Low earth orbit satellite network edge computing unloading and resource allocation joint optimization method

Abstract

The invention provides a joint optimization method for edge computing unloading and resource allocation of a low earth orbit satellite network, and belongs to the technical field of satellite communication and remote sensing. The observation path of the satellite and the adjustment of the side-sway angle are optimized through second-order cone programming, so that shielding and task conflicts are effectively reduced in the observation process. In order to improve the calculation efficiency and adaptability, a Lagrangian relaxation method is adopted to process resource constraints, so that the optimization problem can be decomposed into a plurality of sub-problems to be solved in parallel, and the calculation complexity is reduced. A multi-objective optimization model based on a Pareto leading edge is introduced, and a weight adaptive adjustment mechanism is combined, so that the task completion rate and the energy consumption are balanced. According to the mechanism, the priority among different targets is dynamically adjusted according to the current resource state and task requirements of the satellite network, so that effective execution of tasks is ensured, and energy consumption is saved to the greatest extent. According to the method, the advantages of mixed nonlinear planning and distributed calculation are combined, and efficient collaborative observation task planning in a complex environment is realized.

Description

Technical Field

[0001] The present invention belongs to the field of satellite communication networks and edge computing technologies, and in particular, relates to a joint optimization method for low-orbit satellite network computing offloading and resource allocation based on hierarchical multi-agent reinforcement learning. Background Art

[0002] The observation mission planning of the existing satellite network mainly relies on the unified command and control of the control center of the ground station. The control center collects target area information, mission requests and satellite status data (such as orbital parameters, power and sensor status), and generates a mission planning plan based on this, and sends specific observation instructions to remote sensing satellites and relay satellites. During the observation process, the satellite completes the mission by adjusting the side swing angle, controlling the resolution and the status of the sensor, and transmits the observation data to the relay satellite, which is then transmitted to the ground station via the relay satellite. After the mission is completed, the control center merges and processes all the data at the ground station to generate the final mission results.

[0003] Centralized planning has global coordination and can avoid mission conflicts and redundant observations, but it may be limited by communication delays and computing loads in large-scale missions and complex environments. In recent years, some systems have adopted distributed planning to delegate some decision-making power to each satellite. Satellites plan autonomously based on their own status, orbital position, and mission requirements, and coordinate task allocation through intersatellite links to optimize energy and storage usage and reduce repeated observations. This model improves mission responsiveness and reduces dependence on ground stations, but it also requires efficient intersatellite communications and conflict management.

[0004] In practical applications, mission planning needs to consider both resource optimization and priority allocation. For example, high-priority disaster emergency missions are assigned to satellites with sufficient resources, while routine missions may be postponed or completed by other satellites. The combined use of heuristic algorithms and satellite autonomous optimization algorithms can improve the flexibility and robustness of planning in complex multi-objective missions, and achieve effective observation mission planning that combines centralized and distributed methods. Summary of the invention

[0005] The present invention proposes a multi-satellite multi-observation task collaborative planning method based on hybrid nonlinear programming (MNLP) and distributed optimization framework. Under complex constraints, the method optimizes the satellite's observation path and the adjustment of the sway angle through second-order cone programming (SOCP), thereby effectively reducing occlusion and task conflicts during the observation process. In addition, in order to improve computational efficiency and adaptability, the present invention uses Lagrangian relaxation method to deal with resource constraints, so that the optimization problem can be decomposed into multiple sub-problems for parallel solution, reducing computational complexity.

[0006] In terms of multi-objective optimization, the present invention introduces a multi-objective optimization model based on the Pareto frontier, and combines it with a weight adaptive adjustment mechanism to balance the task completion rate and energy consumption. This mechanism dynamically adjusts the priorities between different objectives according to the current resource status and task requirements of the satellite network, thereby ensuring the effective execution of tasks and saving energy to the greatest extent. The core innovation of the present invention lies in its combination of the advantages of hybrid nonlinear programming and distributed computing, realizing efficient collaborative observation task planning in complex environments. The technical solution adopted is: a joint optimization method for edge computing offloading and resource allocation in a low-orbit satellite network, the method comprising:

[0007] Step 1: Build a link visibility prediction model based on orbit and sub-satellite point parameters;

[0008] Step 1.1: Construct satellite orbit and sub-satellite point model;

[0009] Define orbital parameters. Assuming there are N satellites in the system, the orbital parameters of satellite i include:

[0010] Orbital inclination: I i , in radians; orbit height: h i , in meters; right ascension of ascending node: Ω i , in radians; orbital period: T i , in seconds; orbital semi-major axis: a i , in meters; orbital eccentricity: e i , dimensionless; argument of perigee: ω i , in radians; initial orbital position: θ i0 , in radians;

[0011] The calculation method of the sub-satellite point position is:

[0012] Assume that the orbits of all satellites are circular orbits, that is, the orbital eccentricity e i =0; therefore, the average angular velocity n of satellite i i for:

[0013] n i =2π / T i

[0014] The longitude λ of the subsatellite point of satellite i at time t i (t) and latitude φ i (t) is calculated by the following formula:

[0015] φ i (t) = arcsin(sinI i ·sin(n i t+θ i0 ))

[0016] λ i (t) = Ω i +(n i t+θ i0 )cosI i -ω E t

[0017] Where: E =7.2921150×10 -5 rad / s is the angular velocity of the Earth's rotation, t is the time, starting from the initial epoch time t of the satellite i0 ;

[0018] Step 1.2: Build a visibility model of the target area;

[0019] 1) Definition: The center position of the target area j is represented by the longitude λ j and latitude φ j Determine that the area of ​​the target area is A j , the unit is square meters;

[0020] 2) The calculation method of geocentric angle distance is:

[0021] The geocentric angular distance Δ between satellite i and target area j at time t ij (t) is calculated by the spherical cosine formula:

[0022] cosΔ ij (t) = sinφ i (t)sinφ j +cosφ i (t)cosφ j cos(λ i (t)-λ j )

[0023] Therefore, the geocentric angular distance Δ ij (t) is:

[0024] Δ ij (t) = arccos(sinφ i (t)sinφ j +cosφ i (t)cosφ j cos(λ i (t)-λ j ))

[0025] Geocentric angle distance Δ ij (t) is to determine whether satellite i can observe target area j;

[0026] 3) The calculation method of the maximum observable geocentric angle is:

[0027] Maximum observable geocentric angle of satellite i With its maximum side swing angle and track height h i The relationship is:

[0028]

[0029] Among them, R E =6.371×10 6 m is the average radius of the Earth;

[0030] Maximum observable geocentric angle Indicates that satellite i does not exceed its maximum lateral swing angle Under the condition of , the geocentric angle distance of the farthest target area that can be observed;

[0031] 4) The visibility function is:

[0032] The visibility function V of satellite i to target area j at time t is ij (t) is defined as:

[0033]

[0034] Visibility function V ij (t) is used to indicate whether satellite i can observe target area j at time t; local centroid distance Δ ij (t) is less than or equal to the maximum observable geocentric angle When the satellite can observe;

[0035] Step 1.3: Construct the observation range and side swing angle model;

[0036] 1) The calculation method of ground projection width is:

[0037] The observed ground projection width W of satellite i at time t i (t) is determined by its side swing angle θ i (t) and the field of view angle β of the remote sensor i Decide:

[0038] W i (t) = 2(h i +R E )tan(β i / 2)cosθ i (t)

[0039] Observation ground projection width W i (t) represents the ground width that the remote sensor can cover within time t for satellite i; the side swing angle θ i The adjustment of (t) affects the width of the observation range;

[0040] 2) The satellite ground speed is calculated as follows:

[0041] Satellite ground speed V i (t) is:

[0042] V i (t)=(h i +R E ) i i i / R E

[0043] The orbital speed for:

[0044]

[0045] Satellite ground speed V i (t) reflects the moving speed of satellite i on the ground and determines the ground distance that can be covered per unit time;

[0046] 3) The calculation method of observation area is:

[0047] The observation area A of satellite i at time t i (t) is:

[0048] A i (t) = W i (t)·V i (t)-Δt

[0049] Among them, Δt is the time step, and the observation area A is i (t) represents the ground area that satellite i can cover in time t;

[0050] Step 1.4: Construct energy consumption model;

[0051] Step 1.5: Build a data generation model;

[0052] During the observation process, the remote sensor will generate data volume D i (t), and the observation area A i (t) and resolution R i (t) related; Assume that the amount of data is proportional to the number of pixels, the number of pixels N i (t) is expressed as:

[0053] N i (t) = A i (t) / (R i (t)) 2

[0054] Therefore, the data volume D i (t) is:

[0055] D i (t) = d 0 N i (t) = d 0 A i (t) / (R i (t)) 2

[0056] Where: d 0 is the data generation coefficient for unit pixel; data volume D i (t) represents the amount of data generated by satellite i in time t. The higher the resolution, the more pixels, and the larger the amount of data;

[0057] Step 1.6: Define constraints and optimization goals, including power constraints, storage capacity constraints, observation coverage constraints, swing angle constraints, swing angular velocity constraints, resolution constraints, sensor status constraints, and mission completion status.

[0058] Step 2: Use the alternating direction multiplication method to solve the problem;

[0059] Step 2.1: Problem decomposition;

[0060] The global optimization problem is decomposed into N satellite sub-problems, each of which involves only the decision variable θ corresponding to satellite i. i (t), R i (t), s i (t);

[0061] Step 2.2: Introduce auxiliary variables z and consistency constraints;

[0062]

[0063] Step 2.3: Construct the enhanced Lagrangian function;

[0064] The enhanced Lagrangian function is constructed to include consistency constraints. The terms of the formula are as follows:

[0065]

[0066] Objective function part:

[0067]

[0068] Where: α i and β j are the weight coefficients of energy consumption and task completion rate, E i (t) represents the energy consumption of satellite i at time t, C j Indicates the completion status of task j;

[0069] Lagrange multiplier and penalty part:

[0070]

[0071] is the Lagrange multiplier of the corresponding variable, ρ is the penalty parameter used to control the weight of the consistency constraint, and θ i (t), R i (t), s i (t) represent the sway angle, observation resolution and sensor status of satellite i at time t, is a global variable used to coordinate the solutions of each subproblem; enhanced Lagrangian function Based on the original objective function, Lagrange multipliers and penalty terms are added to deal with the constraints in the optimization problem; the specific explanation is as follows:

[0072] Objective function part:

[0073] Represents the total energy consumption of all satellites at each time step, and the weighting coefficient α i Used to adjust the energy consumption importance of different satellites; It represents the sum of the completion status of all tasks at each time step. Subtracting this part means that we want to maximize the task completion rate. The weight coefficient β j Used to adjust the importance of different tasks;

[0074] Lagrange multiplier and penalty part:

[0075] The consistency constraint of the side swing angle is expressed by the Lagrange multiplier Adjustment; Represents the consistency penalty term of the side swing angle, penalty factor ρ Control the extent of constraint violations;

[0076] Step 2.4: gradually approach the global optimal solution by iteratively updating local variables, global variables and Lagrange multipliers;

[0077] Step 3: Second-order cone programming conversion to simplify optimization;

[0078] Step 3.1: Determine the spherical distance constraint;

[0079] The original spherical distance constraint is a nonlinear form:

[0080] cosΔ ij (t) = sinφ i (t)sinφ j +cosφ i (t)cosφ j cos(λi (t)-λ j )

[0081] Linearize it using Taylor expansion or small angle approximation:

[0082]

[0083] Because Δ ij The value of (t) is extremely small, so we set:

[0084]

[0085] Expressed as a second-order cone constraint:

[0086]

[0087] By approximation, the nonlinear spherical distance constraint is transformed into a second-order cone form;

[0088] Step 3.2: Linearize the energy consumption model;

[0089] Adjust the energy consumption model for the side swing angle:

[0090]

[0091] Introducing auxiliary variables And add linear constraints:

[0092]

[0093] Step 3.3: Construct the second-order cone constrained SOCP problem;

[0094] The optimization problem is in the form of a standard SOCP problem, which includes a linear objective function, linear constraints, and second-order cone constraints:

[0095] mincTx

[0096] st

[0097]

[0098] Among them, c, A k , b k 、c k d k are known parameters, and x is the decision variable;

[0099] Step 4: Use Lagrangian relaxation method to deal with global constraints;

[0100] Step 4.1: Construct the Lagrangian function;

[0101] The global constraints are introduced into the objective function through Lagrange multipliers:

[0102]

[0103] Among them, λ is the Lagrange multiplier for power constraint, μ is the Lagrange multiplier for storage capacity constraint;

[0104] Step 4.2: Multiplier update;

[0105] Through the gradient ascent method, the Lagrange multiplier is dynamically adjusted to gradually meet the constraints:

[0106]

[0107] Among them, η is the step size parameter, which is used to control the update speed of the multiplier;

[0108] Step 4.3: Iterative optimization;

[0109] In each iteration, by updating the Lagrangian multiplier, the power and storage capacity constraints are gradually integrated into the objective function to achieve a balance between the optimization goal and the resource constraints. Through multiple iterations, the Lagrangian relaxation method can effectively integrate the global constraints into the objective function to achieve the optimal task planning under resource constraints. Finally, the optimization process outputs an observation instruction set that satisfies the power and storage capacity constraints, ensuring the maximization of the task completion rate and the minimization of energy consumption.

[0110] Step 5: Pareto optimization using adaptive weights;

[0111] Step 5.1: Define initial weights;

[0112] Set the initial weight coefficient α 0 and β 0 , as the benchmark weights for energy consumption and task completion rate;

[0113] Step 5.2: Adjust the weight according to the remaining resources of the satellite;

[0114] Dynamically adjust the energy consumption weight α according to the remaining power of each satellite i :

[0115]

[0116] Among them, γ is the adjustment coefficient, which is used to control the amplitude of weight adjustment; is the remaining power of satellite i. represents the maximum power of satellite i, E i (t) represents the power of satellite i at time t.

[0117] Step 5.3: Adjust weights based on task priorities;

[0118] According to the priority of each task, dynamically adjust the task completion rate weight β j :

[0119]

[0120] Among them, δ is the adjustment coefficient, which is used to control the amplitude of weight adjustment; Priority j is the priority of task j; max It is the highest priority value among all tasks;

[0121] Step 5.4: Optimize the objective function update;

[0122] As the weight coefficients are adjusted dynamically, the optimization objective function is also updated to reflect the current resource status and task priority:

[0123]

[0124] Through Pareto optimization with adaptive weights, the optimization target is dynamically adjusted according to the real-time satellite resource status and task priority to achieve the best balance between energy consumption and task completion rate; ultimately, the optimization process outputs an observation instruction set that meets resource constraints, ensuring the maximization of task completion rate and minimization of energy consumption.

[0125] Furthermore, the specific method of step 1.4 is:

[0126] 1) Energy consumption of side swing angle adjustment;

[0127] Satellite i adjusts its lateral swing angle θ at time t i (t) Energy consumed Proportional to the absolute value of the angle change:

[0128]

[0129] Where: k 1 is the energy consumption coefficient per unit angle adjustment, in joules / radian; Δt is the time step; the adjustment of the side swing angle consumes energy, and the greater the angle change, the higher the energy consumption;

[0130] 2) Energy consumption when the remote sensor is turned on;

[0131] When the remote sensor is turned on, the energy consumed per unit time is k 2 :

[0132]

[0133] Where: k 2 is the energy consumption coefficient of the remote sensor per unit time; s i(t)∈{0,1} is the state variable of the remote sensor, 1 means on, 0 means off; the remote sensor consumes energy continuously when it is on, and the longer it is on, the higher the energy consumption;

[0134] 3) Resolution adjustment energy consumption;

[0135] Adjusting the resolution of the remote sensor also consumes energy. It is assumed that the energy consumption is proportional to the absolute value of the resolution change:

[0136]

[0137] Where: k 3 is the energy consumption coefficient adjusted for unit resolution, R i (t) is the actual observation resolution of satellite i at time t;

[0138] Adjusting the resolution consumes energy. The greater the change in resolution, the higher the energy consumption.

[0139] 4) Total energy consumption;

[0140] The total energy consumption E of satellite i at time t i (t) is:

[0141]

[0142] The total energy consumption includes three parts: side swing angle adjustment, remote sensor activation and resolution adjustment.

[0143] Furthermore, the specific method of step 1.6 is:

[0144] 1) Power constraints;

[0145] The total energy consumption of satellite i within the mission time window cannot exceed its power capacity

[0146]

[0147] Among them, E i (t) represents the energy consumption of satellite i at a certain moment, ensuring that the total energy consumption of the satellite during the mission does not exceed its power reserve to prevent energy depletion.

[0148] 2) Storage capacity constraints;

[0149] The total amount of data generated by satellite i within the mission time window cannot exceed its storage capacity

[0150]

[0151] Among them, D i(t) represents the amount of data generated by satellite i per unit time, ensuring that the amount of data generated by the satellite during the mission does not exceed the capacity of its storage device to prevent data overflow.

[0152] 3) Observation coverage constraints;

[0153] In order to ensure that task j is completed, the coverage area of ​​the target area must reach its total area A. j :

[0154]

[0155] Among them, s i (t)∈{0, 1} is the state variable of the remote sensor, 1 means on, 0 means off; C j ∈{0, 1} is the completion status of task j; it ensures that the total observed area of ​​each target area at least reaches its actual area to ensure the completion of the task;

[0156] 4) Side swing angle constraint;

[0157] The roll angle θ of satellite i at any time t i (t) must, to the extent physically possible:

[0158]

[0159] where θ i (t) represents the roll angle of satellite i at time t.

[0160] 5) Side swing angular velocity constraint;

[0161] The rate of change of the roll angle of satellite i at any time t cannot exceed its maximum allowable value

[0162]

[0163] in It represents the maximum side swing angle that can be allowed physically for satellite i.

[0164] 6) Resolution constraints;

[0165] The observation resolution R of satellite i at any time t is i (t) must, within its practicable scope:

[0166] R min ≤R i (t)≤R max

[0167] Where R min Indicates the minimum resolution that the satellite's payload equipment can be set to, R maxIndicates the maximum resolution that can be set for satellite payload equipment.

[0168] 7) Remote sensor status constraints;

[0169] Status of the remote sensor i (t) must be a binary variable:

[0170] s i (t)∈{0,1}

[0171] 8) Task completion status;

[0172] Task completion status C j Must be a binary variable:

[0173] C j ∈{0, 1}

[0174] Task j completed C j =1, not completed C j =0;

[0175] Taking energy consumption and task completion rate into consideration, a multi-objective optimization function is established:

[0176]

[0177] Where: α i is the energy consumption weight coefficient of satellite i, β j is the completion rate weight coefficient of task j, E i (t) is the energy consumption of satellite i at time t, C j is the completion status of task j.

[0178] Furthermore, the specific method of step 2.4 is:

[0179] Step 2.4.1: Each satellite independently performs local optimization by:

[0180] Each satellite i independently solves the following optimization problem:

[0181]

[0182] This means that each satellite optimizes its own decision variables based on the current global variable z and the multiplier λ. represents the value of the enhanced Lagrangian function;

[0183] Step 2.4.2: Global variable update:

[0184] The global variable z is updated by the average of the solutions to all subproblems:

[0185]

[0186] Step 2.4.3: Lagrange multiplier update:

[0187] The Lagrange multiplier λ is updated according to the current error:

[0188]

[0189] Through multiple iterations, the global objective function is optimized while satisfying all consistency constraints and resource constraints; finally, the sway angle θ of each satellite at each time step is output. i (t), observation resolution R i (t) and the sensor state s i (t) to achieve optimal planning of multi-satellite collaborative observation tasks.

[0190] Through Pareto optimization with adaptive weights, the algorithm can dynamically adjust the optimization target according to the real-time satellite resource status and mission priority to achieve the best balance between energy consumption and mission completion rate. Ultimately, the optimization process outputs an observation instruction set that meets resource constraints, ensuring the maximization of mission completion rate and the minimization of energy consumption. BRIEF DESCRIPTION OF THE DRAWINGS

[0191] Figure 1 The figure is a schematic diagram of the satellite network task scheduling process in an example of the present invention.

[0192] Figure 2 It is a block diagram of the multi-satellite multi-task planning method based on the Pareto front in an example of the present invention.

[0193] Figure 3 This is a technical roadmap for multi-satellite multi-task planning in the example of the present invention. Specific implementation plan

[0194] Step 1: Build a link visibility prediction model based on orbit and sub-satellite point parameters;

[0195] In order to realize the efficient observation planning of multiple satellites to multiple ground target areas, this problem model (PM) establishes the dynamic relationship between satellite orbit parameters, sub-satellite point position, observation window and target area position. The model aims to achieve comprehensive coverage of multiple target areas by optimizing the satellite's observation instruction set, including observation time, sway angle and sensor status, under limited resources and time constraints, while maximizing the mission completion rate and minimizing energy consumption.

[0196] Step 1.1: Construct satellite orbit and sub-satellite point model;

[0197] 1) Orbital parameters

[0198] Assume that there are N satellites in the system, and the orbital parameters of satellite i include:

[0199] Orbital inclination: I i (Unit: radians)

[0200] Track height: h i (Unit: meter)

[0201] Ascending node right ascension: Ω i (Unit: radians)

[0202] Orbital period: T i (Unit: seconds)

[0203] Orbital semi-major axis: a i (Unit: meter)

[0204] Orbital eccentricity: e i (dimensionless)

[0205] Argument of perigee: ω i (Unit: radians)

[0206] Initial orbital position: θ i0 (Unit: radians)

[0207] 2) Subsatellite point position calculation

[0208] In order to simplify the model, it is assumed that the orbits of all satellites are circular (i.e., the orbital eccentricity e i =0). Therefore, the average angular velocity n of satellite i i for:

[0209] n i =2π / T i

[0210] The longitude λ of the subsatellite point of satellite i at time t i (t) and latitude φ i (t) can be calculated by the following formula:

[0211] φ i (t) = arcsin(sinI i ·sin(n i t+θ i0 ))

[0212] λ i (t) = Ω i +(n i t+θ i0 )cosI i -ω E t

[0213] in:

[0214] ω E =7.2921150×10 -5rad / s is the angular velocity of the Earth's rotation.

[0215] t is the time, starting from the initial epoch time t of the satellite i0 .

[0216] The above formula simplifies the calculation of the sub-satellite point position. It is directly based on the satellite's average angular velocity and orbital parameters, avoiding complex orbital mechanics derivation and ensuring the efficiency and accuracy of the calculation.

[0217] Step 1.2: Build a visibility model of the target area;

[0218] 1) Target area location

[0219] The center position of the target area j is represented by the longitude λ j and latitude φ j OK. The area of ​​the target area is A j (Unit: square meters).

[0220] 2) Geocentric angular distance calculation

[0221] The geocentric angular distance Δ between satellite i and target area j at time t ij (t) can be calculated using the spherical cosine formula:

[0222] cosΔ ij (t) = sinφ i (t)sinφ j +cosφ i (t)cosφ j cos(λ i (t)-λ j )

[0223] Therefore, the geocentric angular distance Δ ij (t) is:

[0224] Δ ij (t) = arccos(sinφ i (t)sinφ j +cosφ i (t)cosφ j cos(λ i (t)-λ j ))

[0225] Geocentric angle distance Δ ij (t) is the key parameter to determine whether satellite i can observe target area j. The feasibility of observation can be determined by calculating the geocentric angular distance between the satellite sub-satellite point and the center of the target area.

[0226] 3) Maximum observable geocentric angle

[0227] Maximum observable geocentric angle of satellite i With its maximum side swing angle and track height h i The relationship is:

[0228]

[0229] Among them, R E =6.371×10 6 m is the mean radius of the Earth.

[0230] Maximum observable geocentric angle Indicates that satellite i does not exceed its maximum lateral swing angle Under the condition of , the geocentric angle distance of the farthest target area that can be observed.

[0231] 4) Visibility function

[0232] The visibility function V of satellite i to target area j at time t is ij (t) is defined as:

[0233]

[0234] Visibility function V ij (t) is used to indicate whether satellite i can observe target area j at time t. The local centroid distance Δ ij (t) is less than or equal to the maximum observable geocentric angle Satellites can observe.

[0235] Step 1.3: Construct the observation range and side swing angle model;

[0236] 1) Ground projection width

[0237] The observed ground projection width W of satellite i at time t i (t) is determined by its side swing angle θ i (t) and the field of view (FOV) of the remote sensor β i Decide:

[0238] W i (t) = 2(h i +R E )tan(β i / 2)cosθ i (t)

[0239] Observation ground projection width W i (t) represents the ground width that the remote sensor can cover within time t. The side swing angle θ i Adjustment of (t) affects the width of the observation range.

[0240] 2) Satellite ground speed

[0241] Satellite ground speed V i (t) is:

[0242] V i (t)=(h i +R E ) i i i / R E

[0243] The orbital speed for:

[0244]

[0245] Satellite ground speed V i (t) reflects the moving speed of satellite i on the ground and determines the ground distance that can be covered per unit time.

[0246] 3) Observation area

[0247] The observation area A of satellite i at time t i (t) is:

[0248] A i (t) = W i (t)·V i (t)·Δt

[0249] Among them, Δt is the time step.

[0250] Observation area A i (t) represents the ground area that satellite i can cover in time t, combining the observation width and ground speed.

[0251] Step 1.4: Construct energy consumption model;

[0252] 1) Energy consumption of side swing angle adjustment

[0253] Satellite i adjusts its lateral swing angle θ at time t i (t) Energy consumed Proportional to the absolute value of the angle change:

[0254]

[0255] in:

[0256] k 1 Energy consumption factor adjusted for unit angle (unit: joule / radian).

[0257] Δt is the time step (unit: seconds).

[0258] Adjusting the side swing angle requires energy. The greater the angle change, the higher the energy consumption.

[0259] 2) Energy consumption when remote sensor is turned on

[0260] When the remote sensor is turned on, the energy consumed per unit time is k 2 :

[0261]

[0262] in:

[0263] k 2 It is the energy consumption coefficient of the remote sensor per unit time (unit: joule / second).

[0264] s i (t)∈{0, 1} is the state variable of the remote sensor, 1 means on and 0 means off.

[0265] Δt is the time step (unit: seconds)

[0266] The remote sensor consumes energy continuously when it is turned on. The longer it is turned on, the higher the energy consumption.

[0267] 3) Resolution adjustment energy consumption

[0268] Adjusting the resolution of the remote sensor also consumes energy. It is assumed that the energy consumption is proportional to the absolute value of the resolution change:

[0269]

[0270] in:

[0271] k 3 Energy consumption factor adjusted for unit resolution (in joules / meter).

[0272] R i (t) is the actual observation resolution of satellite i at time t (unit: meter).

[0273] Δt is the time step (unit: seconds).

[0274] Adjusting the resolution consumes energy. The greater the change in resolution, the higher the energy consumption.

[0275] 4) Total energy consumption

[0276] The total energy consumption E of satellite i at time t i (t) is:

[0277]

[0278] The total energy consumption includes three parts: side swing angle adjustment, remote sensor activation and resolution adjustment, which fully reflects the energy consumption of the satellite during the observation process.

[0279] Step 1.5: Build a data generation model;

[0280] During the observation process, the remote sensor will generate data volume D i (t), and the observation area A i (t) and resolution R i (t). Assuming that the amount of data is proportional to the number of pixels, the number of pixels N i (t) can be expressed as:

[0281] N i (t) = A i (t) / (R i (t)) 2

[0282] Therefore, the data volume D i (t) is:

[0283] D i (t) = d 0 N i (t) = d 0 A i (t) / (R i (t)) 2

[0284] in:

[0285] d 0 Generates coefficients for data per unit pixel (unit: byte / pixel).

[0286] Data volume D i (t) represents the amount of data generated by satellite i in time t. The higher the resolution (R i The smaller (t) is, the more pixels there are and the larger the amount of data is.

[0287] Step 1.6: Define constraints and optimization objectives;

[0288] To ensure the physical feasibility and practical operability of the model, the following constraints need to be met:

[0289] 1) Power Constraint

[0290] The total energy consumption of satellite i within the mission time window cannot exceed its power capacity

[0291]

[0292] Ensure that the satellite's total energy consumption during the mission does not exceed its power reserves to prevent energy depletion.

[0293] 2) Storage capacity constraints

[0294] The total amount of data generated by satellite i within the mission time window cannot exceed its storage capacity

[0295]

[0296] Ensure that the amount of data generated by the satellite during the mission does not exceed the capacity of its storage device to prevent data overflow.

[0297] 3) Observation coverage constraints

[0298] In order to ensure that task j is completed, the coverage area of ​​the target area must reach its total area A. j :

[0299]

[0300] in:

[0301] C j ∈{0, 1} is the completion status of task j.

[0302] Ensure that the total observed area of ​​each target area \(j\) at least reaches its actual area \(A_j\) to ensure the completion of the task.

[0303] 4) Side swing angle constraint

[0304] The roll angle θ of satellite i at any time t i (t) must, to the extent physically possible:

[0305]

[0306] Make sure that the sway angle is not adjusted beyond the physical limitations of the remote sensor to avoid damage to the device or performance degradation.

[0307] 5) Side swing angular velocity constraint

[0308] The rate of change of the roll angle of satellite i at any time t cannot exceed its maximum allowable value

[0309]

[0310] Limit the adjustment speed of the side swing angle to avoid mechanical wear or control system failure due to over-fast adjustment.

[0311] 6) Resolution Constraints

[0312] The observation resolution R of satellite i at any time t is i ( t) must, within its operational scope:

[0313] R min ≤R i (t)≤R max

[0314] Ensure that the resolution of the remote sensor is adjusted within its technical capabilities to avoid degradation of observation quality due to too low or too high resolution.

[0315] 7) Sensor status constraints

[0316] Status of the remote sensor i (t) must be a binary variable:

[0317] s i (t)∈{0,1}

[0318] The remote sensor can only be in the on or off state, not in the half-on state, ensuring the clarity of state control.

[0319] 8) Task completion status

[0320] Task completion status C j Must be a binary variable:

[0321] C j ∈{0, 1}

[0322] Task j is either completed (C j =1), or not completed (C j =0) to ensure the clarity of the task status.

[0323] Taking energy consumption and task completion rate into consideration, a multi-objective optimization function is established:

[0324]

[0325] in:

[0326] α i is the energy consumption weight coefficient of satellite i.

[0327] β j is the completion rate weight coefficient of task j.

[0328] E i (t) is the energy consumption of satellite i at time t.

[0329] C j is the completion status of task j.

[0330] By adjusting the weight coefficient α i and β j, the best balance can be found between minimizing energy consumption and maximizing mission completion rate. The weight coefficient reflects the importance of different satellites and missions, allowing dynamic adjustment to adapt to different optimization needs.

[0331] Step 2: Initialization;

[0332] Set initial variables: θ i (0), R i (0),s i (0)

[0333] Initialize Lagrange multipliers: λ = 0, μ = 0

[0334] Set initial weight: α i =α 0 , β j =β 0

[0335] Set adjustment coefficient: γ, δ

[0336] Set the time step Δt and the maximum number of iterations.

[0337] Step 3: Iterative process;

[0338] like Figure 2 As shown, the present invention will iterate in the planning model, and in each iteration, the following steps are performed until the convergence condition is met or the maximum number of iterations is reached:

[0339] Step 3.1: Local Optimization (ADMM Subproblem)

[0340] Each satellite performs the following operations in parallel:

[0341] 1) Calculate the subsatellite point position φ i (t), λ i (t)

[0342] 2) Determine the visibility V with the target area j ij (t)

[0343] 3) Construct and solve the SOCP subproblem to obtain the optimized θ i (t), R i (t), s i (t)

[0344] 4) Calculate the observation area A i (t) and energy consumption A i (t)

[0345] Step 3.2: Global variable update (ADMM update)

[0346] 1) Calculate global variables

[0347]

[0348]

[0349] 2) Update the Lagrange multipliers λ and μ:

[0350]

[0351] Step 3.3: Adaptive weight adjustment

[0352] Adjust the weight coefficient according to the remaining satellite resources and mission priority:

[0353]

[0354] Step 3.4: Check the convergence bar

[0355] If the objective function change is less than the preset threshold, or the maximum number of iterations is reached, the iteration ends; otherwise, return to step 2 to continue the iteration.

[0356] Step 4: Output the results;

[0357] Generate optimized observation instruction set: θ i (t), R i (t), s i (t)

[0358] Calculate and summarize total energy consumption and task completion: C j

[0359] Output the final observation planning plan to ensure the efficient completion of multi-satellite collaborative observation tasks.

Claims

1. A joint optimization method for edge computing offloading and resource allocation in a low-earth orbit satellite network, the method comprising: Step 1: Construct a link visibility prediction model based on orbital and sub-satellite point parameters; Step 1.1: Construct a satellite orbit and sub-satellite point model; Define orbital parameters. Assume there are N satellites in the system. The orbital parameters of satellite i include: Orbital inclination: I i , in radians; orbit height: h i , in meters; Ascending node right ascension: Ω i , in radians; orbital period: T i , in seconds; orbital semi-major axis: a i , in meters; orbital eccentricity: e i , dimensionless; argument of perigee: ω i , in radians; initial orbital position: θ i0 , in radians; The method for calculating the sub-satellite point position is: Assume that the orbits of all satellites are circular orbits, that is, the orbital eccentricity e i =0; therefore, the average angular velocity n of satellite i i for: n i =2π / T i The longitude λ of the subsatellite point of satellite i at time t i (t) and latitude φ i (t) is calculated by the following formula: <h2 style=";text-align:left;direction:ltr">φ<h2 style=";text-align:left;direction:ltr"> i <h2 style=";text-align:left;direction:ltr"> (t) = arcsin(sinI<h2 style=";text-align:left;direction:ltr"> i <h2 style=";text-align:left;direction:ltr"> sin(n)<h2 style=";text-align:left;direction:ltr"> i <h2 style=";text-align:left;direction:ltr"> t+θ<h2 style=";text-align:left;direction:ltr"> i0 <h2 style=";text-align:left;direction:ltr"> )) l i (t)=Ω i +(n i t+θ i0 )cosI i -oh E t Where: E =7.2921150×10 -5 rad / s is the angular velocity of the Earth's rotation, t is the time, starting from the initial epoch time t of the satellite i0 ; Step 1.2: Construct a target area visibility model; 1) Definition: The center position of the target area j is represented by the longitude λ j and latitude φ j Determine that the area of ​​the target area is A j , the unit is square meters; 2) The method for calculating the geocentric angular distance is: The geocentric angular distance Δ between satellite i and target area j at time t ij (t) is calculated by the spherical cosine formula: cosΔ ij (t)=sinφ i (t)sinφ j +cosφ i (t)cosφ j cos(λ i (t)-λ j ) Therefore, the geocentric angular distance Δ ij (t) is: D ij (t)=arccos(sinφ i (t)sinφ j +cosφ i (t)cosφ j cos(λ i (t)-λ j )) Geocentric angular distance Δ ij (t) is to determine whether satellite i can observe target area j; 3) The method for calculating the maximum observable geocentric angle is: Maximum observable geocentric angle of satellite i With its maximum side swing angle and track height h i The relationship is: Among them, R E =6.371×10 6 m is the average radius of the Earth; Maximum observable geocentric angle Indicates that satellite i does not exceed its maximum lateral swing angle Under the condition of , the geocentric angle distance of the farthest target area that can be observed; 4) The visibility function is: The visibility function V of satellite i to target area j at time t is ij (t) is defined as: Visibility function V ij (t) is used to indicate whether satellite i can observe target area j at time t; local centroid distance Δ ij (t) is less than or equal to the maximum observable geocentric angle When the satellite can observe; Step 1.3: Construct an observation range and slewing angle model; 1) The method for calculating the ground projection width is; The observed ground projection width W of satellite i at time t i (t) is determined by its side swing angle θ i (t) and the field of view angle β of the remote sensor i Decide: W i (t)=2(h i +R E )tan(β i / 2)cosθ i (t) Observation ground projection width W i (t) represents the ground width that the remote sensor can cover within time t for satellite i; the side swing angle θ i The adjustment of (t) affects the width of the observation range; 2) The method for calculating the satellite ground speed is: Satellite ground speed V i (t) is: V i (t)=(h i +R E )n i cosI i / R E The orbital speed for: Satellite ground speed V i (t) reflects the moving speed of satellite i on the ground and determines the ground distance that can be covered per unit time; 3) The method for calculating the observation area is: The observation area A of satellite i at time t i (t) is: A i (t)=W i (t)·V i (t)·Δt Among them, Δt is the time step, and the observation area A is i (t) represents the ground area that satellite i can cover in time t; Step 1.4: Construct an energy consumption model; Step 1.5: Construct a data generation model; During the observation process, the remote sensor will generate data volume D i (t), and the observation area A i (t) and resolution R i (t) related; Assume that the amount of data is proportional to the number of pixels, the number of pixels N i (t) is expressed as: N i (t)=A i (t) / (R i (t)) 2 Therefore, the data volume D i (t) is: D i (t)=d0N i (t)=d0A i (t) / (R i (t)) 2 Where: d0 is the data generation coefficient of the unit pixel; the data volume D i (t) represents the amount of data generated by satellite i in time t. The higher the resolution, the more pixels, and the larger the amount of data; Step 1.6: Define the constraint conditions and optimization objectives; including: power constraint, storage capacity constraint, observation coverage constraint, slewing angle constraint, slewing angular velocity constraint, resolution constraint, remote sensor state constraint, task completion status; Step 2: Use the alternating direction method of multipliers to solve the problem; Step 2.1: Problem decomposition; The global optimization problem is decomposed into N satellite sub-problems, each of which involves only the decision variable θ corresponding to satellite i. i (t), R i (t), s i (t); Step 2.2: Introduce auxiliary variables z and consistency constraints; Step 2.3: Construct an augmented Lagrangian function; Construct an augmented Lagrangian function to include the consistency constraint. The terms of the formula are as follows: Objective function part: Where: α i and β j are the weight coefficients of energy consumption and task completion rate, E i (t) represents the energy consumption of satellite i at time t, C j Indicates the completion status of task j; Lagrange multiplier and penalty term part: is the Lagrange multiplier of the corresponding variable, ρ is the penalty parameter used to control the weight of the consistency constraint, and θ i (t), R i (t), s i (t) represent the sway angle, observation resolution and sensor status of satellite i at time t, is a global variable used to coordinate the solutions of each subproblem; enhanced Lagrangian function Based on the original objective function, Lagrange multipliers and penalty terms are added to deal with the constraints in the optimization problem; Step 2.4: Gradually approximate the global optimal solution by iteratively updating the local variables, global variables, and Lagrange multipliers; Step 3: Second-order cone programming transformation to simplify the optimization; Step 3.1: Determine the spherical distance constraint; The original spherical distance constraint is in a non-linear form: cos△(t)=sino(t)sin中,+cosb;(t)coso,cos(入(t)一入,) Linearize it through Taylor expansion or small angle approximation: Because Δ ij The value of (t) is extremely small, so we set: Express it as a second-order cone constraint: Convert the non-linear spherical distance constraint to a second-order cone form through approximation; Step 3.2: Linearize the energy consumption model; Adjust the energy consumption model for the slewing angle; Introducing auxiliary variables And add linear constraints: Step 3.3: Construct a second-order cone constraint SOCP problem; The optimization problem is in the standard SOCP problem form, including a linear objective function, linear constraints, and second-order cone constraints: minc" min Among them, c, A k 、b k 、c k ,d k are known parameters, and x is the decision variable; Step 4: Use the Lagrangian relaxation method to handle the global constraints; Step 4.1: Construct a Lagrangian function; Introduce the global constraints into the objective function through Lagrange multipliers: Where λ is the Lagrange multiplier for the power constraint, and μ is the Lagrange multiplier for the storage capacity constraint; Step 4.2: Multiplier update; Dynamically adjust the Lagrange multipliers to gradually satisfy the constraint conditions through the gradient ascent method: Where η is the step size parameter used to control the update speed of the multipliers; Step 4.3: Iterative optimization; In each iteration, by updating the Lagrangian multiplier, the power and storage capacity constraints are gradually integrated into the objective function to achieve a balance between the optimization goal and the resource constraints. Through multiple iterations, the Lagrangian relaxation method can effectively integrate the global constraints into the objective function to achieve the optimal task planning under resource constraints. Finally, the optimization process outputs an observation instruction set that satisfies the power and storage capacity constraints, ensuring the maximization of the task completion rate and the minimization of energy consumption. Step 5: Pareto optimization using adaptive weights; Step 5.1: Define initial weights; Set the initial weight coefficients α0 and β0 as the benchmark weights for energy consumption and task completion rate; Step 5.2: Adjust the weight according to the remaining resources of the satellite; Dynamically adjust the energy consumption weight α according to the remaining power of each satellite i : Among them, γ is the adjustment coefficient, which is used to control the amplitude of weight adjustment; is the remaining power of satellite i. represents the maximum power of satellite i, E i (t) represents the power of satellite i at time t. Step 5.3: Adjust weights based on task priorities; According to the priority of each task, dynamically adjust the task completion rate weight β j : Among them, δ is the adjustment coefficient, which is used to control the amplitude of weight adjustment; Priority j is the priority of task j; max It is the highest priority value among all tasks; Step 5.4: Optimize the objective function update; As the weight coefficients are adjusted dynamically, the optimization objective function is also updated to reflect the current resource status and task priority: Through Pareto optimization with adaptive weights, the optimization target is dynamically adjusted according to the real-time satellite resource status and task priority to achieve the best balance between energy consumption and task completion rate; ultimately, the optimization process outputs an observation instruction set that meets resource constraints, ensuring the maximization of task completion rate and minimization of energy consumption.

2. A low-orbit satellite network edge computing offloading and resource allocation joint optimization method as claimed in claim 1, characterized in that: The specific method of step 1.4 is: 1) Energy consumption of side swing angle adjustment; Satellite i adjusts its lateral swing angle θ at time t i (t) Energy consumed Proportional to the absolute value of the angle change: Where: k1 is the energy consumption coefficient per unit angle adjustment, in joules / radian; Δt is the time step; the adjustment of the side swing angle consumes energy, and the greater the angle change, the higher the energy consumption; 2) Energy consumption when the remote sensor is turned on; When the remote sensor is turned on, the energy consumed per unit time is k2: Where: k2 is the energy consumption coefficient of the remote sensor per unit time; s i (t)∈{0,1} is the state variable of the remote sensor, 1 means on, 0 means off; the remote sensor consumes energy continuously when it is on, and the longer it is on, the higher the energy consumption; 3) Resolution adjustment energy consumption; Adjusting the resolution of the remote sensor also consumes energy. It is assumed that the energy consumption is proportional to the absolute value of the resolution change: Where: k3 is the energy consumption coefficient of unit resolution adjustment, R i (t) is the actual observation resolution of satellite i at time t; Adjusting the resolution consumes energy. The greater the change in resolution, the higher the energy consumption. 4) Total energy consumption; The total energy consumption E of satellite i at time t i (t) is: The total energy consumption includes three parts: side swing angle adjustment, remote sensor activation and resolution adjustment.

3. A low-orbit satellite network edge computing offloading and resource allocation joint optimization method as claimed in claim 1, characterized in that: The specific method of step 1.6 is: 1) Power constraints; The total energy consumption of satellite i within the mission time window cannot exceed its power capacity Among them, E i (t) represents the energy consumption of satellite i at a certain moment, ensuring that the total energy consumption of the satellite during the mission does not exceed its power reserve to prevent energy depletion. 2) Storage capacity constraints; The total amount of data generated by satellite i within the mission time window cannot exceed its storage capacity Among them, D i (t) represents the amount of data generated by satellite i per unit time, ensuring that the amount of data generated by the satellite during the mission does not exceed the capacity of its storage device to prevent data overflow. 3) Observation coverage constraints; In order to ensure that task j is completed, the coverage area of ​​the target area must reach its total area A. j : Among them, s i (t)∈{0,1} is the state variable of the remote sensor, 1 means on, 0 means off; C j ∈{0, 1} is the completion status of task j; it ensures that the total observed area of ​​each target area at least reaches its actual area to ensure the completion of the task; 4) Side swing angle constraint; The roll angle θ of satellite i at any time t i (t) must, to the extent physically possible: where θ i (t) represents the roll angle of satellite i at time t. 5) Side swing angular velocity constraint; The rate of change of the roll angle of satellite i at any time t cannot exceed its maximum allowable value in It represents the maximum side swing angle that can be allowed physically for satellite i. 6) Resolution constraints; The observation resolution R of satellite i at any time t is i (t) must, within its practicable scope: R min ≤R i (t)≤R max Where R min Indicates the minimum resolution that the satellite's payload equipment can be set to, R max Indicates the maximum resolution that can be set for satellite payload equipment. 7) Remote sensor status constraints; Status of the remote sensor i (t) must be a binary variable: s i (t)∈{0,1} 8) Task completion status; Task completion status C j Must be a binary variable: C j ∈{0，1} Task j completed C j =1, not completed C j =0; Taking energy consumption and task completion rate into consideration, a multi-objective optimization function is established: Where: α i is the energy consumption weight coefficient of satellite i, β j is the completion rate weight coefficient of task j, E i (t) is the energy consumption of the satellite at time t, C j is the completion status of task j.

4. A low-orbit satellite network edge computing offloading and resource allocation joint optimization method as claimed in claim 1, characterized in that: The specific method of step 2.4 is: Step 2.4.1: Each satellite independently performs local optimization by: Each satellite i independently solves the following optimization problem: This means that each satellite optimizes its own decision variables according to the current global variable z and multiplier λ. represents the value of the enhanced Lagrangian function; Step 2.4.2: Global variable update: The global variable z is updated by the average of the solutions to all subproblems: Step 2.4.3: Lagrange multiplier update: The Lagrange multiplier λ is updated according to the current error: Through multiple iterations, the global objective function is optimized while satisfying all consistency constraints and resource constraints; finally, the sway angle θ of each satellite at each time step is output. i (t), observation resolution R i (t) and the sensor state s i (t) to achieve optimal planning of multi-satellite collaborative observation tasks.

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