Feature inversion method for continuous low-thrust orbit maneuver of space target

Abstract

The invention discloses a feature inversion method for continuous low-thrust orbital maneuver of a space target, and belongs to the technical field of space situation awareness. The method comprises the following steps: firstly, establishing a spacecraft motion dynamics model and a target angle measurement observation model of a tracker; secondly, constructing decision variables for low-thrust maneuvering thrust inversion, including a maneuvering starting time point, a maneuvering ending time point and a maneuvering acceleration vector, and assuming that the maneuvering acceleration vector of the continuous low-thrust maneuvering target is kept unchanged in a maneuvering time period; a distance residual error loss function and an angle measurement residual error loss function are constructed based on the hypothesis, then a low-thrust maneuvering thrust characteristic inversion problem is modeled into a multi-objective optimization problem, a non-dominated sorting multi-population genetic algorithm NSGA-II with an elitist strategy is used for optimizing and solving the multi-objective optimization problem, an optimal decision variable is obtained, and the low-thrust maneuvering thrust characteristic inversion problem is solved. The maneuvering starting time point, the maneuvering ending time point and the maneuvering acceleration vector of the low-thrust maneuvering target are obtained. According to the method, the maneuvering starting time point, the maneuvering ending time point and the maneuvering acceleration vector of the low-thrust maneuvering target are solved only by using the filtering data and the measurement data.

Description

A characteristic inversion method for continuous low-thrust orbital maneuvers of space targets Technical Field

[0001] This invention relates to the field of space situational awareness technology. Specifically, it is a characteristic inversion method for continuous low-thrust orbital maneuvers of space targets. It is applicable to non-cooperative spacecraft maneuvering in low Earth orbit using low-thrust systems, enabling accurate inversion of the maneuver time period and thrust acceleration, and providing key technical support for spacecraft to safely avoid threats. Background Technology

[0002] With the rapid development of aerospace technology and the deepening of human exploration and utilization of space, the number of near-Earth orbit spacecraft has exploded, significantly increasing the complexity of the space environment. Simultaneously, the maturity and widespread adoption of onboard low-thrust systems (such as electric propulsion, cold gas propulsion, solid propulsion, and liquid propulsion) have enabled spacecraft in orbit to perform maneuvering missions such as fly-around, approach, and reconnaissance more flexibly. While this trend enhances the flexibility of space missions, it also exacerbates space safety risks—unknown maneuvers of non-cooperative targets may pose collision threats or other safety hazards to our spacecraft. Therefore, detecting the orbital maneuvering characteristics of potentially threatening space targets and identifying their maneuvering behavior in advance has become one of the core requirements for ensuring the safe operation of spacecraft.

[0003] Currently, research on the detection of orbital maneuvering behavior of space targets has made some progress. Existing technical solutions mainly include three categories: First, by using a weighted fusion method of multiple hypothesis testing of angle measurement innovations, a test statistic is constructed using the deviation (innovation) between observed data and predicted data to detect target orbital maneuvers; Second, by monitoring key orbital parameters of the target orbit (such as semi-major axis and eccentricity), the sudden change characteristics of the orbital parameters are used to determine whether the target has maneuvered; Third, intelligent algorithms such as LSTM (Long Short-Term Memory Network) are used to train and learn from a large amount of measurement data to establish a maneuver detection model.

[0004] Low-thrust maneuvers are a technique where spacecraft change their orbit using sustained low-thrust maneuvers. However, existing techniques have significant limitations: the thrust level of low-thrust maneuvers is extremely small (typically 10). -3 -10 0 m / s 2The slow changes and weak anomalies caused by low-thrust maneuvers make them difficult to detect effectively using traditional methods. Most current methods are essentially designed for "pulse maneuvers" (short-duration, high-magnitude thrust with significant abrupt changes in orbital parameters), and are ill-suited to the "continuous and weak characteristics" of low-thrust maneuvers. This results in insufficient accuracy in "maneuver time period positioning" and "thrust acceleration calculation" for low-thrust maneuvering targets, and even leads to missed or false detections, failing to meet the refined monitoring needs of space situational awareness for low-thrust maneuvering targets.

[0005] To address the shortcomings of the existing technologies, this invention proposes a feature inversion method for continuous low-thrust orbital maneuvers of space targets. Utilizing only filtered data and angle measurement data, it constructs a multi-dimensional residual loss function and a multi-objective optimization model, combined with an improved genetic algorithm, to achieve accurate inversion of maneuver parameters for low-thrust maneuvering targets, filling a gap in the field of low-thrust maneuver detection. Summary of the Invention

[0006] The core objective of this invention is to provide a characteristic inversion method for continuous low-thrust orbital maneuvers of space targets, which solves the problems of inaccurate positioning of the maneuver time period and low thrust acceleration calculation accuracy of existing technologies. It enables high-precision inversion of the start time point, end time point and thrust acceleration vector of continuous low-thrust space maneuver targets using only filtered data and angle measurement data.

[0007] Technical Solution: A feature inversion method for continuous low-thrust orbital maneuvers of space targets, comprising the following steps: S1, establishing a spacecraft motion dynamics model and a tracker angle measurement observation model of the target; S2, constructing decision variables for thrust inversion of low-thrust maneuvers, wherein the decision variables include the maneuver start time point, the maneuver end time point, and the maneuver acceleration vector, and assuming that the maneuver acceleration vector of the continuous low-thrust maneuver target remains unchanged during the maneuver time period; S3, constructing a distance residual loss function; S4, constructing an angle measurement residual loss function to improve the sensitivity to low-thrust maneuver acceleration inversion; S5, modeling the low-thrust maneuver thrust feature inversion problem as a multi-objective optimization problem; S6, using the non-dominated sorting multi-population genetic algorithm NSGA-II with elitist strategy to optimize and solve the multi-objective optimization problem in step S5, obtaining the optimal decision variables, i.e., obtaining the maneuver start time point, maneuver end time point, and maneuver acceleration vector of the low-thrust maneuver target.

[0008] This method uses only filtered and measured data to solve for the start and end times of maneuvering and the acceleration vector of a low-thrust maneuvering target.

[0009] Furthermore, step S1 specifically includes: S11, considering the non-spherical gravitational perturbation of the Earth, mainly including... , and (The perturbation term is the main non-gravitational disturbance source of the motion of near-Earth orbit spacecraft and needs to be included in the model to ensure dynamic accuracy.) Construct a dynamic model of the spacecraft's motion in the Earth's equatorial inertial coordinate system, with the following expression:

[0010] In the formula, The dimension is the motion state quantity of the spacecraft in the Earth's equatorial inertial coordinate system. ; It is the position vector of the spacecraft in the Earth's equatorial inertial coordinate system; These are the velocity vectors of the spacecraft in the Earth's equatorial inertial coordinate system; For the central gravitational acceleration, It is the Earth's gravitational constant; This is the acceleration due to Earth's non-spherical gravitational perturbation. It is the acceleration vector of small thrust;

[0011] S12. In an inertial frame, construct the right ascension of the tracker's line of sight to the target ( ) and declination ( The observation model is expressed as follows:

[0012] In the formula, , These represent the target's positions along the three axes of the inertial coordinate system. , , These represent the three-axis positions of the tracker in the inertial coordinate system (the tracker's trajectory is known and can be accurately obtained through its own orbit measurement data). , The measurement noise for right ascension and declination are respectively. Considering the measurement noise of actual observation equipment, it is modeled as zero-mean Gaussian white noise, i.e., and , and These are the standard deviations of right ascension and declination measurements, respectively.

[0013] Furthermore, step S2 involves constructing the decision variables for small-thrust maneuver inversion, defining the decision variables used for small-thrust maneuver thrust inversion. It includes three core parameters for low-thrust maneuvers, namely the maneuver start time. End time of maneuver and small thrust acceleration vector , These are the components of the small thrust acceleration vector along the three axes of the inertial frame, and thus the decision variables. Represented as:

[0014] To simplify the inversion complexity and ensure engineering practicality, it is assumed that the continuously low-thrust maneuvering target is within the maneuvering time period. Internal acceleration vector The thrust is kept constant (this assumption is consistent with the actual scenarios of most low-thrust maneuver missions, such as trajectory fine-tuning and position holding, where the thrust is usually output stably).

[0015] Further, step S3 involves constructing the distance residual loss function. The distance residual loss function quantifies the deviation between the target position predicted based on filtered data and the actual filtered estimated position, reflecting the impact of target maneuvering on the trajectory position. The specific construction process is as follows: S31, Select the maneuvering time period. The first n target filter estimation states , In the formula They are The filtered estimation vector of the target's position and velocity at any given time; , < Position error Speed ​​error S32. Using each target's filtered estimation state and decision variables, the evolution is performed backward to obtain n groups of target motion states after the maneuvering time period, with each group having m motion states:

[0016] In the formula, Indicates time difference, The spacecraft motion dynamics model in step S1, It is a decision variable; the time difference of evolution. , The moment corresponding to the maneuver, > ; , , They are derived from evolution The target's position and velocity vector at any given time.

[0017] S33, For the n sets of evolutionary motion states in step S32 ( Batch least squares estimation is performed to eliminate the influence of single-pass filtering state error on the prediction results, thus obtaining the predicted motion state of the target after the maneuvering time period. ;

[0018] In the formula , , = , Let n be the motion states of the n groups of targets after the maneuvering time period.

[0019] S34. Take the m target filtered estimation states after the maneuver time period. Using the prediction of motion state and Location data at the same time and Construct the distance residual loss function:

[0020] in, Denotes the Euclidean norm. The smaller the value, the better the maneuver parameters corresponding to the decision variable match the actual maneuver.

[0021] Further, step S4 involves constructing the angle measurement residual loss function. The positional changes caused by small-thrust maneuvers are weak, and the maneuver characteristics cannot be accurately captured solely through distance residuals. Therefore, this step constructs the angle measurement residual loss function, utilizing subtle changes in the line-of-sight direction (deviations in right ascension and declination) to improve the sensitivity to acceleration inversion during small-thrust maneuvers. The specific process is as follows: S41, using the filtered estimation state and decision variables of each target obtained in step S31, evolve backward to obtain the motion states of n sets of targets during the maneuver time period. Combine this with the dynamic model to evolve backward, obtaining the motion states of n sets of targets during the maneuver time period. Each group has k motion states:

[0022] In the formula For the time difference of evolution; It is the time within the maneuver period. ≤ ≤ Furthermore, , It was obtained through evolution. The target position vector at any given moment; S42, the n sets of evolutionary motion states in step S41 ( Batch least squares estimation is performed to obtain the predicted motion state of the target during the maneuvering time period. :

[0023] in, For n sets of evolutionary states in A collection of moments; for The predicted state vector at time t.

[0024] S43, Utilization Position state in and the position state of the tracker at the corresponding time. The target's line-of-sight vector relative to the tracker's predicted unit line-of-sight vector during the maneuvering period is obtained:

[0025] S44. Take k sets of angle measurements within the maneuvering time period. The target's line-of-sight vector relative to the tracker's measurement unit is calculated. S45. Construct the angle measurement residual loss function using the predicted unit line-of-sight vector and the measured unit line-of-sight vector: The smaller the value, the more consistent the prediction of the line-of-sight direction by the maneuver parameters corresponding to the decision variable is with the actual observation, and the sensitivity to small-thrust maneuvers is significantly higher than that of the distance residual.

[0026] Furthermore, step S5 involves modeling a multi-objective optimization problem. The core objective of low-thrust maneuver inversion is to simultaneously minimize the distance residual loss function. Compared with the residual loss function of angle measurement Therefore, it is modeled as a multi-objective optimization problem:

[0027] in, The feasible region of the decision variables must satisfy engineering constraints: machine time constraint: , , Thrust acceleration constraint: , This represents the maximum acceleration of a common small-thrust system.

[0028] Furthermore, the execution process of the non-dominated sorting multi-population genetic algorithm NSGA-II with elite strategy described in step S6 includes initializing the population, fast non-dominated sorting, crowding sorting, population individual selection, crossover and mutation, retaining the elite population strategy, and obtaining the optimal decision variables, namely, obtaining the maneuver start time point, maneuver end time point and maneuver acceleration vector of the low-thrust maneuver target.

[0029] The population is randomly divided into at least 5 independent populations, each with different crossover probabilities, mutation probabilities, distribution indices, and quantification factors.

[0030] Beneficial effects: The method provided by the present invention has the following substantial features and significant progress: (1) The present invention can solve for the start and end time points of maneuvering and the maneuvering acceleration vector of a low-thrust maneuvering target using only filtered data (position and velocity filtering estimation) and measurement data (right ascension and declination). This reduces the requirements for observation equipment and is easy to deploy in existing aerospace observation systems.

[0031] (2) The present invention can accurately calculate the maneuvering time point and maneuvering acceleration of a small thrust maneuvering target in space through an algorithm, providing key support for space situational awareness.

[0032] (3) The present invention has a wide range of applications and has broad requirements for target track type, maneuvering points and maneuvering acceleration vector; (4) The present invention has a high robustness of multi-population genetic algorithm by constructing distance and angle measurement residual function design, and the sensitivity to the influence of filtering data and measurement data error is reduced. Attached Figure Description

[0033] Figure 1 is a flowchart of the algorithm logic of an embodiment of the present invention; Figure 2 is the error distribution of the target maneuvering time point estimation in 10 target engagements in an embodiment of the present invention; Figure 3 is the error distribution of the three-axis thrust estimation of the target in 10 target engagements in an embodiment of the present invention; Figure 4 is the percentage of the thrust amplitude estimation error of the target in 10 target engagements in an embodiment of the present invention. Detailed Implementation

[0034] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. 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 are within the scope of protection of the present invention.

[0035] This invention discloses a feature inversion method for continuous low-thrust orbital maneuvers of space targets. Based on filtered and measured data, distance and angle measurement residual functions are constructed. The NSGA-II non-dominated sorting multi-population genetic algorithm with an elitist strategy can accurately solve for the start and end times of the maneuver and the maneuver acceleration vector of the low-thrust maneuvering target in space. The specific implementation steps are shown in Figure 1.

[0036] A characteristic inversion method for continuous low-thrust orbital maneuvers of space targets includes the following steps: Step S1, establishing a spacecraft motion dynamics model. Angle measurement observation model of the target by the tracker .

[0037] For spacecraft motion dynamics model By differentiating the motion state variables of the spacecraft in the Earth's equatorial inertial coordinate system, the mathematical representation of the model is constructed as follows: , This indicates the calculation of the derivative of the spacecraft's position vector in the Earth's equatorial inertial coordinate system.

[0038] The observation model for right ascension and declination of the target relative to the tracker's line of sight is as follows:

[0039] use This represents the motion state of a spacecraft in the Earth's equatorial inertial coordinate system. and Let S1 and S2 represent the position vector and velocity vector of the spacecraft in the Earth's equatorial inertial coordinate system, respectively; Step S2: Construct decision variables for thrust inversion in small-thrust maneuvers. And assume that the acceleration vector of a continuously low-thrust maneuvering target during the maneuvering time period is... remain unchanged. .

[0040] Step S3: Construct the distance residual loss function as follows:

[0041] Step S4: To improve the sensitivity to the inversion of small-thrust maneuver acceleration, construct the angle measurement residual loss function:

[0042] Step S5: Model the small-thrust maneuver thrust characteristic inversion problem as a multi-objective optimization problem:

[0043] Step S6: Use the non-dominated sorting multi-population genetic algorithm NSGA-II with elitist strategy to find the optimal solution to the multi-objective optimization problem in step S5, and obtain the optimal decision variables. That is, to obtain the start time of the maneuver of a low-thrust maneuvering target. End time of maneuver and the acceleration vector .

[0044] Furthermore, this embodiment sets the following calculation conditions and technical parameters: 1) The initial orbital parameters of the target and tracker are shown in the table below; Table 1 Initial orbital parameters of the target and tracker

[0045] 2) The initial population is randomly divided into 5 independent populations, each with 200 individuals. Different crossover and mutation probabilities are set for each population. Different distribution indices and quantization factors are selected during the simulation of binary crossover and differential evolution. The key parameter settings for the multi-population genetic algorithm are shown in Table 2: Genetic Algorithm Parameters

[0046] 3) Take the number of filtered estimated state data points for the target before the maneuvering period (n=1), the number of filtered estimated state data points after the maneuvering period (m=100), and the number of angle measurement data points during the maneuvering period (k=100); 4) The standard deviation of the position error of the filtered data is 100 m, the standard deviation of the velocity error is 0.1 m / s, and the standard deviation of the right ascension and declination angle measurements is... and All are 5 arcseconds.

[0047] The method for inverting the small thrust of a maneuvering target using filtered data, based on the present invention, was simulated and verified using the aforementioned calculation conditions and technical parameters. The simulation duration for the tracker and target trajectory was 2 hours. A small thrust acceleration of 0.01 m / s was added to the target between 3000 and 4000 s. The thrust vector in the inertial coordinate system was kept constant [0.01; 0; 0]. Then, the method of the present invention was used to calculate the start and end times of the maneuver and the maneuver acceleration vector of the small thrust maneuvering target. Figures 2, 3, and 4 show the error distribution of the estimated maneuvering time points, the error distribution of the three-axis thrust estimation of the target in 10 firing tests, and the percentage error of the thrust amplitude estimation of the target in 10 firing tests, respectively. As can be seen from the figures, the method of the present invention achieves high accuracy in calculating the start and end times of the maneuver and the thrust acceleration vector of the small thrust maneuvering target. Under the method of the present invention, according to 3 In principle, the probability of the estimated start time point of the maneuver falling within (-63.24s, 84.44s) is 99.7%, and the probability of the estimated end time point of the maneuver falling within (-119.31s, 94.11s) is 99.7%; the probability of the estimated x-axis thrust falling within (-0.0015m / s) is also 99.7%. 2 0.0021m / s 2 The probability is 99.7%, and the y-axis thrust estimation error falls within (-0.00033 m / s). 2 -0.00032m / s 2 The probability is 99.7%, and the z-axis thrust estimation error falls within (-0.00020 m / s). 2 0.00023m / s 2 The probability is 99.7%; the percentage of thrust amplitude estimation error falling within (-5.78%, 16.84%) has a probability of 99.7%.

[0048] Therefore, the method of this invention breaks through the characteristic inversion method of continuous low-thrust orbital maneuver of space targets under the condition of passive angle measurement on space. It can accurately calculate the maneuver time point and maneuver acceleration vector of low-thrust maneuvering targets in space using only filtered data and angle measurement data, which improves the accuracy by more than 30% compared with traditional methods.

[0049] Finally, it should be noted that the above descriptions are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A characteristic inversion method for continuous low-thrust orbital maneuvers of space targets, characterized in that, Includes the following steps: S1. Establish a spacecraft motion dynamics model and a tracker angle measurement observation model of the target; S2. Construct decision variables for low-thrust maneuver thrust inversion, including the maneuver start time point, maneuver end time point, and maneuver acceleration vector, assuming that the maneuver acceleration vector of the continuously low-thrust maneuvering target remains unchanged during the maneuver time period; S3. Construct a distance residual loss function; S4. Construct an angle measurement residual loss function to improve the sensitivity to low-thrust maneuver acceleration inversion; S5. Model the low-thrust maneuver thrust characteristic inversion problem as a multi-objective optimization problem; S6. Use the non-dominated sorting multi-population genetic algorithm NSGA-II with elitist strategy to find the optimal decision variables, i.e., the maneuver start time point, maneuver end time point, and maneuver acceleration vector of the low-thrust maneuvering target.

2. The characteristic inversion method for continuous low-thrust orbital maneuvers of space targets according to claim 1, characterized in that, The method described above uses only filtered and measured data to solve for the start and end times of maneuvering and the acceleration vector of a low-thrust maneuvering target.

3. The characteristic inversion method for continuous low-thrust orbital maneuvers of space targets according to claim 1, characterized in that, Step S1 specifically includes: S11, establishing a framework considering the non-spherical shape of the Earth. 、 and The mathematical representation of the spacecraft's motion dynamics model is as follows: In the formula, This represents the motion state of the spacecraft in the Earth's equatorial inertial coordinate system. and These are the spacecraft's position vector and velocity vector in the Earth's equatorial inertial coordinate system, respectively. For the central gravitational acceleration, This is the acceleration due to Earth's non-spherical gravitational perturbation. For small thrust acceleration; S12, establish an observation model of the right ascension and declination of the target relative to the tracker's line of sight in the inertial frame, wherein the observation model is: In the formula, 、 These represent the target's positions along the three axes of the inertial coordinate system. 、 、 These represent the three-axis positions of the tracker in the inertial coordinate system. 、 To measure noise, and 。 4. The characteristic inversion method for continuous low-thrust orbital maneuvers of space targets according to claim 1, characterized in that, Step S3 specifically includes: S31, obtaining the n target filtered estimation states before the maneuver time period. ， In the formula They are The target's position and velocity are filtered and estimated vectors at time t, and the position estimation error is . Speed ​​estimation error S32. Using each target's filtered estimation state and decision variables, the evolution is performed backward to obtain n groups of target motion states after the maneuvering time period, with each group having m motion states: In the formula, Indicates time difference, The spacecraft motion dynamics model in step S1, These are decision variables; S33, perform batch least squares estimation on the n sets of evolving motion states in step S32 to obtain the predicted motion state of the target after the maneuvering time period. S34. Take the m target filtered estimation states after the maneuver time period. Using the prediction of motion state and Location data at the same time and Construct the distance residual loss function: 。 5. The characteristic inversion method for continuous low-thrust orbital maneuvers of space targets according to claim 4, characterized in that, The formula for calculating the least squares estimate in step S33 is as follows: In the formula ， ， = ， Let n be the motion states of the target groups after the maneuvering time period. It is a diagonal matrix.

6. The characteristic inversion method for continuous low-thrust orbital maneuvers of space targets according to claim 1, characterized in that, Step S4 specifically includes: S41, using the target filtering estimation state and decision variables obtained in step S31, and then evolving backward to obtain n groups of target motion states during the maneuvering time period, with each group having k motion states: In the formula For the time difference; S42, perform batch least squares estimation on the n sets of evolving motion states in step S41 to obtain the predicted motion state of the target during the maneuvering time period. S43, Utilizing Position state in and the position state of the tracker at the corresponding time. The target's line-of-sight vector relative to the tracker's predicted unit line-of-sight vector during the maneuvering period is obtained: S44. Take k sets of angle measurements within the maneuvering time period. The target's line-of-sight vector relative to the tracker's measurement unit is calculated. S45. Construct the angle measurement residual loss function using the predicted unit line-of-sight vector and the measured unit line-of-sight vector: 。 7. The characteristic inversion method for continuous low-thrust orbital maneuvers of space targets according to claim 1, characterized in that, The execution process of the non-dominated sorting multi-population genetic algorithm NSGA-II with elitist strategy described in step S6 includes population initialization, fast non-dominated sorting, crowding sorting, population individual selection, crossover and mutation, and the strategy of retaining the elite population.

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