Method for analyzing performance of large-scale low earth orbit satellite constellation system for maritime moving target detection task

Abstract

This invention discloses a performance analysis method for large-scale low-Earth orbit satellite constellation systems for maritime moving target detection missions. It addresses the problems of unrealistic simulation of dense sea surface targets and incomplete performance evaluation index systems, belonging to the field of intelligent shipping and maritime big data processing. The method includes: constructing a large-scale low-Earth orbit satellite constellation and outputting satellite attribute parameters; updating ship speed and correcting acceleration based on the current vessel's track being at sea, and outputting the true track; otherwise, recalculating latitude and longitude; outputting the detection track based on the angle between the target and the satellite payload's field of view axis meeting the visibility threshold; performing Kalman filtering point fusion and track association on the detection track set to obtain a associated track set; and conducting performance analysis using the true track set, the detection track set, and the associated track set to evaluate the average completeness and average accuracy of the point track association. This invention improves the realism of dense sea surface target simulation and rapidly generates performance evaluations for constellation systems of different scales and configurations.

Description

Technical Field

[0001] This invention belongs to the field of satellite constellation system application technology, and relates to a method for performance analysis of large-scale low-Earth orbit satellite constellation systems for maritime moving target detection missions. It is particularly suitable for performance evaluation and optimization of satellite constellation systems in scenarios with dense moving targets on the sea surface. Background Technology

[0002] With the rapid development of marine economic activities and the increasing awareness of maritime rights, real-time monitoring of global sea areas and precise tracking of moving targets at sea (especially ships) have become important requirements in the fields of marine economy and environmental protection. Satellite remote sensing technology, with its advantages of wide coverage, no geographical limitations, and all-weather monitoring capabilities, has become an important means of monitoring moving targets at sea. In recent years, the rapid deployment of large-scale low-Earth orbit satellite constellation systems (such as Starlink and OneWeb) has provided a technological foundation for achieving high-frequency, high-resolution monitoring of global sea areas.

[0003] However, existing methods for evaluating the effectiveness of satellite remote sensing systems are mostly geared towards single-satellite or static observation scenarios, lacking a systematic evaluation framework for the monitoring effectiveness of low-Earth orbit constellations in dense, dynamic, and complex marine environments. Specifically, this manifests in the following ways:

[0004] (1) Unrealistic target scene modeling: Existing methods often use uniform random distribution or idealized motion models when simulating moving targets at sea. They fail to accurately depict the dense distribution characteristics of ships, navigation rules, trajectory interactions, and dynamic behavior of high-density areas such as ports and waterways in the real marine environment. For example, in the invention application No. 202511321815.4 entitled "A Method for Target Track Association in a Multi-Target Environment", the actual implementation is still based on the assumption that "the target moves in uniform linear motion". However, real marine targets often exhibit multi-mode motion characteristics such as speed change, turning, and maneuvering under complex hydrological and meteorological conditions. The uniform speed model is difficult to accurately describe the dynamic behavior of the target, resulting in the disconnect between the performance evaluation scenario and the actual motion mode of moving targets on the sea surface.

[0005] (2) The evaluation indicators lack constellation coordination and dynamic adaptability: Traditional evaluation indicators such as coverage and revisit time are mostly aimed at static or single-target observations, and fail to fully reflect the key capabilities of constellation systems in dense moving target tracking, such as multi-satellite coordination, mission relay, and continuous track correlation. For example, in the invention titled "A Method for Evaluating the Performance of Remote Sensing Satellite Earth Observation" (application number 202410658791.0), although a multi-level indicator system was constructed and an environmental correction factor was introduced, it focused on the comprehensive performance evaluation of static Earth targets and could not realize the continuous tracking and performance analysis of moving targets based on constellation coordinated observation. As another example, in the invention titled "A Method for Evaluating the Search and Tracking Performance of Moving Target Tracking Missions for High-Orbit Remote Sensing Satellites" (application number 202411753419.4), although dynamic indicators of tracking and recapture were designed, it was limited to high-orbit single-satellite scenarios and did not extend to the multi-target and multi-mission coordinated performance evaluation of large-scale low-orbit constellations. Summary of the Invention

[0006] To address the technical problems of unrealistic target scenario modeling and the lack of constellation coordination and dynamic adaptability in evaluation metrics, this invention discloses a performance analysis method for large-scale low-Earth orbit (LEO) satellite constellation systems for maritime moving target detection missions. This method rapidly constructs a large-scale LEO satellite constellation and maritime moving targets for large-scale constellation operation scenarios. It uses wide-swath detection payloads on detection satellites to obtain discrete traces of moving vessel targets over a wide sea area. High-precision positioning is achieved based on the collection, processing, and analysis of industrial big data, driving Kalman filter trace fusion and trajectory association. Combining satellite observation data with fitted moving target traces, performance metrics such as trajectory association accuracy and continuity are output. This invention focuses on scenarios with dense maritime moving targets and large-scale constellation operation, innovatively designing a rapid constellation and target simulation scenario construction method. It utilizes the satellite payload's field of view and the spatiotemporal visibility of moving targets to simulate the satellite payload detection process and efficiently output detection trace results. Furthermore, the constellation system detection results drive multi-target tracking for trajectory association, proposing average completeness and average accuracy performance analysis metrics to rapidly form performance evaluations for constellation systems of different scales and configurations.

[0007] The objective of this invention is specifically achieved through the following technical solutions:

[0008] This invention discloses a method for performance analysis of large-scale low-Earth orbit satellite constellation systems for maritime moving target detection missions, including:

[0009] Step 1: Based on the six root numbers of the seed satellite orbits and the constellation configuration parameters, construct a large-scale low-Earth orbit satellite constellation with the number of orbital planes combined with the number of satellites in each orbital plane, and output the satellite attribute parameters;

[0010] Step two: Determine whether the current vessel's attributes in the maritime moving target detection mission area indicate a turn, and generate a track corresponding to the vessel's attributes according to the kinematic laws and time sequence. Calculate the latitude and longitude from the distance and heading corresponding to the track. Detect whether the current vessel's track is located at sea by using the latitude and longitude in the geographic database. If not, update the heading or reset the total turning angle, and recalculate the latitude and longitude until the current vessel's track is at sea. If yes, update the ship's speed and correct the acceleration based on speed constraints, and output the current vessel's track as the true track.

[0011] Step 3: Use the unit vector of the payload field of view axis of the wide-swath detection payload and the satellite attribute parameters to obtain the angle between the target and the satellite payload field of view axis; determine whether the angle meets the visibility threshold, obtain the constructed edge payload field of view detection model, and output the satellite detection of the current ship's trajectory as the detection trajectory;

[0012] Step four: Iterate through steps two and three to obtain the set of real tracks and the set of detected tracks for all vessels in the maritime moving target detection mission area; perform Kalman filtering on the set of detected tracks to fuse the track data and associate the tracks to obtain the set of associated tracks; conduct performance analysis on the set of real tracks, the set of detected tracks, and the set of associated tracks to evaluate the average recall rate and average accuracy of the track association.

[0013] The beneficial effects of this invention are:

[0014] 1. Traditional Walker constellation construction methods lack a unified mechanism for generating the orbital root numbers and payload parameters of each satellite in the constellation, which is detrimental to subsequent coupling with target visibility analysis. This invention systematically generates simulation parameter elements of the entire constellation of satellites based on the orbital root numbers of seed satellites and constellation configuration parameters. It can quickly construct large-scale low-Earth orbit satellite constellations ranging from dozens to thousands of satellites, providing a basis for performance comparison of different configurations.

[0015] 2. Traditional maritime target simulations use static or straight-line trajectory models, which cannot reflect the dynamic characteristics of ships in realistic dense sea scenarios, such as turning behavior, acceleration constraints, and land-sea boundary limitations. This invention introduces a mechanism of "turning marker + number of turning points + total turning angle" to generate realistic tracks that include straight-line travel and complex turns. It innovatively introduces a dynamic land-sea judgment and correction mechanism, which uses a geographic database to detect in real time whether the latitude and longitude are over the sea. If on land, it automatically regenerates the heading angle until it falls on the sea surface, significantly improving the realism of the simulation. By adopting a speed update model under acceleration constraints, it ensures that ship speed changes conform to physical laws, avoids abrupt changes, enhances temporal continuity, and provides a foundation for boundary testing of system performance under dense target conditions.

[0016] 3. Traditional satellite detection models often simplify to "coverage equals visibility," neglecting the payload's field-of-view cone angle, satellite motion direction, and the dynamic process of the target entering and leaving the field of view. This invention achieves high-precision positioning based on the acquisition, processing, and analysis of industrial big data, by calculating the angle between the target and the payload's field-of-view axis. The relationship with the half-field angle θ is used to accurately determine visibility; an innovative "edge detection timing discrimination" mechanism is implemented. and ,but For the forefront of exploration; if and ,but As the trailing edge detection time, this criterion can accurately capture the discrete times of the target's first / last entry into the field of view, outputting the detection time and position set, providing high-quality observation input for subsequent track association.

[0017] 4. Existing track association methods cannot reflect the continuity of constellation tracking and the accuracy of positioning of moving targets. This invention proposes two new dynamic performance indicators: Average Completeness Rate (ACR), which measures the system's detection coverage capability of real targets; and Average Accuracy Rate (AAR), which measures the spatial matching accuracy between associated tracks and real tracks by introducing a distance error threshold.

[0018] 5. This invention first introduces several innovative modeling methods at each stage of the technology chain. It generates realistic dense tracks through a high-fidelity ship motion model (including turning, acceleration constraints, and land-sea verification), and proposes a dual index of "average completeness + average accuracy" to quantify the system's detection completeness and tracking accuracy of moving targets. Second, based on the current fragmented status quo of the constellation-target-detection-evaluation chain, it constructs an end-to-end simulation analysis framework to achieve a closed loop of the entire process from "constellation construction → target generation → detection simulation → track association → performance evaluation". This effectively solves the industry pain points of "simulation distortion and inaccurate evaluation" in the current field of satellite monitoring of moving targets at sea, and has significant engineering application value and promotion potential. Attached Figure Description

[0019] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments.

[0020] Figure 1 This is a flowchart of a method for performance analysis of a large-scale low-Earth orbit satellite constellation system for maritime moving target detection missions, provided by an embodiment of the present invention.

[0021] Figure 2 This is a schematic diagram of the 20×5 Walker constellation configuration provided in an embodiment of the present invention.

[0022] Figure 3This is a schematic diagram of the 10×10 Walker constellation configuration provided in an embodiment of the present invention. Detailed Implementation

[0023] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0024] like Figure 1 As shown, this invention provides a method for performance analysis of a large-scale low-Earth orbit satellite constellation system for maritime moving target detection missions, including:

[0025] Step 1: Based on the six root numbers of the seed satellite orbits and the constellation configuration parameters, construct a large-scale low-Earth orbit satellite constellation with the number of orbital planes combined with the number of satellites in each orbital plane, and output the satellite attribute parameters;

[0026] The constructed large-scale low-Earth orbit satellite constellation supports flexible configuration of the number of orbital planes, the number of satellites per orbit, and the phase difference, generating Walker constellations with different configurations (p×1 or p×s) or improving constellation layouts, and enabling rapid iterative optimization of constellation configurations.

[0027] Step two: Determine whether the current vessel's attributes in the maritime moving target detection mission area indicate a turn, and generate a track corresponding to the vessel's attributes according to the kinematic laws and time sequence. Calculate the latitude and longitude from the distance and heading corresponding to the track. Detect whether the current vessel's track is located at sea by using the latitude and longitude in the geographic database. If not, update the heading or reset the total turning angle, and recalculate the latitude and longitude until the current vessel's track is at sea. If yes, update the ship's speed and correct the acceleration based on speed constraints, and output the current vessel's track as the true track.

[0028] Based on the kinematic model of ships on the sea surface, a ship maneuvering model is constructed to create a scenario of densely distributed moving ships on the sea surface.

[0029] Step 3: Use the unit vector of the payload field of view axis of the wide-swath detection payload and the satellite attribute parameters to obtain the angle between the target and the satellite payload field of view axis; determine whether the angle meets the visibility threshold, obtain the constructed edge payload field of view detection model, and output the satellite detection of the current ship's trajectory as the detection trajectory;

[0030] Wide-area sea surface detection is carried out using a wide-span detection payload. The visibility of moving targets on the sea surface is analyzed by the payload's field of view to obtain discrete detection points of ships.

[0031] Step four: Iterate through steps two and three to obtain the set of real tracks and the set of detected tracks for all vessels in the maritime moving target detection mission area; perform Kalman filtering on the set of detected tracks to fuse the track data and associate the tracks to obtain the set of associated tracks; conduct performance analysis on the set of real tracks, the set of detected tracks, and the set of associated tracks to evaluate the average recall rate and average accuracy of the track association.

[0032] System performance analysis was conducted, and the optimal estimated points for ships were formed using the Kalman filter algorithm. The scattered detection points were fitted into lines to perform track association. The average coverage rate and average accuracy rate of the track association were evaluated based on the formed track information.

[0033] In step one, the six roots of the seed satellite's orbit are:

[0034] ;

[0035] In the formula, a is the semi-major axis of the seed satellite's orbit, e is the eccentricity of the seed satellite, and inc is the orbital inclination of the seed satellite. The right ascension of the ascending node of the seed satellite, The perigee argument of the seed satellite, For the true anterior angle of the seed satellite, The half-field-of-view angle of the satellite payload is for seed satellites; for detection satellites, which use wide-field-of-view detection, the payload field-of-view model is constructed in a cone shape. The payload detection error of the seed satellite follows a normal distribution, and R is the Earth's radius.

[0036] The constellation configuration parameters are:

[0037] ;

[0038] In the formula, P represents the maximum number of orbital planes, and S represents the maximum number of satellites per orbital plane. This represents the phase difference between corresponding satellites on adjacent orbital planes. This represents the increment of right ascension at the ascending node between orbital planes;

[0039] Based on the six root numbers of seed satellite orbits and constellation configuration parameters, the method for constructing a large-scale low-Earth orbit satellite constellation with a configuration consisting of the number of orbital planes and the number of satellites per orbital plane is as follows:

[0040] When S=1, construct a large-scale low-Earth orbit satellite constellation of type P×1;

[0041] When S≥2, a large-scale low-Earth orbit satellite constellation of type P×S is constructed, with satellites uniformly distributed within the same orbital plane and a phase difference of . / S.

[0042] In step one, the output satellite attribute parameters are:

[0043] ;

[0044] In the formula, For the m-th satellite in the k-th orbital plane of a large-scale low-Earth orbit satellite constellation, Where k is the UTC epoch time, k is the orbital plane number, and m is the satellite number within the orbital plane, m=1,2,…,S; For satellite orbital elements, For satellite payload detection parameters;

[0045] The right ascension of the ascending node of the k-th orbital plane. The calculation method is as follows:

[0046] ;

[0047] In the formula, mod is the modulo operation function;

[0048] True anomaly of the m-th satellite on the k-th orbital plane include and ;in,

[0049] When S=1, the true anomaly angle when constructing a large-scale P×1 type low-Earth orbit satellite constellation The calculation method is as follows:

[0050] ;

[0051] When S≥2, the true anomaly angle when constructing a large-scale P×S type low-Earth orbit satellite constellation The calculation method is as follows:

[0052] .

[0053] In step two, the method for determining whether the current vessel's attributes in the maritime moving target detection mission area are turning, and generating the corresponding track based on the kinematic laws and time sequence, is as follows:

[0054] S21, construct a polygonal simulation region within the latitude range ∈ [-inc, inc] of the maritime moving target detection mission area. The simulation involves establishing a flight path and simultaneously initializing the spatial parameters of the simulation area, the temporal parameters, the motion threshold parameters, and the ship's attribute parameters. The initialization methods include:

[0055] Initialize simulation space region parameters In the formula, A represents the polygonal simulation region. Let A be the coordinates of its vertex. For the first Each latitude, For the first One longitude, This represents the index of a vertex in A, where a is the total number of vertices in A.

[0056] Initialize simulation time parameters: including start time End time and time interval ;

[0057] Initialize simulation motion threshold parameters: initial velocity range, i.e., velocity constraints. The initial heading angle range, i.e., the initial heading angle constraint conditions [ (Unit: degrees, 0° is due north, increasing clockwise), acceleration range, i.e., acceleration constraint conditions. In the formula, For the minimum speed, This represents the maximum speed. For the target at the start of the simulation Minimum allowable heading angle For the target at the start of the simulation Maximum allowable heading angle For the minimum acceleration, This represents the maximum acceleration.

[0058] Initialize ship attribute parameters: whether to turn (isTurnShip∈{0,1}), where 1 indicates turning and 0 indicates going straight; total turning angle. For example, 180°; total number of turning points ;

[0059] S22, according to Initialize target name , express Track sequence index. express The total number of flight tracks;

[0060] S23, based on simulation space region parameters Initial position of the initial track The initial location is randomly generated within A and verified by a geographic database to be located on the sea surface;

[0061] S24, Generate a discrete time point sequence based on the simulation time parameters. :

[0062] ;

[0063] in, Indicates the time step of scene construction. express arrive The number of time steps between, ≥The threshold for the ship's turning time; for example, ;

[0064] S25, Initialize the initial velocity of the trajectory based on the simulation motion threshold parameters. ,express The initial velocity, i.e. The initial velocity at time t, where U represents a uniform velocity distribution;

[0065] At the same time, initialize the initial heading of the track. ,express The initial heading angle at that moment;

[0066] S26. According to the ship attribute parameters, when isTurnShip = 0, the ship attribute is marked as straight. Based on the kinematic laws, a straight track is generated according to the time steps in the time point sequence, that is, the operation steps are repeated for each time step. When isTurnShip = 1, the ship attribute is marked as turning. Based on the kinematic laws, a turning track is generated according to the time steps in the time point sequence.

[0067] In step S26, the heading corresponding to the straight-ahead track is calculated as follows:

[0068] ;

[0069] In the formula, The first of the straight-line flight path The heading angle corresponding to each time step The first of the straight-line flight path The heading angle corresponding to each time step Let be the change in heading angle at the j-th time step of the straight-ahead trajectory. ,express Follow the heading section Uniform distribution on This is the minimum allowable heading change per time step. This represents the maximum allowable change in heading during a single time step.

[0070] Distance corresponding to a straight flight path The calculation method is as follows:

[0071] ;

[0072] In the formula, The first of the straight-line flight path The ship's speed at the start of each time step. For straight-line flight path The ship's speed at the end of each time step The first of the straight-line flight path The time step and the first The difference between the time steps represents the time steps of the straight-line trajectory sorted in ascending order of time;

[0073] In step S26, the turning track is divided into a turning phase and a non-turning phase. A track with significant heading changes needs to be constructed, containing a smooth, phased turning process to simulate the behavior of a real ship making a large-angle turn at sea; and In the formula, This is the time step sequence for the non-turning phase. It simulates the random turning moments of a ship during navigation, avoiding the occurrence of all turns at fixed times. A random starting index for the non-turning phase. , indicating from At least there started The entire turning process is completed in consecutive time steps, and a uniform distribution strategy is used to achieve a smooth turn, that is, ;in,

[0074] S261, the method for calculating the heading corresponding to the non-turning phase of a turning track is as follows:

[0075] ;

[0076] In the formula, The first non-turning phase of the turning trajectory The heading angle corresponding to each time step The first non-turning phase of the turning trajectory The heading angle corresponding to each time step The first non-turning phase of the turning trajectory The change in heading angle at each time step express Follow the heading section Uniform distribution on;

[0077] S262, Distance corresponding to the non-turning phase of a turning track. The calculation method is as follows:

[0078] ;

[0079] In the formula, The first non-turning phase of the turning trajectory The ship's speed at the start of each time step. The first non-turning phase of the turning trajectory The ship's speed at the end of each time step; The first non-turning phase of the turning trajectory The time step and the first The difference between the time steps represents the time steps of the non-turning phase of the turning trajectory, sorted in ascending order of time.

[0080] S263, the method for calculating the heading corresponding to the turning phase of a turning track is as follows:

[0081] ;

[0082] In the formula, The first stage of the turning trajectory The heading angle corresponding to each time step The first stage of the turning trajectory The heading angle corresponding to each time step;

[0083] S264, the distance corresponding to the turning phase of the turning track. The calculation method is as follows:

[0084] ;

[0085] In the formula, The first stage of the turning trajectory The ship's speed at the start of each time step. The first stage of the turning trajectory The ship's speed at the end of each time step The first stage of the turning trajectory The time step and the first The difference between the time steps indicates that the time steps of the turning phase of the turning track are sorted in ascending order of time.

[0086] In step two, latitude and longitude are calculated from the distance and heading corresponding to the flight track. The method is as follows:

[0087] ;

[0088] ;

[0089] In the formula, Let the latitude be the latitude of the j-th time step. Let j be the longitude at the j-th time step. Let the latitude be the latitude of the (j-1)th time step. The longitude at the (j-1)th time step; include , and , indicating the distance corresponding to the flight path; include , and , represents the heading corresponding to the track; R is the Earth's radius.

[0090] In step two, the ship's current trajectory is detected based on its latitude and longitude position in the geographic database to determine if it is at sea, thus avoiding trajectories crossing land. If the ship's trajectory is detected to be on land, then based on... Updated by time step Change in heading angle or Or reset the total turning angle Recalculate the latitude and longitude until the current ship's track is at sea;

[0091] If the current vessel's track is detected to be over the sea, then based on the speed constraint... The core process involves updating the ship's speed and correcting its acceleration, outputting the current ship trajectory as the actual trajectory, and ensuring that the trajectory conforms to physical laws and preset constraints. This achieves precise control over the ship's motion state, ensuring that the generated trajectory not only conforms to actual navigation characteristics but also meets the user-defined parameter range. The method for updating the ship's speed is as follows:

[0092] ;

[0093] In the formula, For acceleration, include , and ,like Exceeding speed constraints Then for acceleration Obtain the corrected acceleration The calculation method is as follows:

[0094] ;

[0095] In the formula, The minimum speed in the speed constraint conditions or maximum speed , include , and If the ship is moving at a reduced speed, then it is If the ship is accelerating, then it is ;

[0096] Output the tracks of all ships in A. ;

[0097] in, For the set of real trajectories, , For namesi The set of trajectories, for Latitude With longitude position .

[0098] Step two simulates the ship's behavior, such as going straight and turning.

[0099] In step three, the method for calculating the angle between the target and the satellite payload's field of view axis is as follows:

[0100] ;in,

[0101] ;

[0102] in, Indicates in The angle between the target and the satellite payload's field of view axis; The name of the target being detected during the simulation is indicated by the satellite detection time index d. sd The moment of being detected by satellite For name sd The time index detected by the satellite, 1≤d≤ , For name sd Total number of times detected by satellite; name sd The name of the target detected by the satellite. for Track sequence index. ≤ ≤ ; Indicates satellite attribute parameters in The line-of-sight vector of the satellite pointing at the target. Indicates in The unit vector of the load field of view axis of the lower wide-swath detection load; for The modulus, for The modulus; Indicates in Lower satellite position vector, Indicates in Lower target position vector;

[0103] Determine the included angle The method for determining whether the edge load field of view detection model meets the visibility threshold is as follows:

[0104] like Then in The target is within the field of view and is visible. Here, θ represents the half-field-of-view angle of the seed satellite's payload, indicating the half-field-of-view angle of the payload when the field of view of the detection satellite is a conical shape for Earth observation. Detection is divided into two types: leading-edge detection (the first half of the circle sweeps across the target) and trailing-edge detection (the second half of the circle sweeps across the target). Then, the detection edge time is determined second by second.

[0105] like and ,but This refers to the moment of forward detection; where forward detection is the leading edge of the field of view in the direction of satellite motion, that is, the first half of the circle sweeping across the target;

[0106] like and ,but The trailing edge detection time; where trailing edge detection is the trailing edge of the field of view in the direction of satellite motion, that is, the latter half of the circle sweeping across the target;

[0107] In the formula, Indicates in The angle between the target and the satellite payload's field of view axis. For the name of the probe time index d-1 during the simulation process sd The moment of being detected by satellite Represents name sd Time index detected by satellite The index of the previous time step;

[0108] The satellite-detected current ship trajectory output by the edge load field-of-view detection model is used as the detection trajectory:

[0109] ;

[0110] in, To detect track sets, , For name sd A collection of ship tracks detected by satellite; To detect the total number of ships detected by satellite in the track set; for Latitude With longitude position .

[0111] The constructed dynamic edge load field-of-view measurement model, combined with satellite orbital motion and target movement trajectory, establishes a geometric visibility criterion and a dynamic detection timing solution method to achieve accurate detection timing determination of moving targets.

[0112] In step four, the set of detection tracks is processed. Methods for performing Kalman filter point fusion and track association to obtain a set of associated tracks include:

[0113] S41, based on the motion model Perform Kalman filter point prediction; the motion model is as follows:

[0114] ;

[0115] ;

[0116] ;

[0117] In the formula, For name sf exist The prior estimate of the target waypoint. The index for fusing and associating time points during the simulation process is: name sf At the moment of being merged and associated, Represents name sf The time index for performing point fusion and association. ≤ ≤ name sf To merge associated target names, sf is Track sequence number index; Here is the state transition matrix. for name under sf The optimal estimate of the dot. The index for fusing and associating time points during the simulation process is: name sf The moment of being integrated and associated, Represents name sf Time index for point fusion and association The index of the previous time step; For the control matrix, for The control input below, for The prior estimate of covariance, for The optimal error covariance matrix under the given conditions, for The transpose of the matrix, The process noise covariance matrix describes the uncertainty of the system model; for The satellite's detection and observation values, , , For the observation matrix, For the true value of the ship, For measuring noise;

[0118] S42, Based on the Kalman filter formula, update the Kalman filter state in the motion model and find the optimal estimation point. The set of associated tracks is obtained. ;

[0119] in, , For name sf The set of associated trajectories, for Latitude With longitude position ; For name sf Total number of associated waypoints This represents the total number of ships associated in the associated track set;

[0120] The update method for Kalman filter state updates in the motion model, based on the Kalman filter formula, is as follows:

[0121] ;

[0122] ;

[0123] ;

[0124] In the formula, for Kalman gain below, Observation matrix transpose, To measure the noise covariance matrix; for The optimal estimate of the ship's position traces. , for The optimal error covariance matrix under the given conditions.

[0125] Based on the generated track information, innovative track correlation performance evaluation indicators are developed to form constellation performance evaluation results.

[0126] In step four, a performance analysis is performed using the real track set, the detected track set, and the associated track set. The method for evaluating the average recall and average accuracy of track association is as follows:

[0127] ;

[0128] ;

[0129] In the formula, The average recall rate of the points associated with each other. The average accuracy of point association; This is an indicator function that takes the value 1 if the condition is true and 0 otherwise; point The meaning of being successfully associated is Used as observation value Kalman filtering is used to obtain the optimal estimate. ; The meaning is ;in, Let it be a distance function. This represents the distance error.

[0130] Verification experiment:

[0131] To verify the effectiveness of the technical solution of the present invention, a verification experiment is provided for illustration:

[0132] Step 1: Construct constellations of different sizes, such as Figure 2 and Figure 3 The figures shown are the Walker constellations, which are 20×5 and 10×10 respectively.

[0133] Step 2: Based on the kinematic model of ships on the sea surface, construct the ship maneuver model and create dense scenarios with an average ship density of 10 ships / 10,000 square kilometers and 30 ships / 10,000 square kilometers on the sea surface.

[0134] Step 3: Use a wide-area detection payload to conduct wide-area sea surface detection, and obtain discrete detection points of ships by analyzing the visibility of moving targets on the sea surface through the field of view of the payload.

[0135] Step 4: Conduct system performance analysis, and evaluate the average completeness and average accuracy of point-track association for the generated track information.

[0136] In this embodiment of the invention, the performance results of different constellation configurations obtained using the technical solution disclosed in this invention are shown in Table 1:

[0137] Table 1

[0138]

[0139] like Figure 2 and Figure 3As shown, this invention successfully constructs two typical Walker constellations based on the six root numbers of seed satellites and constellation configuration parameters. These constellations support uniform satellite distribution within the orbital plane and cross-plane phase difference configuration, providing a comparable basis for subsequent performance comparisons. By employing a velocity update model under acceleration constraints, physically reasonable kinematic continuity is maintained under different densities of 10 ships / 10,000 km² and 30 ships / 10,000 km², effectively simulating densely populated areas such as ports and waterways. Closed-loop simulation results from the entire process of "constellation construction → target generation → detection simulation → track association → performance evaluation" show that in low-density scenarios (10 ships / 10,000 km²), the system achieves almost full target coverage (ACR=0.98) and accurate positioning altitude (AAR=0.99), verifying the high reliability of the method in conventional scenarios. In high-density scenarios (30 ships / 10,000 km²), despite a 3-fold increase in target density, the system still maintains a 76% coverage rate and an 83% accuracy rate, demonstrating strong robustness in dense and complex sea conditions.

[0140] This invention successfully addresses two major industry pain points—simulation distortion and inaccurate evaluation—through an end-to-end simulation implementation process. Experimental results show that the proposed method can not only simulate dense moving targets at sea with high fidelity, but also objectively and quantitatively evaluate the actual performance of different constellation configurations in complex scenarios. This provides scientific and quantifiable decision support for the design, selection, and mission planning of future large-scale low-Earth orbit constellations in fields such as intelligent shipping, maritime supervision, and maritime security.

[0141] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for performance analysis of a large-scale low earth orbit satellite constellation system for maritime moving target detection task, characterized in that, include: Step 1: Based on the six root numbers of the seed satellite orbits and the constellation configuration parameters, construct a large-scale low-Earth orbit satellite constellation with the number of orbital planes combined with the number of satellites in each orbital plane, and output the satellite attribute parameters; Step 2: Determine whether the current vessel's attributes in the maritime moving target detection mission area are turning, and generate the corresponding track based on the kinematic laws and time sequence; calculate the latitude and longitude from the distance and heading corresponding to the track, and detect whether the current vessel's track is located at sea by using the latitude and longitude in the geographic database; No, then update the course or reset the total turning angle, and recalculate the latitude and longitude until the current ship's track is at sea; If yes, then based on the speed constraint, update the ship speed and correct the acceleration, and output the current ship track as the true track; Step 3: Use the unit vector of the payload field of view axis of the wide-swath detection payload and the satellite attribute parameters to obtain the angle between the target and the satellite payload field of view axis; determine whether the angle meets the visibility threshold, obtain the constructed edge payload field of view detection model, and output the satellite detection of the current ship's trajectory as the detection trajectory; Step four: Iterate through steps two and three to obtain the set of real tracks and the set of detected tracks for all vessels in the maritime moving target detection mission area; perform Kalman filtering on the set of detected tracks to fuse the track data and associate the tracks to obtain the set of associated tracks; conduct performance analysis on the set of real tracks, the set of detected tracks, and the set of associated tracks to evaluate the average recall rate and average accuracy of the track association.

2. The method of claim 1, wherein the large-scale LEO satellite constellation system performance analysis for maritime moving target detection task is characterized by, In step one, the six roots of the seed satellite's orbit are: ； In the formula, a is the semi-major axis of the seed satellite's orbit, e is the eccentricity of the seed satellite, and inc is the orbital inclination of the seed satellite. The right ascension of the ascending node of the seed satellite, The perigee argument of the seed satellite, For the true anterior angle of the seed satellite, The half-field-of-view angle of the satellite payload of the seed satellite. The payload detection error of the seed satellite follows a normal distribution, and R is the Earth's radius. The constellation configuration parameters are: ； In the formula, P is the maximum number of orbital planes, S is the maximum number of satellites per orbital plane, is the phase difference value between corresponding satellites between adjacent orbital planes, is the ascending node right ascension increment between orbital planes; Based on the six root numbers of seed satellite orbits and constellation configuration parameters, the method for constructing a large-scale low-Earth orbit satellite constellation with a configuration consisting of the number of orbital planes and the number of satellites per orbital plane is as follows: When S=1, construct a large-scale low-Earth orbit satellite constellation of type P×1; When S≥2, a large-scale low-orbit satellite constellation of P×S is constructed, the satellites are uniformly distributed in the same orbit plane, and the phase difference is / S.

3. The method for performance analysis of a large-scale low-Earth orbit satellite constellation system for maritime moving target detection missions as described in claim 2, characterized in that, In step one, the output satellite attribute parameters are: ； In the formula, For the m-th satellite in the k-th orbital plane of a large-scale low-Earth orbit satellite constellation, Where k is the UTC epoch time, k is the orbital plane number, and m is the satellite number within the orbital plane, m=1,2,…,S; For satellite orbital elements, For satellite payload detection parameters; The right ascension of the ascending node of the k-th orbital plane. The calculation method is as follows: ； In the formula, mod is the modulo operation function; True anomaly of the m-th satellite on the k-th orbital plane include and ;in, When S=1, the true anomaly angle when constructing a large-scale P×1 type low-Earth orbit satellite constellation The calculation method is as follows: ； When S≥2, the true anomaly angle when constructing a large-scale P×S type low-Earth orbit satellite constellation The calculation method is as follows: 。 4. The method for performance analysis of a large-scale low-Earth orbit satellite constellation system for maritime moving target detection missions as described in claim 3, characterized in that, In step two, the method for determining whether the current vessel's attributes in the maritime moving target detection mission area are turning, and generating the corresponding track based on the kinematic laws and time sequence, is as follows: S21, construct a polygonal simulation region within the latitude range ∈ [-inc, inc] of the maritime moving target detection mission area. The simulation involves establishing a flight path and simultaneously initializing the spatial parameters of the simulation area, the temporal parameters, the motion threshold parameters, and the ship's attribute parameters. The initialization methods include: Initialize simulation space region parameters In the formula, A represents the polygonal simulation region. Let A be the coordinates of its vertex. For the first Each latitude, For the first One longitude, This represents the index of a vertex in A, where a is the total number of vertices in A. Initialize simulation time parameters: including start time End time and time interval ; Initialize simulation motion threshold parameters: initial velocity range, i.e., velocity constraints. The initial heading angle range, i.e., the initial heading angle constraint conditions [ Acceleration range, i.e., acceleration constraints. In the formula, For the minimum speed, This represents the maximum speed. For the target at the start of the simulation Minimum allowable heading angle For the target at the start of the simulation Maximum allowable heading angle For the minimum acceleration, This represents the maximum acceleration. Initialize ship attribute parameters: whether to turn (isTurnShip∈{0,1}), where 1 indicates turning and 0 indicates going straight; total turning angle. Total number of turning points ; S22, according to Initialize target name , express Track sequence index. express The total number of flight tracks; S23, based on simulation space region parameters Initial position of the initial track The initial location is randomly generated within A and verified by a geographic database to be located on the sea surface; S24, Generate a discrete time point sequence based on the simulation time parameters. : ； in, Indicates the time step of scene construction. express arrive The number of time steps between, ≥ Threshold for ship turning time; S25, Initialize the initial velocity of the trajectory based on the simulation motion threshold parameters. ,express The initial velocity, i.e. The initial velocity at time t, where U represents a uniform velocity distribution; At the same time, initialize the initial heading of the track. ,express The initial heading angle at that moment; S26. According to the ship attribute parameters, when isTurnShip = 0, the ship attribute is marked as straight, and a straight track is generated according to the time steps in the time point sequence based on the kinematic laws; when isTurnShip = 1, the ship attribute is marked as turning, and a turning track is generated according to the time steps in the time point sequence based on the kinematic laws.

5. The method for performance analysis of a large-scale low-Earth orbit satellite constellation system for maritime moving target detection missions as described in claim 4, characterized in that, In step S26, the heading corresponding to the straight-ahead track is calculated as follows: ； In the formula, The first straight-line flight path The heading angle corresponding to each time step The first straight-line flight path The heading angle corresponding to each time step Let be the change in heading angle at the j-th time step of the straight-ahead trajectory. ,express Follow the heading section Uniform distribution on This is the minimum allowable heading change for a single time step. This represents the maximum allowable change in heading during a single time step. Distance corresponding to a straight flight path The calculation method is as follows: ； In the formula, The first straight-line flight path The ship's speed at the start of each time step. For straight flight path The ship's speed at the end of each time step The first straight-line flight path The time step and the first The difference between the time steps represents the time steps of the straight-line trajectory sorted in ascending order of time; In step S26, the turning trajectory is divided into a turning phase and a non-turning phase; and In the formula, This is the time step sequence for the non-turning phase. ; A random starting index for the non-turning phase. , indicating from At least there started The entire turning process is completed in consecutive time steps, that is, ;in, S261, the method for calculating the heading corresponding to the non-turning phase of a turning track is as follows: ； In the formula, The first non-turning phase of the turning trajectory The heading angle corresponding to each time step The first non-turning phase of the turning trajectory The heading angle corresponding to each time step The first non-turning phase of the turning trajectory The change in heading angle at each time step express Follow the heading section Uniform distribution on; S262, Distance corresponding to the non-turning phase of a turning track. The calculation method is as follows: ； In the formula, The first non-turning phase of the turning trajectory The ship's speed at the start of each time step. The first non-turning phase of the turning trajectory The ship's speed at the end of each time step; The first non-turning phase of the turning trajectory The time step and the first The difference between the time steps represents the time steps of the non-turning phase of the turning trajectory, sorted in ascending order of time. S263, the method for calculating the heading corresponding to the turning phase of a turning track is as follows: ； In the formula, The first stage of the turning trajectory The heading angle corresponding to each time step The first stage of the turning trajectory The heading angle corresponding to each time step; S264, the distance corresponding to the turning phase of the turning track. The calculation method is as follows: ； In the formula, The first stage of the turning trajectory The ship's speed at the start of each time step. The first stage of the turning trajectory The ship's speed at the end of each time step The first stage of the turning trajectory The time step and the first The difference between the time steps indicates that the time steps of the turning phase of the turning track are sorted in ascending order of time.

6. The method for performance analysis of a large-scale low-Earth orbit satellite constellation system for maritime moving target detection missions as described in claim 5, characterized in that, In step two, latitude and longitude are calculated from the distance and heading corresponding to the flight track. The method is as follows: ； ； In the formula, Let the latitude be the latitude of the j-th time step. Let j be the longitude at the j-th time step. Let the latitude be the latitude of the (j-1)th time step. The longitude at the (j-1)th time step; include , and , indicating the distance corresponding to the flight path; include , and , represents the heading corresponding to the track; R is the Earth's radius.

7. The method for performance analysis of a large-scale low-Earth orbit satellite constellation system for maritime moving target detection missions as described in claim 6, characterized in that, In step two, the ship's current trajectory is determined by its latitude and longitude location in the geographic database to determine if it is at sea; if it is detected that the ship's current trajectory is on land, then based on... Updated by time step Change in heading angle or Or reset the total turning angle Recalculate the latitude and longitude until the current ship's track is at sea; If the current vessel's track is detected to be over the sea, then based on the speed constraint... Update the ship's speed and correct its acceleration, then output the current ship's trajectory as the actual trajectory; the method for updating the ship's speed is as follows: ； In the formula, For acceleration, include , and ,like Exceeding speed constraints Then for acceleration Obtain the corrected acceleration The calculation method is as follows: ； In the formula, The minimum speed in the speed constraint conditions or maximum speed , include , and If the ship is moving at a reduced speed, then it is If the ship is accelerating, then it is ; Output the tracks of all ships in A. ; in, For the set of real trajectories, , For name si The set of trajectories, for Latitude With longitude position .

8. The method for performance analysis of a large-scale low-Earth orbit satellite constellation system for maritime moving target detection missions as described in claim 7, characterized in that, In step three, the method for calculating the angle between the target and the satellite payload's field of view axis is as follows: ;in, ； in, Indicates in The angle between the target and the satellite payload's field of view axis; The name of the target being detected during the simulation is indicated by the satellite detection time index d. sd The moment of being detected by satellite For name sd The time index detected by the satellite, 1≤d≤ , For name sd Total number of times detected by satellite; name sd The name of the target detected by the satellite. for Track sequence index. ≤ ≤ ; Indicating satellite attribute parameters in The line-of-sight vector of the satellite pointing at the target. Indicates in The unit vector of the load field of view axis of the lower wide-swath detection load; for The modulus, for The modulus; Indicates in Lower satellite position vector, Indicates in Lower target position vector; Determine the included angle The method for determining whether the edge load field of view detection model meets the visibility threshold is as follows: like Then in The target is within the field of view and is visible. Here, θ represents the half-field-of-view angle of the seed satellite's payload, indicating the half-field-of-view angle of the payload when the field of view of the detection satellite is a conical shape for Earth observation. Detection is divided into two types: leading-edge detection and trailing-edge detection. The detection edge time is then determined second by second. like and ,but This refers to the moment of forward detection; where forward detection is the leading edge of the field of view in the direction of satellite motion, that is, the first half of the circle sweeping across the target; like and ,but The trailing edge detection time; where trailing edge detection is the trailing edge of the field of view in the direction of satellite motion, that is, the latter half of the circle sweeping across the target; In the formula, Indicates in The angle between the target and the satellite payload's field of view axis. For the name of the probe time index d-1 during the simulation process sd The moment of being detected by satellite Represents name sd Time index detected by satellite The index of the previous time step; The satellite-detected current ship trajectory output by the edge load field-of-view detection model is used as the detection trajectory: ； in, To detect track sets, , For name sd A collection of ship tracks detected by satellite; To detect the total number of ships detected by satellite in the track set; for Latitude With longitude position .

9. The method for performance analysis of a large-scale low-Earth orbit satellite constellation system for maritime moving target detection missions as described in claim 8, characterized in that, In step four, the set of detection tracks is processed. Methods for performing Kalman filter point fusion and track association to obtain a set of associated tracks include: S41, based on the motion model Perform Kalman filter point prediction; the motion model is as follows: ； ； ； In the formula, For name sf exist The prior estimate of the target waypoint. The index for fusing and associating time points during the simulation process is: name sf At the moment of being merged and associated, Represents name sf The time index for performing point fusion and association. ≤ ≤ name sf To merge associated target names, sf is Track sequence index; Here is the state transition matrix. for name under sf The optimal estimate of the dot. The index for fusing and associating time points during the simulation process is: name sf The moment of being integrated and associated, Represents name sf Time index for point fusion and association The index of the previous time step; For the control matrix, for The control input below, for The prior estimate of covariance, for The optimal error covariance matrix under the given conditions, for The transpose of the matrix, The process noise covariance matrix describes the uncertainty of the system model; for The satellite's detection and observation values, , , For the observation matrix, For the true value of the ship, For measuring noise; S42, Based on the Kalman filter formula, update the Kalman filter state in the motion model and find the optimal estimation point. The set of associated tracks is obtained. ; in, , For name sf The set of associated trajectories, for Latitude With longitude position ; For name sf Total number of associated waypoints This represents the total number of ships associated in the associated track set; The update method for Kalman filter state updates in the motion model, based on the Kalman filter formula, is as follows: ； ； ； In the formula, for Kalman gain below, Observation matrix transpose, To measure the noise covariance matrix; for The optimal estimate of the ship's location traces. , for The optimal error covariance matrix under the given conditions.

10. The method for performance analysis of a large-scale low-Earth orbit satellite constellation system for maritime moving target detection missions as described in claim 9, characterized in that, In step four, a performance analysis is performed using the real track set, the detected track set, and the associated track set. The method for evaluating the average recall and average accuracy of track association is as follows: ； ； In the formula, The average recall rate of the points associated with each other. The average accuracy of point association; This is an indicator function that takes the value 1 if the condition is true and 0 otherwise; point The meaning of being successfully associated is Used as observation value Kalman filtering is used to obtain the optimal estimate. ; The meaning is ;in, Let be the distance function. This represents the distance error.

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