Space object track association and orbit parameter estimation method

Abstract

The application relates to a space target track correlation and orbit parameter estimation method, and belongs to the space situation awareness field.The application is realized by the following steps: orbit propagation to the observation epoch, calculation of the average normalized information square (NIS) of the track, judgment of whether the track is abnormal according to the average NIS.If the track is not abnormal, the track is directly correlated with the catalog library target, no maneuver occurs, a filtering method is used for updating, and the catalog library is updated.If the track is abnormal, maneuver correlation and maneuver parameter joint estimation are triggered.The joint estimation method takes the maneuver time and the maneuver vector as optimization variables, calculates the average NIS of the track, solves the optimization problem by minimizing the average NIS of the track, obtains the optimal loss function and the maneuver parameter, sets the loss function threshold and the maneuver parameter range to judge the correlation, iteratively judges the maneuver correlation until all the tracks are processed, and then the correlation and the maneuver parameter of the track are obtained.

Description

Technical Field

[0001] This invention relates to a method for correlation of space target tracks and estimation of orbital parameters, belonging to the field of space situational awareness. Background Technology

[0002] With the increasing number of objects in low Earth orbit, near-Earth space has become more crowded, significantly increasing the risk of collisions between spacecraft. Non-cooperative targets, in particular, that may perform unusually close maneuvers, can pose a serious threat to our spacecraft. Given the importance of geostationary orbit (GEO) spacecraft, the safety of the GEO region has become a focus of attention. Due to the great distance between GEO spacecraft and Earth, ground-based and space-based optical observations are typically used to monitor the GEO region. However, the high speed of satellites results in very short tracking observation durations, producing short tracklets. Orbit determination and cataloging using a single tracklet is extremely challenging, and such tracklets that cannot be associated with any cataloged object are often called unassociated short tracklets (UCTs). To address this issue, much research has focused on track association, thereby utilizing multiple associated tracklets for more accurate orbit determination and cataloging. A major challenge in this process is that spacecraft frequently maneuver to maintain their orbital position or perform other tasks. Tracklets resulting from these maneuvers may be mistakenly identified as new targets and incorrectly added to the cataloging database, failing to update the status of previous targets. Considering the trajectory association of target maneuvers is more challenging because it usually requires using limited information to estimate maneuver parameters to determine whether there is an association.

[0003] To address this challenge, many studies have applied optimal control strategies for maneuver association, i.e., evaluating the correlation between tracks obtained before and after a maneuver. The loss function derived from the optimal control strategy can be used as an indicator of correlation. Furthermore, this method can also utilize track information to characterize the maneuver. Serra et al. proposed a track-to-track maneuver association method based on optimal control theory and extended it to track-to-track maneuver association using distance and distance rate constrained admissible regions (CARs).

[0004] The accuracy of association can be improved by estimating maneuver parameters, namely maneuver time and maneuver vector, and using these estimated parameters for association assessment. Some scholars have proposed methods specifically for maneuver parameter estimation. Siminski et al. established an optimization framework aimed at solving for the most probable post-maneuver trajectory state, where the distance and distance rate of the track are optimized variables. This method relies on prior information and is suitable for situations where the pre-maneuver trajectory state is known and sufficient historical maneuver data is available. Pastor et al. proposed a maneuver estimation strategy using the least squares method, assuming that the target's initial trajectory and maneuver direction are known. This method uses multiple post-maneuver track data to estimate maneuver time and velocity changes. These methods can address the challenges of maneuver parameter estimation to some extent. However, they cannot be directly applied to maneuver association and often depend on the results of maneuver association. Without accurate association results, the accuracy of parameter estimation decreases, making it impossible to correctly estimate the target's post-maneuver trajectory state for threat assessment, leading to potential collisions.

[0005] In summary, to accurately determine the correlation of maneuvering tracks, it is essential to estimate maneuvering parameters. Furthermore, resolving maneuvering correlation is crucial for accurate estimation of these parameters. Previous research methods have required substantial prior information for both maneuvering correlation and maneuvering parameter estimation. Therefore, jointly evaluating correlation and estimating maneuvering parameters using optical short-arc observation data under limited prior information is extremely challenging. Moreover, previous research has shown significant promise in transforming the correlation and maneuvering parameter estimation problems into optimization problems, particularly in addressing the challenge of large-scale very short-arc correlation, where optimization methods are highly efficient. Therefore, this invention will, based on limited prior information, construct a reasonable optimization framework to jointly complete track correlation and maneuvering parameter estimation. Summary of the Invention

[0006] To address the coupling issue between maneuver parameter estimation and track correlation, this invention aims to provide a method for space target track correlation and orbit parameter estimation. By calculating the innovation and covariance between track observations and predictions, the method further obtains the NIS and average NIS to detect track anomalies. For anomalous tracks originating from target impulsive maneuvers, the optimal parameters for maneuver time and maneuver vectors are estimated based on a constructed maneuver parameter estimation optimization problem, thereby improving the accuracy of space target track correlation and orbit parameter estimation.

[0007] The objective of this invention is achieved through the following technical solution.

[0008] This invention discloses a method for space target trajectory association and orbital parameter estimation. Given a target orbital catalog database containing the orbital states and covariances of all targets before maneuvering, after obtaining trajectory observations, the orbits are propagated to the observation epochs. The mean normalized innovation square (NIS) of the trajectory is calculated, and the NIS is used to determine whether the trajectory is anomalous, i.e., whether the trajectory is a post-maneuver trajectory or originates from another target. If the trajectory is not anomalous, it is determined that the trajectory is directly associated with the target in the catalog database, and no maneuver has occurred. A filtering method is used to update the trajectory, and the catalog database is also updated. If the trajectory is anomalous, maneuver association and joint estimation of maneuver parameters are triggered. In the joint estimation method, the maneuver time Δt and maneuver vector Δv are set as optimization variables, where Δv = [Δv...]. R ,Δv S ,Δv W ] T The orbital data in the catalog is propagated to the maneuver time Δt, and an impulse maneuver Δv is applied. The maneuvered orbit is then propagated to the observation epoch, and the average NIS of the track is calculated. The optimization objective is to minimize the average NIS of the track. This optimization problem is solved to obtain the optimal loss function and maneuver parameters. A threshold for the loss function and the range of the maneuver parameters are set to determine correlation. The minimum loss function is compared with the set maneuver correlation threshold. If the optimal loss function is higher than the threshold, the track is determined to be a maneuvered and correlated track, and the calculated maneuver parameters are accepted. The track is retained, and iterative processing continues with the observations of the next track. Otherwise, the track is determined to originate from other targets, is not correlated, the calculated maneuver parameters are rejected, and the track is skipped. This iterative maneuver correlation determination continues until all tracks are processed, thus obtaining the correlation of tracks and maneuver parameters, i.e., realizing the correlation of space target tracks and the estimation of orbital parameters.

[0009] The space target trajectory association and orbit parameter estimation method disclosed in this invention includes the following steps:

[0010] Step 1: Anomaly detection based on NIS;

[0011] The orbital data is propagated to the observation epoch using an orbital propagator, and the average NIS of the track observation and the predicted observation of the orbital propagation is calculated. If the calculated average NIS is higher than or equal to the set anomaly threshold, the track is determined to be abnormal. The anomaly indicates that the track was observed after a pulse maneuver or is a track from other targets.

[0012] Step 2: Construct an optimization problem for estimating maneuver parameters;

[0013] Let the maneuver time Δt and maneuver vector Δv be the optimization variables, where Δv = [Δv R ,Δv S ,ΔvW ] T The trajectory is propagated to the maneuver time Δt, and a pulse maneuver Δv is applied. The maneuvered trajectory is then propagated to the observation epoch. The average NIS of the trajectory is calculated, and this average NIS is used as the objective function, with the maneuver parameters as the optimization variables. This constructs an optimization problem for maneuver parameter estimation.

[0014] Step 3: Based on the optimization solution results, estimate the trajectory parameters and determine whether there is a maneuver association.

[0015] The optimization problem in step two is solved using optimization methods to obtain the optimal maneuver parameters between the trajectory and the target, and the corresponding optimal loss function f. min If the optimal loss function value f min Less than the preset evaluation and optimization threshold Then it is determined that the track is associated with the target maneuver, that is, the track was observed and associated with the target after the target maneuvered; otherwise, if This trajectory is determined to be unrelated to the target, and the observations of this trajectory are considered to originate from other targets and are not associated with them.

[0016] Step 4: Iterate through steps 1 to 3 to determine the maneuver correlation until all tracks have been processed, thereby obtaining the correlation and maneuver parameters of the tracks. Subsequently, use filtering methods to determine the trajectory, that is, to achieve trajectory parameter estimation.

[0017] Furthermore, the specific implementation method of step one is as follows:

[0018] Propagate orbital data from the catalog to the observation epochs and calculate the average NIS:

[0019] Calculate new information

[0020]

[0021] Where the subscript k represents the k-th step; y k These are flight track observations; To predict the observed values, an unscented transform is used to obtain:

[0022]

[0023] Where n is the dimension of the orbital state; represents the mean weights in the unscented transformation, and their sum is 1; h(·) is the observation function; For the predicted orbital state; News covariance S k Calculated from the sigma point in the unscented transform:

[0024]

[0025] in, R represents the covariance weights in the unscented transformation; k To observe covariance;

[0026] Based on new information and covariance S k Normalized new information η k Calculated by the following formula:

[0027]

[0028] Normalized new square for:

[0029]

[0030] Normalized new information η k If it is a Gaussian quantity with zero mean and unit covariance, then Will follow Distribution, where N is the dimension of the measurement; the average value of NIS within any time window. for:

[0031]

[0032] Where N is the number of observations of the track;

[0033] if Exceeding the user-defined threshold If the expected measurement value is inconsistent with the actual measurement value, it indicates that there is an anomaly; the anomaly indicates that the track was observed after a pulse maneuver or is a track from another target.

[0034] Furthermore, the specific implementation method of step two is as follows:

[0035] Let the maneuver time Δt and maneuver vector Δv be the optimization variables, where Δv = [Δv R ,Δv S ,Δv W ] T Propagating the cataloged track in the ECI system to the maneuver time Δt, we obtain the maneuver time Δt before the maneuver time. - ECI system lower orbit X - =[r - ,v - ], X - After switching to the RSW orbital coordinate system and applying a pulse maneuver Δv, and then switching back to the ECI frame, the maneuver time Δt can be obtained. + ECI system lower orbit X + =[r + ,v +], where, because it is a pulse maneuver, the orbital position does not change instantaneously, r + =r - Then, the trajectory is propagated to the observation epoch of the track, and the average NIS of the track is calculated using equations (1)-(6), i.e. And use it as the loss function f(Δt,Δv) for the optimization problem:

[0036]

[0037] For the maneuver time Δt, the maneuver occurs within the following boundaries:

[0038] t0<Δt<t end (8)

[0039] Where t0 is the last epoch observed before the maneuver, which is also the time of the last cataloging in the catalog library; t end It is the first epoch observed after the maneuver;

[0040] The range of the maneuver vector is:

[0041] 0≤Δv≤Δv max (9)

[0042] Where ||·|| is the L2 norm, used to calculate the magnitude of the vector; ||Δv|| max This represents the maximum value of the pulse maneuver vector; in summary, this...

[0043] The optimization problem for estimating the maneuver parameters is as follows:

[0044]

[0045] Furthermore, based on the trajectory parameters estimated in step four, the dynamic parameters during the maneuver are corrected, and the trajectory state after the maneuver is estimated using a filtering method to improve trajectory accuracy.

[0046] Furthermore, the process includes the following steps: based on the orbital parameters estimated in step four, iterative processing is performed on all possible maneuver-related tracks to improve the accuracy of maneuver parameter estimation.

[0047] Beneficial effects:

[0048] 1. The space target trajectory association and orbit parameter joint estimation method disclosed in this invention employs propagating the orbit to the observation epoch and calculating the mean normalized information square (NIS) of the trajectory. Based on the NIS, it determines whether the trajectory is abnormal, and decides whether maneuver association and joint estimation are necessary based on the anomaly status. By optimizing maneuver time and maneuver vectors, minimizing the average NIS of the trajectory is used as the optimization objective to obtain the optimal maneuver parameters, further improving the accuracy of trajectory association. This method can accurately determine whether a trajectory is abnormal in complex space environments, promptly identify maneuver trajectories, and reasonably estimate maneuver parameters, thereby effectively improving the accuracy of trajectory association, reducing false or missed associations caused by target maneuvers, and improving the overall reliability of the space target tracking system.

[0049] 2. The space target trajectory association and orbit parameter joint estimation method disclosed in this invention calculates the association probability by inverting possible target maneuvers and using observation information. It performs trajectory association and maneuver parameter estimation by combining a small amount of optical observation data without relying on a large amount of prior information. By reducing dependence on prior information, the data acquisition process is simplified, and the data complexity and acquisition difficulty in practical applications are reduced. This makes the method more applicable and flexible in real-world applications, especially maintaining high accuracy and stability even when data acquisition is limited or incomplete.

[0050] 3. The space target trajectory association and orbit parameter joint estimation method disclosed in this invention judges and optimizes trajectory association by reasonably setting the threshold of the loss function and the range of maneuver parameters. This method maintains high robustness and reliability even in the face of complex space environments and changes in target behavior, effectively handles complex situations, avoids erroneous association judgments, improves the stability of the trajectory association system, and ensures efficient and accurate target trajectory association and maneuver parameter estimation even in dynamic and complex environments.

[0051] 4. The space target trajectory association and orbit parameter joint estimation method disclosed in this invention can accurately estimate maneuver parameters through optimization. This method can accurately correct orbit parameters during maneuvers, improve orbit determination accuracy, and thus achieve more precise target trajectory prediction and tracking. Simultaneously, it can monitor the maneuverability of non-cooperative targets, providing in-depth analysis and prediction of non-cooperative target behavior, and improving the overall performance of the space target identification and tracking system. Attached Figure Description

[0052] Figure 1 Flowchart of a method for joint estimation of space target trajectory association and orbital parameters;

[0053] Figure 2 This is a schematic diagram of NIS-based anomaly detection.

[0054] Figure 3 This is a schematic diagram of the motion correlation judgment for the optimal loss function. Detailed Implementation

[0055] The invention will be further described below with reference to the accompanying drawings and embodiments.

[0056] like Figure 1 As shown in the figure, the specific implementation steps of the space target trajectory association and orbit parameter joint estimation method disclosed in this embodiment are as follows:

[0057] The orbital data is propagated to the observation epoch using an orbital propagator combined with an unscented transform, thus obtaining the predicted orbital state at the k-th sigma point. Calculate the predicted observation value for each observation time point. and its covariance S k :

[0058]

[0059]

[0060] Recalculate the normalized innovation η k and its square

[0061]

[0062]

[0063] After obtaining all NIS within the track, calculate the track average.

[0064]

[0065] and with threshold Compare and judge, if Less than It is then assumed that the track is directly associated with the cataloging target, and the track can be used to update the orbital status of the cataloging target; if Greater than This trajectory is considered abnormal for the secondary target, possibly originating from another target or indicating that the target has maneuvered, requiring further analysis. NIS and thresholds. Judgment such as Figure 2 As shown, the lower subplot represents the NIS at each time point, and the upper subplot represents the average NIS for each track. The horizontal line in the figure represents the threshold. As can be seen, the first 5 flight paths Below the threshold, it indicates that they are directly related tracks; the latter 8 tracks Above the threshold, further judgment is required.

[0066] First, we establish the framework of the optimization problem, setting the maneuver time Δt and maneuver vector Δv as optimization variables, where Δv = [Δv R ,Δv S ,Δv W ] T Propagating the cataloged track in the ECI system to the maneuver time Δt, we obtain the maneuver time Δt before the maneuver time. - ECI system lower orbit X - =[r - ,v - After transforming it to the RSW orbital coordinate system, a pulse maneuver Δv is applied, where the transformation matrix from the ECI coordinate system to the RSW coordinate system is... for:

[0067]

[0068] Switching back to the ECI system, we can obtain the Δt before the maneuver time. + ECI system lower orbit X + =[r + ,v + ], where, because it is a pulse maneuver, the orbital position does not change instantaneously, r + =r - ; in This is the transformation matrix from the RSW coordinate system to the ECI coordinate system. The trajectory is then propagated to the observation epoch of the track, and the average value of the track is calculated. Using this as the loss function f(Δt,Δv) for the optimization problem, and setting constraints on maneuver time and maneuver vector, the optimization problem is established:

[0069]

[0070] The optimization problem is solved using an optimization algorithm to obtain the optimal loss function f. min And optimal maneuver parameters: Δt opt and Δv opt If the optimal loss function value f min Less than another custom evaluation optimization threshold Furthermore, if the maneuvering parameters are within the specified constraints, the trajectory is determined to be associated with the target maneuver; that is, the trajectory is observed and associated with the target after the target maneuver, and the optimal maneuvering parameters obtained from the solution are accepted. In addition, the observations of this trajectory can be filtered to improve trajectory accuracy. Conversely, if... This trajectory is considered irrelevant to the target. Iterative processing is performed on all possible maneuver-related trajectories to improve the accuracy of maneuver parameter estimation. The optimal loss function is f. minWith threshold Comparison such as Figure 3 As shown in the figure, the results of 50 Monte Carlo runs are presented. The dashed line represents the optimal loss function for each Monte Carlo run, the nodal line represents the mean of the 50 Monte Carlo runs, and the horizontal line represents the threshold. As can be seen, tracks 3-5 This indicates that it is maneuver-related, while the other 5 tracks originate from other targets. The average estimation error of the maneuver time is 44.97s, and the average estimation error of the maneuver amplitude is 0.0046m / s.

[0071] The above detailed description further illustrates the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for space object track association and orbit parameter estimation, characterized in that: Comprising the following steps, Step one, abnormality judgment based on NIS; propagating the orbital data to an observation epoch using an orbit propagator and calculating an average NIS of the track observations and predicted observations from the orbit propagation, wherein if the calculated average NIS is greater than or equal to a set threshold of abnormality determining that the track is abnormal, the abnormality indicating that the track was observed after a pulse maneuver or is a track from another target. Step two, constructing optimization problem of maneuver parameter estimation; The maneuver time Δt and the maneuver vector Δv are set as optimization variables, wherein Δv = [Δv R , Δv S , Δv W ] T , and the orbit is propagated to the maneuver time Δt, a pulse maneuver Δv is applied, the orbit after the maneuver is propagated to the observation epoch, the average NIS of the track is calculated, and the average NIS is taken as an optimization objective function, and the maneuver parameters are taken as optimization variables, so that an optimization problem of the maneuver parameter estimation is constructed. Step three, estimating orbit parameters based on optimization solution, judging whether maneuver correlation exists; The optimization method is used to solve the optimization problem in step two to obtain optimal maneuver parameters between the track and the target and a corresponding optimal loss function f min ; if the optimal loss function value f min is less than a preset evaluation optimization threshold , it is determined that the track and the target are maneuver-related, i.e. the track is observed after the target maneuvers and is associated with the target; otherwise, if , it is determined that the track and the target are not related, and it is considered that the track observation value is from other targets and is not associated. Step four, iterating step one to step three to judge maneuver correlation until all tracks are processed, and then obtaining track correlation and maneuver parameters, and subsequently using filtering method to determine orbit, i.e. realizing orbit parameter estimation.

2. The method of claim 1, wherein: Further comprising the following steps, based on orbit parameters estimated in step four, correcting dynamic parameters at maneuver time, and using filtering method to estimate orbit state after maneuver, improving orbit accuracy.

3. The method of claim 1, wherein: Further comprising the following steps, based on orbit parameters estimated in step four, iteratively processing all possible maneuver correlated tracks to improve the accuracy of maneuver parameter estimation.

4. The method of claim 1, 2 or 3, wherein: The specific implementation of step one is as follows: The orbit data in the catalog library is propagated to the observation epoch, and the average NIS is calculated: Computing the innovation where, where the subscript k represents the kth step; y k is the observation value of the track; is the predicted observation value, obtained using the unscented transformation: where n is the dimension of the state of orbit; is the mean weight in the unscented transform, which sums up to 1; h(·) is the observation function; is the predicted state of orbit; innovation covariance S k is calculated from the sigma points in the unscented transform: wherein, is the covariance weight in the unscented transform; R k is the observation covariance; Based on the innovation and the covariance S k , the normalized innovation η k is calculated by the following equation: normalized innovation squared is: normalized innovation η k is a zero-mean, unit-covariance Gaussian quantity, then will follow a distribution where N is the dimension of the measurement; the average value of NIS over any time window is: Wherein, N is the number of observations of the track; If the user-defined threshold is exceeded then the expected measurement does not agree with the actual measurement, indicating an anomaly; the anomaly indicates that the track was observed after a pulse maneuver, or that the track is from another target.

5. The method of claim 4, wherein: The specific implementation of step two is as follows: The maneuver time Δt and the maneuver vector Δv are set as the optimization variables, where Δv = [Δv R , Δv S , Δv W ] T The catalog orbit in ECI is propagated to the maneuver time Δt, and the orbit X - in ECI before the maneuver time Δt is obtained, where X - = [r - , v - ]. After the X - is converted to the RSW orbit coordinate system, the impulse maneuver Δv is applied, and then it is converted to the ECI system, the orbit X + in ECI after the maneuver time Δt is obtained, where X + = [r + , v + ]. Since it is an impulse maneuver, the orbit position is not changed instantaneously, and r + = r - . Then the orbit is propagated to the observation epoch of the track, and the average NIS of the track is calculated using the equations (1)-(6), i.e. and it is used as the loss function f(Δt, Δv) of the optimization problem. For maneuver time Δt, the maneuver occurs within the following boundary: t0 < Δt < t end (8) where t0 is the last observed epoch before the maneuver, i.e. the time of the last catalog entry; t end is the first observed epoch after the maneuver. The range of maneuver vector is: 0 < ||Av|| < ||Av|| max (9) Where ||·|| is the L2 norm, used to calculate the magnitude of the vector; ||Δv|| max Let be the maximum value of the pulse maneuver vector; in summary, the optimization problem for estimating these maneuver parameters is:

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