Non-cooperative spacecraft impulse maneuver inversion method based on orbit determination residual minimization

Abstract

This invention discloses a method for inverting pulse maneuvers in non-cooperative spacecraft based on minimizing orbit determination residuals. Addressing the difficulty in accurately inverting maneuver parameters for non-cooperative spacecraft under conditions of sparse observation data and unknown maneuver times, this invention constructs a sequence of historical orbits and the latest observed orbit states. Within a preset time window, candidate maneuver times are discretized. For each candidate time, orbit propagation is performed under the assumption of no maneuvering to obtain a predicted orbit. A residual vector is constructed based on the position difference between the observed and predicted orbits. A partial derivative matrix is ​​constructed through numerical differentiation. The least squares method is used to solve for the maneuver velocity increment. Candidate intervals and candidate times are selected based on the fitting error. Finally, the maneuver parameters are determined based on the criterion of optimal accuracy within the fit interval. This invention can achieve high-precision estimation of maneuver times and velocity increments under sparse observation conditions, reducing dependence on high-density observation data and prior maneuver information, and significantly improving the stability and reliability of maneuver inversion.

Description

Technical Field

[0001] This invention belongs to the field of space situational awareness (SSA), and in particular relates to a high-precision inversion technique for non-cooperative spacecraft pulse maneuver parameters based on minimizing the sliding orbit determination residual. Background Technology

[0002] Low Earth Orbit (LEO) is the most active region in space situational awareness research, encompassing a large number of in-orbit satellites and space debris targets. With the rapid deployment of large-scale LEO constellations, the number of space targets is increasing rapidly, the orbital environment is becoming increasingly complex, and the potential collision risk between space targets is significantly increasing, placing higher demands on the accuracy and real-time performance of space situational awareness systems. To achieve continuous tracking and risk warning of space targets, it is urgent to construct an autonomous and controllable space situational awareness system. Among these, the determination and prediction of space target orbits is the core foundation of situational awareness, while the maneuvering behavior of space targets is one of the key factors affecting the accuracy of orbit prediction.

[0003] In actual operation, many space targets are non-cooperative targets, meaning their maneuver plans, propulsion parameters, or control information cannot be obtained; orbital data can only be acquired through ground-based or space-based observation methods. In such scenarios, the maneuvering behavior of space targets exhibits significant uncertainty and concealment. In particular, impulse maneuvers typically manifest as sudden changes in velocity over a short period, and their impact on the orbit is instantaneous and discontinuous. This makes it difficult for traditional orbit prediction models based on continuous dynamics assumptions to effectively describe them, leading to a rapid accumulation of prediction errors and severely impacting orbit determination and prediction performance.

[0004] In maneuver inversion problems based on orbital observation data, observation conditions are typically limited by factors such as the field of view (FOV) of the observation equipment, the observation time window, and the observation geometry, resulting in sparse and discontinuous data. Specifically, this manifests as short observation arcs, a limited number of observation points, uneven temporal distribution, and observation interruptions. This sparse data condition leads to insufficient constraints on orbital information, further exacerbating the ill-posedness of the maneuver inversion problem and making it difficult to stably estimate maneuver times and parameters. Summary of the Invention

[0005] To address the challenge of accurately inverting pulse maneuver parameters for non-cooperative spacecraft under conditions of sparse observation data and unknown maneuver times, this invention provides a non-cooperative spacecraft pulse maneuver inversion method based on minimizing orbit determination residuals. This method constructs a sequence of historical orbits and the latest observed orbit state, discretizes candidate maneuver times within a preset time window, performs orbit propagation for each candidate time under the assumption of no maneuvering to construct a predicted orbit, constructs a residual vector based on the position difference between the observed and predicted orbits, constructs a partial derivative matrix using numerical differentiation, solves for the maneuver velocity increment using the least squares method, and selects candidate time intervals based on fitting error and the principle of minimizing the normal component. Finally, the optimal maneuver parameters are selected through internal coincidence accuracy optimization. This invention enables high-precision estimation of maneuver times and velocity increments under sparse observation conditions, reduces dependence on high-density observation data and prior maneuver information, and significantly improves the stability and reliability of maneuver inversion.

[0006] According to one aspect of the present invention, a non-cooperative spacecraft pulse maneuver inversion method based on minimizing orbit determination residuals is provided, comprising: Construct historical orbital state sequences and orbital state sequences derived from the latest observation data; Within a preset time window, potential maneuvering moments are discretized to generate a set of candidate maneuvering moments. For each candidate maneuvering moment, the orbital state at that moment is obtained from the historical orbital state sequence, and the state is propagated to each observation moment under the assumption of no maneuvering to obtain the predicted orbit. Based on the difference between the observed orbit position and the predicted orbit position at each observation time, a residual vector is constructed; Construct the partial derivative matrix of the observation time position with respect to the velocity increment of the candidate maneuver time; Based on the partial derivative matrix and residual vector, the least squares method is used to solve for the speed increment. Calculate the fitting error corresponding to each candidate maneuver time, filter the candidate maneuver time intervals according to the distribution characteristics of the fitting error, and select candidate maneuver times within each candidate interval. Substitute each candidate maneuver time and its corresponding maneuver velocity increment into the piecewise pulse maneuver orbit determination model to obtain the fitted orbit state sequence; calculate the internal consistency accuracy between the fitted orbit state sequence and the observed orbit state sequence, and select the candidate solution with the best internal consistency accuracy as the final maneuver parameters.

[0007] As a further technical solution, when constructing the residual vector, for each observation time, the position deviation at that time is obtained by subtracting the observed orbit position from the predicted orbit position, and the position deviations of all observation times are superimposed to form the overall residual vector.

[0008] As a further technical solution, when constructing the partial derivative matrix, perturbation is applied to each component of the velocity vector at the candidate maneuvering moment, and the perturbed velocity is used as the initial velocity for orbit propagation under the assumption of no maneuvering to obtain the observation moment position under each perturbation condition; the difference between the position obtained after perturbation and the predicted orbit position without perturbation is divided by the perturbation amount to obtain the partial derivative of the observation moment position with respect to the velocity component, thus forming the partial derivative matrix.

[0009] As a further technical solution, when using the least squares method to solve for the maneuver speed increment, the following are included: Establish a linear observation model The least squares method is used to solve the problem. The increase in maneuver speed is obtained. ,in, Represents the partial derivative matrix. This represents the residual vector.

[0010] As a further technical solution, the calculation of the fitting error includes: For each candidate maneuver time, calculate the fitting error. According to the fitting error function Based on the distribution characteristics, the set of candidate intervals containing candidate solutions is selected.

[0011] As a further technical solution, candidate maneuver times are selected within each candidate interval, including: Within each candidate interval, the candidate moment that satisfies the minimum normal component is selected to obtain the set of candidate maneuver moments.

[0012] As a further technical solution, the historical orbital state sequence is derived from historical orbital data, and the orbital state sequence derived from the latest observation data is derived from radar or optical observation data; the preset time window is determined based on the difference between the historical orbital state sequence and the orbital state sequence derived from the latest observation data, and a set of candidate maneuvering moments is generated with a fixed step size.

[0013] According to one aspect of the present invention, a non-cooperative spacecraft pulse maneuver inversion device based on orbit determination residual minimization is provided, comprising: Memory, used to store computer programs; A processor for executing the computer program to implement the method.

[0014] According to one aspect of the present invention, a computer program product is provided, comprising a computer program or computer executable instructions that, when executed by a processor, implement the method described herein.

[0015] According to one aspect of the present invention, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the method described thereon.

[0016] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. Reduced dependence on high-density observation data: This invention can effectively invert the pulse maneuver timing and velocity increment of non-cooperative spacecraft using only historical orbit data and a small amount of the latest observation data, even when observation data is sparse, observation arcs are short, and the number of observation points is limited. This significantly reduces the need for continuous, high-density observation data.

[0017] 2. No prior maneuver information required: This invention does not rely on the spacecraft's maneuver plan, propulsion parameters, or control information. It is applicable to completely non-cooperative target scenarios and can complete maneuver detection and parameter estimation based solely on orbital observation data. It has good versatility and adaptability.

[0018] 3. High accuracy in maneuver timing: By discretely scanning candidate maneuver times, filtering candidate intervals using a fitting error function, and applying the principle of minimizing the normal velocity component, combined with optimized selection based on internal coincidence accuracy, this invention can accurately pinpoint the maneuver occurrence time. Simulation experiments in specific embodiments show that the error range between the estimated maneuver time and the actual maneuver time is 0.01 h ~ 0.03 h, which is far superior to the 0.42 h ~ 0.70 h of the minimum distance method.

[0019] 4. Accurate estimation of maneuver speed increment: This invention obtains a high-precision estimate of maneuver speed increment by constructing a partial derivative matrix and solving using least squares. Simulation results show that the error between the inverted maneuver speed along the track direction and the reference value is small, verifying the accuracy of the maneuver speed estimation.

[0020] 5. Significantly improved orbit determination accuracy: After using the inverted maneuvering parameters for orbit determination, the root mean square error of position can be reduced from several thousand to tens of thousands of meters in the minimum distance method to within several hundred meters, and the root mean square error of velocity is also significantly reduced, effectively improving the consistency of orbit prediction after maneuvering.

[0021] 6. Robust and reliable method: This invention can work stably in various observation scenarios such as radar and optics. By minimizing the sliding orbit determination residual, the robustness of the maneuvering inversion process is enhanced, and excellent results have been achieved on different space targets (such as NORAD ID10520, 10676, and 13149).

[0022] In summary, this invention achieves high-precision and high-reliability inversion of spacecraft pulse maneuver parameters under sparse observation and non-cooperative conditions, providing strong support for space situational awareness and orbit prediction. Attached Figure Description

[0023] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the accompanying drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0024] Figure 1 A schematic flowchart illustrating the non-cooperative spacecraft pulse maneuver inversion method based on orbit determination residual minimization provided in this embodiment of the invention; Figure 2 This is a comparative diagram of the segmented pulse orbit determination results of satellite 10520 provided in an embodiment of the present invention; Figure 3 This is a schematic diagram comparing the segmented pulse orbit determination results of satellite 10676 provided in an embodiment of the present invention; Figure 4 A schematic diagram comparing the segmented pulse orbit determination results of satellite 13149 provided in an embodiment of the present invention. Detailed Implementation

[0025] Addressing the shortcomings of existing technologies, research on inversion methods for non-cooperative target pulse maneuvers under sparse observation data conditions is of great significance. On the one hand, when the maneuver timing is unknown, a reasonable search and discrimination mechanism needs to be constructed to effectively identify the maneuver timing and reduce the uncertainty caused by the lack of prior information. On the other hand, under conditions of sparse, unevenly distributed, and noise-interferenced observation data, it is necessary to fully utilize the inherent relationship between orbital dynamics constraints and limited observation information to establish a stable and efficient maneuver parameter estimation method. This will improve the reliability and robustness of the maneuver inversion results, providing strong support for space target orbit prediction and space situational awareness.

[0026] Therefore, this invention provides a non-cooperative spacecraft pulse maneuver inversion method based on minimizing orbit determination residuals, comprising:

[0027] The first step is to construct the orbital state sequence.

[0028] 1.1 A spacecraft orbital state sequence is constructed based on historical orbital data and the latest observational data, wherein the historical orbital state sequence is... The latest observational data yielded the following orbital state sequence: , , Represents a position vector. This represents the velocity vector.

[0029] The second step is to construct the residual equation.

[0030] When constructing the residual equations in this step, the time window for the maneuver is first determined based on the difference between the initial trajectory before and after the maneuver. Within the time window, the maneuvering moments are discretely scanned; for each candidate maneuvering moment, the orbital state at that moment is obtained based on historical orbital data, and orbital propagation is performed under the assumption of no maneuvering to construct the predicted orbit. The details are as follows:

[0031] 2.1, within the preset time window The potential maneuver moments are discretized and processed according to a fixed step size. Generate a set of candidate maneuver times: , For each candidate maneuver moment The corresponding state is obtained from the historical orbit sequence through orbit interpolation. This state serves as the initial trajectory before the maneuver occurs. Without considering the maneuver, the state is... Propagation from the moment of maneuver to the current observation moment This yields a predicted trajectory: , in: This represents the orbital dynamics propagation function, and the corresponding position is... . This indicates the extrapolation result of the orbit if no maneuver occurs.

[0032] 2.2, for each observation time The observation residual is defined as: , For the observation time The position of the observation orbit, For the observation time The predicted orbital position. By superimposing all observed times, a global residual vector is constructed: , in, This indicates the number of observation data.

[0033] 2.3 To describe the effect of maneuver speed on position, an instantaneous position vector (i.e., the position at the time of observation) is constructed. Speed ​​increment relative to maneuver moment The partial derivative matrix is ​​used to describe the effect of the velocity change at the maneuver moment on the position change at the current observation moment: , The numerical differentiation method is used for calculation, for the velocity... Each component is subjected to a small perturbation. : , Dissemination Then the matrix elements are: , j represents the j-th component in the position component. This step involves applying a small perturbation to the velocity component at the maneuvering moment and performing orbital propagation under the assumption of no maneuvering to obtain the position change before and after the perturbation at each observation moment, thereby calculating the sensitivity relationship between position and velocity and constructing the state transition partial derivative matrix of position with respect to velocity.

[0034] The third step is to solve for the maneuvering amount using least squares.

[0035] 3.1 Establishing a linear observation model: , in, This represents the velocity increment vector generated by the pulse maneuver. It is solved using the least squares method: , Obtain the speed increment .in, These represent the velocity increment components of the target in the track direction, normal direction, and radial direction, respectively.

[0036] The fourth step is residual evaluation and optimal solution selection.

[0037] 4.1, for each candidate maneuver time Calculate the fitting error: , Based on the fitting error function Based on the distribution characteristics, a set of candidate intervals containing candidate solutions is selected. Within each candidate interval, the candidate time point that satisfies the minimum N-component is selected, thus obtaining a set of candidate maneuver times. Segmented pulse maneuver orbit determination is performed based on each candidate maneuver moment to obtain the fitted orbit state sequence. .

[0038] 4.2 Calculate the internal consistency accuracy between the segmented pulse maneuver orbit determination results and the observed orbit:

[0039] Calculate the internal consistency accuracy between the segmented orbit determination results and the observed orbit: , The candidate solution with the best internal consistency accuracy is selected as the final maneuver parameter. .

[0040] Through the above method, the present invention can effectively estimate key maneuver parameters such as maneuver timing, velocity increment, and orbit change amplitude of non-cooperative spacecraft in scenarios with sparse observation data and radar and optical observation. This reduces the dependence on high-density observation data and prior maneuver information, and improves the stability and reliability of maneuver detection and parameter inversion.

[0041] It should be noted that when selecting the second, third, or fourth step, the selection of the maneuver timing is not directly based on the single minimum residual principle. Instead, the candidate maneuver timings are evaluated by constructing a fitting error function, and candidate time intervals with smaller errors are prioritized. Within the candidate interval, the candidate timings are further constrained and screened by combining the principle of minimizing the normal component of the maneuver velocity in the orbital coordinate system to obtain optimized candidate solutions. The candidate solutions are then substituted into the segmented maneuver orbit determination model to determine the orbit. By comparing the internal consistency accuracy of each candidate solution, the optimal maneuver timing and the corresponding maneuver velocity increment are finally determined.

[0042] The terms “comprising” and “having”, and any variations thereof, in the specification, claims, and accompanying drawings of this invention are intended to cover a non-exclusive inclusion, such as a process, method, system, product, or apparatus that includes a series of steps or units, not necessarily limited to those explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0043] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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, 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. In addition, the technical features of the various embodiments or individual embodiments provided by the present invention can be arbitrarily combined to form new technical solutions. Such combinations are not bound by the order of steps and / or structural composition patterns, but must be based on the ability of those skilled in the art to implement them. When the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection claimed by the present invention.

[0044] See Figure 1 The specific implementation process of the non-cooperative spacecraft pulse maneuver inversion method based on minimizing orbit determination residuals provided in this embodiment of the invention is as follows.

[0045] The first step is to construct the orbital state sequence. Historical orbital data is generated based on the initial orbital parameters of TLE (Transient Earth Array), which are shown in Table 1. Gaussian-distributed observation noise is superimposed to simulate actual orbital errors. Considering the target is a low-Earth orbit space target, Gaussian noise with zero mean, a standard deviation of 100, and 0.1 m / s is superimposed on the position and velocity components, respectively. Based on this, orbital dynamics propagation is performed to obtain the historical orbital data state sequence. In this example, the simulated pulse maneuver time is set to 2024-04-04 00:00:00, and only one observation arc segment is acquired after the maneuver. The observation data is generated from simulated ground-based radar observations. The station location is set at 114.3°E, 30.5°N, and an altitude of 39.3 m. Relevant parameter settings are shown in Table 2. The observation arc length is 120s, and the observations include angle and distance information. The angle observation noise is Gaussian noise with zero mean and a standard deviation of 100", and the distance observation noise is Gaussian noise with zero mean and a standard deviation of 50m. First, the initial trajectory is determined using the observation data to obtain the initial trajectory value after maneuvering. Then, the trajectory is refined using the least squares method to obtain the latest trajectory state sequence based on the observation data.

[0046] Table 1 Initial orbital parameters .

[0047] Table 2 Simulation Parameter Settings for Observations .

[0048] The second step is to construct the residual equation. First, based on the difference between the initial orbits in historical orbital data and the initial orbits in the latest observation data, a time window for maneuvering is determined. This window is approximately 6 hours long and is used to cover the range of possible maneuvering times. Within this time window, maneuvering times are discretely scanned at a preset time step of 1 minute to obtain a series of candidate maneuvering times.

[0049] For each candidate maneuver time, based on the pre-maneuver orbit data, the orbital state information at that time is obtained through orbital dynamics propagation. This information is then used as initial conditions to propagate the orbit to each observation time after the maneuver, under the assumption of no maneuver, thus constructing the corresponding predicted orbit. Subsequently, the predicted orbit is compared with the latest observation data orbit, and the positional deviation at each observation time is calculated, forming a residual sequence. The residuals from all observation times are then uniformly organized to construct an overall residual vector. Based on the linearization concept of orbital dynamics, an approximately linear relationship is established between the residuals and the maneuver velocity increment, thereby transforming the maneuver problem into a parameter estimation problem.

[0050] The third step is to solve for the velocity increment corresponding to each candidate maneuver moment.

[0051] The fourth step is residual evaluation and optimal solution selection. For each candidate maneuver moment, the corresponding maneuver velocity increment is calculated using the aforementioned method, and the fitting residual between the observed trajectory and the propagation trajectory is calculated. Based on the residual distribution characteristics, candidate maneuver moment intervals with smaller errors are first selected. Within each candidate interval, representative candidate moments are determined by combining the principle of minimizing the N-direction component of the maneuver velocity in the UNW coordinate system. Subsequently, each candidate moment and its corresponding maneuver quantity are substituted into the segmented maneuver orbit determination model for trajectory determination. The internal consistency accuracy of the observed data is used as the evaluation index to compare and analyze different candidate solutions. Finally, the maneuver moment and maneuver velocity increment with the best internal consistency accuracy are selected as the final solution. Taking the space target with NORAD ID 10676 as an example, the orbit determination results for different candidate maneuver moments are shown in Table 3.

[0052] Table 3. Orbit determination accuracy at different candidate maneuver times .

[0053] The "--" indicates the orbit determination result without considering maneuvers. The results in the table show that the candidate maneuver time 2024-04-03 23:58:39 has the best internal consistency accuracy; therefore, this time is selected as the final maneuver time. Compared with the simulated maneuver time 2024-04-04 00:00:00, there is only a time deviation of about 3 minutes, indicating that this method has high accuracy in maneuver time positioning. Furthermore, comparing the inverted maneuver velocity increment with the actual maneuver quantity set in the simulation, the inverted maneuver quantity along the track direction is 1.17 m / s, which is smaller than the reference maneuver quantity of 1.00 m / s, further verifying the accuracy of the maneuver quantity estimation.

[0054] To verify the effectiveness of the method of this invention, the minimum distance method is introduced as a comparative method. This method propagates the trajectory before and after the maneuver, calculates the relative distance between the two trajectories, and uses the moment of minimum relative distance as the estimated maneuver time. The method of this invention is based on residual construction and parameter estimation, and uses all observation data to invert the maneuver time and velocity increment. Figures 2 to 4 A comparison of the results of the two methods in maneuver timing estimation and segmented pulse orbit determination is presented, where blue represents the minimum distance method and red represents the method of this invention.

[0055] Depend on Figures 2 to 4 It can be seen that the orbit determination error of the method of the present invention is smaller than that of the minimum distance method in all components along the track direction, radial direction, and normal direction, with the improvement being more significant along the track direction. Furthermore, a statistical analysis was performed on the deviations between the estimated maneuver times and the actual maneuver times of the two methods, and the results are shown in Table 4. By comparing the root mean square error of orbit determination and the error of maneuver time, the performance of the two methods in maneuver detection and parameter estimation can be evaluated.

[0056] Table 4 Comparison of residuals for segmented pulse orbit determination using two methods .

[0057] Table 4 compares the performance of the minimum distance method and the inversion method proposed in this invention in terms of maneuver timing estimation error and orbit determination accuracy. The results show that the maneuver timing estimation error obtained by the method of this invention ranges from 0.01 h to 0.03 h, while the error range of the minimum distance method is 0.42 h to 0.70 h. Regarding orbit determination accuracy, the root mean square error of position obtained by the method of this invention is reduced from several kilometers to tens of thousands of meters by the minimum distance method to within several hundred meters, and the root mean square error of velocity is also significantly reduced. For targets with large maneuver timing estimation errors, the orbit determination accuracy of the minimum distance method decreases significantly, while the method of this invention maintains a small error for all targets. This indicates that the estimated maneuver timing and maneuver magnitude have good extrapolation consistency and physical rationality, thus verifying the effectiveness and reliability of this method.

[0058] The present invention also provides a non-cooperative spacecraft pulse maneuver inversion device based on minimizing orbit determination residuals. The device includes a memory and a processor. The memory stores a computer program; the processor executes the computer program to implement the steps in the foregoing method embodiments.

[0059] In a specific instance, this device can be deployed in a ground-based telemetry and control center or a space situational awareness system. The processor can be a high-performance computing server, such as one configured with an Intel Xeon Gold 6248R processor, 256GB of RAM, and 1TB of SSD storage. Historical orbit data and real-time received ground-based radar observation data are pre-stored in the memory. Upon receiving the latest observation data, the processor automatically triggers the following operations: constructing a historical orbit state sequence and an orbit state sequence derived from the latest observation data; discretizing potential maneuvering moments within a preset time window to generate a set of candidate maneuvering moments; for each candidate maneuvering moment, obtaining the orbit state at that moment from the historical orbit state sequence and propagating it to each observation moment under the assumption of no maneuvering to obtain the predicted orbit; constructing a residual vector based on the positional difference between the observed and predicted orbits; constructing a partial derivative matrix through numerical differentiation; solving for the maneuvering velocity increment using the least squares method; calculating the fitting error and screening candidate intervals, selecting candidate maneuvering moments based on the principle of minimizing the normal component; substituting the candidate parameters into the piecewise pulse maneuvering orbit determination model to obtain the fitted orbit state sequence; calculating the internal consistency accuracy and selecting the optimal solution. The final output includes the maneuver timing and velocity increment, which are used for subsequent trajectory prediction and collision warning.

[0060] The device has advantages such as high automation, fast computing speed, and adaptability to sparse observation data, and can be directly integrated into existing space target monitoring systems.

[0061] The present invention also provides a computer program product, including a computer program or computer-executable instructions. When the computer program or computer-executable instructions are executed by a processor, they implement the steps in the foregoing method embodiments.

[0062] In a specific example, the computer program product can manifest as a DVD, USB flash drive, or software installation package on a network server containing the computer program. The user inserts the disc into the ground station's computer optical drive and follows the prompts to install the program. After installation, a "Maneuver Inversion Tool" icon appears on the computer desktop. Double-clicking to run the program guides the user to import historical orbit TLE files and the latest radar observation data files. The background program automatically performs pulse maneuver parameter inversion according to the method of this invention, ultimately displaying the optimal maneuver timing and velocity increment on the interface, and generating an orbit determination accuracy report. The program also provides log recording and result export functions, supporting batch processing of multiple space targets.

[0063] This computer program product enables the method of the present invention to be easily deployed in various computing environments, improving the portability and commercial potential of the technology.

[0064] The present invention also provides a computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, it implements the steps in the foregoing method embodiments.

[0065] In a specific example, the storage medium can be a solid-state drive (SSD), an embedded multimedia card (eMMC), a secure digital card (SD card), or a virtual block device in cloud storage. Taking a data server deployed at a satellite ground station as an example, the server has a built-in 480GB SATA interface SSD as its system disk, which pre-stores the operating system and the executable program of the method of this invention. When the server receives new observation arc data, the operating system calls the program instructions in the SSD, loads them into memory, and executes them by the CPU. The program first reads the TLE orbit data from the historical database for the past week, combines it with the latest observation data to perform residual minimization calculations, and finally writes the inverted maneuver parameters into a designated log file on the SSD. Because the storage medium is in firmware form, it has advantages such as vibration resistance, low power consumption, and fast read speed, making it particularly suitable for unattended automated observation stations.

[0066] In another example, the storage medium can be a portable USB flash drive. Staff can carry the USB flash drive containing the program of this invention to the field mobile telemetry and control station, insert it into a portable computer to run it, without the need for complicated software installation, thus achieving rapid deployment and flexible application.

[0067] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the technical solutions of the embodiments of the present invention.

Claims

1. A non-cooperative spacecraft impulsive maneuver inversion method based on orbit determination residual minimization, characterized in that, The method comprises the following steps: constructing a historical orbit state sequence and an orbit state sequence derived from latest observation data; discretizing potential maneuver time within a preset time window to generate a candidate maneuver time set; for each candidate maneuver time, obtaining the orbit state at the time from the historical orbit state sequence, and propagating the state to each observation time under the assumption of no maneuver to obtain a predicted orbit; constructing a residual vector according to the difference between the observed orbit position and the predicted orbit position at each observation time; when constructing the residual vector, subtracting the predicted orbit position from the observed orbit position at each observation time to obtain the position deviation at the time, and superimposing the position deviations at all observation times to form an overall residual vector; constructing a partial derivative matrix of the observation time position relative to the velocity increment of the candidate maneuver time; when constructing the partial derivative matrix, perturbing each component of the velocity vector of the candidate maneuver time, taking the perturbed velocity as the initial velocity to propagate the orbit under the assumption of no maneuver to obtain the observation time position under each perturbation; dividing the difference between the position obtained after perturbation and the predicted orbit position without perturbation by the perturbation amount to obtain the partial derivative of the observation time position to the velocity component, which constitutes the partial derivative matrix; Based on the partial derivative matrix and the residual vector, a least square method is used to solve the maneuvering velocity increment, comprising: establishing a linear observation model , using a least square method to solve , obtaining the maneuvering velocity increment , wherein, represents the partial derivative matrix, represents the residual vector; The fitting error corresponding to each candidate maneuver time is calculated, candidate maneuver time intervals are selected according to the distribution characteristics of the fitting error, and candidate maneuver times are selected in each candidate interval; when the fitting error is calculated, the fitting error is calculated for each candidate maneuver time ; the candidate interval set in which the candidate solution is located is selected according to the distribution characteristics of the fitting error function ; the candidate maneuver times are selected in each candidate interval, including: the candidate times that meet the minimum normal component are selected in each candidate interval to obtain the candidate maneuver time set; substituting each candidate maneuver time and the corresponding maneuver velocity increment into the segmented pulse maneuver orbit determination model to obtain a fitted orbit state sequence; calculating the internal consistency accuracy between the fitted orbit state sequence and the observed orbit state sequence, and selecting the candidate solution with the optimal internal consistency accuracy as the final maneuver parameter.

2. The non-cooperative spacecraft pulse maneuver inversion method based on residual minimization of orbit determination according to claim 1, characterized in that: the historical orbit state sequence is derived from historical orbit data, and the orbit state sequence derived from latest observation data is derived from radar or optical observation data; the preset time window is determined according to the difference between the historical orbit state sequence and the orbit state sequence derived from latest observation data, and the candidate maneuver time set is generated at a fixed step.

3. A non-cooperative spacecraft impulsive maneuver inversion apparatus based on orbit determination residual minimization, characterized in that, The memory is configured to store a computer program. The processor is configured to execute the computer program to implement the method according to any one of claims 1 to 2. The computer program or computer executable instructions are executed by the processor to implement the method according to any one of claims 1 to 2.

4. A computer program product, characterized in that, The computer program is stored on the computer readable medium and is executed by the processor to implement the method according to any one of claims 1 to 2.

5. A computer readable storage medium, characterized in that, ​

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