Mobile ship tracking task optimization method and system based on ADMM algorithm

Abstract

The application provides a mobile ship tracking task optimization method and system based on an ADMM algorithm, relates to the technical field of satellite task planning, and solves the technical problems of high calculation complexity, dynamic response lag, and observation blind area caused by multi-satellite resource competition in the prior art. The method comprises the following steps: acquiring a target sea area image to be observed; dividing the target sea area image into a plurality of grid cells; setting an observation time period and dividing the observation time period into a plurality of observation sub-periods; acquiring a plurality of visible satellites corresponding to the observation sub-periods, assigning grid cells to each visible satellite, and obtaining a corresponding observation ship list; initializing algorithm parameters; optimizing and detecting conflicts of the plurality of observation ship lists through the ADMM algorithm to obtain an optimal observation list; and observing and sorting the plurality of ships in the optimal observation list in chronological order to obtain an observation task plan table. The application is used in the process of tracking mobile ships at sea.

Description

Technical Field

[0001] This application relates to the field of satellite mission planning technology, and in particular to a method and system for optimizing moving vessel tracking missions based on the ADMM algorithm. Background Technology

[0002] In missions involving the tracking and monitoring of moving vessels at sea using synthetic aperture radar (SAR) satellite constellations, existing technologies primarily rely on centralized mission planning methods. These methods typically require aggregating all information, including satellite status and vessel dynamics, at a ground station or a single primary satellite for unified processing to generate a global observation plan. However, as the constellation size and the number of vessels increase, this centralized planning faces severe computational bottlenecks. The problem complexity increases exponentially with the number of satellites and vessels, making it difficult to complete the planning within a limited timeframe. Furthermore, the continuous movement of vessels at sea demands that the observation plan possess a high degree of dynamic responsiveness, while communication delays between satellites and ground stations make it difficult for centralized systems to update and issue adjustment commands in a timely manner. In addition, in multi-satellite collaborative scenarios, the lack of efficient conflict resolution mechanisms easily leads to multiple satellites competing for the same observation target, while other targets are overlooked, resulting in resource waste and observation blind spots. Summary of the Invention

[0003] This application provides an optimization method and system for tracking moving ships based on the ADMM algorithm, which solves the technical problems of high computational complexity, lag in dynamic response, and blind spots caused by competition for multi-satellite resources when facing large-scale scenarios with multiple satellites and multiple ships.

[0004] To achieve the above objectives, this application adopts the following technical solution:

[0005] Firstly, an optimization method for tracking moving ships based on the ADMM algorithm is provided, including:

[0006] Acquire images of the target sea area to be observed;

[0007] Based on the working mode of SAR satellites, constellation revisit characteristics, and ship speed, the target sea area image is divided into multiple grid cells;

[0008] The observation time period is set, and the observation time period is divided into multiple observation sub-periods based on grid coverage and ship monitoring frequency;

[0009] Multiple visible satellites are acquired based on the observation sub-cycle, and grid cells and corresponding list of observation vessels are assigned to each visible satellite based on the visible duration.

[0010] Initialize algorithm parameters; wherein, the algorithm parameters include ship priority weights, ADMM parameters, and global variables;

[0011] The optimal observation list is obtained by optimizing and detecting conflicts in multiple observation vessel lists using the ADMM algorithm.

[0012] The observation task plan table is obtained by sorting the multiple ships in the optimal observation list according to time.

[0013] Based on the above technical solutions, the mobile vessel tracking task optimization method based on the ADMM algorithm provided in this application firstly transforms the complex global continuous optimization problem into a discrete distributed sub-problem by dividing the target sea area into grids and combining it with a time sub-period partitioning strategy, significantly reducing computational complexity and enabling the system to meet the real-time planning requirements in large-scale scenarios. Secondly, through a responsibility area allocation mechanism based on visible duration and a conflict detection module integrating an auction algorithm, the resource competition problem in multi-satellite collaborative observation is effectively solved, achieving load balancing of observation tasks. While ensuring key monitoring of high-priority vessels, the overall utilization efficiency of constellation resources is significantly improved. Finally, through iterative coordination of the ADMM algorithm, this method effectively converges the local optimization results of each satellite to a globally approximate optimal solution, generating a coordinated and orderly observation plan. Thus, under the constraint of limited onboard resources, it achieves continuous, stable, and efficient tracking and monitoring capabilities for multiple mobile vessels in a wide sea area.

[0014] In conjunction with the first aspect above, in one possible implementation, the initialization algorithm parameters include:

[0015] Historical observation data is acquired, and ship priority weights are set based on the historical observation data; wherein, the historical observation data includes ship type, navigation area, and historical behavior;

[0016] Initialize the penalty coefficient, maximum number of iterations, and convergence threshold;

[0017] Initialize decision variables, global consistency variables, and Lagrange multipliers; wherein the initial state of the decision variables is an unobserved task.

[0018] In conjunction with the first aspect above, in one possible implementation, the optimization and conflict detection of multiple observed vessel lists using the ADMM algorithm includes:

[0019] S31. Solve the optimization problem for the observation vessel list of each visible satellite to obtain multiple observation sublists;

[0020] S32. Perform observation conflict detection on multiple observation sublists and update the observation tasks through a bidding auction mechanism to obtain the optimal observation list;

[0021] S33. Update the global consistency variables and Lagrange multipliers, and perform a convergence test on the optimal observation list; if the preset convergence condition is not met, repeat steps S31-S32; if the convergence condition is met, exit the loop.

[0022] In conjunction with the first aspect above, in one possible implementation, the optimization problem of the observation vessel list for each visible satellite includes:

[0023] A target optimization function is constructed for the list of observation vessels for each visible satellite; wherein the expression of the target optimization function is:

[0024] ;

[0025] In the formula, For the first One ship, For the first One visible satellite, For visual satellites List of observation vessels; For binary decision variables, Indicates visual satellite execution vessel The k Second observation; For ships Total number of observations This is a time cost penalty coefficient. For visual satellites execution vessel The k The time cost required for each observation For the execution of ships The k The second observation and the first k -1 time interval between observations;

[0026] Define global constraints By introducing an augmented Lagrangian function, global constraints are incorporated into the objective optimization function, resulting in a satellite-level subproblem; wherein, the expression of the augmented Lagrangian function is:

[0027] ;

[0028] In the formula, For all decision variables The set, For Lagrange multipliers; This is a globally consistent variable used to enforce the decision variables of each visible satellite. Satisfy global constraints; This is the penalty coefficient, used to balance the original objective function with the constraints; and This is a coefficient matrix used to organize decision variables. and globally consistent variables Associated with constraints; This is a constant vector used to represent the boundary values ​​of the constraints;

[0029] The expression for the satellite-level subproblem is:

[0030] ;

[0031] In the formula, This represents the current iteration number. and For the first Global consistency variables and Lagrange multipliers in each iteration;

[0032] A heuristic algorithm is used to solve the satellite-level subproblems, resulting in multiple lists of observations.

[0033] In conjunction with the first aspect above, in one possible implementation, the step of detecting observation conflicts in multiple observation sublists and updating the observation task through a bidding auction mechanism includes:

[0034] S51. Sort the observation plans for the same target ship by time. If the time interval between adjacent observation sub-cycles is less than the preset time resolution and the observations are performed by different visible satellites, mark them as conflicting tasks; mark multiple conflicting tasks as a conflicting task set.

[0035] S52. Initialize bidding information for each pair of conflicting tasks in the conflicting task set; submit bids for conflicting targets based on observation costs; wherein the bids are inversely proportional to the observation costs;

[0036] S53. The coordinator selects the visual satellite with the highest bid to perform the corresponding observation task; other visual satellites participating in the bidding remove the corresponding conflicting observation tasks and update their observation plans;

[0037] S54. Repeat steps S51-S53 to traverse all target ships and generate the optimal observation list.

[0038] In conjunction with the first aspect above, in one possible implementation, the heuristic algorithm for solving the satellite-level subproblem is a genetic algorithm, including:

[0039] Initialize the population and encode the chromosomes to represent the ship task allocation scheme;

[0040] Fitness is calculated using a fitness function to evaluate the merits of task allocation schemes; wherein, the fitness function integrates the objectives of maximizing the number of observations and minimizing time cost;

[0041] Perform selection, crossover, and mutation operations to generate a new generation of population;

[0042] Iterate and optimize until the preset stopping condition is met.

[0043] In conjunction with the first aspect above, in one possible implementation, the convergence detection includes calculating the decision variables in two adjacent iterations using the Euclidean norm. The algorithm is considered to have converged when the amount of iterative change is less than the convergence threshold.

[0044] In conjunction with the first aspect above, in one possible implementation, the time cost ;in, For ships The speed of travel; A function relating to the payload system parameters of the SAR satellite, derived from time intervals. The required imaging swath width and resolution mode for this observation are determined by the calculations; the time cost is also related to the satellite's motion speed.

[0045] In conjunction with the first aspect above, in one possible implementation, the method for obtaining the list of observed vessels includes:

[0046] S91. Calculate the visibility duration between the grid cell and multiple visible satellites;

[0047] S92. Assign grid cells to visible satellites whose visible duration reaches more than 70% of the longest visible duration, and generate a satellite responsibility area mapping table;

[0048] S93. Obtain the location of the target ship and its corresponding grid cell;

[0049] S94. Assign target vessels to corresponding visible satellites based on the satellite area of ​​responsibility mapping table;

[0050] S95. Repeat steps S93-S94 to traverse all target ships and generate a list of observed ships.

[0051] Secondly, a moving vessel tracking task optimization system based on the ADMM algorithm is provided, including:

[0052] Satellite constellation module: Composed of multiple low-Earth orbit SAR satellites, each equipped with an onboard processing unit for performing local task optimization;

[0053] Command Satellite Module: Located in geosynchronous orbit, it is used for global resource coordination, ADMM parameter allocation, and conflict resolution;

[0054] Grid partitioning module: used to discretize the target sea area into a grid and store the grid geographic information;

[0055] Time management module: used to divide the observation time period and synchronize the clocks of each satellite;

[0056] Communication module: Supports inter-satellite data transmission for exchanging ship status, observation plans, and ADMM global variables;

[0057] Task generation module: Used to output an observation task plan table sorted by time and visualize it.

[0058] This application provides a method and apparatus for optimizing moving vessel tracking tasks based on the ADMM algorithm. By introducing a distributed optimization framework based on the ADMM algorithm, it effectively overcomes the inherent defects of centralized planning. First, by decomposing the complex global problem into local subproblems that can be solved in parallel by each satellite, and utilizing a command satellite for high-level coordination, the computational complexity is greatly reduced, enabling the system to respond quickly to dynamic changes in vessels. Second, the designed temporal and spatial discretization strategy, along with an auction conflict resolution mechanism combining priority and observation history, achieves intelligent and balanced allocation of satellite resources among multiple targets. This maximizes the total number of observations while avoiding resource competition and internal friction, thus improving overall tracking efficiency and success rate. Finally, this method fully leverages the distributed characteristics of the satellite constellation, forming a computationally efficient, responsive, and resource-utilization-efficient on-orbit autonomous mission planning solution.

[0059] It should be understood that the descriptions of technical features, technical solutions, beneficial effects, or similar language in this application do not imply that all features and advantages can be achieved in any single embodiment. Rather, it is understood that the description of a feature or beneficial effect means that a specific technical feature, technical solution, or beneficial effect is included in at least one embodiment. Therefore, the descriptions of technical features, technical solutions, or beneficial effects in this specification do not necessarily refer to the same embodiment. Furthermore, the technical features, technical solutions, and beneficial effects described in this embodiment can be combined in any suitable manner. Those skilled in the art will understand that embodiments can be implemented without one or more specific technical features, technical solutions, or beneficial effects of a particular embodiment. In other embodiments, additional technical features and beneficial effects may be identified in specific embodiments that do not embody all embodiments. Attached Figure Description

[0060] Figure 1A system architecture diagram of a moving vessel tracking task optimization system based on the ADMM algorithm is provided for embodiments of this application;

[0061] Figure 2 A flowchart illustrating an optimization method for a moving vessel tracking task based on the ADMM algorithm provided in this application embodiment;

[0062] Figure 3 This is a schematic diagram illustrating the coverage of the observation area by the satellite constellation under different observation sub-cycles provided in the embodiments of this application;

[0063] Figure 4 This is a schematic diagram illustrating the number of visible satellites under different observation sub-periods provided in the embodiments of this application;

[0064] Figure 5 A schematic diagram illustrating the number of grids handled by each visible satellite during the first observation sub-cycle provided in this application embodiment;

[0065] Figure 6 A schematic diagram showing the number of ships covered by each visible satellite during the first observation sub-period provided in this application embodiment;

[0066] Figure 7 A schematic diagram showing the number of visible satellites corresponding to each ship in the first observation sub-period provided in this application embodiment;

[0067] Figure 8 A schematic diagram of a ship observation mission plan provided in an embodiment of this application;

[0068] Figure 9 A schematic diagram illustrating the total working time of each visible satellite provided in the embodiments of this application. Detailed Implementation

[0069] The moving vessel tracking task optimization method based on the ADMM algorithm provided in this application can be applied to, for example... Figure 1 In the ADMM algorithm-based mobile vessel tracking task optimization system 100 shown, as follows: Figure 1 As shown, the communication system includes: a satellite constellation module 10, a command satellite module 20, a grid partitioning module 30, a time management module 40, a communication module 50, and a task generation module 60.

[0070] Among them, satellite constellation module 10 is used to perform local task optimization;

[0071] Command Star Module 20: Used for global resource coordination, ADMM parameter allocation, and conflict resolution;

[0072] Grid partitioning module 30: used to discretize the target sea area into a grid and store grid geographic information;

[0073] Time management module 40: Used to divide the observation time period and synchronize the clocks of each satellite;

[0074] Communication module 50: Used to exchange ship status, observation plan and ADMM global variables;

[0075] Task generation module 60: Used to output an observation task plan table sorted by time and to visualize it.

[0076] To address the technical problems of high computational complexity, slow dynamic response, and observation blind spots caused by multi-satellite resource competition in large-scale scenarios involving multiple satellites and ships, this application provides an optimization method for moving ship tracking tasks based on the ADMM algorithm. The method includes:

[0077] Acquire images of the target sea area to be observed;

[0078] Based on the working mode of SAR satellites, constellation revisit characteristics, and ship speed, the target sea area image is divided into multiple grid cells;

[0079] The observation time period is set, and the observation time period is divided into multiple observation sub-periods based on grid coverage and ship monitoring frequency;

[0080] Multiple visible satellites are acquired based on the observation sub-cycle, and grid cells and corresponding list of observation vessels are assigned to each visible satellite based on the visible duration.

[0081] Initialize algorithm parameters; wherein, the algorithm parameters include ship priority weights, ADMM parameters, and global variables;

[0082] The optimal observation list is obtained by optimizing and detecting conflicts in multiple observation vessel lists using the ADMM algorithm.

[0083] The observation task plan table is obtained by sorting the multiple ships in the optimal observation list according to time.

[0084] Based on this, the technical problems of high computational complexity, slow dynamic response, and blind spots caused by competition for multi-satellite resources when facing large-scale scenarios with multiple satellites and ships are solved.

[0085] like Figure 2 As shown in the embodiments of this application, the method for optimizing a moving vessel tracking task based on the ADMM algorithm includes:

[0086] S201. Obtain images of the target sea area to be observed.

[0087] For example, a simulation experiment spanning three days was conducted in a sea area of ​​approximately 2000km × 2000km. This sea area is vast and representative, allowing for thorough testing of the algorithm's performance in a large-scale scenario. Fifty ships were placed in this sea area, their trajectories following a certain random pattern, with a maximum ship speed set at 20 knots. This random motion characteristic simulates the real-world navigation of ships in the marine environment, increasing the complexity and realism of the simulation experiment.

[0088] S202, based on the working mode of SAR satellites, constellation revisit characteristics, and ship speed, divides the target sea area image into multiple grid cells.

[0089] It should be noted that for the sea area observed by satellite collaboratively, the region is divided into grids, each assigned a unique ID, and the center latitude and longitude coordinates of each grid are recorded. The grid division of the target sea area serves as the basis for optimizing the multi-satellite collaborative observation mission of spaceborne SAR satellites. The determination of its grid size and coverage must fully consider key factors such as the SAR satellite's operating mode, the constellation's revisit characteristics of the region, and the ship's movement speed. A balance between computational complexity and resource utilization efficiency is achieved while meeting observation accuracy and coverage requirements.

[0090] It is important to note that the operating mode of a SAR satellite has a significant impact on grid division. The satellite's observation capabilities and coverage vary considerably depending on the operating mode. Taking strip mode, scan mode, and spotlight mode as examples, the imaging swath width and resolution differ significantly in these three modes. In strip mode, if the grid is too large, exceeding the satellite's observation range, some grids will not be fully observed, creating blind spots. In spotlight mode, while the satellite can acquire high-resolution images, the observation range is relatively narrow. If the grid is too small, it will significantly increase the need for the satellite to frequently switch observation areas, which will not only reduce observation efficiency but may also significantly increase the computational complexity of the entire system. Therefore, the grid size must be scientifically and rationally determined based on the SAR satellite's operating mode to ensure that the grid range, satellite observation capabilities, and actual application scenarios are matched.

[0091] It's important to note that constellation revisit characteristics and ship speed are also key factors in grid partitioning. The constellation's revisit performance determines the observation repetition interval for ships. For high-speed ships, if the grid is too small, the ship may traverse multiple grids in a very short time, making it difficult for satellites to continuously and stably track the ship's trajectory. Conversely, if the grid is too large, it will be impossible to capture changes in the ship's trajectory in a timely and accurate manner, affecting the accuracy and continuity of observations. Furthermore, given the uncertainty of ship motion, a certain buffer space needs to be reserved during grid partitioning to cope with sudden changes in ship direction or speed, ensuring the stability and reliability of observations.

[0092] For example, the main parameters of the satellite constellation are shown in Table 1. This embodiment uses a low-Earth orbit SAR satellite constellation consisting of 72 satellites. Under this constellation layout, the coordinated observation of the satellites can achieve efficient coverage of the target area. Each satellite operates in its own orbit and cooperates with each other to conduct coordinated observation of a large area of ​​target sea area.

[0093] It should be noted that, in practice, by utilizing the flexible scanning capability of phased array antennas, satellites can achieve combinations of different resolutions and arbitrary swath widths within the SAR system's capability envelope.

[0094] Table 1

[0095]

[0096] For example, for the sea area observed by this constellation, key factors such as the working mode of SAR satellites, the revisit characteristics of the constellation to the region, and the speed of ship movement are fully considered. A balance is achieved between computational complexity and resource utilization efficiency while meeting the requirements for observation accuracy and coverage. Combining ship movement speed, satellite mode, and algorithm complexity, this embodiment uses a 40km × 40km grid, dividing the target sea area into a total of 7509 grids.

[0097] S203. Set the observation time period and divide the observation time period into multiple observation sub-periods based on grid coverage and ship monitoring frequency.

[0098] It is important to note that in the tracking and observation missions of moving ships at sea by spaceborne SAR satellite constellations, the rational division of observation time periods is a core element for achieving efficient mission planning and optimal resource allocation. From a computational complexity perspective, dividing the continuous observation process into discrete time periods transforms the originally complex dynamic optimization problem into multiple relatively independent sub-problems, significantly reducing the dimensionality and difficulty of the algorithm's solution and effectively avoiding combinatorial explosion. From a resource utilization perspective, a clear division of observation periods facilitates the fine-grained scheduling of satellite resources, enabling the constellation system to flexibly allocate remaining resources and accommodate other tasks while ensuring the core mission of ship tracking and monitoring.

[0099] It should be noted that determining the observation time interval is a complex process involving multiple coupled factors, primarily influenced by three key factors: the number of satellites in the constellation, the size of the scene area, and the number of ships. The division of the observation time period must follow Criterion 1 and Criterion 2;

[0100] Criterion 1 states that within a given time period, the SAR satellite constellation must achieve complete coverage of all grids within the target area. This criterion provides a fundamental guarantee for the comprehensiveness and integrity of the observation mission. If any grids are not covered, target vessels may be missed, negatively impacting overall monitoring effectiveness. From a mathematical programming perspective, this criterion requires that in each observation period, the satellite's observation trajectory and coverage area must satisfy the spatial constraints of the target area grids to ensure that all grids are observed at least once.

[0101] Guideline 2 states that the observation repetition period should be less than the vessel's monitoring frequency requirements. For example, if the required repetition monitoring frequency for a vessel is higher than once every 2 hours, the observation period can be set between 1 and 1.5 hours. Limiting the observation period to a reasonable range helps to promptly capture vessel position migrations and status changes, ensuring the timeliness and accuracy of the observation data, which aligns with the high-precision requirements of marine monitoring for vessel dynamic tracking. Furthermore, the carrying capacity of satellite resources must be considered when setting this guideline. While ensuring monitoring accuracy, it is crucial to avoid excessive consumption of satellite resources due to excessively short observation periods, which could adversely affect the long-term stable operation of the constellation system.

[0102] For example, the ship monitoring cycle needs to be less than 2 hours, therefore the algorithm's observation sub-cycle needs to be controlled within 2 hours. By simulating the orbital parameters, the percentage of coverage of the observation area by the satellite constellation under different observation time cycles can be calculated, such as... Figure 3 As shown in the figure, after the observation sub-period is divided into 45-minute intervals, the SAR satellite constellation can completely cover the target area within that time period.

[0103] For example, considering increasing the flexibility of mission planning within the satellite constellation, for this application scenario, an observation period of 1 hour is selected. This allows the 3-day simulation period to be divided into 72 sub-cycles. Choosing an observation period of 1 hour ensures high-frequency monitoring of ships, timely acquisition of their dynamic information, and achieves a good balance between satellite resources and computational complexity, thereby improving the flexibility and efficiency of mission planning.

[0104] S204. Based on the observation sub-cycle, obtain the corresponding multiple visible satellites, and based on the visible duration, assign grid cells and the corresponding list of observation vessels to each visible satellite.

[0105] In some implementations, the method for obtaining the list of observed vessels includes:

[0106] S91. Calculate the visibility duration between the grid cell and multiple visible satellites;

[0107] S92. Assign grid cells to visible satellites whose visible duration reaches more than 70% of the longest visible duration, and generate a satellite responsibility area mapping table;

[0108] S93. Obtain the location of the target ship and its corresponding grid cell;

[0109] S94. Assign target vessels to corresponding visible satellites based on the satellite area of ​​responsibility mapping table;

[0110] S95. Repeat steps S93-S94 to traverse all target ships and generate a list of observed ships.

[0111] It should be noted that satellite responsibility area allocation is an important step in achieving multi-satellite collaborative observation. It aims to rationally allocate ship observation tasks in the target sea area to various satellites, thereby improving observation efficiency and resource utilization.

[0112] For example, the time window for a satellite to pass over the target sea area within a time-divided period (e.g., one hour) is calculated using an orbit prediction model. The satellite combination that can observe the passing of the area within that period is then selected from the constellation system. The visible duration between the center point of each grid and all passing satellites is calculated. Considering the overlap during system optimization, the grid is assigned to satellites with a visible duration of more than 70% of the longest visible duration, thereby generating a satellite responsibility area mapping table. Based on the location of the vessel during its last observation and the mapping relationship between the grids, the vessel is assigned to the corresponding satellite. Finally, a list of observing vessels for each satellite within that observation period is generated.

[0113] For example, based on the observation sub-period division scheme in S203, the target area grid responsibility division within 72 sub-periods can be obtained. First, the number of satellites capable of observing the target vessel within each observation sub-period is analyzed, i.e., the visible satellites requiring mission planning, such as... Figure 4 As shown in the figure, the number of visible satellites observed during one observation sub-cycle is between 27 and 32. Further analysis is conducted on the number of satellite grids responsible for each sub-cycle; taking the first sub-cycle as an example... Figure 5 As shown, the area of ​​responsibility for different satellites varies in size, which will affect the subsequent allocation of responsible vessels.

[0114] For example, taking the initial situation as an example, the responsibility area allocation of 50 ships can be obtained. Figure 6 This indicates the number of ships each satellite is responsible for. Figure 7 This indicates the number of satellites assigned to different vessels. It can be seen that during the initial allocation, each vessel is assigned at least one responsible satellite. Therefore, various conflicts will arise in actual mission planning. Subsequent ADMM main loop steps will use conflict resolution to achieve optimal global mission allocation. This conflict resolution mechanism is one of the core advantages of the ADMM algorithm, effectively solving mission allocation conflicts in multi-satellite, multi-vessel scenarios and improving the execution efficiency and quality of observation missions.

[0115] S205. Initialize algorithm parameters, including ship priority weights, ADMM parameters, and global variables.

[0116] In some implementations, the initialization algorithm parameters include:

[0117] Historical observation data is acquired, and ship priority weights are set based on the historical observation data; wherein, the historical observation data includes ship type, navigation area, and historical behavior;

[0118] Initialize the penalty coefficient, maximum number of iterations, and convergence threshold;

[0119] Initialize decision variables, global consistency variables, and Lagrange multipliers; wherein the initial state of the decision variables is an unobserved task.

[0120] It should be noted that before assigning priority weights to vessels within the target sea area, vessels that have already left the target sea area need to be removed from the observation task sequence, and then priority weights need to be assigned to each vessel. The priority weight of ships is determined by a comprehensive evaluation based on factors such as ship type, navigation area, and historical behavior.

[0121] For example, vessels navigating in sensitive waters or fishing boats with a history of illegal fishing are assigned higher priority weights to ensure they receive focused monitoring. This embodiment uses the default rule for important vessels. ordinary ships In practice, different ship priorities can be defined according to changes in mission requirements.

[0122] It should be noted that the penalty coefficient is used to balance the strictness of the constraints, and its value needs to be adjusted according to the size of the problem and the complexity of the constraints. A larger penalty coefficient can speed up the convergence of the algorithm, but may cause the algorithm to get stuck in local optima; a smaller penalty coefficient may slow down the convergence. The maximum number of iterations sets the maximum number of loops the algorithm can run to avoid infinite loops due to failure to converge. The convergence threshold is used to determine whether the algorithm has reached the optimal solution. When the change in the objective function during the algorithm's iterations is less than the convergence threshold, the algorithm is considered to have converged. When initializing these parameters, the optimal range of parameter values ​​is determined through a combination of theoretical analysis and simulation experiments to ensure the efficient operation of the algorithm.

[0123] It should be noted that the ADMM-based mobile vessel tracking and monitoring optimization algorithm takes "breaking down the whole into parts and solving collaboratively" as its core design idea. Through strategies of spatial discretization, time segmentation, and hierarchical task allocation, it systematically deconstructs the complex multi-satellite collaborative observation optimization problem.

[0124] For example, parameter configuration mainly includes key parameters of the ADMM algorithm, such as the penalty coefficient, maximum number of iterations, and convergence threshold, determining the initial range of parameter values. In solving the satellite-level subproblems, a genetic algorithm is used, requiring the setting of parameters such as population size, crossover probability, and mutation probability to balance the algorithm's search capability and convergence speed. Table 2 shows sample parameter configuration values ​​for the algorithm; in practice, different values ​​need to be set for specific scenarios and tasks.

[0125] Table 2

[0126]

[0127] For example, initializing decision variables , indicating no observation task; globally consistent variables and Lagrange multipliers This provides the initial state for subsequent algorithms.

[0128] S206. The ADMM algorithm is used to optimize and detect conflicts in multiple observation vessel lists to obtain the optimal observation list.

[0129] In some implementations, the optimization and collision detection of multiple observed vessel lists using the ADMM algorithm includes:

[0130] S31. Solve the optimization problem for the observation vessel list of each visible satellite to obtain multiple observation sublists;

[0131] S32. Perform observation conflict detection on multiple observation sublists and update the observation tasks through a bidding auction mechanism to obtain the optimal observation list;

[0132] S33. Update the global consistency variables and Lagrange multipliers, and perform a convergence test on the optimal observation list; if the preset convergence condition is not met, repeat steps S31-S32; if the convergence condition is met, exit the loop.

[0133] It should be noted that the ADMM main loop is the core part of the algorithm, which iteratively updates the variables to gradually approach the global optimum. Each iteration mainly includes solving satellite-level subproblems, boundary conflict detection and auction mechanisms, and global consistency updates and convergence checks.

[0134] For example, after resolving boundary conflicts, based on the updated decision variables It can update globally consistent variables. Furthermore, the global residual can be calculated. The global residual reflects the degree of deviation of the current solution from satisfying the constraints. Based on the global residual, the Lagrange multipliers can be updated:

[0135] ;

[0136] The updated Lagrange multipliers will guide each satellite to better satisfy the global constraints when solving the next satellite subproblem.

[0137] In some implementations, the optimization problem of solving the observation vessel list for each visible satellite includes:

[0138] A target optimization function is constructed for the list of observation vessels for each visible satellite; wherein the expression of the target optimization function is:

[0139] ;

[0140] In the formula, For the first One ship, For the first One visible satellite, For visual satellites List of observation vessels; For binary decision variables, Indicates visual satellite execution vessel The k Second observation; For ships Total number of observations This is a time cost penalty coefficient. For visual satellites execution vessel The k The time cost required for each observation For the execution of ships The k The second observation and the first k -1 time interval between observations;

[0141] Define global constraints By introducing an augmented Lagrangian function, global constraints are incorporated into the objective optimization function, resulting in a satellite-level subproblem; wherein, the expression of the augmented Lagrangian function is:

[0142] ;

[0143] In the formula, For all decision variables The set, For Lagrange multipliers; This is a globally consistent variable used to enforce the decision variables of each visible satellite. Satisfy global constraints; This is the penalty coefficient, used to balance the original objective function with the constraints; and This is a coefficient matrix used to organize decision variables. and globally consistent variables Associated with constraints; This is a constant vector used to represent the boundary values ​​of the constraints;

[0144] The expression for the satellite-level subproblem is:

[0145] ;

[0146] In the formula, This represents the current iteration number. and For the first Global consistency variables and Lagrange multipliers in each iteration;

[0147] A heuristic algorithm is used to solve the satellite-level subproblems, resulting in multiple lists of observations.

[0148] It should be noted that by decomposing complex global problems into satellite-level subproblems using the ADMM framework, the computational complexity of a single solution is significantly reduced, making real-time onboard computing possible. Combined with the heuristic solution strategy of genetic algorithms, the combinatorial explosion problem is effectively avoided while ensuring the quality of the solution. The distributed optimization structure and conflict resolution mechanism work together to ensure continuous tracking coverage of multiple vessels and achieve efficient use of satellite energy and working time through time cost control, thereby improving the autonomy and robustness of the constellation system in dynamic ocean monitoring missions.

[0149] It should be noted that sets The task allocation scheme for the entire constellation is encoded and is the core output of the optimization problem; the globally consistent variable z is used to enforce the local decision variables of each visible satellite. Satisfying global constraints, such as ensuring the same ship is not observed repeatedly by multiple visible satellites; Lagrange multipliers. Used to adjust the degree to which global constraints are satisfied, for example, if a constraint is violated (such as resource overrun). An increase in the penalty coefficient will force subsequent iterations to revise the decision; a larger penalty coefficient It imposes strict constraints, but this may lead to numerical instability; the penalty coefficient is relatively small. Slower convergence but more robust; in practice, the penalty coefficient... It can be dynamically fine-tuned based on the real-time status of satellite resources to cope with sudden changes in ship movement; coefficient matrix A Encoding the impact of local decisions on global constraints, such as satellite resource usage; coefficient matrix. B Encoding the global coordination role of the globally consistent variable z, such as the consistency requirements in conflict resolution; constant vector c The physical limitations of the system were quantified.

[0150] For example, when solving the optimization problem for the observation vessel list of each visible satellite, the objective optimization function for the vessel observation task within the responsibility area of ​​each satellite is first constructed. This function aims to maximize the total number of observations, while introducing a time cost penalty term related to the observation time interval to balance resource consumption. Subsequently, by introducing auxiliary variables and Lagrange multipliers, an augmented Lagrange function is constructed to incorporate global constraints (including time windows, resource budgets, and observation mutual exclusion conditions) into the optimization model, forming a satellite-level subproblem that can be solved in a distributed manner. Finally, a genetic algorithm is used as a heuristic solver to perform selection, crossover, and mutation operations on chromosomes encoded as task sequences. After iterative optimization, the optimal observation sublist for each satellite is obtained, thereby achieving autonomous and rapid on-board task planning.

[0151] In some implementations, the step of detecting observation conflicts in multiple observation sublists and updating the observation task through an auction mechanism includes:

[0152] S51. Sort the observation plans for the same target ship by time. If the time interval between adjacent observation sub-cycles is less than the preset time resolution and the observations are performed by different visible satellites, mark them as conflicting tasks; mark multiple conflicting tasks as a conflicting task set.

[0153] S52. Initialize bidding information for each pair of conflicting tasks in the conflicting task set; submit bids for conflicting targets based on observation costs; wherein the bids are inversely proportional to the observation costs;

[0154] S53. The coordinator selects the visual satellite with the highest bid to perform the corresponding observation task; other visual satellites participating in the bidding remove the corresponding conflicting observation tasks and update their observation plans;

[0155] S54. Repeat steps S51-S53 to traverse all target ships and generate the optimal observation list.

[0156] For example, an empty conflict task set is created to store conflicting ship observation tasks. For each ship, all its observation plans are sorted according to the observation start time. Then, it is checked that the time interval between adjacent observation plans is less than the set time resolution (e.g., 1 hour) and that these observation plans are executed by different satellites. If both conditions are met, these observation tasks are added to the conflict task set. For each conflict task in the conflict task set (i.e., a conflicting pair of ship observation tasks), bidding information is initialized for each satellite participating in the conflict. For each conflict target, different satellites submit bids, the coordinator selects the satellite with the highest bid to execute the observation, updates the task allocation, and after the winning satellite obtains the right to execute the observation task, other satellites participating in the conflict need to update their own observation plans. The conflicting observation task is removed from their own observation plans, and the time schedule of the remaining observation tasks is re-evaluated and adjusted to ensure that their own time windows and resource budget constraints are met. For example, if a satellite loses its ship observation task in a conflict, it will no longer consider observing that ship in the next ADMM cycle optimization.

[0157] In some implementations, the heuristic algorithm for solving the satellite-level subproblems is a genetic algorithm, including:

[0158] Initialize the population and encode the chromosomes to represent the ship task allocation scheme;

[0159] Fitness is calculated using a fitness function to evaluate the merits of task allocation schemes; wherein, the fitness function integrates the objectives of maximizing the number of observations and minimizing time cost;

[0160] Perform selection, crossover, and mutation operations to generate a new generation of population;

[0161] Iterate and optimize until the preset stopping condition is met.

[0162] It should be noted that satellite-level subproblems can be solved primarily through linear approximation and heuristic algorithm embedding. Considering that satellite-level subproblems are mainly implemented autonomously within each satellite of the constellation, exact solution methods (such as MILP and nonlinear programming algorithms) would consume significant computing power from the onboard computer; therefore, heuristic algorithms are used as alternatives. Genetic algorithms are a type of heuristic algorithm, and their feasibility is analyzed based on the independence of the problem, the adaptability of the algorithm, and the scalability of the algorithm.

[0163] The independence of the problem: In actual satellite observation missions, each satellite is typically assigned a specific observation area, also known as its area of ​​responsibility. The areas of responsibility for different satellites are independent of each other. This independence allows each satellite to independently plan its observation mission within its own area of ​​responsibility, only needing to consider the impact of ADMM global consistency variables, without needing to consider the situation of ships within the areas of responsibility of other satellites.

[0164] The algorithm's adaptability: The genetic algorithm is itself a search algorithm suitable for solving complex optimization problems, and it can perform efficient searches within a given search space. When each satellite optimizes only for ships within its area of ​​responsibility, the search space is significantly reduced, allowing the genetic algorithm to converge to a better solution more quickly.

[0165] The algorithm's scalability is enhanced by its regional optimization approach, which can be easily scaled up as the number of satellites increases. Each satellite only needs to focus on its own area of ​​responsibility, without needing to process information from the entire system, thus significantly improving the system's scalability.

[0166] In summary, genetic algorithms can effectively solve satellite-level subproblems.

[0167] For example, the main implementation flow of a genetic algorithm includes:

[0168] Population initialization: Chromosome encoding is designed to be the task allocation order, that is, the gene representation of the chromosome is the task allocation scheme;

[0169] Fitness assessment: Calculate fitness, which measures the quality of the task allocation scheme represented by each chromosome.

[0170] Selection operations: Tournament selection can select relatively superior individuals from the population, while elite retention ensures that the best individuals in each generation can directly enter the next generation, thereby avoiding the loss of excellent genes.

[0171] Crossover operation: This operation combines the genes of the parent generation to generate offspring individuals through sequential crossover. During the crossover process, new conflicts may be introduced, but illegal solutions will be filtered out in the subsequent fitness evaluation stage.

[0172] Mutation operation: By randomly adjusting the gene sequence, new solution space is explored. The main mutation operation is to randomly swap the positions of two ships.

[0173] In some implementations, the convergence test includes calculating the decision variables in two adjacent iterations using the Euclidean norm. The algorithm is considered to have converged when the amount of iterative change is less than the convergence threshold.

[0174] It should be noted that convergence detection is mainly used to determine the changes in decision variables between two adjacent iterations, and then to evaluate the stability of the solution of the algorithm, and whether it can be considered as a sign of convergence.

[0175] For example, the change in the decision variable between two adjacent iterations is calculated, and the Euclidean norm is used to evaluate the change:

[0176] ;

[0177] Where N is the total number of satellites.

[0178] In some implementations, the time cost ;in, For ships The speed of travel; A function relating to the payload system parameters of the SAR satellite, derived from time intervals. The required imaging swath width and resolution mode for this observation are determined by the calculations; the time cost is also related to the satellite's motion speed.

[0179] It should be noted that the observation time cost of a constellation system over a target sea area determines the consumption of multiple resources, including energy and data volume. Therefore, observation time cost is a key system performance indicator. Since ships are in motion, the size of their potential movement area varies at different observation intervals, and the required imaging swath width for each ship in a subsequent observation also differs.

[0180] It should be noted that by establishing an adaptive cost model that considers spatiotemporal correlation, the system can dynamically adjust its observation strategy according to the target's motion characteristics, ensuring both the ability to continuously lock onto moving targets and avoiding resource waste in a fixed mode. Secondly, by deeply coupling the payload's physical parameters with the optimization algorithm, the mission planning results become more engineering feasible, significantly reducing the risk of planning failure due to model mismatch. Finally, this refined cost control mechanism enables the constellation system to maintain a better energy balance during long-term monitoring missions, providing key technical support for achieving onboard autonomous mission planning.

[0181] For example, the time cost of a single observation is calculated through an established composite function model, in which the satellite's velocity is calculated in real time based on satellite orbit parameters, while the real-time speed provided by the Automatic Identification System (AIS) is received. The key function encapsulates the core parameters of the SAR payload, including the antenna scanning angle, signal processing delay, and imaging time under different resolution modes. This function dynamically determines the optimal imaging mode based on the time interval between the previous and current observations—when the interval is large, which increases the uncertainty of the ship's position, a wide-swath scanning mode is automatically selected, corresponding to a higher time cost value; when the interval is short, a spotlight mode can be enabled to obtain higher resolution. Finally, this precisely calculated time cost value is embedded into the penalty term of the ADMM optimization framework, guiding the algorithm to intelligently balance tracking frequency and resource consumption when planning observation tasks.

[0182] S207. Sort the observations of multiple ships in the optimal observation list according to time order to obtain the observation task plan table.

[0183] For example, after completing algorithm initialization, task simulation is performed on the application scenario, such as... Figure 8 The image shows the final ship observation task plan, with different colored dots representing different visible satellites. Since some ships have already left the target area, they will not be assigned satellites for observation after they have departed. The observation task sequence results clearly demonstrate the algorithm's allocation of ship observation tasks, verifying the algorithm's feasibility and effectiveness in real-world scenarios.

[0184] For example, based on a pre-set mission scenario, the constellation can track and detect all ships, thus achieving a 100% mission completion rate. Simultaneously, statistical analysis of the satellite operating time resources consumed by the mission yields the total operating time of the entire constellation system dedicated to that mission. Figure 9As shown in the figure, the inclusion of a penalty term for operating time in the objective optimization function effectively controls the system's operating time overhead. Based on the pre-set SAR satellite payload capacity (5 minutes of operation per orbit), the maximum operating time resource consumption per satellite over the entire simulation period (3 days) is 13.60% of the available resources (approximately 240 minutes). The remaining operating time resources can better ensure the constellation system completes other tasks. This demonstrates that the algorithm can rationally allocate satellite resources and improve resource utilization efficiency while ensuring the completion of observation tasks.

[0185] For example, the hardware requirements for running the simulation program are as follows:

[0186] CPU: Intel(R) Core(TM) Ultra 5 125H 3.60 GHz;

[0187] Memory: 16GB; Hard Drive: 1TB;

[0188] Software version: Matlab 2022b;

[0189] The total program execution time for the entire simulation cycle was 9180.69 s, of which satellite responsibility area allocation took 3521.40 s, with a single satellite responsibility area allocation taking 0.68 s. Solving satellite-level subproblems took a total of 5657.27 s. Over 72 observation cycles, a total of 10944 satellite-level subproblems were solved, translating to approximately 0.51 s per subproblem solution. In actual satellite systems, onboard computation will be implemented using faster GPUs or FPGAs, fully realizing large-scale parallel processing of responsibility area allocation and satellite-level subproblem solving, further improving efficiency. In summary, the algorithm proposed in this application can meet the mission requirements of future spaceborne SAR constellations in tracking moving ships. Detailed analysis of the algorithm's runtime, combined with a discussion of actual hardware implementation methods, verifies the algorithm's advantages and feasibility in terms of time performance.

[0190] It should be noted that, for the task optimization problem of SAR satellite constellation tracking moving ships at sea, this application mainly reconstructs the problem based on the ADMM algorithm. First, the global optimization objective is decomposed into satellite-level sub-problems, with each satellite corresponding to one sub-problem, independently solving for its own optimal allocation scheme for observation tasks. In this process, a globally consistent variable is introduced to represent the information that needs to be coordinated among satellites, such as the target observation matrix. Then, an augmented Lagrangian function is constructed, incorporating the constraints of the original problem into the objective function through Lagrange multipliers and penalty terms. In this way, the original problem is transformed into a series of sub-problems that can be solved in parallel, with information exchange and collaborative optimization achieved between the sub-problems through updates of the Lagrange multipliers. This problem reconstruction method not only fully utilizes the distributed computing advantages of the ADMM algorithm but also effectively handles complex factors such as satellite resource constraints and dynamic changes in the target, ensuring the efficient execution of the algorithm.

[0191] Based on the above technical solutions, the mobile vessel tracking task optimization method based on the ADMM algorithm provided in this application effectively overcomes the inherent defects of centralized planning by introducing a distributed optimization framework based on the ADMM algorithm. First, by decomposing the complex global problem into local subproblems that can be solved in parallel by each satellite, and utilizing a command satellite for high-level coordination, the computational complexity is greatly reduced, enabling the system to respond quickly to the dynamic changes of the vessel. Second, the designed temporal and spatial discretization strategy, along with an auction conflict resolution mechanism combining priority and observation history, achieves intelligent and balanced allocation of satellite resources among multiple targets. This maximizes the total number of observations while avoiding resource competition and internal friction, improving overall tracking efficiency and success rate. Finally, this method fully leverages the distributed characteristics of the satellite constellation, forming a computationally efficient, responsive, and resource-utilization-efficient on-orbit autonomous mission planning solution.

[0192] In one possible implementation, this application embodiment also provides a moving vessel tracking task optimization system based on the ADMM algorithm, including:

[0193] Satellite constellation module: Composed of multiple low-Earth orbit SAR satellites, each equipped with an onboard processing unit for performing local task optimization;

[0194] Command Satellite Module: Located in geosynchronous orbit, it is used for global resource coordination, ADMM parameter allocation, and conflict resolution;

[0195] Grid partitioning module: used to discretize the target sea area into a grid and store the grid geographic information;

[0196] Time management module: used to divide the observation time period and synchronize the clocks of each satellite;

[0197] Communication module: Supports inter-satellite data transmission for exchanging ship status, observation plans, and ADMM global variables;

[0198] Task generation module: Used to output an observation task plan table sorted by time and visualize it.

[0199] For example, the grid partitioning module first discretizes the target sea area into standard grid cells and establishes a geographic information database; the time management module divides the observation period into cooperative sub-periods based on the constellation revisit characteristics and maintains the system time reference through inter-satellite synchronization protocols; the command satellite module is deployed in geostationary orbit, decomposes the global optimization problem into satellite-level sub-problems based on the ADMM framework, and distributes optimization parameters to each satellite through the communication module; each SAR satellite in the satellite constellation module independently solves the observation plan within its area of ​​responsibility using its onboard processing unit, and uploads local decisions through the communication module; when the command satellite module detects multi-satellite observation conflicts, it initiates a priority-based auction mechanism for coordination, and finally the task generation module integrates all optimization results, generates a visualized observation plan, and distributes it to the executing satellites.

[0200] Based on the above technical solutions, firstly, by constructing a hybrid architecture of "centralized coordination and distributed execution," the coordination of global optimization is maintained, while the system's computational load is significantly reduced through distributed computing. Secondly, by adopting an inter-satellite collaborative conflict resolution mechanism, the overlap and conflict of multi-satellite observation tasks are effectively avoided, significantly improving the overall observation efficiency of the constellation. Finally, through standardized module design and onboard autonomous processing capabilities, continuous and accurate monitoring and rapid mission response of moving vessels are achieved, providing a complete system solution for the autonomous collaborative operation of large-scale satellite constellations.

Claims

1. A method for mobile vessel tracking task optimization based on ADMM algorithm, characterized in that, The method comprises the following steps: acquiring a target sea area image to be observed; dividing the target sea area image into a plurality of grid units based on the working mode of a SAR satellite, constellation revisit characteristics and the speed of a ship; setting an observation time period, and dividing the observation time period into a plurality of observation sub-periods based on grid coverage and ship monitoring frequency; acquiring a plurality of visible satellites corresponding to the observation sub-periods, and assigning grid units and a corresponding observation ship list to each visible satellite based on the visible time length; initializing algorithm parameters; wherein the algorithm parameters comprise ship priority weight, ADMM parameter and global variable; optimizing and detecting conflicts in the plurality of observation ship lists through an ADMM algorithm to obtain an optimal observation list; sequentially observing the plurality of ships in the optimal observation list to obtain an observation task plan table; the initializing algorithm parameters comprise: acquiring historical observation data, and setting ship priority weight based on the historical observation data; wherein the historical observation data comprises ship type, sailing area and historical behavior; initializing penalty coefficient, maximum iteration number and convergence threshold; initializing decision variable, global consistency variable and Lagrange multiplier; wherein the initial state of the decision variable is no observation task; the optimizing and detecting conflicts in the plurality of observation ship lists through the ADMM algorithm comprise: S31. solving an optimization problem for each observation ship list of each visible satellite to obtain a plurality of observation sub-lists; S32. detecting observation conflicts in the plurality of observation sub-lists, and updating observation tasks through a bidding auction mechanism to obtain an optimal observation list; S33. updating the global consistency variable and the Lagrange multiplier, and detecting convergence of the optimal observation list; if the preset convergence condition is not met, repeating steps S31-S32; if the convergence condition is met, exiting the loop.

2. The ADMM algorithm based mobile vessel tracking task optimization method according to claim 1, wherein, the solving an optimization problem for each observation ship list of each visible satellite comprises: constructing a target optimization function for each observation ship list of each visible satellite; wherein the expression of the target optimization function is: ； wherein is the number of vessels, is the number of visible satellites, is the number of visible satellites, is the list of observed vessels for the visible satellite is the list of observed vessels for the visible satellite is the list of observed vessels for the visible satellite is a binary decision variable, denotes the number of observations performed by the visible satellite for the vessel is the number of observations performed by the visible satellite k for the vessel is the total number of observations performed by the vessel is the time cost penalty coefficient, is the time cost required for performing the observation number by the visible satellite for the vessel is the time interval between the observation number k and the observation number -1 performed by the visible satellite for the vessel k is the time interval between the observation number k and the observation number -1 performed by the visible satellite for the vessel Defining global constraints , introducing an augmented Lagrangian function to fuse the global constraints into the objective optimization function, to obtain a satellite-level subproblem; wherein, the expression of the augmented Lagrangian function is: ； wherein, is a set of all decision variables , is a Lagrange multiplier; is a global consistency variable for forcing the decision variables of each visible satellite to satisfy global constraints; is a penalty coefficient for balancing the original objective function and the constraints; and are coefficient matrices for associating the decision variables and the global consistency variable to the constraints; is a constant vector for representing the boundary values of the constraints; the expression of the satellite-level sub-problem is: ； wherein is the number of the current iteration, and is the global consistency variable and Lagrange multiplier for the iteration. solving the satellite-level sub-problem through a heuristic algorithm to obtain a plurality of observation sub-lists.

3. The ADMM algorithm based mobile vessel tracking task optimization method according to claim 1, wherein, the detecting observation conflicts in the plurality of observation sub-lists and updating observation tasks through the bidding auction mechanism comprise: S51. sorting observation plans of the same target ship by time, and marking as a conflict task if the time interval between adjacent observation sub-periods is less than a preset time resolution and the observation is performed by different visible satellites; marking a plurality of conflict tasks as a conflict task set; S52. initializing bidding information for each pair of conflict tasks in the conflict task set; and submitting a bid for a conflict target based on observation cost; wherein the bid is inversely proportional to the observation cost; S53. selecting a visible satellite with the highest bid through a coordinator to perform the corresponding observation task; and removing the corresponding conflict observation task and updating the observation plan of other visible satellites participating in the bidding; S54. repeating steps S51-S53 to traverse all target ships to generate an optimal observation list.

4. The ADMM algorithm based mobile vessel tracking task optimization method according to claim 2, wherein, The heuristic algorithm for solving the satellite-level sub-problem is a genetic algorithm, comprising: initializing a population, encoding a chromosome for representing a task allocation scheme of a ship; calculating fitness through a fitness function for evaluating the pros and cons of the task allocation scheme; wherein the fitness function fuses the maximization of the number of observations and the minimization of the time cost; performing selection, crossover and mutation operations to generate a new generation of population; iteratively optimizing until a preset stopping condition is met.

5. The ADMM algorithm based mobile vessel tracking task optimization method according to claim 1, wherein, The convergence test includes calculating the decision variables in two adjacent iterations using the Euclidean norm. The algorithm is considered to have converged when the amount of iterative change is less than the convergence threshold.

6. The ADMM algorithm based mobile vessel tracking task optimization method according to claim 2, wherein, the time cost ; wherein is the speed of travel of the vessel; is a function related to the payload system parameters of the SAR satellite, determined by the imaging swath and resolution mode required for the present observation, calculated from the time interval ; the time cost is also related to the satellite motion speed.​ 7. The ADMM algorithm based mobile vessel tracking task optimization method according to claim 1, wherein, The method for obtaining the observation ship list comprises: S91. calculating the visible duration of the grid cell and the plurality of visible satellites; S92. assigning the grid cell to the visible satellite with a visible duration reaching more than 70% of the longest visible duration to generate a satellite responsibility area mapping table; S93. obtaining the location of the target ship and the corresponding grid cell; S94. assigning the target ship to the corresponding visible satellite based on the satellite responsibility area mapping table; S95. repeating steps S93-S94 to traverse all target ships to generate the observation ship list.

8. A system of the method for optimizing the task of tracking moving vessels based on ADMM algorithm, applied to the method for optimizing the task of tracking moving vessels based on ADMM algorithm according to any one of claims 1-7, characterized in that, Comprise: Satellite constellation module: composed of multiple low-orbit SAR satellites, each satellite is equipped with a satellite-borne processing unit for performing local task optimization; Command star module: set in geosynchronous orbit for global resource coordination, ADMM parameter distribution and conflict resolution; Grid division module: for discretizing the target sea area into grids and storing grid geographic information; Time management module: for dividing observation time periods and synchronizing satellite clocks; Communication module: supporting inter-satellite data transmission for exchanging ship status, observation plans and ADMM global variables; Task generation module: for outputting time-ordered observation task plans and visualizing the display; The initialization of the ADMM parameters and the ADMM global variables comprises: obtaining historical observation data, and setting ship priority weights according to the historical observation data; wherein the historical observation data includes ship type, sailing area and historical behavior; initializing the penalty coefficient, the maximum number of iterations and the convergence threshold; initializing the decision variable, the global consistency variable and the Lagrange multiplier; wherein the initial state of the decision variable is no observation task; The local task optimization and conflict resolution comprise: S31. solving the optimization problem for each observation ship list of the visible satellite to obtain a plurality of observation sub-lists; S32. detecting observation conflicts for the plurality of observation sub-lists and updating observation tasks through a bidding auction mechanism to obtain an optimal observation list; S33. updating the global consistency variable and the Lagrange multiplier, and detecting the convergence of the optimal observation list; if the preset convergence condition is not met, repeating steps S31-S32; if the convergence condition is met, exiting the loop.

Images