-constellation Coni. i,mi,q :

[0334] △Ω i,mi,q =(21n i ·J2·Re 2 ·T d ·cos(inc i )·△a i,mi,q ) / (4a i 3 ), m i ∈[1,M i ],q∈[1,N i ]

[0335] In the formula, a i n i 、inc i These represent the semi-major axis, angular velocity, and tilt angle of the sub-constellation Coni, respectively.

[0336] The RAAN adjustment corresponding to the satellite with the smallest RAAN adjustment is taken as the RAAN adjustment that can be achieved in this orbital plane:

[0337] △Ω i,mi =min(△Ω i,mi,q ), m i ∈[1,M i ],q∈[1,N i ]

[0338] 2.8.2.4 The RAAN of each orbit of the sub-constellation Coni is Ω. i,mi m i ∈[1,M i Calculate the RAAN interval for each orbital plane. If the interval is less than ΔΩ... i,mi If so, they can be launched together. Assume that the sub-constellation Coni requires a total of G launches.

[0339] 2.8.2.5 Currently, multiple satellite launches typically employ a cost-sharing approach. The base cost of each launch is shared by the carried satellites according to their weight, and the total satellite weight should be within the payload capacity. Therefore, the cost of each launch can be considered related to the initial orbital semi-major axis, inclination, and total satellite mass. Calculate the launch cost of the sub-constellation Coni:

[0340] Clau i =∑ G g+1 (w1inc i +w2a i +w3Mass+ε g )

[0341] In the formula, Mass is the total weight of the satellite, determined by the satellite selection scheme for each orbital plane and SatLib. w1, w2, and w3 are weighting parameters, and ε g The base cost for the g-th launch will be determined based on the actual situation.

[0342] 2.8.2.6 Calculate the launch cost (Clau) of all sub-constellations within the constellation:

[0343] Clau=∑ I i=1 Clau i

[0344] 2.8.3 The total cost of a constellation consists of manufacturing and launch costs. Calculate the total cost of the constellation, Ctot:

[0345] Ctot=Cman+Clau

[0346] 2.9 Iterative Solution Using Genetic Algorithm

[0347] The total cost of the constellation is used as the fitness value of the current solution and fed into the genetic algorithm for subsequent selection, crossover, and mutation operations. The algorithm will automatically generate new solutions and corresponding populations, and then proceed with optimization iterations.

[0348] 3. Design of Heterogeneous Constellation Deployment Scheme

[0349] Step 3 involves determining the design of a heterogeneous constellation deployment scheme through satellite target position allocation, target orbit parameter calculation, fuel calculation, and deployment scheme, and outputting the deployment fuel consumption.

[0350] This invention employs a planar control approach, deploying only the semi-major axis and AoL of satellites in the same orbit. Within each sub-constellation, the deployment scheme is consistent across all orbital planes. Assuming that after configuration design, the constellation has I sub-constellations, for i∈[1,I], the deployment scheme for each orbital plane of each sub-constellation is calculated sequentially.

[0351] 3.1 Satellite target location allocation

[0352] 3.1.1 Assuming that after the constellation configuration is designed, the total number of satellites in a certain orbital plane of sub-constellation i is N. i The tilt angle is inc i The nominal semi-major axis is a i For q∈[1,N] i ] Query SatLib, and in the information column of satellite q, look for a match with a i The total fuel Δv corresponding to the closest characteristic semi-major axis q And fuel demand estimate △v per q Calculate the fuel adequacy value for satellite q:

[0353] γ q =△v q / △v per q , q∈[1,N i ]

[0354] 3.1.2 For q∈[1,N] i The standard AoL for calculating the target location is:

[0355]

[0356] 3.1.3, u0 q The absolute values ​​are arranged in ascending order. The satellites are then arranged according to their γ values. q Arranged in ascending order. (For γ) q Minimum satellite allocation | u0 q The position with the minimum value is γ. q Second smallest satellite allocation | u0 q The position with the second smallest value is assigned, and so on, to all satellites. Assume that after assignment, satellites 1 to N... i The standard AoL for the target location is u1 q , q∈[1,N i ].

[0357] 3.2 Calculation of Target Orbit Parameters

[0358] For satellite q∈[1,N] i Calculate the following values ​​one by one:

[0359] 3.2.1 Query SatLib and find the column containing information about satellite q that matches a. i The orbital decay parameter k1 within the target maintenance period corresponding to the closest feature semi-major axis mp q k2 mp q .

[0360] 3.2.2 Calculate the initial working semi-major axis of satellite q during its first sustainment period, which is also the target deployment semi-major axis:

[0361] a mai q,0 =a i -(k1 mp q ·T mp 2 ) / 3-(k2 mp q ·T mp ) / 2

[0362] In the formula, a mai q,0 a represents the target deployment semi-major axis of satellite q, that is, the initial operational semi-major axis of satellite q during its first sustainment cycle. i a represents the semi-major axis of the sub-constellation to which satellite q belongs. iObtained by configuration design method, k1 mp q k2 mp q Let T represent the second-order and first-order semi-major axis attenuation coefficients of satellite q during the maintenance phase, respectively. mp Indicates the target maintenance period.

[0363] The reason for setting the initial semi-major axis of the maintenance period in this way is that the aforementioned initial semi-major axis allows the satellite to maintain a certain position during the maintenance period T. mp The total offset of AoL within the constellation is 0, meaning that the satellites move symmetrically during the maintenance period, which facilitates constellation maintenance.

[0364] 3.2.3 Calculate satellite q with respect to a mai q,0 For the semi-major axis, the target maintenance period T mp Maximum AoL offset within:

[0365] △u max,q =[(7λ'+3n i ) / 12a i ]·[-2k1 mp q T mid 3 -3k2 mp q T mid 2 +(2k1 mp q T mp 2 +3k2 mp q T mp )T mid ]

[0366] λ'=[(3n e J2R e 2 ) / 2a i 2 ]·(4cos 2 inc i -1)

[0367]

[0368] In the formula, △u max,q λ' represents the maximum AoL offset of satellite q, λ' represents the long-term rate of change of the mean anomaly angle, and n i a represents the orbital angular velocity corresponding to the semi-major axis of the sub-constellation to which satellite q belongs. i k1 represents the semi-major axis of the sub-constellation to which satellite q belongs. mpq k2 mp q Let T represent the second-order and first-order semi-major axis attenuation coefficients of satellite q during the maintenance phase, respectively. mid T represents the time required to reach the maximum AoL offset. mp Indicates the target maintenance period. inc i This indicates the inclination angle of the sub-constellation where satellite q is located.

[0369] 3.2.4 Calculate the initial AoL of satellite q during its first sustainment period, which is also the target AoL for deployment:

[0370] u mai q =u1 q +△u max,q / 2

[0371] 3.3 Fuel Calculation and Deployment Scheme Determination

[0372] For satellite q∈[1,N] i Perform the following steps one by one:

[0373] 3.3.1 Query SatLib and find the column containing information about satellite q that matches a. i The orbital attenuation parameter k1 corresponding to the deployment phase of the closest feature semi-major axis d q k2 d q .

[0374] 3.3.2 Calculate the deployment time T of each satellite on the target. d Internally, the value of AoL is adjusted to u by relying on the difference semi-major axis. mai q At that time, the required initial semi-major axis for deployment is:

[0375] a dep q =a i -(2a i u mai q ) / [(7λ'+3n i )T d ]-(k1 d q ·T d 2 ) / 3-(k2 d q ·T d ) / 2

[0376] 3.3.3 Calculate the fuel consumption required for satellite q's deployment orbital maneuver:

[0377] △v dep q =(n i ·|a i -a dep q |) / 2+[n i ·|(a dep q +k1 d q ·T d 2 +k2 d q T d )-a mai q,0 |] / 2

[0378] 3.3.4 The deployment scheme for satellite q is as follows: at the start of deployment, from the semi-major axis a... i The first orbital maneuver is performed at the entry point, adjusting the semi-major axis to a. dep q Free Run T d After a certain time, the relative AoL difference with the orbital insertion point is u. mai q At this point, a second orbital maneuver is performed to adjust the semi-major axis to a. mai q,0 Satellite q deployment is complete. The same applies to the remaining satellites.

[0379] Step 4: Design of Heterogeneous Constellation Maintenance Scheme

[0380] Step 4 involves designing a heterogeneous constellation maintenance scheme by calculating the expected value of sustained fuel consumption, the expected value of semi-major axis adjustment, the working semi-major axis, fuel calculation and maintenance scheme determination, and condition judgment, and outputting the sustained fuel consumption. Simulation-based verification and correction are used to check whether the constellation meets constraints throughout its entire life cycle, and configuration modifications are performed (if necessary).

[0381] This invention employs a plane-based control approach, maintaining only the semi-major axis and AoL of satellites in the same orbit. Within the sub-constellation, the maintenance scheme is consistent across all orbital planes, and during each maintenance period T... mp Maintenance is performed at the end. Assume the constellation has I sub-constellations. For i ∈ [1, I], calculate the maintenance scheme for each orbital plane of each sub-constellation. Assume that the total number of satellites in a certain orbital plane of sub-constellation i is N. i For q∈[1,N] i Perform the following steps one by one:

[0382] 4.1 Calculation of Expected Fuel Consumption

[0383] 4.1.1 Query SatLib and record the total fuel Δv of satellite q. q Considering potential future reconfiguration and deorbiting contingencies, a portion of fuel is reserved for deployment and maintenance. The total available fuel for deployment and maintenance is Δv. q '=η△v q Where η is the fuel redundancy ratio, which is selected manually.

[0384] 4.1.2 Assuming this is the h-th maintenance cycle, what is the expected fuel consumption Δv for this maintenance cycle? mai_exp q,h for:

[0385] △v mai_exp q,h =△v left q / [floor(T m / T mp )-h+1]

[0386] In the formula, △v left q The remaining available fuel for satellite q.

[0387] If h=1, then Δv left q =△v q '-△v dep q Otherwise, △v left q Calculated from step 4.4.3.

[0388] 4.2 Calculation of Expected Value of Semi-Major Axis Adjustment

[0389] 4.2.1 Assume that the semi-major axis of satellite q before the h-th maintenance is a. beg q,h angular velocity is n beg q,h Using no more than △v mai_exp q,h The fuel is sufficient to adjust the working half-length shaft to the following range:

[0390] a work q,h ∈[a beg q,h -(2△v mai_exp q,h ) / n beg q,h a beg q,h +(2△v mai_exp q,h ) / n beg q,h ]

[0391] Among them, a work q,h This represents the range of the working semi-major axis of satellite q after the h-th maintenance.

[0392] 4.2.2 To ensure the imaging resolution constraint, in a work q,h Within the range, exclude those that do not satisfy the maximum value constraint of the semi-major axis a. max =δ·(f / p max )+R e Update a to the range of the semi-major axis. work q,h .

[0393] 4.2.3 Calculate a work q,h The corresponding nominal semi-major axis range:

[0394] a sta q,h ∈[a work q,h +(k1 mp q ·T mp 2 ) / 3+(k2 mp q ·T mp ) / 2-(2△v mai_exp q,h ) / n beg q,h ,

[0395] a work q,h +(k1 mp q ·T mp 2 ) / 3+(k2 mp q ·T mp ) / 2+(2△v mai_exp q,h ) / n beg q,h ]

[0396] 4.3 Calculation of the semi-major axis of the working part

[0397] 4.3.1 To ensure the relative position control effect of satellites within this orbit, the nominal semi-major axis a of all satellites... sta q,h Consistency is required. Therefore, refer to the nominal semi-major axis a of each satellite. sta q,h Choose a value as the nominal semi-major axis a for the h-th maintenance of this orbit. stah The selection principle is: when all satellites' a sta q,h If all satellites have a union, then the maximum value in the union is selected; if some satellites do not have a union, then the maximum value in the union of the other satellites is selected. sta q,h And concentrate, select a with no union satellites sta q,h The minimum value of the sum of Euclidean distances across the range; when all satellites' a sta q,h There is no union of any satellites, so take a with all satellites. sta q,h The minimum sum of Euclidean distances over a given range.

[0398] 4.3.2 Calculate the working semi-major axis of satellite q during the h-th maintenance:

[0399] a mai q,h =a sta h -(k1 mp q ·T mp 2 ) / 3-(k2 mp q ·T mp ) / 2

[0400] 4.4 Fuel Calculation and Sustainability Scheme Determination

[0401] 4.4.1 Calculate the sustainment burnup of satellite q for the h-th time:

[0402] △v mai q,h =(n beg q,h |a mai q,h -a beg q,h |) / 2

[0403] 4.4.2 The maintenance plan is as follows: the execution time of the h-th maintenance is hT. mp Perform an orbital maneuver to move the semi-major axis of satellite q from a beg q,h Adjust to a mai q,h AoL is automatically corrected through adjustments to the semi-major axis. The h-th maintenance cycle for satellite q ends. The same applies to the remaining satellites. A schematic diagram of the relative changes in the semi-major axis and AoL (relative to standard AoL and nominal semi-major axis) of a satellite during one maintenance cycle is shown below. Figure 7 .

[0404] 4.4.3 Update the current remaining available fuel for satellite q:

[0405] △v left’ q =△v left q -△v mai q,h

[0406] In the formula, △v left’ q Δv represents the remaining usable fuel after the h-th maintenance period. left q Δv represents the remaining available fuel before the h-th sustaining cycle. mai q,h This represents the sustain fuel consumption for the hth cycle.

[0407] 4.5 Conditional Judgment

[0408] If h≥floor(T) m / T mp If h = h + 1, then the design is complete, proceed to step 4.6. Otherwise, let h = h + 1, proceed to step 4.1.

[0409] 4.6 Inspection and Correction

[0410] 4.6.1 Perform a full-process simulation of the complete constellation, including all orbits, to verify whether all direct constraints within the maintenance duration are met. If they are met, the constellation full-process design is complete; otherwise, continue with this step.

[0411] 4.6.2 If the mission phase and duration are not met, identify the satellite with insufficient fuel and execute step 2.4.1 to reselect the satellite with insufficient fuel, reduce the value of β, and select the satellite with the second lowest manufacturing cost to replace the satellite with insufficient fuel.

[0412] 4.6.3 If the revisit time requirement is not met, locate the coverage hole. If the coverage hole appears on an adjacent satellite within the orbital plane, it indicates that the number of satellites is too small. Proceed to step 2.4 to increase the number of satellites within the orbital plane and complete satellite selection. If the coverage hole appears on an adjacent orbital plane, it indicates that the number of orbits is too small. Proceed to step 2.4, then step 2.5 or 2.7 to increase the number of orbital planes and complete satellite selection.

[0413] It should be noted that performing step 2.4, followed by step 2.5 or 2.7, specifically refers to adding an orbital plane to the subconstellation containing the satellite. The selection and number of satellites within this orbital plane can be directly copied from existing orbits in the subconstellation, or it can be performed according to step 2.4. Other parameters for the new and existing orbits need to be calculated and verified according to 2.5 or 2.7. Specifically, the RAAN parameters are calculated based on 2.5.1 and 2.7.4; other parameters are consistent with (shared with) other orbital planes in the subconstellation, and the other steps are verification steps.

[0414] 4.6.4. Execute steps 4.6.1 to 4.6.3 until the constraints are satisfied, update the constellation's configuration design scheme, deployment scheme, and maintenance scheme, calculate the total cost of the constellation, and the entire constellation design process is completed.

[0415] In summary, this invention provides a comprehensive design method for heterogeneous Earth coverage constellations, encompassing configuration design, deployment scheme design, and maintenance scheme design, to optimize overall performance. Using an optimization method primarily based on intelligent optimization algorithms, it solves for the heterogeneous constellation configuration that satisfies coverage indicators, has acceptable control costs, and meets expected fuel consumption under high-dimensional heterogeneous parameters and complex constraints, minimizing overall cost. Furthermore, it considers factors such as fuel and control costs to provide constellation deployment and maintenance schemes. This invention provides an effective integrated design method for the entire process design of low-to-medium orbit circular heterogeneous Earth coverage constellations, achieving comprehensive performance optimization based on manufacturing costs, control costs, and complex constraints. This avoids the resource waste and repeated manual iterations caused by the decoupling of traditional configuration design and control scheme design. Simulation results demonstrate that, in terms of overall constellation cost, to achieve the same coverage indicators, the optimized configuration's overall cost is only 70-74% of that of a traditional uniform configuration with the same semi-major axis and inclination angle. Moreover, the revisit time decreases with latitude variations, an advantage that is more significant in large-latitude span scenarios such as near-global coverage.

[0416] In summary, this invention can achieve synergistic optimization of coverage effectiveness and overall cost, and has scalability when the constellation scale is expanded. It can support the efficient design of thousands of constellations in scenarios such as emergency remote sensing and global Internet of Things, and reduce the overall cost and design difficulty throughout the entire life cycle.

[0417] The above description is only a preferred embodiment of the present invention. Therefore, all equivalent changes or modifications made to the structure, features and principles described in the claims of this patent application are included in the scope of this patent application.

Claims

1. An integrated design method for the configuration, deployment, and maintenance of heterogeneous constellations for ground coverage, characterized in that, Includes the following steps: Step 1: Determine the direct constraints, calculate the indirect constraints, and construct a pool of candidate satellites; The direct constraints include one or more combinations of the following constraints: a) Target deployment duration, target maintenance duration, target maintenance cycle, and target design life; b) The highest and lowest target latitudes; c) Ideal revisit time; d) Highest optical image resolution; e) Multiple alternative satellites and their total manufacturing cost, total mass, windward surface-to-mass ratio, total fuel, payload focal length to probe size ratio, and payload coverage half-angle; The indirect constraints include one or more combinations of the following constraints: a) Semi-major axis constraint interval; b) Inclination constraint range, where the maximum inclination angle corresponds to the highest target latitude and the minimum inclination angle corresponds to the lowest target latitude; Step 2: Using a genetic algorithm with the goal of minimizing the total cost of the constellation, and combining direct and indirect constraints, the number of sub-constellations and the configuration parameters of each sub-constellation are solved hierarchically to obtain the optimal number of sub-constellations and the configuration parameters of each sub-constellation. The configuration parameters include inclination angle, semi-major axis, number of orbital planes, set of right ascension of ascending nodes, number of satellites per orbit, and satellite selection. In step 2, each individual mainly consists of the number of sub-constellations, the tilt angle of each sub-constellation, and the semi-major axis of the sub-constellation with the largest tilt angle. The tilt angle of the sub-constellation with the largest tilt angle is set as the highest target latitude. The reciprocal of the fitness value of each individual is the total cost of the constellation. The hierarchical stepwise solution refers to: stepwise solving other configuration parameters and the total constellation cost based on the configuration parameter values ​​in an individual, and using the reciprocal of the total constellation cost as the fitness value; Step 3: For each sub-constellation, determine the deployment plan for each orbital plane; The deployment plan for each satellite is as follows: At the start of deployment, the satellite performs its first orbital maneuver from its entry point to adjust its semi-major axis to the initial semi-major axis of deployment; after the satellite has been freely orbiting the target deployment for a long time, the difference between its relative AoL and the entry point is equal to the target AoL. At this point, a second orbital maneuver is performed to adjust it to the target deployment semi-major axis, and the satellite deployment ends. The deployment scheme includes the target AoL of each satellite on the orbital plane, the initial semi-major axis of deployment, and the target deployment semi-major axis; Step 4: For each sub-constellation, determine the maintenance scheme for each orbital plane; the maintenance scheme includes the working semi-major axis of each satellite after each maintenance.

2. The integrated design method for the configuration, deployment, and maintenance of heterogeneous constellations for ground coverage according to claim 1, characterized in that: The hierarchical step-by-step solution process is specifically as follows: Calculate the semi-major axes of the remaining sub-constellations based on the semi-major axis of the sub-constellation with the largest tilt angle; Based on the semi-major axis of the sub-constellation, select all satellites that meet the imaging resolution constraints from the candidate satellite pool to form an optional satellite pool; determine the latitude of the two observation points based on the optional satellite pool of the sub-constellation; For each sub-constellation, the number of satellites per orbit and the satellite type are determined through star selection; For the sub-constellation with the largest inclination angle, the sub-constellation configuration is designed according to the independent covering method, and the number of orbital planes and the set of right ascension of the ascending nodes of the sub-constellation with the largest inclination angle are obtained; For the sub-constellations other than the one with the largest inclination, the sub-constellation configuration is designed in sequence according to the combination coverage method, with the goal of maintaining the ideal revisit time for ground targets at lower latitudes and arbitrary longitudes within the cycle. This results in the number of orbital planes and the set of right ascension of ascending nodes for each sub-constellation. The inclination, semi-major axis, number of orbital planes, set of right ascension of ascending nodes, number of satellites per orbit, and satellite selection of each sub-constellation constitute the configuration parameters of the sub-constellation; The manufacturing and launch costs are determined based on the configuration parameters of each sub-constellation. The manufacturing and launch costs of all sub-constellations are then tallied to obtain the total cost of the constellation.

3. The integrated design method for the configuration, deployment, and maintenance of heterogeneous constellations for ground coverage according to claim 2, characterized in that: The process of obtaining satellite selection through star selection is as follows: First, the total fuel and fuel requirement estimates for each optional satellite are selected from the pool of optional satellites for the sub-constellation; Subsequently, optional satellites that do not meet the following criteria are removed, resulting in an updated pool of optional satellites: △v j ≤(△v per j / b) In the formula, △v j Δv represents the total fuel of the j-th optional satellite. per j β represents the estimated fuel requirement of the j-th optional satellite, and β represents the preset fuel coefficient. Finally, from the updated pool of available satellites, select a satellite using either method: a) Select the satellite with the lowest total manufacturing cost; when manufacturing costs are the same, select the satellite with the larger total fuel; when both total manufacturing cost and total fuel are the same, select the satellite with the larger ratio of payload focal length to probe size. b) Select a combination of multiple satellites to form an orbit based on actual needs or preferences.

4. The integrated design method for the configuration, deployment, and maintenance of heterogeneous constellations for ground coverage according to claim 2, characterized in that: The process of obtaining the number of satellites per orbit through satellite selection is as follows: First, take any longitude at each of the two observation points to form the first and second ground targets; then, obtain the number of satellites per orbit based on the revisit time threshold of each sub-constellation for the first and second ground targets; finally, use simulation methods to iteratively correct the number of satellites per orbit of the sub-constellation with the largest inclination angle until the revisit time of any orbit of the sub-constellation with the largest inclination angle for the first and second ground targets is less than the corresponding revisit time threshold. During the iterative correction process, the revisit time of each orbital face to the first and second ground targets is obtained through simulation. If both revisit times are less than the corresponding threshold, the current number of satellites per orbit is taken as the corrected number of satellites per orbit, and the correction ends. Otherwise, the number of satellites per orbit of the sub-constellation with the largest inclination is increased by a preset step size, the satellite selection is obtained again, and the simulation and comparison process is executed again.

5. The integrated design method for the configuration, deployment, and maintenance of heterogeneous constellations for ground coverage according to claim 1, characterized in that: In step 3, the deployment scheme of satellites on each orbital plane in the sub-constellation is determined through the following process: First, for each satellite in the orbital plane, the total fuel and fuel requirement estimates of the satellites are selected from the pool of candidate satellites, and the ratio of total fuel to fuel requirement estimates is obtained as the fuel adequacy value; based on the number of satellites per orbit of the sub-constellation, the standard AoL for each target deployment location is calculated; Subsequently, the satellites are arranged in ascending order of fuel adequacy, and the target deployment locations are arranged in ascending order of standard AoL absolute value. The satellites and target deployment locations are then deployed in sequence one by one. Subsequently, the half-major axis attenuation parameters of the satellites within the target deployment duration are selected from the candidate satellite pool, and then the target deployment half-major axis of the satellites is calculated. Based on the target deployment half-major axis, the maximum AoL offset of the satellites within the target maintenance period is calculated. Finally, based on the satellite's standard AoL and maximum AoL offset, the target AoL, initial semi-major axis of deployment, and fuel consumption required for deployment orbital maneuvers are calculated using the following formulas: u mai q =u1 q +△u max,q / 2 △v dep q =(n i ·|a i -a dep q |) / 2+[n i ·|(a dep q +k1 d q ·T d 2 +k2 d q T d )-a mai q,0 |] / 2 a dep q =a i -(2a i u mai q ) / [(7λ’+3n i )T d ]-(k1 d q ·T d 2 ) / 3-(k2 d q ·T d ) / 2 In the formula, u mai q u1 q , △u max,q Let Δv represent the target AoL, standard AoL, and maximum AoL offset of satellite q, respectively. dep q a represents the fuel consumption required for the deployment orbital maneuver of satellite q. dep q n represents the initial semi-major axis of satellite q during deployment; i a represents the orbital angular velocity corresponding to the semi-major axis of the sub-constellation to which satellite q belongs. i k1 represents the semi-major axis of the sub-constellation to which satellite q belongs. d q k2 d q Let a represent the second-order semi-major axis attenuation coefficient and the first-order semi-major axis attenuation coefficient of satellite q during the deployment phase, respectively. mai q,0 The initial working semi-major axis represents the first sustaining period of satellite q, || denotes taking the absolute value, u mai q Let AoL represent the target angle of satellite q, λ' represent the long-term rate of change of the mean anomaly angle, and T represent the target angle of satellite q. d Indicates the target deployment time.

6. The integrated design method for the configuration, deployment, and maintenance of heterogeneous constellations for ground coverage according to claim 1, characterized in that: In step 4, the maintenance scheme for satellites on each orbital plane in the sub-constellation is determined through the following process: 4.1 For each satellite, based on the satellite's current remaining available fuel and the current number of sustaining operations, obtain the expected fuel consumption value for the current sustaining operation; 4.2 For each satellite, based on the current expected burnup and the working semi-major axis and angular velocity before the current maintenance, combined with the imaging resolution constraint, determine the working semi-major axis range after the current maintenance, and then obtain the nominal semi-major axis range based on the working semi-major axis range after the current maintenance and the semi-major axis attenuation parameters of the satellite during the target deployment period. 4.

3. Determine a common nominal semi-major axis based on the nominal semi-major axis range of all satellites on the orbital plane, and then combine the semi-major axis attenuation parameters of each satellite during the target deployment period to obtain the current working semi-major axis after maintenance. 4.4 For each satellite, calculate the sustainment burnup during the current sustainment period and update the current remaining available fuel, then return to step 4.1; 4.5 Repeat steps 4.1 to 4.4 until the target number of maintenance cycles is reached.

7. The integrated design method for the configuration, deployment, and maintenance of heterogeneous constellations for ground coverage according to claim 6, characterized in that: Step 4 further includes step 4.6: 4.6.1 Perform a full-process simulation of the complete heterogeneous constellation, including all orbits, and check whether the direct constraints within the maintenance duration are met. If they are met, the full-process design of the constellation is completed. If the mission phase and duration are not met, proceed to step 4.6.

2. If the revisit time constraint is not met, proceed to step 4.6.

3. 4.6.

2. Identify satellites with insufficient fuel, and reselect satellites for the sub-constellation to obtain the number of satellites per orbit and satellite type for the sub-constellation. Return to step 4.6.

1. 4.6.

3. Locate the location of the coverage hole. If the coverage hole appears on adjacent satellites in the same orbital plane, increase the number of satellites per orbit in the orbital plane and complete the satellite selection. If the covering hole appears on an adjacent orbital plane, increase the number of orbital planes of the sub-constellation where the orbital plane is located, and redesign the star selection and sub-constellation configuration, update the number of orbital planes of the sub-constellation where the orbital plane is located, and return to step 4.6.1; 4.6.

4. Execute steps 4.6.1 to 4.6.3 until all direct constraints are met, update the constellation's configuration design, deployment plan, and maintenance plan, calculate the total cost of the constellation, and the entire constellation design process is complete.

8. The integrated design method for the configuration, deployment, and maintenance of heterogeneous constellations for ground coverage according to claim 1, characterized in that: The pool of candidate satellites includes the total manufacturing cost, total fuel, total mass, payload focal length to probe size ratio, payload coverage half-angle, semi-major axis attenuation parameter set, and fuel requirement estimate set for satellites with different surface-to-mass ratios; the fuel requirement estimate set includes fuel requirement estimates under different characteristic semi-major axes.

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