A method for predicting the uncertain trajectory of a target using a low-Earth orbit satellite network

Abstract

This invention relates to a method for predicting uncertain trajectories of targets in a low-Earth orbit (LEO) satellite network, belonging to the field of detection and tracking technology. The method comprises the following steps: Step 1: Establishing a multi-target dynamic model under space motion; Step 2: Establishing a satellite-perturbed orbit dynamic model; Step 3: Calculating the position and velocity of satellite i in the geocentric inertial coordinate system based on the satellite-perturbed orbit dynamic model in Step 2; Step 4: Determining whether the target is within the detection range of the satellite's optical sensor based on the multi-target dynamic model in Step 1 and the position and velocity of satellite i in the geocentric inertial coordinate system in Step 3; Step 5: Establishing the measurement equation of the target in the geocentric inertial coordinate system; and using the measurement equation of the target in the geocentric inertial coordinate system, predicting the uncertain trajectory of the target. This invention realizes target trajectory prediction under uncertain conditions encountered when a LEO satellite network collaboratively detects moving targets in space.

Description

Technical Field

[0001] This invention belongs to the field of detection and tracking technology, and relates to a method for predicting the uncertain trajectory of a target using a low-orbit satellite network. Background Technology

[0002] When low-Earth orbit satellite networks detect and track small targets in space, they face uncertainties in information such as the target's maneuvering time and thrust magnitude. When using traditional multi-satellite centralized cooperative detection filters to measure space targets, the constellation cannot autonomously adjust its structure when the observation modes of multiple satellites change dynamically, making it difficult to guarantee the stability of the detected target signals. Furthermore, the estimated target trajectory values ​​may diverge, making it difficult to effectively assess the target's entire flight status.

[0003] In target tracking tasks, the target state and the measurements from satellite sensors at a given moment are two distinct random vectors, exhibiting uncertainty. Furthermore, the observed geometric relationship between the target and the satellites is constantly changing, constituting an uncertain set of relationships. Due to clutter and the possibility of false or missed detections by satellite sensors, the number of measurements generated by multiple satellite sensors may not equal the number of targets. The target state and the number of elements in the multi-satellite measurement set may change, and each element will evolve over time. For the sensors, measurements generated by the target are indistinguishable from those generated by clutter, and the sensors themselves do not have a direct correspondence between the target and the measurements; therefore, the order of elements in the measurement set is uncertain.

[0004] Under these conditions, it is a challenge to correlate the raw detection data of different satellites in the StarNet to achieve target trajectory prediction. Summary of the Invention

[0005] The technical problem solved by this invention is to overcome the shortcomings of the prior art and propose a method for predicting the uncertain trajectory of a target using a low-Earth orbit satellite network, thereby realizing the prediction of the target trajectory under uncertain conditions when the low-Earth orbit satellite network is used to collaboratively detect moving targets in space.

[0006] The solution of the present invention is:

[0007] A method for predicting the uncertain trajectory of a target using a low-Earth orbit satellite network includes:

[0008] Step 1: Establish a multi-objective dynamic model under spatial motion;

[0009] Step 2: Establish a dynamic model of the satellite's perturbed orbit;

[0010] Step 3: Based on the satellite's perturbation orbit dynamics model in Step 2, calculate the position and velocity of satellite i in the geocentric inertial coordinate system;

[0011] Step 4: Based on the multi-target dynamics model in Step 1 and the position and velocity of satellite i in the geocentric inertial coordinate system in Step 3, determine whether the target is within the detection range of the satellite's optical sensor.

[0012] Step 5: Establish the measurement equation of the target in the geocentric inertial coordinate system; based on the measurement equation of the target in the geocentric inertial coordinate system, predict the uncertain trajectory of the target.

[0013] In the aforementioned method for predicting the uncertain trajectory of a target using a low-Earth orbit satellite network, the method for establishing the multi-target dynamic model in step one is as follows:

[0014] After multiple space-moving targets leave the atmosphere, they enter a free flight phase, where their motion is only affected by gravity and thrust. In a geocentric inertial coordinate system, the target is defined as j, j = 1, 2…N. t N t Let t be the total number of targets at time t;

[0015] Since low-Earth orbit satellite network detection cannot predict the true motion sequence of non-cooperative targets, let the state vector of target j be... Wherein, the position vector r (j) =[x (j) ,y (j) ,z (j) ] T velocity vector Thrust acceleration vector

[0016] The establishment of a multi-objective dynamic model is described as follows:

[0017]

[0018] In the formula, μ e The gravitational constant of Earth;

[0019] f (j) (·) represents the dynamic function;

[0020] R (j) (t) represents the current radius of the Earth;

[0021] W (j) (t) represents the system noise as the target.

[0022] In the above-mentioned method for predicting the uncertain trajectory of a target using a low-Earth orbit satellite network, in step two, the low-Earth orbit satellite network adopts the Walker constellation configuration; it is described by N, P, and f; where N is the total number of satellites, P is the number of orbital planes in which the satellites are distributed, and f is the relative phase factor between satellites on adjacent orbital planes.

[0023] Let satellite i be numbered in the constellation. Then the right ascension of the ascending node and the angular distance from perigee of satellite i are expressed as follows:

[0024]

[0025] In the formula, Ω i Let the right ascension of the ascending node of satellite i be _i_.

[0026] ω i Angular distance from perigee to satellite i;

[0027] P i The number of the orbital plane where the satellite is located;

[0028] N i The satellite's designation within its orbital plane;

[0029] S is the number of satellites on each orbital plane.

[0030] In the aforementioned method for predicting the uncertain trajectory of a target using a low-Earth orbit satellite network, based on the Walker constellation configuration, a dynamic model of the satellite's perturbed orbit considering only Earth's gravity is established:

[0031]

[0032] In the formula, μ e The gravitational constant of Earth;

[0033] t0 is the initial time;

[0034] r0 is the position vector from the Earth's center to the satellite's center of mass;

[0035] The satellite velocity vector;

[0036] This is the satellite's acceleration vector;

[0037] r0 is the initial position;

[0038] r (i) (t0) is the initial position vector of satellite i in the geocentric inertial coordinate system;

[0039] To be based on constellation configuration and r (i) (t0) is the initial position vector of satellite i.

[0040] To be based on constellation configuration and The initial velocity vector of satellite i is obtained;

[0041] Let be the acceleration vector of satellite i.

[0042] In the aforementioned method for predicting the uncertain trajectory of a target in a low-Earth orbit satellite network, considering the combined effects of gravity, thrust, and atmospheric drag on the satellite's on-orbit detection operation, the total acceleration vector a of the satellite in the geocentric inertial frame is calculated:

[0043] a = a T +a A +a G

[0044] In the formula, a T This is the vector of the maneuvering acceleration caused by the thrust in the geocentric inertial frame;

[0045] a A This is the drag acceleration vector caused by atmospheric drag in the geocentric inertial frame;

[0046] a G This is the vector of gravitational acceleration caused by gravity in the geocentric inertial frame.

[0047] Substitute 'a' into formula (3) Make corrections:

[0048]

[0049] This yields the final dynamic model of the satellite's perturbed orbit:

[0050]

[0051] In the aforementioned method for predicting the uncertain trajectory of a target using a low-Earth orbit satellite network, the drag acceleration vector a caused by atmospheric drag in the geocentric inertial frame is... A for:

[0052]

[0053] In the formula, v is the magnitude of the satellite's velocity relative to the atmosphere;

[0054] u v The satellite velocity unit vector;

[0055] ρ(h) is the atmospheric density at the satellite's altitude h.

[0056] β is the damping coefficient.

[0057] In the aforementioned method for predicting the uncertain trajectory of a target using a low-Earth orbit satellite network, the thrust-induced maneuvering acceleration vector a T for:

[0058] a T =a′ T u v

[0059] In the formula, a′ TThis refers to the magnitude of the acceleration.

[0060] u v The target's maneuvering acceleration is represented by a unit vector.

[0061] In the aforementioned method for predicting the uncertain trajectory of a target using a low-Earth orbit satellite network, step three involves calculating the position and velocity of satellite i in the geocentric inertial coordinate system as follows:

[0062] Establish the equations for calculating the position of satellite i in the geocentric inertial coordinate system:

[0063]

[0064] In the formula, Let i be the three coordinates of satellite i in the geocentric inertial coordinate system;

[0065] The coordinate transformation matrix from the orbital plane coordinate system of satellite i to the geocentric inertial coordinate system;

[0066] x p y p z p Let i be the three coordinates of satellite i in the orbital plane coordinate system;

[0067] Establish the velocity calculation equation for satellite i in the geocentric inertial coordinate system:

[0068]

[0069] In the formula, · represents differentiation;

[0070] In formula (6) Substituting into formula (5), the value in formula (4) is... Substituting into formula (6), we can obtain the position and velocity of satellite i in the geocentric inertial coordinate system.

[0071] In the aforementioned method for predicting the uncertain trajectory of a target using a low-Earth orbit satellite network, step four, the method for determining that the target is within the detection range of the satellite's optical sensors, is as follows:

[0072] For target j, it is determined that it has been detected by satellite i if the following condition is met:

[0073]

[0074] In the formula, α (i) Let be the half field of view of satellite i;

[0075] η (ij) The angle between satellite i and target j;

[0076] This is the satellite-to-target position vector;

[0077] This is the satellite's position vector relative to the origin of the geocentric inertial coordinate system;

[0078] This is the vector from the origin of the geocentric inertial coordinate system to the satellite's position.

[0079] This is the vector from the origin of the geocentric inertial coordinate system to the target position.

[0080] According to the Law of Cosines:

[0081]

[0082] and

[0083]

[0084] In the formula, [x s y s z s [ ] represents the position vector of satellite i;

[0085] When the satellite and the target satisfy formulas (7) and (8), it means that the target is within the detection range of the satellite's optical sensor.

[0086] In the aforementioned method for predicting the uncertain trajectory of a target using a low-Earth orbit satellite network, step five involves establishing the measurement equations for the target in the geocentric inertial coordinate system as follows:

[0087] Based on the state vectors of the target and the satellite in the geocentric inertial coordinate system, by simultaneously solving equations (7) and (8), the measurement equation of the target in the geocentric inertial coordinate system is obtained:

[0088]

[0089] In the formula, Z ij These are the measurement values ​​obtained by the satellite in the geocentric inertial coordinate system for target detection;

[0090] h ij (·) represents the measurement function of satellite i on target j;

[0091] X j (t) represents the state value of target j at time t;

[0092] Let be the state value of satellite i at time t;

[0093] Let be the measurement noise variance matrix of satellite i to target j;

[0094] Where h ij The equation is solved as follows:

[0095]

[0096] In the formula, [x s y s z s ] T This indicates the satellite's position in the geocentric inertial coordinate system;

[0097] [xyz] T This indicates the target's position in the geocentric inertial coordinate system; i is the satellite number, and j is the target number.

[0098] The advantages of this invention compared to the prior art are:

[0099] (1) The prediction method based on the measurement information of the uncertain trajectory of the target by the low-orbit star network provided by the present invention solves the problem of target trajectory prediction under the uncertainty constraint when the low-orbit star network is used to detect moving targets in space.

[0100] (2) This invention establishes a dynamic model of space moving targets, a dynamic model of satellite-perceived orbits, a low-orbit star network observation model of space moving targets, and a multi-star detection target information model, and realizes the analysis of the relative dynamic characteristics of star-target random vectors;

[0101] (3) The present invention constructs a time window and uses a logical method to form a set of target flight trajectory prediction sequences for output, which can be used for simulation modeling and verification evaluation of the detection capabilities of large-scale low-Earth orbit satellite network systems. Attached Figure Description

[0102] Figure 1 This is a schematic diagram illustrating the observation between the satellite and the maneuvering target according to the present invention;

[0103] Figure 2 This is a schematic diagram of the satellite measurement angle of the present invention;

[0104] Figure 3 This is a flowchart of the low-orbit satellite network for predicting the trajectory of a target with uncertainty, as presented in this invention. Detailed Implementation

[0105] The present invention will be further described below with reference to the embodiments.

[0106] This invention provides a method for predicting the uncertain trajectory of a target using a low-Earth orbit (LEO) satellite network. Combining the characteristics of distributed observations by multiple satellites within the LEO network, it establishes dynamic models for moving space targets, satellite-perturbed orbits, LEO network observations of moving space targets, and multi-satellite target information models. Relative dynamic characteristics of the star-target random vector are analyzed, and time windows are constructed to generate a set of target flight trajectory prediction sequences using a logical method, resulting in the output results.

[0107] Low-Earth orbit satellite networks provide methods for predicting uncertain target trajectories, such as... Figure 3 As shown, the specific steps include the following:

[0108] Step 1: Establish a multi-objective dynamic model under spatial motion.

[0109] In step one, the method for establishing the multi-objective dynamic model is as follows:

[0110] After multiple space-moving targets leave the atmosphere, they enter a free flight phase, where their motion is only affected by gravity and thrust. In a geocentric inertial coordinate system, the target is defined as j, j = 1, 2... N. t N t Let t be the total number of targets at time t.

[0111] Since low-Earth orbit satellite network detection cannot predict the true motion sequence of non-cooperative targets, let the state vector of target j be... Wherein, the position vector r (j) =[x (j) ,y (j) ,z (j) ] T velocity vector Thrust acceleration vector

[0112] The establishment of a multi-objective dynamic model is described as follows:

[0113]

[0114] In the formula, μ e is the Earth's gravitational constant.

[0115] f (j) (·) represents the dynamic function.

[0116] R (j) (t) represents the current radius of the Earth.

[0117] W (j) (t) represents the system noise as the target.

[0118] Step 2: Establish a dynamic model of the satellite's perturbed orbit.

[0119] In step two, the low-Earth orbit satellite network adopts the Walker constellation configuration; it is described by N, P, and f; where N is the total number of satellites, P is the number of orbital planes on which the satellites are distributed, and f is the relative phase factor of satellites on adjacent orbital planes.

[0120] Let satellite i be numbered in the constellation. Then the right ascension of the ascending node and the angular distance from perigee of satellite i are expressed as follows:

[0121]

[0122] In the formula, Ω i Let be the right ascension of the ascending node of satellite i.

[0123] ω i Let be the perigee angular distance of satellite i.

[0124] P i This refers to the number of the orbital plane where the satellite is located.

[0125] N i This refers to the satellite's designation within its orbital plane.

[0126] S is the number of satellites on each orbital plane.

[0127] Based on the Walker constellation configuration, a satellite perturbed orbit dynamics model considering only Earth's gravity is established:

[0128]

[0129] In the formula, μ e is the Earth's gravitational constant.

[0130] t0 is the initial time.

[0131] r0 is the position vector from the Earth's center to the satellite's center of mass.

[0132] This is the satellite velocity vector.

[0133] This is the satellite acceleration vector.

[0134] r0 is the initial position.

[0135] r (i) (t0) is the initial position vector of satellite i in the geocentric inertial coordinate system.

[0136] To be based on constellation configuration and r (i) (t0) is the initial position vector of satellite i.

[0137] To be based on constellation configuration and The initial velocity vector of satellite i is obtained.

[0138] Let be the acceleration vector of satellite i.

[0139] Considering the combined effects of gravity, thrust, and atmospheric drag on the satellite's on-orbit operation, calculate the total acceleration vector a of the satellite in the geocentric inertial frame:

[0140] a = a T +aA +a G

[0141] In the formula, a T This is the vector of the maneuvering acceleration caused by the thrust in the geocentric inertial frame.

[0142] a A This is the drag acceleration vector caused by atmospheric drag in the geocentric inertial frame.

[0143] a G It is the vector of gravitational acceleration caused by the Earth's gravity in the geocentric inertial frame.

[0144] Substitute 'a' into formula (3) Make corrections:

[0145]

[0146] This yields the final dynamic model of the satellite's perturbed orbit:

[0147]

[0148] The drag acceleration vector a caused by atmospheric drag in a geocentric inertial frame A for:

[0149]

[0150] In the formula, v represents the magnitude of the satellite's velocity relative to the atmosphere.

[0151] u v This is a unit vector representing the satellite's velocity.

[0152] ρ(h) is the atmospheric density at the satellite's altitude h.

[0153] β is the damping coefficient.

[0154] The thrust-induced acceleration vector a T for:

[0155] a T =a′ T u v

[0156] In the formula, a′ T For the magnitude of the motor acceleration,

[0157] u v The target's maneuvering acceleration is represented by a unit vector.

[0158] Step 3: Based on the satellite's perturbed orbit dynamics model in Step 2, calculate the position and velocity of satellite i in the geocentric inertial coordinate system.

[0159] In step three, the method for calculating the position and velocity of satellite i in the geocentric inertial coordinate system is as follows:

[0160] Establish the equations for calculating the position of satellite i in the geocentric inertial coordinate system:

[0161]

[0162] In the formula, Let be the three coordinates of satellite i in the geocentric inertial coordinate system.

[0163] The coordinate transformation matrix from the orbital plane coordinate system of satellite i to the geocentric inertial coordinate system.

[0164] x p y p z p Let be the three coordinates of satellite i in the orbital plane coordinate system.

[0165] Establish the velocity calculation equation for satellite i in the geocentric inertial coordinate system:

[0166]

[0167] In the formula, · represents differentiation;

[0168] In formula (6) Substituting into formula (5), the value in formula (4) is... Substituting into formula (6), we can obtain the position and velocity of satellite i in the geocentric inertial coordinate system.

[0169] Step 4: Based on the multi-target dynamics model in Step 1 and the position and velocity of satellite i in the geocentric inertial coordinate system in Step 3, determine whether the target is within the detection range of the satellite's optical sensor.

[0170] In step four, the method for determining that the target is within the detection range of the satellite optical sensor is as follows:

[0171] The relationship between low-Earth orbit satellite networks and observations of moving targets in space is as follows: Figure 1 As shown, for target j, it is determined that it has been detected by satellite i if the following condition is met:

[0172]

[0173] In the formula, α (i) Let be the half field of view of satellite i.

[0174] η (ij) Let be the angle between satellite i and target j.

[0175] This is the satellite's position vector to the target.

[0176] This is the position vector of the satellite relative to the origin of the geocentric inertial coordinate system.

[0177] This is the vector from the origin of the geocentric inertial coordinate system to the satellite's position.

[0178] This is the vector from the origin of the geocentric inertial coordinate system to the target position.

[0179] According to the Law of Cosines:

[0180]

[0181] and

[0182]

[0183] In the formula, [x s y s z s [ ] represents the position vector of satellite i;

[0184] When the satellite and the target satisfy formulas (7) and (8), it indicates that the target is within the detection range of the satellite's optical sensor. The azimuth and elevation angles of the target in the star-fixed coordinate system can then be obtained. The satellite's measurement angle of the target is as follows: Figure 2 As shown.

[0185] Step 5: Establish the measurement equation of the target in the geocentric inertial coordinate system; based on the measurement equation of the target in the geocentric inertial coordinate system, predict the uncertain trajectory of the target.

[0186] In step five, the method for establishing the measurement equations of the target in the geocentric inertial coordinate system is as follows:

[0187] Based on the state vectors of the target and the satellite in the geocentric inertial coordinate system, by simultaneously solving equations (7) and (8), the measurement equation of the target in the geocentric inertial coordinate system is obtained:

[0188]

[0189] In the formula, Z ij These are the measurements obtained by the satellite from the target detection in the geocentric inertial coordinate system.

[0190] h ij (·) is the measurement function of satellite i to target j.

[0191] X j (t) represents the state value of target j at time t.

[0192] Let be the state value of satellite i at time t.

[0193] Let be the measurement noise variance matrix of satellite i to target j.

[0194] Where h ij The equation is solved as follows:

[0195]

[0196] In the formula, [x s y s z s ] T This indicates the satellite's position in the geocentric inertial coordinate system.

[0197] [xyz] T This indicates the target's position in the geocentric inertial coordinate system; i is the satellite number, and j is the target number.

[0198] This equation includes not only the target's position information but also the satellite's position information. Therefore, the target state estimate obtained using this measurement information is necessarily related to the satellite's own orbit determination accuracy. To achieve collaborative tracking of multiple targets under the observation conditions of a space-based satellite network, in addition to the orbit determination accuracy of the satellite constellation, it is also necessary to ensure the unification of the time and space references of each satellite. Only observation information acquired under a unified spatiotemporal architecture can be used for data association and state updates of multiple targets.

[0199] In a single-target tracking task, the target state x at a certain time (time k) k A collection of measurements from multiple satellite detection sensors (z k Let be two random vectors of uncertain dimension. Due to clutter and the possibility of false or missed detections by satellite sensors, the number of measurements generated by a multi-satellite sensor may not equal the number of targets. The target state and the number of elements contained in the multi-satellite measurement set may change, and each element will also evolve over time. For the sensor, there is no difference between measurements generated by the target and measurements generated by clutter, and the sensor itself has no correspondence between the target and the measurements; therefore, the order of elements in the target measurement set is also uncertain. Therefore, a random finite set is used to describe it, i.e.:

[0200]

[0201] In the formula, and Let N represent the state of the i-th target and the satellite detection measurement at time k, respectively. k and M k Let X be a random finite set at time k. k and Z k The number of elements, and They are the target state space and the satellite multi-target measurement space, respectively, which are composed of the single-target state space. and single-target measurement space The set consisting of all finite subsets of .

[0202] The initial trajectory is calculated in real time using a logical method. First, the value of N is set, and the measurements Z at the first N time points are... i (i = 1, 2, ..., N) are processed. A time window of length M is set, and the starting point of the time window is the starting point of the measurement time. When a stable track is formed within the time window, the initial track prediction is considered complete; otherwise, the entire time window is shifted forward by one sampling interval. Specific execution steps:

[0203] 1. Take the measurement at the first moment within the time window as the track header, establish a tracking gate as a constraint, and combine all measurements at the second moment that meet the conditions to confirm the state of the new target and establish a possible track.

[0204] 2. Compare the motion characteristics (e.g., location information) of newly generated targets with the location information of target trajectory predictions within the existing time window, associate targets with the same motion characteristics, and remove irrelevant values.

[0205] 3. Combining the dynamics of the moving target, extrapolate and predict a time step for each track obtained in the previous step, and establish a tracking gate centered on the prediction point. The size of the tracking gate is determined by the extrapolation variance of the track. The measurement at the third time step, which falls into each target tracking gate and is closest to the extrapolation point, is incorporated into the corresponding track.

[0206] 4. If no third measurement occurs in the tracking gate of a certain track in the previous step, the track can be cancelled. Considering the possibility of target maneuvering, a tracking gate containing acceleration can be established to further screen the measurements at the third moment, and to check whether any measurements fall into the tracking gate containing acceleration.

[0207] 5. Repeat the first two steps until a stable track is formed within the time window.

[0208] 6. Take the measurements that do not fall into each step of the tracking gate as new track heads (called free measurements) and repeat the above process.

[0209] 7. Update and form a new set of target flight trajectory prediction sequences. Repeat the above process until the target motion ceases. The output set of target flight trajectory prediction sequences is the flight trajectory prediction value for multiple targets.

[0210] In target tracking tasks, the target state and satellite sensor measurements at a given moment are two distinct random vectors, exhibiting uncertainty. Furthermore, the observational geometry between the target and satellites is constantly changing, constituting an uncertain set of relationships. Due to clutter and the possibility of false or missed detections by satellite sensors, the number of measurements from multiple satellite sensors may not match the number of targets. The target state and the number of elements in the multi-satellite measurement set may change, and each element will evolve over time. For the sensors, measurements generated by the target are indistinguishable from those generated by clutter, and the sensors themselves do not have a direct correspondence between the target and the measurements; therefore, the order of elements in the measurement set is uncertain. Under these conditions, target trajectory prediction in satellite networks faces significant challenges.

[0211] This invention proposes a prediction method based on the measurement information of uncertain target trajectories from low-Earth orbit (LEO) satellite networks. This method solves the problem of target trajectory prediction under uncertainty constraints when LEO satellite networks are used to collaboratively detect moving targets in space. It can be used in the simulation modeling and verification evaluation of the detection capabilities of large-scale LEO satellite network systems.

[0212] Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make possible changes and modifications to the technical solutions of the present invention by utilizing the methods and techniques disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solutions of the present invention shall fall within the protection scope of the technical solutions of the present invention.

Claims

1. A method for predicting the uncertain trajectory of a target using a low-Earth orbit satellite network, characterized in that: include: Step 1: Establish a multi-objective dynamic model under spatial motion; Step 2: Establish a dynamic model of the satellite's perturbed orbit; Step 3: Based on the satellite's perturbation orbit dynamics model in Step 2, calculate the position and velocity of satellite i in the geocentric inertial coordinate system; Step 4: Based on the multi-target dynamics model in Step 1 and the position and velocity of satellite i in the geocentric inertial coordinate system in Step 3, determine whether the target is within the detection range of the satellite's optical sensor. Step 5: Establish the measurement equation of the target in the geocentric inertial coordinate system; based on the measurement equation of the target in the geocentric inertial coordinate system, predict the uncertain trajectory of the target.

2. The method for predicting the uncertain trajectory of a target using a low-Earth orbit satellite network according to claim 1, characterized in that: In step one, the method for establishing the multi-objective dynamic model is as follows: After multiple space-moving targets leave the atmosphere, they enter a free flight phase, where their motion is only affected by gravity and thrust. In a geocentric inertial coordinate system, the targets are defined as j, j = 1, 2…N. t N t Let t be the total number of targets at time t; Since low-Earth orbit satellite network detection cannot predict the true motion sequence of non-cooperative targets, let the state vector of target j be... Wherein, the position vector r (j) =[x (j) ,y (j) ,z (j) ] T velocity vector Thrust acceleration vector The establishment of a multi-objective dynamic model is described as follows: In the formula, μ e The gravitational constant of Earth; f (j) (·) represents the dynamic function; R (j) (t) represents the current radius of the Earth; W (j) (t) represents the system noise as the target.

3. The method for predicting the uncertain trajectory of a target using a low-Earth orbit satellite network according to claim 2, characterized in that: In step two, the low-Earth orbit satellite network adopts the Walker constellation configuration; The terms N, P, and f are used to describe the satellites; where N is the total number of satellites, P is the number of orbital planes on which the satellites are distributed, and f is the relative phase factor between satellites on adjacent orbital planes. Let satellite i be numbered in the constellation. Then the right ascension of the ascending node and the angular distance from perigee of satellite i are expressed as follows: In the formula, Ω i Let the right ascension of the ascending node of satellite i be _i_. ω i Angular distance from perigee to satellite i; P i The number of the orbital plane where the satellite is located; N i The satellite's designation within its orbital plane; S is the number of satellites on each orbital plane.

4. The method for predicting the uncertain trajectory of a target using a low-Earth orbit satellite network according to claim 3, characterized in that: Based on the Walker constellation configuration, a satellite perturbed orbit dynamics model considering only Earth's gravity is established: In the formula, μ e The gravitational constant of Earth; t0 is the initial time; r0 is the position vector from the Earth's center to the satellite's center of mass; The satellite velocity vector; This is the satellite's acceleration vector; r0 is the initial position; r (i) (t0) is the initial position vector of satellite i in the geocentric inertial coordinate system; To be based on constellation configuration and r (i) (t0) is the initial position vector of satellite i. To be based on constellation configuration and The initial velocity vector of satellite i is obtained; Let be the acceleration vector of satellite i.

5. The method for predicting the uncertain trajectory of a target using a low-Earth orbit satellite network according to claim 4, characterized in that: Considering the combined effects of gravity, thrust, and atmospheric drag on the satellite's on-orbit operation, calculate the total acceleration vector a of the satellite in the geocentric inertial frame: a=a T +a A +a G In the formula, a T This is the vector of the maneuvering acceleration caused by the thrust in the geocentric inertial frame; a A This is the drag acceleration vector caused by atmospheric drag in the geocentric inertial frame; a G This is the vector of gravitational acceleration caused by gravity in the geocentric inertial frame. Substitute 'a' into formula (3) Make corrections: This yields the final dynamic model of the satellite's perturbed orbit:

6. The method for predicting the uncertain trajectory of a target using a low-Earth orbit satellite network according to claim 5, characterized in that: The drag acceleration vector a caused by atmospheric drag in the geocentric inertial frame is described. A for: In the formula, v is the magnitude of the satellite's velocity relative to the atmosphere; u v The satellite velocity unit vector; ρ(h) is the atmospheric density at the satellite's altitude h. β is the damping coefficient.

7. The method for predicting the uncertain trajectory of a target using a low-Earth orbit satellite network according to claim 5, characterized in that: The thrust-induced acceleration vector a T for: a T =a′ T u v In the formula, a′ T This refers to the magnitude of the acceleration. u v The target's maneuvering acceleration is represented by a unit vector.

8. The method for predicting the uncertain trajectory of a target using a low-Earth orbit satellite network according to claim 5, characterized in that: In step three, the method for calculating the position and velocity of satellite i in the geocentric inertial coordinate system is as follows: Establish the equations for calculating the position of satellite i in the geocentric inertial coordinate system: In the formula, Let i be the three coordinates of satellite i in the geocentric inertial coordinate system; The coordinate transformation matrix from the orbital plane coordinate system of satellite i to the geocentric inertial coordinate system; x p y p z p Let i be the three coordinates of satellite i in the orbital plane coordinate system; Establish the velocity calculation equation for satellite i in the geocentric inertial coordinate system: In the formula, · represents differentiation; In formula (6) Substituting into formula (5), the value in formula (4) is... Substituting into formula (6), we can obtain the position and velocity of satellite i in the geocentric inertial coordinate system.

9. The method for predicting the uncertain trajectory of a target using a low-orbit satellite network according to claim 1, characterized in that: In step four, the method for determining that the target is within the detection range of the satellite optical sensor is as follows: For target j, it is determined that it has been detected by satellite i if the following condition is met: In the formula, α (i) Let be the half field of view of satellite i; η (ij) The angle between satellite i and target j; This is the satellite-to-target position vector; This is the satellite's position vector relative to the origin of the geocentric inertial coordinate system; This is the vector from the origin of the geocentric inertial coordinate system to the satellite's position. This is the vector from the origin of the geocentric inertial coordinate system to the target position. According to the Law of Cosines: and In the formula, [x s y s z s [ ] represents the position vector of satellite i; When the satellite and the target satisfy formulas (7) and (8), it means that the target is within the detection range of the satellite's optical sensor.

10. A method for predicting the uncertain trajectory of a target using a low-Earth orbit satellite network according to claim 1, characterized in that: In step five, the method for establishing the measurement equation of the target in the geocentric inertial coordinate system is as follows: Based on the state vectors of the target and the satellite in the geocentric inertial coordinate system, by simultaneously solving equations (7) and (8), the measurement equation of the target in the geocentric inertial coordinate system is obtained: In the formula, Z ij These are the measurement values ​​obtained by the satellite in the geocentric inertial coordinate system for target detection; h ij (·) represents the measurement function of satellite i on target j; X j (t) represents the state value of target j at time t; Let be the state value of satellite i at time t; Let be the measurement noise variance matrix of satellite i to target j; Where h ij The equation is solved as follows: In the formula, [x s y s z s ] T This indicates the satellite's position in the geocentric inertial coordinate system; [xyz] T This indicates the target's position in the geocentric inertial coordinate system; i is the satellite number, and j is the target number.

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