Trajectory segment reconstruction method and apparatus

Abstract

The application relates to the field of aerospace navigation positioning technology, and provides a trajectory segmentation reconstruction method and device. The trajectory segmentation reconstruction method comprises the following steps: acquiring a discrete sampling trajectory of an aircraft obtained through measurement, and segmenting the discrete sampling trajectory according to maneuvering intensity to obtain at least two discrete flight trajectory segments, wherein the discrete sampling trajectory comprises a plurality of trajectory discrete sampling points; reconstructing an initial trajectory by using the trajectory discrete sampling points in each discrete flight trajectory segment to obtain each initial reconstructed trajectory; and correcting the initial reconstructed trajectory of the discrete flight trajectory segment whose maneuvering intensity meets a preset high maneuvering intensity requirement to obtain a trajectory reconstruction correction result. The trajectory segmentation reconstruction method can improve the accuracy of aircraft trajectory reconstruction on the basis of ensuring the trajectory reconstruction efficiency.

Description

Technical Field

[0001] This application relates to the field of aerospace navigation and positioning technology, specifically to a trajectory segmentation reconstruction method and apparatus. Background Technology

[0002] In aircraft signal simulation and system verification, it is necessary to obtain the parameters of the aircraft's continuous flight trajectory.

[0003] Due to limitations in measurement and control sampling, the ground can only obtain trajectory data at discrete moments. The trajectory within the sampling interval cannot be directly observed. Therefore, it is necessary to reconstruct the trajectory information such as continuous position, velocity, and acceleration through trajectory reconstruction.

[0004] In related technologies, a globally unified interpolation method is commonly used to reconstruct the trajectory across the entire segment. However, since the flight state of an aircraft is constantly changing, it is difficult to balance the accuracy and efficiency of trajectory reconstruction using a globally unified interpolation method. Summary of the Invention

[0005] In view of this, this application aims to propose a trajectory segmentation reconstruction method to improve the accuracy of aircraft trajectory reconstruction while ensuring the efficiency of trajectory reconstruction.

[0006] To achieve the above objectives, the technical solution of this application is implemented as follows: a trajectory segmentation reconstruction method, comprising: acquiring a measured discrete sampled trajectory of an aircraft, and segmenting the discrete sampled trajectory according to maneuver intensity to obtain at least two discrete flight trajectory segments, wherein the discrete sampled trajectory includes multiple discrete trajectory sampling points; using the discrete trajectory sampling points in each of the discrete flight trajectory segments to perform initial trajectory reconstruction to obtain each initial reconstructed trajectory; and correcting the initial reconstructed trajectory of the discrete flight trajectory segment whose maneuver intensity meets a preset high maneuver intensity requirement to obtain a trajectory reconstruction correction result.

[0007] Furthermore, the step of segmenting the discrete sampled trajectory according to maneuver intensity to obtain at least two discrete flight trajectory segments includes: taking two adjacent discrete sampling points of the trajectory as a sampling interval, calculating the maneuver intensity index corresponding to each sampling interval; determining the maneuver intensity corresponding to each sampling interval based on the relative magnitude of the maneuver intensity index corresponding to each sampling interval and a preset maneuver intensity segmentation threshold; and segmenting the discrete sampled trajectory based on the maneuver intensity corresponding to each sampling interval to obtain at least two discrete flight trajectory segments.

[0008] Furthermore, the calculation formula for the mobility intensity index includes:

[0009] ;

[0010] ; ; ;

[0011] ;

[0012] in, The aforementioned mobility strength index, Represents the sampling interval [t] k , t k+1 The dimensionless normalized eigenvalue corresponding to the q-th derivative increment of ] This represents the dimensionless normalized characteristic quantity corresponding to curvature. The weighting coefficients represent the increments of the q-th derivative. Represents the weighting coefficients of the curvature-related terms, where, ; For the increment of the q-th derivative, Represents the L2 norm, For the spacecraft at sampling time t k The trajectory state vector below, Indicates at sampling time t k The lower position, Indicates at sampling time t k The speed of the drop Indicates at sampling time t k The acceleration below, Indicates at sampling time t k The q-th time derivative of B; q Let q be the qth order dynamic capability boundary of the aircraft; The maximum curvature allowed for the aircraft; , To prevent tiny positive numbers with a denominator of 0; This represents the cross product of vectors.

[0013] Furthermore, the step of segmenting the discrete sampling trajectory based on the maneuver intensity corresponding to each sampling interval to obtain at least two discrete flight trajectory segments includes: performing preliminary segmentation of the discrete sampling trajectory according to the maneuver intensity corresponding to each sampling interval to obtain preliminary flight trajectory segments; determining the interval duration of each preliminary flight trajectory segment; and merging any preliminary flight trajectory segment with an adjacent preliminary flight trajectory segment if the interval duration corresponding to any preliminary flight trajectory segment is lower than a preset minimum duration to obtain at least two discrete flight trajectory segments.

[0014] Furthermore, the maneuver intensity includes high maneuver intensity and stable maneuver intensity; wherein, determining the maneuver intensity corresponding to each sampling interval based on the relative magnitude of the maneuver intensity index corresponding to each sampling interval and the preset maneuver intensity segmentation threshold includes: determining the maneuver intensity corresponding to the sampling interval as high maneuver intensity when the maneuver intensity index is greater than the preset maneuver intensity segmentation threshold; and determining the maneuver intensity corresponding to the sampling interval as stable maneuver intensity when the maneuver intensity index is not greater than the preset maneuver intensity segmentation threshold.

[0015] Furthermore, the initial trajectory reconstruction using discrete sampling points in each of the discrete flight trajectory segments to obtain each initial reconstructed trajectory includes: establishing a benchmark local trajectory reconstruction model; using the benchmark local trajectory reconstruction model to solve for the initial reconstructed trajectory corresponding to each of the sampling intervals, with the endpoints of the discrete flight trajectory segments having the same derivative before and after trajectory reconstruction as a constraint.

[0016] Furthermore, the baseline local trajectory reconstruction model includes: ;in, The initial reconstructed trajectory of the i-th discrete flight trajectory segment at time t; are basis functions; Denotes the coefficients of the l-th power basis polynomial;

[0017] The constraints include: ;in, Wherein, L and R represent the two endpoints of the discrete flight trajectory segment, This indicates that the initial reconstructed trajectory of the i-th segmented interval is at the start time T of the segmented interval. i The value of the q-th derivative at point , This indicates that the initial reconstructed trajectory of the i-th segmented interval is at the termination time T of the segmented interval. i+1 The value of the q-th derivative at point , Let T be the starting time of the i-th segmented interval. i The observed value of the qth order boundary derivative of the discrete sampling trajectory at the corresponding location; Let T be the termination time of the i-th segmented interval. i+1 The observed value of the qth order boundary derivative of the discrete sampling trajectory at the corresponding location.

[0018] Furthermore, the correction of the initial reconstructed trajectory of the discrete flight trajectory segment whose maneuverability meets the preset high maneuverability requirement includes: for the discrete flight trajectory segment whose maneuverability meets the preset high maneuverability requirement, setting a preset number of virtual nodes in the segmented interval corresponding to the discrete flight trajectory segment; establishing a trajectory correction model with the goal of minimizing the fitting residual and the constraint that the derivatives of the endpoints of the segmented interval are consistent before and after correction; and solving the virtual node trajectory parameters corresponding to each virtual node in the segmented interval based on the trajectory correction model to obtain the corrected reconstructed trajectory.

[0019] Furthermore, the trajectory correction model includes: ;in, ; For the i-th segment interval [T] i ,T i+1 Energy cost of the q-th derivative within the inner quadrant; For fitting residual penalty term The weighting coefficients, For the i-th segment interval [T] i ,T i+1 Energy cost of the q-th derivative The weighting coefficients, and The sum is 1;

[0020] in, ; ; This is the set of state parameters to be estimated for all virtual nodes. Let represent the local modified basis function matrix corresponding to the j-th virtual node; where ; This represents the q-th derivative of the modified basis function with respect to time. , and These are the maximum permissible limits for the aircraft's speed, acceleration, and other higher-order parameters.

[0021] Compared to related technologies, this application has at least the following advantages: The trajectory segmentation reconstruction method of this application first segments the discrete sampled trajectory according to the maneuver intensity of the aircraft. Then, during trajectory reconstruction, an initial trajectory reconstruction is performed first. After obtaining the initial reconstructed trajectory, the discrete flight trajectory segments whose maneuver intensity meets the preset high maneuver intensity requirements are then corrected. In this way, for discrete flight trajectory segments that do not belong to high maneuver intensity, a unified initial trajectory reconstruction method can be directly used for trajectory reconstruction. For discrete flight trajectory segments that belong to high maneuver intensity, correction is performed separately after the initial trajectory reconstruction. This improves the trajectory reconstruction accuracy of high maneuver intensity flight segments without increasing the trajectory reconstruction complexity of stable maneuver intensity flight segments.

[0022] Another objective of this application is to provide a trajectory segmentation and reconstruction device, comprising: a trajectory segmentation module, used to acquire the measured discrete sampled trajectory of an aircraft, and segment the discrete sampled trajectory according to the maneuver intensity to obtain at least two discrete flight trajectory segments, wherein the discrete sampled trajectory includes multiple discrete trajectory sampling points; an initial reconstruction module, used to perform initial trajectory reconstruction using the discrete trajectory sampling points in each of the discrete flight trajectory segments to obtain each initial reconstructed trajectory; and a trajectory correction module, used to correct the initial reconstructed trajectory of the discrete flight trajectory segment whose maneuver intensity meets a preset high maneuver intensity requirement to obtain a trajectory reconstruction correction result.

[0023] The trajectory segment reconstruction device described in this application can directly reconstruct the trajectory using a unified initial trajectory reconstruction method for discrete flight trajectory segments that do not meet the preset high maneuverability requirements (i.e., discrete flight trajectory segments that do not belong to high maneuverability). For discrete flight trajectory segments that meet the preset high maneuverability requirements (i.e., discrete flight trajectory segments that belong to high maneuverability), a separate correction is performed after the initial trajectory reconstruction. In this way, the trajectory reconstruction accuracy of high maneuverability flight segments can be improved without increasing the trajectory reconstruction complexity of stable maneuverability flight segments. Attached Figure Description

[0024] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings:

[0025] Figure 1 This is a flowchart illustrating the trajectory segmentation reconstruction method described in an embodiment of this application.

[0026] Figure 2 This is a schematic diagram of the process for correcting the initial reconstructed trajectory in the trajectory segmentation reconstruction method described in the embodiments of this application.

[0027] Figure 3This is a schematic diagram of the overall process of the trajectory segmentation reconstruction method described in the embodiments of this application.

[0028] Figure 4 This is a schematic diagram of the trajectory segmentation reconstruction device described in the embodiments of this application.

[0029] Explanation of reference numerals in the attached diagram: 410, trajectory segmentation module; 420, initial reconstruction module; 430, trajectory correction module. Detailed Implementation

[0030] To make the technical solution and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0031] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other.

[0032] Furthermore, it should be noted that in the description of this application, if terms such as "upper," "lower," "inner," or "outer" appear, indicating orientation or positional relationship, these are based on the orientation or positional relationship shown in the accompanying drawings and are only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation on this application. In addition, if terms such as "first" or "second" appear, they are also used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0033] Furthermore, in the description of this application, unless otherwise expressly defined, the terms "installation," "connection," "joining," and "connector" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection between two components. Those skilled in the art can understand the specific meaning of the above terms in this application in light of the specific circumstances.

[0034] In this application, the terms "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., refer to a specific feature, structure, material, or characteristic described in connection with that embodiment or example, which is included in at least one embodiment or example of this application. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0035] The present application will now be described in detail through exemplary embodiments. However, it should be understood that, without further description, elements, structures, and features in one embodiment may be advantageously incorporated into other embodiments.

[0036] An embodiment of the first aspect of this application provides a trajectory segmentation reconstruction method. First, the discrete sampled trajectory is segmented according to the aircraft's maneuvering intensity. Then, during trajectory reconstruction, an initial trajectory reconstruction is performed first. After obtaining the initial reconstructed trajectory, the discrete flight trajectory segments with high maneuvering intensity (also known as strong maneuvering intensity) are further corrected. Thus, for discrete flight trajectory segments that do not belong to high maneuvering intensity, trajectory reconstruction can be performed directly using a unified initial trajectory reconstruction method. For discrete flight trajectory segments belonging to high maneuvering intensity, correction is performed separately after the initial trajectory reconstruction. This improves the trajectory reconstruction accuracy of high maneuvering intensity flight segments without increasing the complexity of trajectory reconstruction for stable maneuvering intensity flight segments.

[0037] In related technologies, signal simulation and system performance verification tasks for spacecraft, launch vehicles, and airborne platforms require obtaining flight trajectory information such as position, velocity, and acceleration of the spacecraft over continuous time. However, actual measurement systems can usually only obtain trajectory sampling results at discrete moments (i.e., flight trajectory information at discrete moments), such as measuring the position, velocity, and acceleration of the spacecraft at each discrete moment.

[0038] The flight trajectory information between these discrete moments cannot be actually measured. In other words, the real flight trajectory between discrete moments is in an unobservable state. Therefore, in order to obtain the flight trajectory information of the aircraft in continuous time, it is necessary to reconstruct the trajectory based on the trajectory sampling results of each discrete moment.

[0039] Trajectory reconstruction refers to the process of reconstructing flight trajectory information, such as position, velocity, acceleration, and attitude, at any consecutive time points between sampling moments, by using discrete observation sampling points as constraints and combining them with the aircraft's dynamic motion model.

[0040] Currently, most trajectory reconstruction methods in related technologies adopt a unified reconstruction approach. For example, a unified reconstruction model (such as using low-order polynomial interpolation or B-spline interpolation) is used to reconstruct the flight trajectory information at each discrete time point.

[0041] However, for aircraft, the trajectory of an aircraft has time-varying characteristics. For example, it exhibits stable flight in some discrete periods, while it exhibits high-maneuver flight such as significant acceleration and turning in other discrete periods.

[0042] If a unified reconstruction model is used for flight trajectory information at all discrete moments in accordance with the methods in related technologies, on the one hand, in order to meet the accuracy requirements of trajectory reconstruction during high maneuvers, the reconstruction model needs to adopt a high-precision reconstruction model, which will result in higher computational complexity for the trajectory reconstruction process during stable flight periods; on the other hand, if the computational complexity of trajectory reconstruction during stable flight periods is reduced, the accuracy of the reconstruction model will be weaker, and the reconstructed trajectory during high maneuver periods will produce larger errors.

[0043] In view of this, in order to overcome the shortcomings of related technologies, the trajectory segmentation reconstruction method in this embodiment combines... Figure 1 In terms of overall design, it includes the following steps S110-S130.

[0044] Step S110: Obtain the measured discrete sampling trajectory of the aircraft, and divide the discrete sampling trajectory into segments according to the maneuver intensity to obtain at least two discrete flight trajectory segments.

[0045] The discrete sampling trajectory includes multiple discrete sampling points, each corresponding to a sampling time. The discrete sampling point includes the flight trajectory information of the aircraft at that sampling time (equivalent to the trajectory state of the aircraft), such as the three-dimensional position of the aircraft, the velocity of the aircraft, and the acceleration of the aircraft.

[0046] Specifically, the flight trajectory information of the aircraft corresponding to the discrete sampling points of the trajectory can be represented by a trajectory state vector.

[0047] More specifically, assuming the spacecraft is at sampling time t k The trajectory state vector below is ,in Representing three-dimensional position, Indicates speed, Indicates acceleration. Let q represent the q-th time derivative.

[0048] For adjacent sampling times, such as t k t k+1 Define the normalized continuous-time variable within this sampling interval. .

[0049] The trajectory reconstruction objective is: based on the trajectory state vector at different sampling times... Output the trajectory state estimation results for any continuous time period. The continuous time trajectory state estimation results This is the result of trajectory reconstruction and correction.

[0050] More specifically, given the discrete sampled trajectory of the aircraft, the different flight states of the aircraft (i.e., the maneuver intensity of the aircraft) are first identified based on the discrete sampled trajectory, and then the discrete sampled trajectory is segmented according to the maneuver intensity of the aircraft.

[0051] Among them, maneuver intensity is used to characterize the degree of drastic change in the motion state of an aircraft within adjacent sampling intervals.

[0052] In this embodiment, the maneuver intensity can include high maneuver intensity and steady maneuver intensity. When the aircraft's speed, acceleration, and higher-order dynamic parameters change significantly, the trajectory exhibits significant nonlinear changes, the motion attitude and displacement change rapidly within a short period, and the overall motion dynamics within the interval are turbulent, it indicates that the aircraft is in the flight period corresponding to high maneuver intensity.

[0053] When the aircraft's speed, acceleration, and higher-order dynamic parameters change gradually, its motion state is approximately uniform or changes gradually, its trajectory is smooth and continuous without drastic changes, and its overall dynamic characteristics are stable within a given interval, it indicates that the aircraft is in a flight period corresponding to a stable maneuver intensity.

[0054] When segmenting the discrete sampled trajectory, the process can be as follows: The interval between two adjacent sampling times is considered as one sampling interval. Starting from the sampling interval between the first and second sampling times (i.e., the first sampling interval), the maneuver intensity corresponding to each sampling interval is determined sequentially. During the traversal, if the maneuver intensity of the next sampling interval is the same as that of the current sampling interval, the next sampling interval is merged with the current sampling interval into the same discrete flight trajectory segment. If the maneuver intensity changes, the merging of the current trajectory segment is terminated, and the next sampling interval is used as the starting point for a new discrete flight trajectory segment to continue segmenting until all sampling intervals have been processed, resulting in discrete flight trajectory segments with high maneuver intensity and discrete flight trajectory segments with stable maneuver intensity.

[0055] More specifically, in some embodiments, step S110, segmenting the discrete sampled trajectory according to maneuver intensity to obtain at least two discrete flight trajectory segments, may specifically include: taking two adjacent discrete sampled points of the trajectory as a sampling interval, calculating the maneuver intensity index corresponding to each sampling interval; determining the maneuver intensity corresponding to each sampling interval based on the relative magnitude of the maneuver intensity index corresponding to each sampling interval and a preset maneuver intensity segmentation threshold; and segmenting the discrete sampled trajectory based on the maneuver intensity corresponding to each sampling interval to obtain at least two discrete flight trajectory segments.

[0056] Among them, the maneuver intensity index is a set index used to measure the maneuver intensity of the aircraft corresponding to each sampling interval. It is used to determine the maneuver intensity corresponding to each sampling interval based on the relative size of the maneuver intensity index and the preset maneuver intensity segmentation threshold, so as to facilitate the subsequent segmentation of the discrete sampling trajectory.

[0057] Specifically, the maneuver intensity corresponding to each sampling interval is determined based on the relative magnitude of the maneuver intensity index corresponding to each sampling interval and the preset maneuver intensity segmentation threshold. This includes: if the maneuver intensity index is greater than the preset maneuver intensity segmentation threshold, the maneuver intensity corresponding to the sampling interval is determined to be high maneuver intensity; if the maneuver intensity index is not greater than the preset maneuver intensity segmentation threshold, the maneuver intensity corresponding to the sampling interval is determined to be stable maneuver intensity.

[0058] For example, the time interval between the first and second sampling times is taken as the first sampling interval. The maneuver intensity index of the first sampling interval is calculated. If the maneuver intensity index is greater than the preset maneuver intensity segmentation threshold, the maneuver intensity corresponding to the first sampling interval is determined to be high maneuver intensity. Conversely, if it is not greater than the preset maneuver intensity segmentation threshold, the maneuver intensity corresponding to the first sampling interval is determined to be steady maneuver intensity.

[0059] Then, the maneuver intensity index corresponding to the sampling interval (second sampling interval) between the second and third sampling times is calculated, and its corresponding maneuver intensity is determined in the same way as the first sampling interval. This is used as an example to determine the maneuver intensity index and maneuver intensity of the next sampling interval, until the maneuver intensity index of the last sampling interval is determined, and the maneuver intensity corresponding to the last sampling interval is determined accordingly.

[0060] Specifically, the determination of this maneuver intensity index can be achieved by constructing the maneuver intensity index based on the derivative increment corresponding to the sampling interval. This is used to measure the dynamic increments of each order in the flight trajectory information within the sampling interval, as well as the instantaneous trajectory turning intensity of the aircraft, in order to determine whether the aircraft is in steady motion or high-maneuvering motion within the sampling interval.

[0061] More specifically, in some embodiments, the sampling time t k With sampling time t k+1 Taking the sampling interval between [t] as an example, this sampling interval [t] is used for explanation. k , t k+1 The calculation process for the mobility strength index is as follows:

[0062] First, for the sampling interval [t] k , t k+1 Define its q-th order derivative increment. Formula 1 is given below. In Formula 1, q is an integer between 0 and m, representing the order of the input discrete sampling trajectory. For example, if each discrete sampling point in the discrete sampling trajectory includes the corresponding aircraft's position, velocity, and acceleration, then q can take values ​​of 0, 1, and 2. When q is 0, This represents the increment of the 0th derivative, i.e., the increment of the derivative corresponding to the position; when q is 1, This represents the increment of the first derivative, i.e., the increment of the derivative corresponding to the velocity; when q is 2, This represents the increment of the second derivative, that is, the increment of the derivative corresponding to the acceleration.

[0063] (Formula 1).

[0064] Based on the increment of the qth derivative Construct a maneuvering strength index that considers the increment of multi-order trajectory state derivatives and flight curvature. Considering the significant changes in position, velocity, acceleration, and higher-order dynamic quantities of a highly maneuverable flight trajectory at adjacent sampling times, and the corresponding changes in trajectory curvature, a maneuver intensity index is constructed based on the multi-order derivative increments of the flight trajectory and its curvature (corresponding curvature term). The multi-order derivative increments characterize the intensity of dynamic abrupt changes in the trajectory state within the discrete sampling interval, while the curvature term characterizes the intensity of the flight trajectory's turning maneuvers. Together, they describe the degree of maneuverability of the flight trajectory within the current sampling interval from the perspectives of tangential dynamic changes and normal geometric changes.

[0065] To avoid numerical instability in the maneuverability index caused by inconsistent dimensions and large differences in numerical scales of the incremental terms and curvature terms of different orders, this embodiment first performs dimensionless normalization on the trajectory state feature terms (such as position, velocity, acceleration, etc.) before constructing the maneuverability index. Furthermore, based on the significance of each feature term and the corresponding dynamic capability boundary of the aircraft, the weighting coefficients of the incremental terms and curvature terms of each order are adaptively set. Specifically, the maneuverability calculation formula is shown in Formula 2 below.

[0066] (Formula 2)

[0067] in, Represents the sampling interval [t] k , t k+1 The dimensionless normalized feature quantity corresponding to the q-th derivative increment of the two discrete sampling points of the trajectory. Represents curvature (for the sampling interval [t]). k , t k+1 The dimensionless normalized characteristic quantity corresponding to the curvature of this trajectory segment. The weighting coefficients represent the increments of the q-th derivative. This represents the weighting coefficient of the curvature-related terms.

[0068] The dimensionless normalized eigenvalue corresponding to the increment of the q-th derivative is defined as: .

[0069] Among them, B q Let B be the q-th order dynamic capability boundary of the aircraft. For example, if the first-order parameter is velocity and the second-order parameter is acceleration, and q=1, then B... q This represents the maximum permissible speed limit for an aircraft; if q=2, then B... q This indicates the maximum permissible limit for acceleration. To prevent tiny positive numbers with a denominator of 0.

[0070] The dimensionless normalized characteristic of curvature is defined as follows: .

[0071] in This is the maximum curvature allowed for the aircraft. To prevent tiny positive numbers with a denominator of 0.

[0072] The weighting coefficients reflect the contribution of each normalized feature and satisfy the following constraints: .

[0073] Considering that the higher the order of the trajectory derivative increment, the greater the noise, the stronger the sensitivity, and the smaller the weight should be, the weight coefficients of the q-th order derivative increment and the feature term corresponding to curvature are set as follows: .

[0074] in Indicates the first The increment of the first derivative corresponds to the standard deviation of the feature term in the entire flight trajectory sample (i.e., the entire discrete flight trajectory), and is a statistical scale parameter characterizing the feature. This represents the standard deviation of the curvature term, corresponding to the standard deviation of the characteristic term across the entire flight trajectory sample.

[0075] Based on Formula 1 and Formula 2, the sampling interval [t] can be calculated. k , t k+1 Corresponding mobility intensity index Then, based on the sampling interval [t], k , t k+1 Corresponding mobility intensity index Compared with the preset maneuver intensity segment threshold (in this embodiment, it is...) The sampling interval [t] is determined by comparing the two values. k , t k+1 The corresponding mobility intensity.

[0076] It is worth noting that in this embodiment, the preset maneuver intensity segment threshold can be set independently based on the aircraft's maximum dynamic range and flight trajectory type. Specifically, it can be determined by combining theoretical boundaries and simulation / actual calibration, based on the aircraft's maximum maneuverability (i.e., the maximum dynamic range) and the sensitivity of reconstruction error to maneuver intensity, while ensuring that the smooth maneuver segment is not overly subdivided and the high-maneuver segment is not missed. This will not be elaborated upon here.

[0077] It is also worth noting that in this embodiment, after segmenting the discrete sampling trajectory in the manner described in the above embodiment, the discrete flight trajectory segments after the initial segmentation can be merged into short-term segments to perform minimum duration length constraint processing and obtain the final discrete flight trajectory segments.

[0078] That is, based on the maneuver intensity corresponding to each sampling interval, the discrete sampling trajectory is segmented to obtain at least two discrete flight trajectory segments. Specifically, this may include: performing preliminary segmentation of the discrete sampling trajectory according to the maneuver intensity corresponding to each sampling interval to obtain preliminary flight trajectory segments; then determining the interval duration of each preliminary flight trajectory segment, and merging any preliminary flight trajectory segment with the adjacent preliminary flight trajectory segment if the interval duration corresponding to any preliminary flight trajectory segment is lower than the preset minimum duration to obtain at least two discrete flight trajectory segments.

[0079] Among them, the adjacent preliminary flight trajectory segment is the trajectory segment adjacent to the preliminary flight trajectory segment whose interval duration is less than the preset minimum duration (for ease of description, it is referred to as the target preliminary flight trajectory segment).

[0080] It is worth noting that if the initial flight trajectory segment of the target corresponds to only one adjacent initial flight trajectory segment (for example, its preceding / following initial flight trajectory segment), then the adjacent initial flight trajectory segment is the preceding / following initial flight trajectory segment of the target's initial flight trajectory segment.

[0081] If the target's initial flight trajectory segment is preceded by an adjacent previous initial flight trajectory segment and followed by an adjacent subsequent initial flight trajectory segment, then the adjacent initial flight trajectory segment can be the one with the shorter duration between the preceding and subsequent initial flight trajectory segments, or either one of them, or it can be the initial flight trajectory segment whose maneuverability index is closer to the maneuverability index corresponding to the target's initial flight trajectory segment among these two adjacent initial flight trajectory segments, without any limitation here.

[0082] It is also worth noting that if the interval duration corresponding to a certain preliminary flight trajectory segment is not less than the preset minimum duration, then it is not necessary to merge the preliminary flight trajectory segment with the adjacent preliminary flight trajectory segments, but to treat it as a separate discrete flight trajectory segment.

[0083] This approach avoids isolated misjudgments that could lead to segment jitter. Specifically, it suppresses spurious short-duration trajectory segments caused by discrete sampling noise and single-point anomalous observations, preventing frequent alternations and chaotic jitter in the segmentation results, and ensuring smooth and stable trajectory segment boundaries and consistent segment types. Furthermore, since an aircraft in real continuous flight will not immediately transition from a stable state to a high-maneuver state and then back to a stable state, this short-duration segmentation and merging of the initially divided trajectory segments, applying a minimum duration constraint, makes the final trajectory segmentation results more reasonable, ensuring that the final discrete flight trajectory segments better reflect the aircraft's real, stable, and continuously changing high-maneuver conditions.

[0084] Thus, in step S110, after segmenting the discrete sampled trajectory according to the maneuver intensity to obtain at least two discrete flight trajectory segments, the following steps S120 and S130 can be executed to perform trajectory reconstruction processing for each discrete flight trajectory segment respectively.

[0085] Step S120: Using the discrete sampling points of each discrete flight trajectory segment, perform initial trajectory reconstruction to obtain each initial reconstructed trajectory.

[0086] Specifically, in this embodiment, each discrete flight trajectory segment obtained in step S110 corresponds to a segmented interval, for example, the segmented interval [T i ,T i+1 ] Corresponding to the i-th discrete flight trajectory segment after partitioning, T i T represents the starting time of the i-th segment interval. i+1 This represents the termination time of the i-th segment interval. Wherein, this segment interval [T]... i ,T i+1 The corresponding local trajectory reconstruction time is H. i =T i+1 -T i .

[0087] Let the segmented interval [T] be... i ,T i+1 The trajectory vector at any given moment (a vector composed of flight trajectory information at any given moment) is: In this embodiment, initial trajectory reconstruction of the discrete flight trajectory segment of any segmented interval means calculating the flight trajectory information at any time within that segmented interval (i.e., obtaining the trajectory vector at that any time). That is, solving for the trajectory vector. The expression is equivalent to solving for the flight trajectory information at any time within the segmented interval, thus equivalent to obtaining the segmented interval [T]. i ,T i+1 The corresponding initial reconstructed trajectory.

[0088] in, The trajectory vector at time t is composed of the aircraft's position, velocity, acceleration, and other flight trajectory information at time t. Position is the 0th-order component, velocity is the 1st-order component, acceleration is the 2nd-order component, and so on.

[0089] In some embodiments, step S120, using the discrete sampling points of the trajectory in each discrete flight trajectory segment to perform initial trajectory reconstruction and obtain each initial reconstructed trajectory may specifically include: establishing a benchmark local trajectory reconstruction model; using the constraint that the endpoints of the discrete flight trajectory segment have the same derivative before and after trajectory reconstruction, and using the benchmark local trajectory reconstruction model to solve for the initial reconstructed trajectory corresponding to each sampling interval.

[0090] Specifically, in order to solve for this trajectory vector In this embodiment, the segmented interval [T] is defined. i ,T i+1 The corresponding local normalized time variable .

[0091] Suppose that the start and end times of this segmented interval can be used up to Boundary conditions for the first derivative, where This indicates the order of the local boundary constraints used in the i-th segment interval (the start and end times of each segment interval have discrete trajectory sampling points, and these discrete trajectory points have position, velocity, etc.). Third-order dynamic information, for example, assuming that the flight trajectory information corresponding to the discrete sampling point of the trajectory only includes position, velocity, and acceleration, the discrete sampling point of the trajectory corresponds to third-order dynamic information, with the third order being position, velocity, and acceleration respectively. The starting point and ending point boundaries are defined by the following formula three.

[0092] (Formula 3).

[0093] In Formula 3 above, the subscripts L and R represent the left endpoints (i.e., T) of the segmented interval. i The corresponding time) and the right endpoint (i.e., T) i+1 (corresponding time). In Formula 3, q ​​takes the value 0- The positive integers between 0 and 1 represent the trajectory order after reconstruction of the baseline local trajectory. Generally, It is equal to m (the order of the discrete sampling trajectory of the input). Wherein, in Formula 3... Let represent the trajectory vector at time t. T represents i The q-th order component in the trajectory vector at time t, for example, s represents the position, velocity, acceleration, etc. at time t. (1) (t) represents the velocity at time t, s (2) (t) is the acceleration at time t.

[0094] Formula 3 represents the trajectory vector corresponding to the i-th sampling interval (i-th discrete flight trajectory segment) obtained from the initial reconstruction. The trajectory vector corresponding to its left endpoint is the trajectory vector of the corresponding discrete sampling point of the trajectory input before reconstruction. The trajectory vector corresponding to its right endpoint is the trajectory vector of the corresponding discrete sampling point of the trajectory input before reconstruction, thus ensuring that the trajectory vector of the starting point (or ending point) of the segmented interval remains consistent before and after reconstruction.

[0095] It is worth noting that not only must the trajectory vectors of the starting (or ending) points of the segmented interval remain consistent before and after reconstruction, but the two endpoints of the segmented interval must also satisfy the derivative consistency condition. That is, the constraint condition includes: the derivatives of the endpoints of the discrete flight trajectory segment before and after trajectory reconstruction are consistent. Specifically, this constraint condition includes the following formula four.

[0096] (Formula 4).

[0097] in, This represents the initial reconstructed trajectory of the i-th segmented interval (the reconstructed trajectory obtained after initial trajectory reconstruction using the reference local trajectory reconstruction model) at the start time T of the interval. i The value of the q-th derivative at point ; This indicates that the initial reconstructed trajectory of the i-th segmented interval is at the interval termination time T. i+1 The value of the q-th derivative at point , Let T be the starting time of the i-th segmented interval. i The observed value of the q-th boundary derivative of the discrete sampling trajectory at that point (equivalent to the initial time T in the discrete sampling trajectory). i The q-th derivative corresponding to the discrete sampling points of the trajectory). Let T be the termination time of the i-th segmented interval. i+1 The observed value of the qth order boundary derivative of the discrete sampling trajectory at the corresponding location.

[0098] By combining Equation 3 and Equation 4, we can obtain the constraints used in the initial trajectory reconstruction in step S120.

[0099] To reconstruct the initial trajectory, a baseline local trajectory reconstruction model needs to be used for solving. In this embodiment, within the segmented interval [T]... i ,T i+1 Construct a 2n i +1 order baseline local trajectory reconstruction model.

[0100] Specifically, the baseline local trajectory reconstruction model includes the following formula five.

[0101] (Formula 5).

[0102] in, Let be the initial reconstructed trajectory (i.e., the trajectory vector mentioned above) of the i-th discrete flight trajectory segment at time t. Formula 5 uses... Construct a baseline local power basis polynomial for the independent variable. This represents the coefficients of the l-th power basis polynomial. l represents the order of the index, taking values ​​from 0 to 2n. i +1. It should be noted that the power basis in Formula 5... It can be replaced by other equivalent families of local basis functions, such as Chebyshev polynomial bases, closely related polynomial bases, or other polynomial bases. In this embodiment, the locally normalized time variable in Formula 5... This will be illustrated using a basis function as an example.

[0103] Thus, by combining Equations 4 and 5, and substituting the polynomial of the reconstructed local trajectory into the derivative consistency condition, a system of linear equations is established. ,in, This represents the coefficient matrix generated by the boundary derivative conditions. This represents the vector of coefficients of the polynomial to be determined. This represents the observation vector defined by the derivative boundaries at the left and right endpoints. It is solved using Equation 5. The initial trajectory reconstruction results of each trajectory component in the i-th segment interval are obtained respectively (where the discrete flight trajectory segment is a three-dimensional trajectory, which is composed of trajectory components in three directions: x, y, and z. x and y are along the horizontal plane, and z is the vertical direction perpendicular to the horizontal plane. The initial trajectory reconstruction of the trajectory component in the x direction, the trajectory component in the y direction, and the trajectory component in the z direction are performed respectively using Formula 5 to obtain the initial trajectory reconstruction results of the three trajectory components respectively). Then, the initial trajectory reconstruction results of each trajectory component are spliced ​​together to obtain the initial trajectory reconstruction result of any continuous time in the i-th segment interval. This means obtaining the initial reconstructed trajectory.

[0104] It is worth noting that any continuous and differentiable function can be represented by a polynomial. In this embodiment, within each segmented interval, a (2n) polynomial is constructed using a normalized time basis function expansion. i +1) order local polynomial (i.e., Formula 5 above, the baseline local trajectory reconstruction model), and using the positions of the left and right endpoints of the interval up to n i The boundary conditions of the first derivative establish a set of coefficient constraint equations (that is, the constraint conditions composed of Formula 3 and Formula 4 above). Since the number of polynomial coefficients matches the number of boundary constraints, the coefficients of each term can be uniquely obtained, and thus the initial trajectory reconstruction result at any time in the segmented interval can be obtained, that is, the initial reconstructed trajectory in the segmented interval can be obtained.

[0105] After calculating the initial reconstructed trajectory for each discrete flight trajectory segment in step S120, this method of trajectory reconstruction using a reference trajectory reconstruction model has good trajectory reconstruction accuracy for the stable flight period of the aircraft. However, for the period when the aircraft is in high-maneuver flight, the obtained initial reconstructed trajectory will deviate significantly from the actual situation of the aircraft, resulting in lower trajectory reconstruction accuracy. Therefore, after obtaining each initial reconstructed trajectory in step S120, step S130 is also required to correct the initial reconstructed trajectory of the discrete flight trajectory segment with high maneuver intensity.

[0106] Step S130: Correct the initial reconstructed trajectory of the discrete flight trajectory segment that meets the preset high maneuverability requirements to obtain the trajectory reconstruction correction result.

[0107] The preset high maneuverability requirement refers to a maneuverability level that is considered high. In other words, the maneuverability index corresponding to a discrete flight trajectory segment is greater than the preset maneuverability threshold. Discrete flight trajectory segments that do not meet the preset high maneuverability requirement are not considered high maneuverability discrete flight trajectory segments, such as the discrete flight trajectory segments corresponding to the aforementioned steady maneuverability level.

[0108] In some embodiments, refer to Figure 2 In step S130, the initial reconstructed trajectory of the discrete flight trajectory segment that meets the preset high maneuverability requirements is corrected, which may specifically include the following steps S131-S133.

[0109] Step S131: For discrete flight trajectory segments with high maneuverability, set a preset number of virtual nodes in the segmented intervals corresponding to the discrete flight trajectory segments.

[0110] Specifically, using segmented intervals [T] i ,T i+1 For example (assuming this segmented interval corresponds to high maneuver intensity), in this segmented interval [T] i ,T i+1 [M is set inside]i There are 10 virtual nodes. The number of virtual nodes (i.e., the preset number) can be set according to the length of the segment interval. The longer the interval, the more virtual nodes are set. The number of virtual nodes can also be set according to the maneuver intensity index of the discrete flight trajectory segment corresponding to the segment interval. The higher the maneuver intensity index, the more virtual nodes are set.

[0111] Define the normalized position of the j-th virtual node within this segmented interval as: ,in This indicates that the j-th virtual node within the segmented interval is relative to the left endpoint (T) of the segmented interval. i The normalized time position of ) satisfies Furthermore, the actual time corresponding to the j-th virtual node is .in, In this context, K represents an integer, meaning that j can take values ​​from 1 to M (the preset number).

[0112] Furthermore, the state parameters of the trajectory to be estimated (also called the trajectory vector to be estimated) at the j-th virtual node are defined as follows: The trajectory state parameters at the j-th virtual node calculated by step S120 above (i.e., the trajectory vector at the j-th virtual node position obtained from the initial trajectory reconstruction) are as follows: Then the corrected offset corresponding to the j-th virtual node is: .

[0113] Step S132: With the goal of minimizing the fitting residuals and the constraint that the derivatives of the endpoints of the segmented intervals are consistent before and after the correction, a trajectory correction model is established.

[0114] Specifically, to prevent the virtual nodes from deviating significantly from the initial trajectory reconstruction result in step S120, which could lead to significant oscillations in the corrected reconstructed trajectory, a minimum fitting residual penalty (i.e., minimizing the sum of squared fitting residuals) is introduced in step S132. To fit the residual penalty term, this The calculation formula is shown in Formula Six below.

[0115] (Formula 6).

[0116] in, It is a symmetric positive definite weight matrix used to adjust the penalty intensity of different state parameters of virtual nodes (state parameters such as position, velocity, acceleration and other flight trajectory information).

[0117] Next, the set of estimated state parameters for all virtual nodes is defined, which is the set of estimated trajectory vectors corresponding to each virtual node. Suppose that after correction by virtual nodes, in the segmented interval [T] i ,T i+1 The corrected trajectory on ] is The corrected trajectory The formula is shown in Equation 7 below.

[0118] (Formula 7).

[0119] in, This represents the local correction basis function matrix corresponding to the j-th virtual node, used to map discrete state offsets to continuous-time trajectory corrections. The correction offset for each virtual node... As a correction coefficient, multiply by the local correction basis function matrix corresponding to the virtual node. Then, the contributions of all virtual nodes are linearly superimposed, so that at any given time... Continuous trajectory correction values ​​are generated, and thus the corrected trajectory is obtained. The formula is also known as Formula Seven above.

[0120] Wherein, the local modified basis function matrix B-spline functions or Bernstein polynomials with local support can be selected. These basis functions are superior to those used in the aforementioned baseline local trajectory reconstruction model. (Using basis functions such as closely spaced polynomials and Chebyshev polynomials), it is more sensitive to the instantaneous maneuvering changes of the aircraft (such as pulse maneuvers and non-standard maneuvers), and can quickly capture and fit the local features of the flight trajectory. Therefore, by using Formula 7 to perform initial trajectory reconstruction correction on discrete flight trajectory segments with high maneuvering intensity, the trajectory reconstruction accuracy under high maneuvering periods can be improved.

[0121] It is worth noting that in this embodiment, only the trajectory vectors of each virtual node within the segmented interval are corrected; the flight trajectory information at the boundaries (i.e., the left and right endpoints) of the segmented interval is not corrected. Therefore, the local correction basis function matrix in Formula 7... The boundary disappearance condition shown in Formula 8 below should be satisfied.

[0122] (Formula 8).

[0123] in, Represents the local modified basis function matrix The q-th derivative with respect to time, where, in Formula 8 K represents an integer, meaning q can take values ​​from 0 to n. iThe integers between these ranges. This ensures that introducing virtual nodes does not disrupt the boundary consistency at the left and right endpoints of the segmented intervals.

[0124] Furthermore, in order to suppress higher-order derivative oscillations in the corrected reconstructed trajectory, in this embodiment, the i-th segment interval [T] is also defined. i ,T i+1 The energy cost of the qth derivative within the inner domain is given by the following formula (nine).

[0125] (Formula 9).

[0126] Where q represents the order of the derivative to which the smoothing constraint is applied. For example, if q is 2, it means that the energy cost of the derivative is used to suppress excessive fluctuations in the rate of change of acceleration.

[0127] Based on the above embodiments, a trajectory correction model as shown in Formula 10 is constructed based on the discrete sampling points of the two endpoints of the segmented interval (i.e., the flight trajectory information of the two endpoints).

[0128] (Formula 10).

[0129] in, , and These are the maximum permissible limits for the vehicle's speed, acceleration, and other higher-order parameters (such as rate of change of acceleration, jerk, and acceleration jerk). These maximum permissible limits are set based on the dynamic performance boundaries of the trajectory carrier (vehicle, rocket) to limit the vehicle's speed, acceleration, and other higher-order parameters within their dynamic performance boundaries.

[0130] For fitting residual penalty term The weighting coefficients, For the i-th segment interval [T] i ,T i+1 Energy cost of the q-th derivative The weighting coefficients, and When the sum is 1, and the interval maneuver intensity is high and the reference trajectory truncation error is large, Set a smaller value to allow virtual nodes to generate more thorough local corrections.

[0131] Wherein, the i-th segment interval [T] i ,T i+1 Energy cost of the q-th derivative In Equation 10, this serves as a smoothing term for higher-order derivatives. Equation 10 minimizes this cost. Achieve smoothing of higher-order derivatives.

[0132] The trajectory correction model aims to minimize the fitting residual. It uses the consistency of the derivatives of the flight trajectory information corresponding to the two endpoints of the reconstructed trajectory in the segmented interval with the discrete sampling points of the trajectory as the correction constraint. Combined with the condition of suppressing the oscillation of higher-order derivatives in the reconstructed trajectory, the trajectory correction model as shown in Equation 10 above is obtained.

[0133] In this way, the initial reconstructed trajectory within the segmented interval can be modified under constraints, so that the modified reconstructed trajectory not only meets the boundary consistency condition and satisfies the requirement of continuity of higher-order derivatives, but also avoids the problem of trajectory reconstruction error divergence caused by the increase of degrees of freedom.

[0134] Step S133: Based on the trajectory correction model, solve for the virtual node trajectory parameters corresponding to each virtual node in the segmented interval to obtain the corrected reconstructed trajectory corresponding to the segmented interval.

[0135] Specifically, in step S133, the above formula can be solved by sequential quadratic programming or Gauss-Newton iteration to obtain the trajectory parameters of all virtual nodes (i.e., the trajectory vectors of the virtual nodes). Thus, the corrected reconstructed trajectory corresponding to the segmented interval is obtained. .

[0136] Thus, through steps S110-S130, the discrete sampling trajectory is first segmented according to the aircraft's maneuver intensity. Then, during trajectory reconstruction, an initial trajectory reconstruction is performed first. After obtaining the initial reconstructed trajectory, the discrete flight trajectory segments with high maneuver intensity are then corrected. This way, for discrete flight trajectory segments that do not belong to high maneuver intensity, a unified initial trajectory reconstruction method can be used directly for trajectory reconstruction. For discrete flight trajectory segments belonging to high maneuver intensity, separate corrections are performed after the initial trajectory reconstruction. This improves the trajectory reconstruction accuracy of high maneuver intensity flight segments without increasing the complexity of trajectory reconstruction for stable maneuver intensity flight segments.

[0137] It is worth noting that, assuming that after the segmentation process in step S110 above, S segmented intervals are obtained, and the time boundary set of each segmented interval is {T0, ..., T...} s}

[0138] Since each segmented interval satisfies the consistency condition of the derivatives at its left and right boundaries, the entire reconstructed trajectory satisfies the condition up to n at the boundaries of the segmented intervals. i The continuity of order. Therefore, for any given continuous time... When determining the trajectory reconstruction result at a certain moment, we can first determine the index of the interval to which that moment belongs. Then you can find the trajectory reconstruction result corresponding to that moment. .

[0139] It is worth noting that, regarding the trajectory segmentation reconstruction method of this embodiment, based on the above exemplary implementations, in specific implementations, as a preferred embodiment, it may include, for example:

[0140] Reference Figure 3 , Figure 3 This document illustrates the overall process of the trajectory segmentation reconstruction method. First, upon receiving the discrete trajectory, a maneuver intensity assessment is performed. Following the assessment, the trajectory is segmented, with the segment time boundaries assumed to be {T0, ..., Ts}. Then, initial trajectory reconstruction is performed for each segment interval; that is, the initial reconstructed trajectory for each segment interval is calculated using Formula 5 above, and the baseline trajectory reconstruction result is output. .

[0141] Subsequently, for the segmented intervals with high maneuverability, the baseline trajectory reconstruction results for these segmented intervals are corrected using Formula 10 above, resulting in the corrected baseline trajectory results. .

[0142] Then the reconstructed trajectory at each time point within a continuous time period can be output, that is, the trajectory reconstruction result can be output. .

[0143] In the preferred embodiment of the above trajectory segmentation reconstruction method, the specific implementation of each step can still be found in the descriptions of the above exemplary embodiments. Furthermore, the beneficial effects brought about by the design of each step in this preferred embodiment can also be found in the descriptions of the above exemplary embodiments, and will not be repeated here.

[0144] The trajectory segmentation reconstruction method in this embodiment adopts the design described above. First, the discrete sampled trajectory is segmented according to the aircraft's maneuver intensity. Then, during trajectory reconstruction, an initial trajectory reconstruction is performed first. After obtaining the initial reconstructed trajectory, the discrete flight trajectory segments with high maneuver intensity are then corrected. This way, for discrete flight trajectory segments that do not belong to high maneuver intensity, a unified initial trajectory reconstruction method can be directly used for trajectory reconstruction. For discrete flight trajectory segments with high maneuver intensity, correction is performed separately after the initial trajectory reconstruction. This improves the trajectory reconstruction accuracy of high maneuver intensity flight segments without increasing the complexity of trajectory reconstruction for stable maneuver intensity flight segments.

[0145] An embodiment of the second aspect of this application provides a trajectory segmentation reconstruction apparatus, such as... Figure 4 As shown, the trajectory segmentation reconstruction device includes a trajectory segmentation module 410, an initial reconstruction module 420, and a trajectory correction module 430.

[0146] The trajectory segmentation module 410 is used to acquire the measured discrete sampled trajectory of the aircraft and segment the discrete sampled trajectory according to the maneuver intensity to obtain at least two discrete flight trajectory segments, wherein the discrete sampled trajectory includes multiple discrete trajectory sampling points. The initial reconstruction module 420 is used to reconstruct the initial trajectory using the discrete trajectory sampling points in each discrete flight trajectory segment to obtain each initial reconstructed trajectory. The trajectory correction module 430 is used to correct the initial reconstructed trajectory of the discrete flight trajectory segment whose maneuver intensity meets the preset high maneuver intensity requirement to obtain the trajectory reconstruction correction result.

[0147] Specifically, in the implementation of the trajectory segmentation reconstruction device of this embodiment, the above-mentioned modules can be existing module products with data transmission, storage or computation processing functions.

[0148] In practical applications, the specific implementation process of the functions of each module in the trajectory segmentation reconstruction device of this embodiment can be found in the relevant descriptions in the above method embodiments, and will not be repeated here.

[0149] The trajectory segment reconstruction device in this embodiment can directly reconstruct the trajectory using a unified initial trajectory reconstruction method for discrete flight trajectory segments that do not belong to high maneuver intensity. For discrete flight trajectory segments that belong to high maneuver intensity, it can make separate corrections after the initial trajectory reconstruction. In this way, the trajectory reconstruction accuracy of high maneuver intensity flight segments can be improved without increasing the trajectory reconstruction complexity of stable maneuver intensity flight segments.

[0150] The above are merely some embodiments of this application and are not intended to limit this application. The technical features or structures in the foregoing different embodiments can be arbitrarily combined to form other specific technical solutions as needed. For those skilled in the art, this application can have various modifications and variations. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principle of this application should be included within the protection scope of the claims of this application.

Claims

1. A trajectory segmentation reconstruction method, characterized in that, include: The discrete sampling trajectory of the aircraft is obtained by measurement, and the discrete sampling trajectory is segmented according to the maneuver intensity to obtain at least two discrete flight trajectory segments, wherein the discrete sampling trajectory includes multiple discrete sampling points; Using the discrete sampling points of each discrete flight trajectory segment, the initial trajectory of each discrete flight trajectory segment is reconstructed to obtain each initial reconstructed trajectory; The initial reconstructed trajectory of the discrete flight trajectory segment whose maneuverability meets the preset high maneuverability requirement is corrected to obtain the trajectory reconstruction correction result.

2. The trajectory segmentation reconstruction method according to claim 1, characterized in that, The step of segmenting the discrete sampled trajectory according to the maneuver intensity to obtain at least two discrete flight trajectory segments includes: Take two adjacent discrete sampling points of the trajectory as a sampling interval, and calculate the maneuver intensity index corresponding to each sampling interval; The maneuver intensity corresponding to each sampling interval is determined based on the relative magnitude of the maneuver intensity index corresponding to each sampling interval and the preset maneuver intensity segmentation threshold. Based on the maneuver intensity corresponding to each sampling interval, the discrete sampling trajectory is segmented to obtain at least two discrete flight trajectory segments.

3. The trajectory segmentation reconstruction method according to claim 2, characterized in that, The calculation formula for the mobility intensity index includes: ； ； ； ； ； in, The aforementioned mobility strength index, Represents the sampling interval [t] k , t k+1 The dimensionless normalized eigenvalue corresponding to the q-th derivative increment of ] This represents the dimensionless normalized characteristic quantity corresponding to curvature. The weighting coefficients represent the increments of the q-th derivative. Represents the weighting coefficients of the curvature-related terms, where, ; For the increment of the q-th derivative, Represents the L2 norm, For the spacecraft at sampling time t k The trajectory state vector below, Indicates at sampling time t k The three-dimensional position below, Indicates at sampling time t k The speed of the drop Indicates at sampling time t k The acceleration below, Indicates at sampling time t k The q-th time derivative; B q Let q be the qth order dynamic capability boundary of the aircraft; The maximum curvature allowed for the aircraft; , To prevent tiny positive numbers with a denominator of 0; This represents the cross product of vectors.

4. The trajectory segmentation reconstruction method according to claim 2, characterized in that, Based on the maneuver intensity corresponding to each of the sampling intervals, the discrete sampling trajectory is segmented to obtain at least two discrete flight trajectory segments, including: Based on the maneuver intensity corresponding to each sampling interval, the discrete sampling trajectory is initially segmented to obtain an initial flight trajectory segment; Determine the interval duration of each of the aforementioned preliminary flight trajectory segments; If the duration of the interval corresponding to any of the initial flight trajectory segments is less than the preset minimum duration, the initial flight trajectory segment is merged with the adjacent initial flight trajectory segment to obtain at least two discrete flight trajectory segments.

5. The trajectory segmentation reconstruction method according to claim 2, characterized in that, The maneuver intensity includes high maneuver intensity and steady maneuver intensity; The step of determining the maneuver intensity corresponding to each sampling interval based on the relative magnitude of the maneuver intensity index corresponding to each sampling interval and the preset maneuver intensity segmentation threshold includes: If the maneuver intensity index is greater than the preset maneuver intensity segmentation threshold, the maneuver intensity corresponding to the sampling interval is determined to be high maneuver intensity. If the maneuver intensity index is not greater than the preset maneuver intensity segmentation threshold, the maneuver intensity corresponding to the sampling interval is determined to be a stable maneuver intensity.

6. The trajectory segmentation reconstruction method according to claim 1, characterized in that, The step of using the discrete sampling points of each discrete flight trajectory segment to reconstruct the initial trajectory of each discrete flight trajectory segment, resulting in each initially reconstructed trajectory, includes: Establish a baseline local trajectory reconstruction model; Using the constraint that the derivatives of the endpoints of the discrete flight trajectory segments before and after trajectory reconstruction are consistent, the initial reconstructed trajectories corresponding to each sampling interval are solved using the benchmark local trajectory reconstruction model.

7. The trajectory segmentation reconstruction method according to claim 6, characterized in that, The baseline local trajectory reconstruction model includes: ； in, The initial reconstructed trajectory of the i-th discrete flight trajectory segment at time t; are basis functions; Denotes the coefficients of the l-th power basis polynomial; The constraints include: ; in, ; Wherein, L and R represent the two endpoints of the discrete flight trajectory segment, respectively. This indicates that the initial reconstructed trajectory of the i-th segmented interval is at the start time T of the segmented interval. i The value of the q-th derivative at point , This indicates that the initial reconstructed trajectory of the i-th segmented interval is at the termination time T of the segmented interval. i+1 The value of the q-th derivative at point , Let T be the starting time of the i-th segmented interval. i The observed value of the qth order boundary derivative of the discrete sampling trajectory at the corresponding location; Let T be the termination time of the i-th segmented interval. i+1 The observed value of the qth order boundary derivative of the discrete sampling trajectory at the corresponding location.

8. The trajectory segmentation reconstruction method according to claim 1, characterized in that, The initial reconstructed trajectory of the discrete flight trajectory segment whose maneuverability meets the preset high maneuverability requirement is corrected to obtain the trajectory reconstruction correction result, including: For discrete flight trajectory segments that meet the preset high maneuverability requirements, a preset number of virtual nodes are set in the segmented intervals corresponding to the discrete flight trajectory segments; With the goal of minimizing the fitting residuals and the constraint that the endpoints of the segmented intervals have the same derivatives before and after the correction, a trajectory correction model is established. Based on the trajectory correction model, the trajectory parameters of the virtual nodes corresponding to each virtual node in the segmented interval are solved to obtain the corrected reconstructed trajectory.

9. The trajectory segmentation reconstruction method according to claim 8, characterized in that, The trajectory correction model includes: ； in, ; For the i-th segment interval [T] i ,T i+1 Energy cost of the q-th derivative within the inner quadrant; For fitting residual penalty term The weighting coefficients, For the i-th segment interval [T] i ,T i+1 Energy cost of the q-th derivative The weighting coefficients, and The sum is 1; in, ; ; This is the set of state parameters to be estimated for all virtual nodes. This represents the local modified basis function matrix corresponding to the j-th virtual node; in, ; This represents the q-th derivative of the modified basis function with respect to time. , and These are the maximum permissible limits for the aircraft's speed, acceleration, and other higher-order parameters.

10. A trajectory segmentation reconstruction device, characterized in that, include: The trajectory segmentation module is used to acquire the measured discrete sampled trajectory of the aircraft and segment the discrete sampled trajectory according to the maneuver intensity to obtain at least two discrete flight trajectory segments, wherein the discrete sampled trajectory includes multiple discrete trajectory sampling points; The initial reconstruction module is used to reconstruct the initial trajectory using the discrete sampling points of the trajectory in each of the discrete flight trajectory segments, so as to obtain each initial reconstructed trajectory. The trajectory correction module is used to correct the initial reconstructed trajectory of discrete flight trajectory segments whose maneuverability meets the preset high maneuverability requirements, and obtain the trajectory reconstruction correction result.

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