Space object maneuvering multi-hypothesis sequential blind reconstruction method and system

Abstract

The application discloses a space target maneuvering multi-hypothesis sequential blind reconstruction method and system, and belongs to the field of orbit maneuvering parameter estimation and reconstruction. The method comprises the following steps: acquiring reference two-line element (TLE) of a space target and a sparse arc segment after an epoch of the reference TLE; determining a candidate maneuvering time window, configuring a corresponding preset maneuvering model; calculating a conditional residual cost, and forming a cost landscape; extracting multiple candidate maneuvering hypotheses according to the cost landscape, and forming an initial multi-maneuvering hypothesis candidate set; when a subsequent sparse arc segment arrives, performing sequential probability arbitration based on a current residual cost; performing discrimination according to the type of the preset maneuvering model, and outputting a maneuvering reconstruction result. The application retains multiple candidate branches by constructing a multi-hypothesis parallel evolution framework, and performs sequential probability arbitration by using a subsequent sparse arc segment, so that the risk of a traditional single-solution method prematurely falling into a false local optimum is reduced, and the blind reconstruction adaptability under a sparse observation condition is improved.

Description

Technical Field

[0001] This invention belongs to the technical fields of space situational awareness, space target trajectory determination, orbital maneuver parameter estimation and reconstruction, analytical orbital propagation and sparse observation data processing, and specifically relates to a method and system for sequential blind reconstruction of space target maneuvers with multiple hypotheses. Background Technology

[0002] With the rapid increase in the number of low-Earth orbit targets, operational spacecraft frequently perform maneuvers for reasons such as orbit lifting, orbit maintenance, collision avoidance, and mission adjustments. Once a maneuver occurs, conventional orbit predictions based on the two-line elements (TLE) before the maneuver quickly become invalid, thereby affecting target cataloging updates, collision risk assessments, and subsequent precise orbit determination.

[0003] Existing space target maneuver analysis and reconstruction techniques mainly include statistical analysis methods based on historical orbital element sequences or updated orbital products, and observational inversion methods based on numerical dynamics, optimal control, or full-state optimization. The former can extract long-term orbital change trends, but relies on data accumulation after the maneuver, making it difficult to provide timely maneuver timing and control variables. The latter has higher accuracy potential, but usually relies on good initial guesses, involves significant computational load, and is not conducive to the rapid processing of large-scale targets. Furthermore, existing research has attempted to improve the efficiency of maneuver parameter estimation using analytical propagation, average elements, or simplified dynamic models, providing a useful foundation for rapid reconstruction. However, when the observation arcs before and after the maneuver are sparse, the maneuver time is in a long blind zone, and multiple candidate residuals are close, further solutions are needed for issues such as candidate retention, sequential arbitration, normal aliasing discrimination, and reconstruction via continuous low-thrust start-stop.

[0004] Several solutions exist in this field regarding short-arc initial orbit determination, orbit matching, and orbit change determination. For example, short-arc orbit determination methods typically recover orbit parameters from single or multiple short-arc observations, and then select or match parameters based on residual statistics, orbital surface differences, radial / alongline / normal differences, and other indicators. Orbit matching methods typically propagate two sets of orbit parameters to a common moment or multiple decision moments, and determine whether they belong to the same target based on semi-major axis differences, orbital surface angles, or spatial position differences. Orbit change determination methods based on TLE matching typically propagate the cataloged TLE to the observation moment, calculate the theoretical observation value, and then use the residual between the observed value and the calculated value to determine whether the observed arc segment matches the cataloged target. The above methods are valuable for reference in orbit matching and orbit change determination, but most still focus on determining "whether a match has occurred" or "whether an orbit change has occurred," and do not directly address the problem of robustly reconstructing maneuver moments and control variables in unobserved blind zones under known or pre-set maneuver models.

[0005] Furthermore, some orbit matching methods rely on orbit error covariance or covariance propagation, while others depend on historical TLE sequences, historical maneuver files, manually given initial maneuver values, or relatively well-defined posterior orbit products. For non-cooperative targets and sparse observation data, this information is often unavailable or lacks sufficient reliability. Even if multi-segment orbit determination or TLE matching can indicate deviations from the target orbit, it is difficult to directly provide stable maneuver timing and control quantity estimates in the initial stage, and it is even more difficult to handle situations where the residuals of multiple candidate maneuver timings are similar.

[0006] In the analytical processing chain based on TLE and Simplified General Perturbation Model 4 (SGP4), the first-order rate of change of the average motion is usually denoted as... In traditional cataloging practices, More often considered as natural drag or long-term perturbation related terms, it is not explicitly used as an estimable control variable for continuous low-thrust maneuvers. For low-thrust maneuvers spanning multiple observation blind zones, directly estimating the complete thrust vector or piecewise acceleration requires strong priors and a large amount of observational data; however, if it is equivalent to the long-term rate of change of the mean motion, the macroscopic changes in orbital energy can be captured while maintaining the analytical propagation structure of SGP4. Therefore, how to... One of the technical problems that this invention needs to solve is to transform conventional propagation parameters into an equivalent expression of continuous low thrust and to place it in the same multi-hypothesis sequential framework as pulse velocity increment reconstruction.

[0007] A contrasting approach to single-solution processing considers both the fit of the observation residuals and the magnitude of fuel consumption or control parameters within the candidate maneuver time window. The residuals and fuel consumption are weighted and summed, and the candidate with the lowest overall cost is selected as the unique maneuver solution. This approach has a clear output and is simple to implement; however, under sparse arc conditions, both the residual term and the fuel-optimal term may be affected by the overlapping effects of observation geometry, noise, and maneuver time, causing the algorithm to prematurely lock into a false local optimum.

[0008] In real-world sparse observation scenarios, maneuvering events are often difficult to capture continuously by sensors. Available data typically consists of a reliable reference time interval (TLE) that does not contain the maneuvering effect to be reconstructed, and several sparse arcs acquired after its reference epoch with relatively long intervals and short durations; the maneuver to be reconstructed occurs between the reference TLE epoch and the start time of the first sparse arc. In this case, a single initial arc is insufficient to uniquely determine the maneuver's occurrence time and control variables, and multiple erroneous candidates may have residuals similar to or even smaller than the actual maneuver. If traditional methods lock in a single solution based on the principle of minimizing residuals in the initial stage, they are prone to mistaking mathematical fitting artifacts for physically consistent branches, leading to errors in orbital plane, phase, or energy reconstruction.

[0009] Therefore, a blind reconstruction technique for sparse arc segments is needed. This technique should be able to retain multiple physically feasible assumptions when initial information is insufficient, perform sequential arbitration as subsequent sparse arc segments arrive, and handle the problems of half-cycle aliasing in normal pulse maneuvers and unknown start-stop times in continuous low-thrust maneuvers under a pre-defined maneuver model. Simultaneously, this technique should remain as analytical and lightweight as possible to meet the requirements of batch target processing and near-real-time maneuver parameter recovery. Summary of the Invention

[0010] This invention addresses the problems of traditional single-solution reconstruction methods under sparse observation conditions, such as premature locking of false local optima, strong dependence on initial values, and difficulty in handling normal pulse half-cycle aliasing and unknown termination times of continuous low thrust. It provides a multi-hypothesis sequential blind reconstruction method for space target maneuvers, which takes the reference TLE (Time Limit Expiration) epoch that does not contain the maneuver effect to be reconstructed and the sparse arc segment after it as the main input. The time interval between the reference TLE epoch and the start time of the first sparse arc segment is used as the candidate time window for the maneuver to be reconstructed. It does not require orbital error covariance, historical maneuver files, or manually given maneuver times and initial values ​​of control variables as necessary conditions. It is suitable for the rapid reconstruction of maneuver parameters and subsequent orbit updates of non-cooperative targets.

[0011] According to one aspect of this specification, a multi-hypothesis sequential blind reconstruction method for space target maneuvering is provided, comprising:

[0012] Obtain the reference double orbit elements of the space target and at least one sparse arc segment after the epoch of the reference double orbit elements;

[0013] The time interval between the epoch of the reference double-track elements and the start time of the first sparse arc segment is determined as the candidate maneuver time window, and the corresponding preset maneuver model is configured according to the preset maneuver type.

[0014] Each candidate moment within the candidate maneuver time window is fixed, and the maneuver control variables are estimated under a preset maneuver model to obtain the conditional residual cost. A cost landscape is constructed based on all candidate moments and the corresponding conditional residual costs. Multiple candidate maneuver hypotheses are extracted based on the cost landscape to form an initial multi-maneuver hypothesis candidate set.

[0015] When subsequent sparse arc segments arrive, orbit propagation, observation prediction and parameter correction are performed on the initial multi-maneuver hypothesis candidate set or each candidate maneuver hypothesis retained after screening in the previous sequential stage to obtain the observation residual vector. The residual cost is obtained based on the observation residual vector and mapped to the normalized posterior probability.

[0016] Sequential probability arbitration is performed based on the normalized posterior probability, confirmation boundary, elimination boundary, and candidate merging condition of each candidate maneuver hypothesis; wherein, the confirmation boundary and elimination boundary are set based on the normalized posterior probability; the candidate merging condition is that, after parameter correction, the differences in candidate maneuver time, candidate maneuver control quantity, and residual cost of different candidate maneuver hypotheses are less than the corresponding preset thresholds.

[0017] Based on the type of the preset maneuver model, the candidate maneuver assumptions after sequential probability arbitration are discriminated or the parameters are completed to obtain the processing results, and the maneuver reconstruction results are output according to the processing results.

[0018] As a further technical solution, a preset maneuver model is configured according to a pre-defined maneuver type, including:

[0019] When the preset maneuver type is pulse maneuver, configure the pulse maneuver model;

[0020] When the pre-set maneuver type is continuous low thrust maneuver, configure the continuous low thrust maneuver model.

[0021] As a further technical solution, the multiple candidate maneuver hypotheses are extracted through at least one of the following methods:

[0022] For cost landscapes exhibiting a multi-peak structure, all residual local minima and their neighborhoods are extracted as candidate maneuver hypotheses.

[0023] For cost landscapes exhibiting a single-valley structure, the global minimum of the residual and its adjacent time points are extracted as candidate maneuver hypotheses.

[0024] For cost landscapes where no significant dominant basin has formed, local minima are dispersed, or the residual costs of multiple candidate points are close, a dynamic admission threshold condition is set, and a minimum time interval constraint is introduced among the candidate points that meet the dynamic admission threshold condition to perform sparse sampling to extract candidate maneuver hypotheses.

[0025] As a further technical solution, the method includes: if the normalized posterior probability of the current candidate maneuver hypothesis is greater than the confirmation boundary, it is determined to be a dominant candidate maneuver hypothesis and input into a preset maneuver model.

[0026] As a further technical solution, the method further includes: if the normalized posterior probability of the current candidate maneuver hypothesis is lower than the elimination boundary for multiple consecutive sequential stages, and the number of consecutive times it is lower than the elimination boundary is greater than the preset elimination duration, then the candidate maneuver hypothesis is eliminated.

[0027] As a further technical solution, the method also includes:

[0028] If the normalized posterior probability of the current candidate maneuver hypothesis is in the retention interval, then determine whether it satisfies the candidate merging condition with other candidate maneuver hypotheses:

[0029] If satisfied, the hypothesis is merged into an equivalent candidate maneuver hypothesis and only the candidate maneuver hypothesis with the highest normalized posterior probability is retained to enter the next sequential stage.

[0030] If the conditions are not met, the candidate maneuver hypotheses are retained and the process proceeds to the next sequential stage.

[0031] As a further technical solution, based on the type of the preset maneuver model, the candidate maneuver hypotheses after sequential probability arbitration are discriminated or their parameters are completed:

[0032] For track-based pulse maneuvers, candidate maneuver hypotheses with normalized posterior probabilities greater than the confirmation boundary are identified as dominant candidate maneuver hypotheses.

[0033] For normal pulse maneuvers, when there are still multiple candidate maneuver hypotheses that are difficult to distinguish based on residual cost alone after sequential probability arbitration, half-cycle aliasing is performed on the candidate maneuver hypotheses, and the physically consistent dominant candidate maneuver hypotheses are determined by calculating the topological consistency cost.

[0034] For continuous low-thrust maneuvers, after determining the assumption of continuous low-thrust dominant candidate maneuvers, the residual drift along the track in the subsequent sparse arc segment is analyzed to determine and locate the thrust termination time in order to complete the parameters of continuous low-thrust maneuvers.

[0035] As a further technical solution, for normal pulse maneuvers, half-cycle aliasing is performed on the candidate maneuver hypotheses, and physically consistent dominant candidate maneuver hypotheses are determined by calculating the topological consistency cost, including:

[0036] Candidate maneuvers whose time differences are set to integer multiples of the orbital period and whose normal velocity increments have alternating signs are clustered into an aliasing family.

[0037] A topological consistency cost is constructed based on the long-term drift rate change of the ascending node, and the candidate maneuver hypothesis with the minimum topological consistency cost is selected within the aliasing family as the physical consistency preferred candidate maneuver hypothesis.

[0038] As a further technical solution, the residual drift along the track in subsequent sparse arc segments is analyzed to determine and locate the thrust termination time, including:

[0039] For continuous low-thrust maneuvers, a track residual baseline is established based on the historical sparse arc segments of the stable thrust phase.

[0040] When the average residual along the track of the new sparse arc segment satisfy When the direction of the average along-track residual is consistent with the theoretical drift direction after thrust removal, the thrust termination candidate determination is triggered; wherein, For the residual baseline along the track, This is a preset threshold coefficient;

[0041] After triggering the thrust termination candidate determination, the thrust continuation hypothesis and the thrust termination hypothesis are constructed. Based on the average track residual of the current sparse arc segment, a standardized residual is constructed. The likelihood weights of the thrust continuation hypothesis and the thrust termination hypothesis are calculated, and the likelihood weights are normalized to the thrust termination hypothesis probability.

[0042] When the probability of the thrust termination hypothesis is greater than a preset confirmation threshold, it is determined that the thrust termination occurred in the candidate unobserved interval; when the probability of the thrust termination hypothesis is lower than a preset rejection threshold, the current thrust termination candidate determination is cancelled.

[0043] When the probability of the thrust termination assumption is between the preset rejection threshold and the preset confirmation threshold, it is included in the subsequent sparse arc segment for delayed confirmation.

[0044] Once it is determined that the thrust termination occurs in a candidate unobserved interval, a trial termination time is introduced within the candidate unobserved interval. The average along-track residual of the sparse arc segment after the first effective thrust termination located after the candidate unobserved interval is used to calculate the equivalent residual acceleration, and the thrust termination time is estimated by minimizing the equivalent dynamic cost.

[0045] According to one aspect of this specification, a space target maneuvering multi-hypothesis sequential blind reconstruction system is provided, comprising:

[0046] The first processing module is used to obtain the reference double orbit elements of the space target and at least one sparse arc segment after the epoch of the reference double orbit elements.

[0047] The second processing module is used to determine the time interval between the epoch of the reference double-track elements and the start time of the first sparse arc segment as the candidate maneuver time window, and configure the corresponding preset maneuver model according to the preset maneuver type.

[0048] The third processing module is used to fix each candidate moment within the candidate maneuver time window, estimate the maneuver control variables under the preset maneuver model, obtain the conditional residual cost, construct a cost landscape based on all candidate moments and the corresponding conditional residual costs, and extract multiple candidate maneuver hypotheses based on the cost landscape to form an initial multi-maneuver hypothesis candidate set.

[0049] The fourth processing module is used to perform orbit propagation, observation prediction and parameter correction on the initial multi-maneuver hypothesis candidate set or each candidate maneuver hypothesis retained after screening in the previous sequential stage when the subsequent sparse arc segment arrives, to obtain the observation residual vector, and to obtain the residual cost based on the observation residual vector, and to map the residual cost to the normalized posterior probability.

[0050] The fifth processing module is used to perform sequential probability arbitration based on the normalized posterior probability, confirmation boundary, elimination boundary, and candidate merging condition of each candidate maneuver hypothesis; wherein the confirmation boundary and elimination boundary are set based on the normalized posterior probability; the candidate merging condition is that after parameter correction, the differences in candidate maneuver time, candidate maneuver control quantity, and residual cost of different candidate maneuver hypotheses are less than the corresponding preset thresholds.

[0051] The sixth processing module is used to discriminate or complete the parameters of the candidate maneuver hypotheses after sequential probability arbitration based on the type of the preset maneuver model, obtain the processing results, and output the maneuver reconstruction results based on the processing results.

[0052] Compared with the prior art, the beneficial effects of the present invention are:

[0053] 1. This invention mainly relies on the reference TLE (Time Limit Exceeded) and its subsequent sparse arc segments that do not contain the maneuver effects to be reconstructed. It constrains the timing of the pulse maneuver or the start time of the continuous low-thrust maneuver to be reconstructed between the reference TLE epoch and the start time of the first sparse arc segment. It does not require prior provision of the orbital error covariance, historical maneuver files, or manually given maneuver timing and initial values ​​of control variables, thus reducing prior dependence. When the initial arc segment information is insufficient, it retains multiple candidate branches by constructing a multi-hypothesis parallel evolution framework and uses subsequent sparse arc segments for sequential probability arbitration, thereby reducing the risk of traditional single-solution methods falling into false local optima too early and improving the adaptability of blind reconstruction under sparse observation conditions.

[0054] 2. This invention addresses the potential semi-orbital periodic symmetric aliasing that may occur during normal pulse maneuvers under sparse observations by introducing a topological consistency cost based on the long-term drift difference of the ascending node. This allows multiple mirror candidates to obtain additional physical discrimination criteria when their fitting residuals are similar, which helps to screen out false branches that are inconsistent with the long-term orbital plane evolution and improves the spatial geometric aliasing discrimination capability of normal pulse maneuvers.

[0055] 3. This invention equates the long-term energy effect of continuous low thrust to the average rate of change of motion, and combines it with three-stage analytical propagation to incorporate continuous low thrust maneuvers into a candidate generation, propagation evolution, and sequential arbitration process consistent with pulse maneuvers. At the same time, by analyzing the parabolic drift of the residual along the track after thrust removal, the thrust termination time is determined and located, reducing the dependence on the prior of the complete thrust vector, and realizing a unified analytical representation and start-stop reconstruction of continuous low thrust maneuvers.

[0056] 4. This invention takes SGP4 analytical propagation and parallel evolution of finite candidate maneuver assumptions as its core, and performs trajectory prediction, maneuver mapping and residual evaluation under a unified coordinate framework. It avoids repeatedly calling high-precision numerical dynamics integration in the candidate search stage, reduces computational overhead, and thus improves the engineering applicability of batch target processing and near real-time maneuver parameter recovery, which is convenient for subsequent cataloging and updating. Attached Figure Description

[0057] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0058] Figure 1 A flowchart of a space target maneuvering multi-hypothesis sequential blind reconstruction method provided in an embodiment of the present invention.

[0059] Figure 2 This is a schematic diagram of model-driven temporal search and multi-maneuver hypothesis candidate set extraction provided in an embodiment of the present invention, wherein... Figure 2 (a) in the image represents a typical landscape of along-track pulse cost. Figure 2 (b) in the image represents a typical landscape of normal pulse cost. Figure 2 (c) in the text represents a typical landscape with continuous low thrust costs.

[0060] Figure 3 A flowchart of the sequential probability arbitration process for a multi-maneuver hypothesis candidate set provided in an embodiment of the present invention. Detailed Implementation

[0061] It should be noted that: space targets refer to man-made on-orbit targets that operate in Earth orbit, have a usable reference TLE, and can obtain observation data through radar, optics, or other measurement systems. They mainly include remote sensing satellites, communication satellites, navigation satellites, and low-Earth orbit constellation satellites.

[0062] 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.

[0063] Example 1

[0064] like Figure 1As shown, this embodiment of the invention proposes a sequential blind reconstruction method for multiple hypotheses of space target maneuvering, including: Step S1, obtaining the reference double-track orbit elements of the space target and at least one sparse arc segment after the epoch of the reference double-track orbit elements, and constructing observation residuals based on the reference double-track orbit elements and the sparse arc segment. Step S2, determining the time interval between the epoch of the reference double-track orbit elements and the start time of the first sparse arc segment as a candidate maneuvering time window, and configuring a corresponding preset maneuvering model according to a pre-set maneuvering type. Step S3, fixing each candidate moment within the candidate maneuvering time window, estimating the maneuvering control variables under the preset maneuvering model, obtaining the conditional residual cost, constructing a cost landscape based on all candidate moments and the corresponding conditional residual costs; extracting multiple candidate maneuvering hypotheses based on the cost landscape to form an initial multi-maneuvering hypothesis candidate set. Step S4: When subsequent sparse arc segments arrive, perform trajectory propagation, observation prediction, and parameter correction on the initial multi-maneuver hypothesis candidate set or each candidate maneuver hypothesis retained after screening in the previous sequential stage to obtain the observation residual vector. Calculate the residual cost based on the observation residual vector and map the residual cost to a normalized posterior probability. Step S5: Perform sequential probability arbitration based on the normalized posterior probability, confirmation boundary, elimination boundary, and candidate merging condition of each candidate maneuver hypothesis. The confirmation boundary and elimination boundary are set based on the normalized posterior probability. The candidate merging condition is that after parameter correction, the differences in candidate maneuver time, candidate maneuver control quantity, and residual cost among different candidate maneuver hypotheses are less than corresponding preset thresholds. Step S6: Based on the type of the preset maneuver model, discriminate or complete the parameters of the candidate maneuver hypotheses after sequential probability arbitration to obtain the processing result. Output the maneuver reconstruction result based on the processing result.

[0065] Specifically, step S1 includes the following:

[0066] Step S1.1: Obtain the reference TLE of the space target, and at least the time elapsed after the reference TLE epoch obtained by the radar measurement system or optical measurement system. A sparse arc segment, ,in, Indicates the first A sparse arc segment. The reference TLE refers to the last reliable reference TLE whose epoch is earlier than the moment of the pulse maneuver to be reconstructed or the start time of the continuous low-thrust maneuver, and which does not contain the effect of the maneuver to be reconstructed; the moment of the pulse maneuver to be reconstructed or the start time of the continuous low-thrust maneuver is located between the epoch of the reference TLE and the start time of the first sparse arc segment; the sparse arc segment refers to a sequence of observation data records that is relatively short in duration relative to the orbital period of the space target and has an unobserved interval between adjacent arc segments; each sparse arc segment It consists of multiple time-stamped observation data records. Specifically, when the preset maneuver type is a pulse maneuver, the time of the pulse maneuver to be reconstructed is located between the epoch of the reference double-track elements and the start time of the first sparse arc segment; when the preset maneuver type is a continuous low-thrust maneuver, the start time of the continuous low-thrust maneuver to be reconstructed is located between the epoch of the reference double-track elements and the start time of the first sparse arc segment.

[0067] The observation data is either radar observation data or optical observation data. The radar observation data includes range, azimuth, and elevation angle observations, while the optical observation data includes right ascension and declination observations. The observation timescale, observation type, and input observation value, along with the corresponding station information or observation platform status, are read from each observation data record. The observation data records are then sorted by time, formatted uniformly, and have their coordinates standardized.

[0068] Step S1.2: Input the reference TLE into the SGP4 propagation model to calculate the theoretical orbital state of the space target at each observation time; based on the station location or observation platform status and observation type corresponding to each observation time, convert the theoretical orbital state into theoretical observation values. Theoretical observation values ​​include radar theoretical observation values ​​and optical theoretical observation values; the radar theoretical observation values ​​include range, azimuth, and elevation angle, and the optical theoretical observation values ​​include right ascension and declination.

[0069] Step S1.3: Represent the actual observed values ​​and the corresponding theoretical observed values ​​according to the same observation type, unit of measurement, and observation reference coordinate system, and construct the observation residual by subtracting the two representations. The actual observed value is the input observed value relative to the theoretical calculated value. This input observed value is obtained by a ground-based station or a space-based observation platform; in the simulation verification of this embodiment, this input observed value is a simulated observed value based on precise ephemeris. Step S1 is applicable to ground-based stations or space-based observation platforms, as long as the observation time, the corresponding station location or observation platform status, and the input observed value can be obtained.

[0070] Specifically, step S2 includes the following:

[0071] Step S2.1: Refer to the epoch of TLE The starting time of the first sparse arc segment The time interval between these points is determined as the candidate maneuver time window. The expression is as follows:

[0072] (1)

[0073] For pulse maneuvers, the candidate maneuver time window is the candidate range of the pulse maneuver time, and the maneuver control variable to be estimated is the pulse velocity increment; for continuous low-thrust maneuvers, the candidate maneuver time window is the candidate range of the thrust initiation time, and the maneuver control variable to be estimated is the equivalent average rate of change of motion.

[0074] Step S2.2: Configure the corresponding preset maneuver model according to the preset maneuver type: when the preset maneuver type is pulse maneuver, configure the pulse maneuver model; when the preset maneuver type is continuous low-thrust maneuver, configure the continuous low-thrust maneuver model. The preset maneuver type can be provided by mission configuration, manual interpretation, or an independent pre-maneuver detection and classification module. This embodiment of the invention does not limit the specific method of obtaining the maneuver type. The maneuver type is used to select the corresponding preset maneuver model. This embodiment of the invention reconstructs the maneuver timing and maneuver control variables under the selected preset maneuver model.

[0075] The embodiments of the present invention do not require automatic detection of maneuver occurrence or automatic identification of maneuver type as necessary steps. Instead, they reconstruct the maneuver timing and control variables under the configured preset maneuver model, as follows:

[0076] For the configured preset maneuver model, the maneuver coupling propagation relationship is established, expressed as:

[0077] (2)

[0078] in, For the goal at all times Position and velocity state, For candidate maneuver parameters, This is a maneuvering coupled propagation operator. The maneuvering coupled propagation operator uses SGP4 as the basic propagation kernel and performs state propagation, observation prediction, and residual evaluation within a unified coordinate framework.

[0079] When SGP4 is used in conjunction with TLE, it typically outputs the state in the true equatorial vernal equinox coordinate system (TEME). In practice, the propagation state can be converted to one of the following coordinate systems: the true equatorial daily coordinate system (TOD), the geocentric inertial coordinate system (ECI), or the J2000 coordinate system, before performing maneuver mapping, observation prediction, and residual evaluation. Alternatively, the theoretical orbital state can be further mapped to the station's local observation coordinate system and compared with actual radar or optical observations. These coordinate unification steps are used to avoid systematic biases introduced by inconsistencies between propagation coordinates, maneuver coordinates, and observation coordinates.

[0080] For the kinematic parameters of pulse maneuver The expression is:

[0081] (3)

[0082] in, For candidate maneuver moments, The pulse velocity increment can be represented in radial, along-track, and normal coordinate systems. Preferably, at the candidate maneuver moment, the pre-maneuver position and velocity state of the space target is obtained according to the reference TLE, the pulse velocity increment is transformed to a coordinate system consistent with the velocity state and superimposed on the velocity vector, and the average orbital elements adapted to the SGP4 propagation model are updated according to the post-maneuver position and velocity state for use in post-maneuver orbit propagation.

[0083] For continuous low-thrust maneuvers, the maneuver parameters The expression is:

[0084] (4)

[0085] in, At the moment of thrust initiation, The equivalent average rate of change of motion caused by continuous low thrust. The thrust termination time is defined as the equivalent average motion change rate, which characterizes the long-term cumulative effect of continuous low thrust on orbital energy and average motion, without discretizing the continuous low thrust process into multiple pulses. This allows continuous low thrust maneuvers to participate in the search for the thrust initiation time, the evolution of candidate maneuver hypotheses, and the location of the thrust termination time as scalar control quantities.

[0086] For a near-circular orbit, a constant thrust acceleration along the track The equivalent average rate of change of motion satisfies the following condition:

[0087] (5)

[0088] in, For average motion, Let be the orbital velocity. For orbital lifting thrust along the track, the semi-major axis increases and the average motion decreases; therefore, under the above notation conventions... It is usually negative; its sign changes accordingly for reverse braking or track descent. During the thrust phase, the equivalent average rate of change of motion is used as an additional term to the first-order rate of change of the average motion, to update the long-term terms of the average motion and the mean anomaly angle:

[0089] (6)

[0090] (7)

[0091] in, During the thrust phase Average motion, Let the angle be the approximate point angle at that moment. and These are the average motion and the angle of approach at the moment of thrust initiation, respectively. The time interval between the start of relative thrust. This represents the long-term average motion variation term corresponding to the natural trajectory change. Continuous low-thrust maneuvers employ a three-stage propagation model: natural propagation before thrust, equivalent propagation during the thrust application phase, and natural propagation after thrust. After the thrust termination moment, Set it to zero, and use the average orbital elements accumulated at the termination time as the initial condition for subsequent natural propagation.

[0092] Specifically, step S3 includes the following:

[0093] Step S3.1: Select candidate maneuver time windows According to the preset step size Discretize to obtain the candidate time set :

[0094] (8)

[0095] in, Indicates the sequence number of the candidate time grid point. Indicates the first candidate maneuver within the corresponding time window. One candidate moment, This indicates that the candidate maneuver time window is set according to a preset step size. The total number of candidate moments obtained after discretization is determined by the length of the candidate maneuver time window and the preset time step.

[0096] For each candidate time Fix the candidate time and estimate the maneuver control variables under the corresponding preset maneuver model. The conditional residual cost at this candidate time point is obtained. :

[0097] (9)

[0098] The weighted root mean square residual is defined as follows:

[0099] (10)

[0100] in, To observe the residual vector, The observation weight matrix is ​​constructed based on the standard deviations of various observation errors. These are the maneuver control variables corresponding to the configured preset maneuver model. The number of equivalent observation equations involved in residual calculation; when When constructed based on the reciprocals of the variances of each observation error, the weighted root mean square residual is a dimensionless index. For the pulse maneuver model, the maneuver control variable is the pulse velocity increment. For the continuous low-thrust maneuver model, the maneuver control variable is the equivalent average rate of change of motion. For continuous low-thrust maneuvers, during the initial time search phase, the candidate thrust start time is fixed and the equivalent average rate of change of motion is estimated, and candidate maneuver hypotheses are constructed based on the continuous action of thrust. Since determining the thrust termination time requires information on the along-track residual drift exhibited by the sparse arc segment after thrust termination, the thrust termination time is not considered as a variable to be estimated during the initial time search phase; when subsequent sparse arc segments arrive and thrust termination characteristics appear, the thrust termination candidate determination, probability confirmation, and thrust termination time location are then performed according to step S6.

[0101] Step S3.2: Select all candidate times. and the corresponding conditional residual cost Arranged in chronological order of candidate times, they form a discrete relationship in which the conditional residual cost changes with the candidate times. This discrete relationship is called the cost landscape.

[0102] Step S3.3: Extract multiple candidate maneuver hypotheses based on the morphology of the cost landscape to form an initial multi-maneuver hypothesis candidate set. This embodiment of the invention does not directly use the global minimum of the conditional residual cost as the unique maneuver solution, but rather employs a corresponding candidate maneuver hypothesis extraction method based on the number, distribution, and relative size of local minima in the cost landscape.

[0103] The candidate maneuver hypothesis extraction method includes at least one of the following:

[0104] For a cost landscape that presents multiple local minima, candidate points corresponding to each local minima of the residual and their neighborhood candidate points are extracted to form candidate maneuver hypotheses.

[0105] For cost landscapes that present a single significant valley, candidate points corresponding to the global minimum of the conditional residual cost and their adjacent candidate times are extracted to form candidate maneuver hypotheses, in order to retain candidate time biases caused by observation noise, time discretization or parameter compensation.

[0106] For cost landscapes that do not form significant dominant basins, have dispersed local minima, or have similar conditional residual costs among multiple candidate points, a dynamic admission threshold condition is set:

[0107] (11)

[0108] in, Denotes the first set of conditional residual costs Quantile threshold. Among the candidate points that satisfy the dynamic admission threshold, a minimum time interval constraint is further introduced, wherein... The minimum allowed time interval between two extracted candidate maneuvers:

[0109] (12)

[0110] in, and These represent any two different candidate times that satisfy the dynamic admission threshold condition. .

[0111] Based on the minimum time interval constraint, sparse sampling is performed on candidate points that meet the dynamic admission threshold to form candidate maneuver hypotheses that are distributed in a dispersed manner within the candidate maneuver time window.

[0112] Each candidate maneuver hypothesis It includes at least the candidate maneuver timing, the candidate maneuver control quantity, and the corresponding conditional residual cost, and uses the candidate maneuver timing and the candidate maneuver control quantity as the initial values ​​for subsequent sequential parameter correction.

[0113] Specifically, Figure 2 This represents the typical cost landscape and candidate extraction methods under different preset maneuver models. For track-side pulse maneuvers, there is a parameter compensation relationship between the candidate maneuver time and the pulse velocity increment, causing the cost landscape to present multiple close local minima. Therefore, candidate points corresponding to multiple local minima and their neighboring candidate points are retained, instead of determining a unique maneuver result solely based on the global minimum in the initial stage.

[0114] For normal pulse maneuvers, the cost landscape may exhibit characteristics such as dispersed local minima, a lack of significant dominant basins, and similar conditional residual costs across multiple candidate points. This phenomenon may be due to the relatively weak constraint of the current finite sparse arc segments on the orbital surface changes caused by the normal maneuver, as well as the half-cycle geometric aliasing of the normal pulse maneuver, which allows different candidate maneuver times and normal velocity increments to form similar observational fitting results. Therefore, we extract dispersed candidate maneuver hypotheses using dynamic admission thresholds and minimum time interval constraints, rather than directly determining the maneuver outcome based on a single global minimum.

[0115] For continuous low-thrust maneuvers, the cost landscape may present a single significant valley. We retain the candidate point corresponding to the global minimum of the conditional residual cost and its neighborhood candidate points to support the sequential evolution of subsequent continuous thrust candidate maneuver hypotheses and the location of the thrust termination time. Figure 2 In (c), only the global minimum of the conditional residual cost is representatively marked. The neighborhood candidate point refers to the candidate maneuver hypothesis located at the candidate time or the adjacent time grid point of the global minimum. They are not marked one by one in the figure.

[0116] Figure 2 The verification reference time indicated in the middle is only used to illustrate the relative relationship between the cost landscape and the reference maneuver time, and does not participate in the candidate time search, candidate maneuver hypothesis extraction or parameter estimation process.

[0117] Specifically, step S4 includes the following:

[0118] Step S4.1, when the subsequent (the first) When the sparse arc segment reaches the current sequential stage, denote the current sequential stage as the th stage. The first sequential update uses the initial set of candidate maneuver hypotheses as input, and subsequent sequential updates use the candidate maneuver hypotheses retained after screening in the previous sequential stage as input. For each candidate maneuver hypothesis, orbit propagation, observation prediction, and parameter correction are performed separately. After the parameter correction converges, the first sequential update is obtained. The candidate maneuver hypothesis is in the... Stage observation residual vector Based on the observed residual vector, the weighted root mean square residual is used to characterize the first... The candidate maneuver hypothesis is in the... Stage residual cost The expression is as follows:

[0119] (13)

[0120] in, For the first The observation weight matrix corresponding to the stage observation data, For the first The number of equivalent observation equations involved in residual calculation at each stage.

[0121] Step S4.2: Obtain the residual cost based on the observed residual vector, and map the residual cost to the normalized posterior probability.

[0122] Candidate maneuver hypotheses that fail to converge after parameter correction or whose residual cost exceeds a preset anomaly threshold are eliminated and not included in the posterior probability normalization calculation in this stage.

[0123] For the remaining candidate maneuver hypotheses, assuming all candidate maneuver hypotheses use the same prior probability, the residual cost is mapped to a normalized posterior probability:

[0124] (14)

[0125] (15)

[0126] in, Indicates the first The candidate maneuver hypothesis is in the... The unnormalized residual score of the stage is used to integrate the residual cost, data volume weight and adaptive annealing factor of the current stage, and serves as an intermediate quantity for the normalized posterior probability mapping. For the first The candidate maneuver hypothesis is in the... The normalized posterior probability of the stage; This represents the number of candidate maneuver hypotheses participating in the probability normalization calculation at this stage, after parameter-corrected convergence and residual anomaly checks. The weights are related to the current amount of sparse arc segment data. The adaptive annealing factor, which varies with the sequential stage, is expressed as follows:

[0127] (16)

[0128] in, This is the initial annealing factor.

[0129] In a preferred embodiment, the data weight of the current sparse arc segment It can be set as follows:

[0130] (17)

[0131] in, For the first The number of equivalent observation equations for sparse arc segments in a given stage. To reference the number of equivalent observation equations, This is the upper limit of the weight. This is a data volume weighting adjustment index. The data volume weight is used to reduce the excessive influence of extremely short arc segments or arc segments with insufficient observations on the probability arbitration results.

[0132] Based on the normalized posterior probabilities of each candidate maneuver hypothesis, a confirmation boundary is set. and elimination boundary In a preferred embodiment, the confirmation boundary and the elimination boundary are respectively:

[0133] (18)

[0134] (19)

[0135] in, To confirm the lower bound parameter of the baseline as the boundary changes with the sequential stage, To confirm the boundary attenuation coefficient, This is the elimination boundary ratio coefficient.

[0136] Specifically, step S5 includes the following:

[0137] Sequential probability arbitration is performed based on the normalized posterior probability, confirmation boundary, elimination boundary, and candidate merging conditions of each candidate maneuver hypothesis in order to retain, merge, eliminate, or confirm the corresponding candidate maneuver hypothesis.

[0138] Sequential probabilistic arbitration includes:

[0139] If the normalized posterior probability of the current candidate maneuver hypothesis is lower than the elimination threshold for multiple consecutive sequential stages, and the number of consecutive times it is lower than the elimination threshold is greater than the preset elimination duration, then the candidate maneuver hypothesis is eliminated (in specific implementation, pulse maneuver: 2 consecutive sequential stages; continuous low thrust maneuver: 3 consecutive sequential stages).

[0140] If the current candidate maneuver hypothesis is in the retention interval (the retention interval is greater than or equal to the elimination boundary and less than or equal to the confirmation boundary), then the candidate maneuver hypothesis is retained and continues to evolve. The determination is whether the candidate merging condition is met: if it is met, the corresponding candidate maneuver hypothesis is merged into an equivalent candidate maneuver hypothesis and enters the next sequential stage; if it is not met, the corresponding candidate maneuver hypothesis is retained and enters the next sequential stage.

[0141] If the normalized posterior probability of the current candidate maneuver hypothesis is greater than the confirmation boundary, it is determined to be a dominant candidate maneuver hypothesis and output to the preset maneuver model. Here, retention, merging, elimination, and confirmation are not four steps that the same candidate maneuver hypothesis must go through sequentially, but rather different arbitration results that may correspond to different candidate maneuver hypotheses after being included in the new sparse arc segment. The candidate merging condition refers to the fact that, after parameter correction, the differences in candidate maneuver timing, candidate maneuver control quantity, and residual cost among different candidate maneuver hypotheses are less than the corresponding preset thresholds. Candidate maneuver hypotheses that meet the candidate merging condition are considered equivalent candidate maneuver hypotheses, and only the candidate maneuver hypothesis with the highest normalized posterior probability is retained to enter the next sequential stage.

[0142] As a preferred approach, during the evolution of multiple maneuver assumptions, parameter correction includes iterative differential correction of candidate maneuver moments and candidate maneuver control variables. It can also selectively correct the drag term, mean approach angle, or mean motion in the reference TLE based on the time interval between the reference TLE epoch and the current arc segment, to absorb phase or model biases caused by long-term propagation. For continuous low-thrust maneuvers, candidates at adjacent starting moments may gradually exhibit equivalent trajectories under sustained thrust. The processing program can merge kinematically converging candidates based on the stability of the residual index and the equivalent mean motion rate of change to avoid redundant branches occupying computational resources for extended periods.

[0143] Figure 3 This is a flowchart of the sequential probability arbitration process for the candidate set of multiple maneuver hypotheses, corresponding to steps S4 and S5.

[0144] Specifically, step S6 includes the following:

[0145] Step S6.1: Based on the type of the preset maneuver model, the candidate maneuver hypotheses after sequential probability arbitration are discriminated or their parameters are completed to obtain the processing results, as follows:

[0146] 1. For track-based pulse maneuvers, candidate maneuvers with normalized posterior probabilities greater than the confirmation boundary are identified as dominant candidate maneuvers (at which point the reconstruction can be considered complete).

[0147] 2. For normal pulse maneuvers, when there are still multiple candidate maneuver hypotheses that are difficult to distinguish based on residual cost alone after sequential probability arbitration, half-cycle aliasing is performed on the candidate maneuver hypotheses, and the physically consistent dominant candidate maneuver hypotheses are determined by calculating the topological consistency cost.

[0148] Candidate maneuvers whose timing differs by approximately half an orbital period and whose normal velocity increments have alternating signs are clustered into an aliasing family. Let the first... The candidate maneuver times for each candidate maneuver hypothesis are: The long-term drift rate of the ascending node right ascension caused by the maneuver, obtained from parameter correction, is: The unified evaluation time is .

[0149] Since different aliasing candidates correspond to different maneuver times, in order to fit a common set of subsequent observations, each candidate will generate different long-term drift rate compensations for the right ascension of the ascending node during the parameter correction process. A topological consistency cost is constructed based on the change in the long-term drift rate of the ascending node, including:

[0150] With the first Taking the candidate maneuver hypothesis as a reference, its prediction of the first... The candidate and the first Cumulative difference between nodes among candidates for:

[0151] (20)

[0152] Based on the long-term drift rate changes of the ascending node after correction of the parameters of the two candidate maneuver assumptions, the actual cumulative difference between the two at the unified evaluation time is... for:

[0153] (twenty one)

[0154] The cumulative difference of the actual nodes is compared with the first... The cumulative difference of predicted nodes obtained from the candidate nodes is compared, and the nth node is defined as... The candidate relative to the first Targeted topological differences of each candidate for:

[0155] (twenty two)

[0156] No. The cost of each candidate maneuver hypothesis relative to the topological consistency of the entire aliasing family Defined as:

[0157] (twenty three)

[0158] in, This represents the number of candidate maneuver hypotheses within the aliasing family.

[0159] Within the aliasing family, the candidate maneuver hypothesis with the lowest topological consistency cost is selected as the physical consistency advantage candidate maneuver hypothesis for normal pulse maneuvers.

[0160] For continuous low-thrust maneuvers, after determining the assumption of continuous low-thrust dominant candidate maneuvers, the track residual drift of subsequent sparse arc segments is analyzed to determine and locate the thrust termination time in order to complete the parameters of continuous low-thrust maneuvers (at which point the reconstruction can be considered complete).

[0161] For continuous low-thrust maneuvers, during the phase where thrust is considered stable, a residual baseline along the track is established using historical sparse arc segments that have been confirmed to be in a stable thrust phase. Equivalent thrust acceleration during the stable thrust phase It is obtained by converting the current estimated equivalent average rate of change of motion:

[0162] (twenty four)

[0163] When the actual thrust has terminated but the candidate propagation still assumes that the thrust continues to act, the theoretical along-track drift between the thrust continuation assumption and the actual ballistic motion is approximated as follows:

[0164] (25)

[0165] in, The time interval is relative to the candidate thrust termination time. For the reason The calculated current equivalent thrust acceleration.

[0166] When the centroid of the new sparse arc segment is at time Average along-track residual at point satisfy:

[0167] (26)

[0168] And the direction of the average residual along the track is... When the directions are consistent, the thrust termination candidate determination and probability arbitration process is triggered, wherein... This is the preset threshold coefficient.

[0169] After triggering the thrust termination candidate determination, a thrust persistence hypothesis is constructed. and thrust termination assumption .in, This indicates that continuous low thrust is still in effect. This indicates that the continuous low thrust has terminated within the candidate unobserved interval. The candidate unobserved interval is determined by the unobserved time interval between the last sparse arc segment confirmed to be in the thrust phase and the first sparse arc segment that triggered the thrust termination candidate determination.

[0170] For the assumption Standardized residuals are constructed based on the average residuals along the track of the current sparse arc segments. :

[0171] (27)

[0172] in, The expected along-rail residual under the thrust sustaining assumption can be determined based on the along-rail residual baseline during the thrust stabilization phase. This represents the expected along-track residual under the thrust termination assumption. For the thrust termination assumption, based on different trial termination times within the candidate unobserved interval, the theoretical along-track drift range corresponding to the currently evaluated sparse arc segment is calculated, and the value within this theoretical along-track drift range that is closest to the current average along-track residual is taken as the expected along-track residual. .

[0173] To reduce the impact of anomalous observations on thrust termination determination, Cauchy likelihood weights for the thrust continuation and thrust termination assumptions are calculated. :

[0174] (28)

[0175] When the thrust sustaining hypothesis and the thrust termination hypothesis use the same prior probability, the Cauchy likelihood weights are normalized to the thrust termination hypothesis probability. :

[0176] (29)

[0177] when When the value exceeds a preset confirmation threshold, thrust termination is determined to have occurred during the candidate unobserved interval; when If the thrust is below the preset rejection threshold, the candidate for thrust termination is cancelled; when When the value is between the preset rejection threshold and the preset acceptance threshold, it continues to be included in subsequent sparse arc segments for delayed acceptance.

[0178] Once it is determined that thrust termination occurred within the candidate unobserved interval, a trial termination time is introduced within the candidate unobserved interval. The equivalent residual acceleration is calculated using the average along-track residual of the sparse arc segment following the termination of the first effective thrust after the candidate unobserved interval. :

[0179] (30)

[0180] The thrust termination time is estimated by minimizing the equivalent dynamic cost through binary search or monotonic search. And complete the continuous low-thrust maneuver parameters. The expression for the dynamic equivalent cost is:

[0181] (31)

[0182] Step S6.2: Output the motor reconstruction results based on the processing results.

[0183] For pulse maneuvers, the maneuver reconstruction result includes at least the pulse maneuver time and the pulse velocity increment; for continuous low-thrust maneuvers, the maneuver reconstruction result includes at least the thrust initiation time, the thrust termination time, and the equivalent average rate of change of motion. The equivalent thrust acceleration can also be calculated and output based on the equivalent average rate of change of motion.

[0184] The maneuver reconstruction result may also include a type label corresponding to the preset maneuver model, as well as residual statistics, topology consistency cost, or thrust termination positioning cost for verifying the reconstruction process.

[0185] The method does not require track error covariance, historical maneuver files, or manually given maneuver times and initial control values ​​as necessary inputs, nor does it require automatic detection of maneuver occurrence or automatic identification of maneuver type as necessary steps.

[0186] To verify the implementation effect of the method in the embodiments of the present invention, Examples 2 to 4 below respectively select the International Space Station (ISS), Sentinel-3A, and Starlink-34961 as example targets. The above target names are only used to identify verification examples under different maneuver types and orbital conditions, and do not constitute a limitation on the applicable objects of the embodiments of the present invention. Each embodiment uses a simulated sparse observation arc segment generated based on the precise ephemeris of the corresponding target. The input for maneuver reconstruction is the pre-maneuver reference TLE and the simulated sparse observation arc segment. The reference maneuver parameters are obtained through precise ephemeris inversion or mission maneuver files. The precise ephemeris and reference maneuver parameters are only used for simulation data generation and reconstruction error assessment, and do not participate in candidate time search, parameter estimation, multiple hypothesis evolution, or sequential probability arbitration processes.

[0187] Example 2

[0188] In this embodiment of the invention, the International Space Station (ISS) is used as an example target to obtain the pre-maneuver reference time interval (TLE) and the simulated radar sparse arc segment generated based on precise ephemeris. The processing program uses the blind zone between the reference TLE epoch and the first observation time as a candidate maneuver time window, configures the pulse maneuver model, and generates candidate times within this window at fixed step sizes. For each candidate time, the processing program estimates the pulse velocity increment and calculates the conditional residual cost.

[0189] Under sparse arc conditions and noise, the cost landscape of grid search may exhibit a multi-peak structure, with a typical form as follows: Figure 2 As shown in (a) above. At this point, the global minimum point of the residual may deviate from the reference maneuver time due to geometric aliasing or measurement noise. If the traditional single-solution approach of residual minimization is adopted, the algorithm will directly lock a single candidate and discard other branches in the initial stage, which may lead to deviations in subsequent trajectory predictions.

[0190] To address this issue, the processing procedure in this embodiment of the invention extracts the maneuver timing and velocity increments corresponding to each local minimum point as candidate maneuver hypotheses, constructing a parallel multi-hypothesis solution set. Subsequently, as the second, third, and subsequent arc segments arrive, each currently retained candidate maneuver hypothesis performs trajectory prediction and iterative differential correction by assimilating the new arc segment data. The processing procedure performs a horizontal comparability evaluation of each competing hypothesis branch based on adaptive annealing posterior probability. Candidates with continuously low probabilities are eliminated by a double-boundary probability arbitration mechanism, while candidates with consistently dominant probabilities, satisfying physical consistency, and stable residuals are confirmed as maneuver reconstruction results.

[0191] Specifically, taking a near-Earth orbit target at an altitude of approximately 400 km performing an orbital pulse maneuver as an example, the reference TLE epoch before the maneuver is 2025-10-14 18:31:38 UTC, and the delay of the first simulated orbital measurement arc relative to the reference maneuver time is approximately 1.96 hours. The processing program sets the search grid step size to 15 minutes and selects three initial candidate maneuver hypotheses from the search results according to the candidate extraction rules of the cost landscape to enter the subsequent sequential evolution. Through parallel evolution of multiple hypotheses and sequential probability arbitration, the posterior probability of the candidate maneuver hypotheses is greater than 0.88 at the third sparse arc and is greater than the confirmation boundary. In this embodiment, the final output maneuver timing error is -74 seconds, the along-orbit velocity increment estimation error is 1.05%, and the average computation time per execution is approximately 51.2 milliseconds. The reference maneuver parameters used for calculating the maneuver timing error and velocity increment error are obtained from precise ephemeris inversion before and after the maneuver and are not used as reconstruction input.

[0192] Example 3

[0193] In this embodiment of the invention, Sentinel-3A is used as an example target, and the space target undergoes a normal pulse maneuver. The processing program generates multiple normal pulse candidates within a candidate maneuver time window, and the candidate parameters include the maneuver timing. and normal velocity increment .

[0194] Since normal maneuvers primarily cause instantaneous rotation of the orbital plane, observability within a single simulated sparse observation arc segment generated based on precise ephemeris is weak. The cost landscape constructed by its grid search may exhibit irregular morphology and lack a dominant basin, with typical morphologies such as... Figure 2 As shown in (b) in the figure. At this time, multiple candidate solutions with a time difference of about half an orbital period and opposite signs of normal velocity increments will exhibit similar instantaneous fitting residuals, forming a half-cycle geometric aliasing.

[0195] To address this issue, the processing procedure in this embodiment of the invention is based on a dynamic admission quantile threshold. Perform coarse screening and utilize minimum time interval constraints. By filtering out densely overlapping points, sparse sampling is performed across the entire candidate window to extract a multi-maneuver hypothesis candidate set containing semi-periodic geometric mirror points.

[0196] First, candidate maneuver hypotheses that satisfy the half-cycle interval relationship are selected and clustered into an aliasing family. Then, with the sequential assimilation of multiple subsequent orbital arcs, although the instantaneous short-arc residuals of each mirror hypothesis remain close after differential correction, the half-cycle time difference at the assumed orbital change time leads to variations in the branches. The long-term cumulative precession pattern of the right ascension of the ascending node under long-term perturbation diverges. The processing procedure calculates the precession rate changes recovered from each hypothetical branch and evaluates them at a unified evaluation time. The topology consistency cost of each hypothesis is evaluated relative to the entire aliasing family. The processor selects the candidate with the smaller topology consistency cost and the satisfactory residual as the physically consistent solution for the normal pulse maneuver, and marks the other candidates as mirror candidates.

[0197] Specifically, taking a typical remote sensing satellite's normal pulse maneuver as an example, the acquisition delay for the first observation arc is 27.13 hours, and the average interval for subsequent arcs is 11.93 hours. In this embodiment, the processing program extracts a candidate set of mirror images containing half-cycle intervals and filters the normal pulse maneuver branches based on the aforementioned topology consistency discrimination mechanism. The final reconstructed maneuver timing error is -42 seconds, the estimated dominant normal velocity increment is approximately 2.005 m / s, the relative error is 2.11%, and the average computation time for this process is approximately 870.0 milliseconds. The reference maneuver timing and normal velocity increment in this embodiment are determined based on publicly available or obtainable mission maneuver files and are only used to calculate the reconstruction error, not to participate in the reconstruction process.

[0198] Example 4

[0199] In this embodiment of the invention, Starlink-34961 is used as an example target. The space target performs a continuous low-thrust maneuver along its orbit with an unknown duration. The processing program first searches for candidate start times within the maneuver initiation window and represents the thrust effect as an equivalent average rate of change of motion. Each candidate is used for trajectory prediction according to a three-stage propagation pattern: natural propagation before thrust, equivalent propagation during the thrust phase, and natural propagation after thrust. Since adjacent time-time candidates will exhibit kinematic convergence characteristics under continuous thrust, the algorithm implements an early merging strategy during the sequential evolution process, ultimately retaining the assumption of a single continuous thrust candidate maneuver.

[0200] During the stable thrust phase, the processing program establishes a baseline of along-track residuals using several arc segments. If natural trajectory slippage occurs after thrust termination, the position of subsequent arc segments will deviate from the original dynamic envelope. The processing program analyzes the average along-track residuals of the new sparse arc segments. Whether there is a significant deviation from the baseline, and whether the direction of deviation is consistent with the theoretical secondary drift direction after thrust removal, triggers the thrust termination candidate determination and probability arbitration process. The processing program calculates the likelihood weights of the thrust continuation hypothesis and the thrust termination hypothesis, respectively, and obtains the posterior probability of the thrust termination hypothesis. When the posterior probability is greater than the confirmation threshold, a candidate unobserved interval containing the thrust termination time is confirmed, and a trial termination time is introduced within the confirmed candidate unobserved interval. Extract the equivalent residual acceleration and locate the thrust termination time by minimizing the equivalent dynamic cost. Finally, the relevant arc segments are jointly corrected to output an equivalent profile of continuous low-thrust maneuvering.

[0201] Specifically, taking the trans-day continuous orbital lifting maneuver performed by a low-Earth orbit internet constellation satellite as an example, due to the slow accumulation of kinematic characteristics of continuous thrust, the processing program triggers kinematic convergence merging in the early stage of sequential evolution and determines the unique dominant continuous thrust candidate maneuver hypothesis in the third orbital measurement arc. During the natural coasting phase after thrust termination, the average along-track residual in the 11th arc produces a positive drift of approximately +98.74 km. Based on the aforementioned residual parabolic drift determination mechanism, this drift direction is consistent with the theoretical direction, and the posterior probability of the thrust termination hypothesis is greater than 0.99. This confirms the candidate unobserved interval containing the thrust termination time and triggers the termination time positioning process within the candidate unobserved interval. The processing program then performs a binary search positioning, and after joint correction, the thrust start time error is 36 seconds, the termination time error is -35 seconds, and the equivalent thrust acceleration estimation error is 1.92%. The average computation time of this embodiment is approximately 307.9 milliseconds. The reference thrust start time, thrust termination time, and reference thrust effect parameters in this embodiment of the invention are determined based on the long-term orbital changes obtained from precise ephemeris inversion before and after the maneuver, and are used only for implementation effect verification.

[0202] For continuous low-thrust maneuvers, the relative errors in the control quantity reconstruction in Table 1 are expressed as the relative errors in equivalent thrust acceleration obtained from the equivalent average rate of change of motion. All reconstruction errors listed in Table 1 are compared against reference maneuver parameters obtained through precise ephemeris inversion or maneuver files; these reference parameters are not used as inputs to the method of this invention.

[0203] To illustrate the supporting role of the above three embodiments in the beneficial effects of the present invention, Table 1 summarizes the verification results for three example target objects and different maneuver types. ISS, Sentinel-3A, and Starlink-34961 correspond to the verification examples of Embodiments 2, 3, and 4, respectively, and are used to illustrate the implementation effects of the present invention under different orbital targets and different preset maneuver models, and do not constitute a limitation on the applicable objects. The sparse arc delay time in Table 1 represents the time interval from the corresponding reference maneuver time to the start time of the first available sparse arc segment thereafter. For pulse maneuvers, the delay time is calculated from the reference pulse maneuver time; for continuous low-thrust maneuvers, the start delay time is calculated from the reference thrust start time, and the end delay time is calculated from the reference thrust end time.

[0204] Table 1 Summary of Validation Results for the Three Example Targets

[0205]

[0206] The implementation of the various embodiments of the present invention is based on programmed processing through a device with processor functionality. Therefore, in practical engineering, the technical solutions and functions of the various embodiments of the present invention are encapsulated into various modules. Based on this reality, and building upon the above embodiments, the embodiments of the present invention provide a space target maneuvering multi-hypothesis sequential blind reconstruction system, which is used to execute a space target maneuvering multi-hypothesis sequential blind reconstruction method from the above method embodiments.

[0207] The system includes: a first processing module for acquiring the reference double-track elements of a space target and at least one sparse arc segment after the epoch of the reference double-track elements; a second processing module for determining the time interval between the epoch of the reference double-track elements and the start time of the first sparse arc segment as a candidate maneuver time window, and configuring a corresponding preset maneuver model according to a pre-defined maneuver type; a third processing module for fixing each candidate moment within the candidate maneuver time window, estimating maneuver control variables under the preset maneuver model, obtaining conditional residual costs, constructing a cost landscape based on all candidate moments and corresponding conditional residual costs, and extracting multiple candidate maneuver hypotheses based on the cost landscape to form an initial multi-maneuver hypothesis candidate set; and a fourth processing module for processing the initial multi-maneuver hypothesis candidate set or the previous... After sequential screening, each candidate maneuver hypothesis retained undergoes trajectory propagation, observation prediction, and parameter correction to obtain an observation residual vector. The residual cost is then calculated based on this vector and mapped to a normalized posterior probability. The fifth processing module performs sequential probability arbitration based on the normalized posterior probability, confirmation boundary, elimination boundary, and candidate merging condition for each candidate maneuver hypothesis. The confirmation boundary and elimination boundary are set based on the normalized posterior probability. The candidate merging condition is that, after parameter correction, the differences in candidate maneuver timing, candidate maneuver control quantity, and residual cost among different candidate maneuvers are less than corresponding preset thresholds. The sixth processing module, based on the type of the preset maneuver model, discriminates or completes the parameters of the candidate maneuver hypotheses after sequential probability arbitration, obtaining the processing result and outputting the maneuver reconstruction result.

[0208] The space target maneuver multi-hypothesis sequential blind reconstruction system provided in this invention addresses the problems of traditional single-solution reconstruction methods under sparse observation conditions, such as premature locking of false local optima, strong dependence on initial values, and difficulty in handling normal pulse half-cycle aliasing and unknown termination times of continuous low thrust. It provides a space target maneuver multi-hypothesis sequential blind reconstruction method that obtains the reference double-track orbit elements of the space target and the sparse arc segments after the epoch of the reference double-track orbit elements. The pulse maneuver time to be reconstructed or the start time of the continuous low thrust maneuver is located between the epoch of the reference double-track orbit elements and... Between the start time of the first sparse arc segment, an observation residual is constructed; the time interval between the epoch of the reference double-track elements and the start time of the first sparse arc segment is determined as the candidate maneuver time window, and a corresponding preset maneuver model is configured according to the pre-defined maneuver type; the conditional residual cost is calculated to form a cost landscape; multiple candidate maneuver hypotheses are extracted based on the cost landscape to form an initial multi-maneuver hypothesis candidate set; when subsequent sparse arc segments arrive, sequential probabilistic arbitration is performed based on the current residual cost; additional discrimination is performed according to the type of the preset maneuver model; and the maneuver reconstruction result is output. This invention reduces the risk of traditional single-solution methods falling into false local optima too early and improves the adaptability of blind reconstruction under sparse observation conditions by constructing a multi-hypothesis parallel evolution framework to retain multiple candidate branches and using subsequent sparse arc segments for sequential probabilistic arbitration.

[0209] Finally, it should be noted that the above specific embodiments are merely representative examples of the present invention. Obviously, the present invention is not limited to the above specific embodiments and many variations are possible. Any simple modifications, equivalent changes, and alterations made to the above specific embodiments based on the technical essence of the present invention should be considered within the protection scope of the present invention.

Claims

1. A multi-hypothesis sequential blind reconstruction method for space target maneuvering, characterized in that, include: Obtain the reference double orbit elements of the space target and at least one sparse arc segment after the epoch of the reference double orbit elements; The time interval between the epoch of the reference double-track elements and the start time of the first sparse arc segment is determined as the candidate maneuver time window, and the corresponding preset maneuver model is configured according to the preset maneuver type. Each candidate moment within the candidate maneuver time window is fixed, and the maneuver control variables are estimated under a preset maneuver model to obtain the conditional residual cost. A cost landscape is constructed based on all candidate moments and the corresponding conditional residual costs. Multiple candidate maneuver hypotheses are extracted based on the cost landscape to form an initial multi-maneuver hypothesis candidate set. When subsequent sparse arc segments arrive, orbit propagation, observation prediction and parameter correction are performed on the initial multi-maneuver hypothesis candidate set or each candidate maneuver hypothesis retained after screening in the previous sequential stage to obtain the observation residual vector. The residual cost is obtained based on the observation residual vector and mapped to the normalized posterior probability. Sequential probability arbitration is performed based on the normalized posterior probability, confirmation boundary, elimination boundary, and candidate merging condition of each candidate maneuver hypothesis; wherein, the confirmation boundary and elimination boundary are set based on the normalized posterior probability; the candidate merging condition is that, after parameter correction, the differences in candidate maneuver time, candidate maneuver control quantity, and residual cost of different candidate maneuver hypotheses are less than the corresponding preset thresholds. Based on the type of the preset maneuver model, the candidate maneuver assumptions after sequential probability arbitration are discriminated or the parameters are completed to obtain the processing results, and the maneuver reconstruction results are output according to the processing results.

2. The method for sequential blind reconstruction of space target maneuvers based on multiple hypotheses according to claim 1, characterized in that, Configure the corresponding preset maneuver model according to the pre-defined maneuver type, including: When the preset maneuver type is pulse maneuver, configure the pulse maneuver model; When the pre-set maneuver type is continuous low thrust maneuver, configure the continuous low thrust maneuver model.

3. The method for sequential blind reconstruction of space target maneuvers based on multiple hypotheses according to claim 1, characterized in that, The multiple candidate maneuver hypotheses are extracted through at least one of the following methods: For cost landscapes exhibiting a multi-peak structure, all residual local minima and their neighborhoods are extracted as candidate maneuver hypotheses. For cost landscapes exhibiting a single-valley structure, the global minimum of the residual and its adjacent time points are extracted as candidate maneuver hypotheses. For cost landscapes where no significant dominant basin has formed, local minima are dispersed, or the residual costs of multiple candidate points are close, a dynamic admission threshold condition is set, and a minimum time interval constraint is introduced among the candidate points that meet the dynamic admission threshold condition to perform sparse sampling to extract candidate maneuver hypotheses.

4. The method for sequential blind reconstruction of space target maneuvers based on multiple hypotheses according to claim 1, characterized in that, The method includes: if the normalized posterior probability of the current candidate maneuver hypothesis is greater than the confirmation boundary, it is determined to be a dominant candidate maneuver hypothesis and input into a preset maneuver model.

5. The method for sequential blind reconstruction of space target maneuvers based on multiple hypotheses according to claim 1, characterized in that, The method includes: if the normalized posterior probability of the current candidate maneuver hypothesis is lower than the elimination boundary for multiple consecutive sequential stages, and the number of consecutive times it is lower than the elimination boundary is greater than a preset elimination duration, then the candidate maneuver hypothesis is eliminated.

6. The method for sequential blind reconstruction of space target maneuvers based on multiple hypotheses according to claim 1, characterized in that, The method includes: If the normalized posterior probability of the current candidate maneuver hypothesis is in the retention interval, then determine whether it satisfies the candidate merging condition with other candidate maneuver hypotheses: If satisfied, the hypothesis is merged into an equivalent candidate maneuver hypothesis and only the candidate maneuver hypothesis with the highest normalized posterior probability is retained to enter the next sequential stage. If the conditions are not met, the candidate maneuver hypotheses are retained and the process proceeds to the next sequential stage.

7. The method for sequential blind reconstruction of space target maneuvers based on multiple hypotheses according to claim 1, characterized in that, Based on the type of the preset maneuver model, the candidate maneuver hypotheses after sequential probability arbitration are judged or their parameters are completed: For track-based pulse maneuvers, candidate maneuver hypotheses with normalized posterior probabilities greater than the confirmation boundary are identified as dominant candidate maneuver hypotheses. For normal pulse maneuvers, when there are still multiple candidate maneuver hypotheses that are difficult to distinguish based on residual cost alone after sequential probability arbitration, half-cycle aliasing is performed on the candidate maneuver hypotheses, and the physically consistent dominant candidate maneuver hypotheses are determined by calculating the topological consistency cost. For continuous low-thrust maneuvers, after determining the assumption of continuous low-thrust dominant candidate maneuvers, the residual drift along the track in the subsequent sparse arc segment is analyzed to determine and locate the thrust termination time in order to complete the parameters of continuous low-thrust maneuvers.

8. The method for sequential blind reconstruction of space target maneuvers based on multiple hypotheses according to claim 7, characterized in that, For normal pulse maneuvers, half-cycle aliasing is performed on the candidate maneuver hypotheses, and physically consistent dominant candidate maneuver hypotheses are determined by calculating the topological consistency cost, including: Candidate maneuvers whose time differences are set to integer multiples of the orbital period and whose normal velocity increments have alternating signs are clustered into an aliasing family. A topological consistency cost is constructed based on the long-term drift rate change of the ascending node, and the candidate maneuver hypothesis with the minimum topological consistency cost is selected within the aliasing family as the physical consistency preferred candidate maneuver hypothesis.

9. The method for sequential blind reconstruction of space target maneuvers based on multiple hypotheses according to claim 7, characterized in that, Analyze the residual drift along the track in subsequent sparse arc segments to determine and locate the thrust termination time, including: For continuous low-thrust maneuvers, a track residual baseline is established based on the historical sparse arc segments of the stable thrust phase. When the average residual along the track of the new sparse arc segment satisfy When the direction of the average along-track residual is consistent with the theoretical drift direction after thrust removal, the thrust termination candidate determination is triggered; wherein, For the residual baseline along the track, This is a preset threshold coefficient; After triggering the thrust termination candidate determination, the thrust continuation hypothesis and the thrust termination hypothesis are constructed. Based on the average track residual of the current sparse arc segment, a standardized residual is constructed. The likelihood weights of the thrust continuation hypothesis and the thrust termination hypothesis are calculated, and the likelihood weights are normalized to the thrust termination hypothesis probability. When the probability of the thrust termination hypothesis is greater than a preset confirmation threshold, it is determined that the thrust termination occurred in the candidate unobserved interval; when the probability of the thrust termination hypothesis is lower than a preset rejection threshold, the current thrust termination candidate determination is cancelled. When the probability of the thrust termination assumption is between the preset rejection threshold and the preset confirmation threshold, it is included in the subsequent sparse arc segment for delayed confirmation. Once it is determined that the thrust termination occurs in a candidate unobserved interval, a trial termination time is introduced within the candidate unobserved interval. The average along-track residual of the sparse arc segment after the first effective thrust termination located after the candidate unobserved interval is used to calculate the equivalent residual acceleration, and the thrust termination time is estimated by minimizing the equivalent dynamic cost.

10. A multi-hypothesis sequential blind reconstruction system for space target maneuvering, characterized in that, A method for implementing a space target maneuvering multi-hypothesis sequential blind reconstruction method according to any one of claims 1-9 includes: The first processing module is used to obtain the reference double orbit elements of the space target and at least one sparse arc segment after the epoch of the reference double orbit elements. The second processing module is used to determine the time interval between the epoch of the reference double-track elements and the start time of the first sparse arc segment as the candidate maneuver time window, and configure the corresponding preset maneuver model according to the preset maneuver type. The third processing module is used to fix each candidate moment within the candidate maneuver time window, estimate the maneuver control variables under the preset maneuver model, obtain the conditional residual cost, construct a cost landscape based on all candidate moments and the corresponding conditional residual costs, and extract multiple candidate maneuver hypotheses based on the cost landscape to form an initial multi-maneuver hypothesis candidate set. The fourth processing module is used to perform orbit propagation, observation prediction and parameter correction on the initial multi-maneuver hypothesis candidate set or each candidate maneuver hypothesis retained after screening in the previous sequential stage when the subsequent sparse arc segment arrives, to obtain the observation residual vector, and to obtain the residual cost based on the observation residual vector, and to map the residual cost to the normalized posterior probability. The fifth processing module is used to perform sequential probability arbitration based on the normalized posterior probability, confirmation boundary, elimination boundary, and candidate merging condition of each candidate maneuver hypothesis; wherein the confirmation boundary and elimination boundary are set based on the normalized posterior probability; the candidate merging condition is that after parameter correction, the differences in candidate maneuver time, candidate maneuver control quantity, and residual cost of different candidate maneuver hypotheses are less than the corresponding preset thresholds. The sixth processing module is used to discriminate or complete the parameters of the candidate maneuver hypotheses after sequential probability arbitration based on the type of the preset maneuver model, obtain the processing results, and output the maneuver reconstruction results based on the processing results.

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