A Multi-Radar Handover Tracking Method for Space Targets Based on Forecast Error Covariance Propagation

Abstract

This invention belongs to the field of radar target tracking technology and relates to a multi-radar handover tracking method for space targets based on the propagation of prediction error covariance. The method includes the following steps: a first radar performs filtering tracking on the space target to obtain the first position, first velocity, and first covariance information at the last observation time; transforms to a geocentric inertial coordinate system; constructs the initial prediction state and the initial prediction error covariance information, and extrapolates the prediction to obtain the prediction state and prediction error covariance information for future times; determines the time when the target enters the airspace covered by the second radar; the second radar plans the interception position and interception area and tracks the target, obtaining candidate states and candidate covariance information; constructs a test statistic, combines it with multi-time-time association quality evaluation, determines the cross-radar association result, and completes the space target handover tracking. The technical solution of this application can improve the trajectory coherence, error consistency, and association reliability in space target handover.

Description

Technical Field

[0001] This invention belongs to the field of radar target tracking technology, and specifically relates to a multi-radar handover tracking method for space targets based on the propagation of prediction error covariance. Background Technology

[0002] In existing technologies, multi-radar space target surveillance typically relies on each radar independently completing tracking, and the handover requirement is met by extrapolating the target state near the coverage boundary. However, existing handover methods have some significant shortcomings in terms of trajectory consistency between different dynamic models, coherent expression of cross-coordinate system error statistics, and stability of cross-radar track association.

[0003] In existing technologies, since the forecasting process is mostly based on ground-fixed coordinates or measurement coordinates, the covariance information is usually limited to the single radar, and the error statistical structure between radars is weak. At the same time, the extrapolation model is not uniform in the processing of perturbation forces, which makes the trajectory continuity in the handover stage poor, and the forecast performance entering the coverage airspace is easily affected by changes in perturbation forces and fluctuates.

[0004] In addition, traditional correlation methods often rely on a single comparison of positional or velocity differences, resulting in weak statistical support for the correlation. Under conditions of weak measurement or error accumulation, the stability of correlation judgment is low, and the quality of correlation is prone to instability.

[0005] It is evident that existing technologies often suffer from problems such as poor consistency in forecast status, weak consistency in error statistics, and low reliability of cross-radar correlation. These are the shortcomings of existing technologies.

[0006] In view of this, it is very necessary to provide a multi-radar handover tracking method for space targets based on the propagation of prediction error covariance, so as to solve the above-mentioned defects in the prior art. Summary of the Invention

[0007] The purpose of this invention is to address the shortcomings of existing technologies, such as poor forecast consistency, weak error statistical consistency, and low reliability of cross-radar correlation, by providing a multi-radar handover tracking method for space targets based on forecast error covariance propagation, thereby solving the aforementioned technical problems.

[0008] To achieve the above objectives, the present invention provides the following technical solution:

[0009] A multi-radar handover tracking method for space targets based on forecast error covariance propagation includes the following steps:

[0010] The space target is filtered and tracked in the northeast-sky coordinate system of the first radar to obtain the first position, first velocity, and first covariance information including the first position covariance, the first velocity covariance, and the first position-velocity cross-covariance at the last observation time.

[0011] The first position, first velocity, and first covariance information are transformed to the geocentric inertial coordinate system to obtain the second position, second velocity, and second covariance information;

[0012] The initial state and initial covariance of the forecast error are constructed using the second position, second velocity, and second covariance information, and the forecast is extrapolated to obtain the forecast state and forecast error covariance information for future times.

[0013] The entry time of a space target into the airspace covered by the second radar is determined based on the forecast status and forecast error covariance information, and the forecast status and forecast error covariance information corresponding to the entry time are sent to the second radar.

[0014] The second radar plans the interception position and interception area based on the forecast state and forecast error covariance information, and performs tracking to obtain candidate state and candidate covariance information.

[0015] Based on the forecast state, forecast error covariance information, candidate state and candidate covariance information, a test statistic is constructed, and combined with multi-time-time correlation quality evaluation, the cross-radar correlation result is determined to complete the handover tracking of space targets.

[0016] By adopting the above technical solution, and by constructing a continuous state extrapolation and error expression link among multiple radars, consistent processing of state and covariance information under cross-coordinate system can be achieved. This enables the predicted trajectory to exhibit higher consistency, error statistics to maintain stronger uniformity, and correlation judgment to have better stability, thus meeting the requirements of high trajectory consistency, strong error consistency, and high correlation reliability in space target handover.

[0017] Specifically, after the first radar obtains the target's position, velocity, and covariance information, the state and error basis are made continuous from the source and can be used for subsequent calculations. After the state is transformed to the geocentric inertial coordinate system, it obtains a unified form under an independent coordinate system, establishing a consistent reference framework for subsequent extrapolation. When performing forecast extrapolation based on this state, the evolution of the trajectory at future moments maintains a consistent trend under unified dynamic conditions, and the evolution of the error is consistent with the state. When determining the time to enter the airspace covered by the second radar based on the forecast state and forecast error covariance information, the selection of the handover node is based on the spatiotemporal extrapolation results of the previous radar to form a coordinated entry basis. When the second radar conducts interception and tracking based on this, it can perform initial search and state acquisition based on the forecast state and error expression. When constructing test statistics and combining them with multi-time correlation quality evaluation, cross-radar correlation is carried out under a unified state difference metric and error structure, thereby forming a more stable correlation result. Overall, the handover performance of space targets is more continuous, consistent, and has a more reliable trend.

[0018] Preferably, the step of transforming the first position, first velocity, and first covariance information to a geocentric inertial coordinate system to obtain the second position, second velocity, and second covariance information includes:

[0019] A coordinate transformation matrix is ​​constructed based on the geodetic longitude, geodetic latitude, geodetic elevation, and Earth's rotation angular velocity of the location of the first radar station;

[0020] The first position, first velocity, and first covariance information are linearly transformed using a coordinate transformation matrix to obtain the second position, second velocity, and second covariance information. The second covariance information includes the second position covariance, the second velocity covariance, and the cross-covariance between the second position and velocity.

[0021] This technical solution achieves the following technical effects by constructing a continuous geographic and physical parameter framework using a single reference station during coordinate transformation:

[0022] First, by uniformly expressing the state information derived from the local observation environment into a coordinate form suitable for three-dimensional spatial dynamics, the directional relationship between position and velocity in the spatial reference system can be kept more stable, thereby maintaining good geometric consistency in subsequent state extrapolation. This improves the accuracy of subsequent extrapolation calculations in expressing state changes and provides a structurally complete input basis for error propagation, enabling the state to be expressed coherently under different reference frames.

[0023] Second, by utilizing the structural characteristics of linear transformation, various statistical quantities formed by radar measurements can maintain their intrinsic correlation during the transformation process, thereby strengthening the correspondence between error components and ensuring that the statistical characteristics of velocity and position directions remain consistent in the spatial reference system. This lays a unified statistical structure for subsequent covariance derivation and also ensures that the distribution characteristics of errors in high-dimensional state space maintain good orthogonality and consistency, which is beneficial for subsequent dynamic models to handle error distribution.

[0024] Third, by reconstructing covariance information in a geocentric inertial coordinate system, each error component can obtain a structure that can be directly used in the prediction model under a global reference frame. This gives the state variables a stronger consistency basis when they are involved in perturbations, long-arc motions, or cross-radar links. Consequently, it maintains a more robust numerical performance in subsequent trajectory calculations, error extrapolation, and handover node determination, forming a more coordinated error and state expression system for continuous tracking of space targets.

[0025] As a preferred option, forecast extrapolation is performed, including: using a space dynamics model to calculate the acceleration vector of the space target in the geocentric inertial coordinate system based on the Earth's gravitational field parameters and the forecast initial state, and updating the forecast state with the forecast initial state and the acceleration vector. The space dynamics model includes the Earth's non-spherical gravity term.

[0026] This forecast extrapolation technique achieves the following technical effects by continuously predicting the target motion within a unified dynamics framework:

[0027] First, by utilizing the structural features of the space dynamics model, the motion state of the target in the geocentric inertial coordinate system is made more consistent with the actual trajectory evolution trend, thereby maintaining higher trajectory coherence in the state prediction at future moments and maintaining stable evolution accuracy in long arc motion affected by perturbation, so that the prediction results have more reliable temporal consistency in subsequent use.

[0028] Second, by adopting an acceleration construction method based on gravitational field parameters, the state update process can fully reflect the influence of the Earth's non-spherical gravity on the target trajectory, effectively suppressing the deviation between the future state trend and the real dynamic environment, and maintaining stronger coordination of the dynamic model's performance in different altitude regions. This gives the extrapolated trajectory a more complete physical logic basis and provides consistent state input for subsequent prediction links.

[0029] Third, by combining the initial state with the acceleration vector for state updates, the state evolution can reflect the coupling relationship between velocity changes and gravitational perturbations, making the trajectory evolution exhibit a smoother change pattern in the high-dimensional state space, and making the future trajectory estimation based on dynamic conditions maintain a more robust extensibility over time, thus forming a state extrapolation capability suitable for cross-time domain prediction in multi-radar environments.

[0030] As a preferred option, forecast extrapolation also includes: constructing a linearized error propagation relationship based on the Jacobian matrix of the space dynamics model, propagating the initial covariance information of the forecast error in the form of a combination of the Jacobian matrix and the state transition matrix, and introducing process noise covariance information during the propagation process to obtain the forecast error covariance information at future times.

[0031] This error propagation technique utilizes the locally linearized structure of the dynamic model to construct an error inference link, achieving the following technical effects:

[0032] First, by using an error expansion method based on the Jacobi matrix, the propagation path of the error during the state change process presents a more explicit linear structure, thereby maintaining a high degree of evolution consistency in the error prediction at future moments, and maintaining the structural stability of the error information in scenarios where the state dimension increases or the trajectory changes rapidly, so that the propagation trend of the error is coordinated with the spatial dynamics environment.

[0033] Second, by using the Jacobian matrix in conjunction with the state transition matrix, the error change can simultaneously reflect the local dynamic influence and the overall state update law, so that the covariance maintains the continuous expression of correlation in matrix operations and exhibits a higher positive definite preservation ability in the error evolution process. Thus, the error structure in the future time step still has a clear statistical relationship under high-dimensional operations, providing a stable error input basis for subsequent state deduction and correlation judgment.

[0034] Third, by introducing process noise covariance information during error propagation, the model becomes more resistant to external disturbances, trajectory deviations, or small model uncertainties. This allows the error estimate for future moments to maintain a more robust expression in a dynamically changing environment and forms an adaptive error structure when there are model approximations or perturbation fluctuations. The resulting forecast error covariance information is more closely aligned with the actual state distribution, thus providing a more reliable error description system for subsequent processing links.

[0035] As a preferred method, the step of determining the entry time of a space target into the airspace covered by the second radar based on the forecast state and forecast error covariance information includes: converting the forecast states of multiple future times into coordinate representations based on the second radar, comparing them with the airspace covered by the second radar, and selecting the earliest time when the second radar detects the target from the forecast times that satisfy the airspace coverage constraints as the entry time.

[0036] This entry time determination technology achieves the following technical effects by selecting the optimal entry time from the unified prediction link:

[0037] First, by using a coordinate representation method based on the second radar, the state at future moments has a consistent basis for expression in subsequent judgments, thereby maintaining a clearer geometric correspondence under different spatial location conditions and making the spatial relationship between radars present a more stable matching effect, thus enhancing the ability to interpret position changes in dynamic environments.

[0038] Second, by adopting a screening method based on coverage spatial constraints, the adaptability of each candidate time in terms of geometric conditions is improved, the relationship between the predicted state and the effective detection area is more determinable, and a more coordinated entry basis is formed in the comparison of multiple times, so that the selection of the handover node has higher spatial adaptability and the predicted time corresponds well with the actual detectable conditions.

[0039] Third, by using the covariance of the prediction error in the position direction, the selection of the entry time can take into account both the spatiotemporal relationship and the error distribution trend, and reflect the constraint of error information in the time series extrapolation, so that the final selected entry time can maintain more reliable stability in the future state extrapolation, thereby providing a clearer time reference for the subsequent interception and correlation process.

[0040] Preferably, the second radar plans the interception location and interception area based on the forecast state and forecast error covariance information, including: transforming the forecast error covariance information into coordinates in the measurement space of the second radar, constructing a three-dimensional envelope region around the forecast state based on the eigenvectors and eigenvalues ​​of the transformed covariance matrix, and performing an interception search within the three-dimensional envelope region.

[0041] The interception area planning technology solution achieves the following technical effects by constructing a three-dimensional envelope based on an error structure within the measurement space:

[0042] First, by utilizing the coordinate transformation of the forecast error covariance information, the error information can be consistently expressed in the second radar measurement space, so that the error distribution maintains the continuity of directional characteristics in the new coordinate system and reflects the integrity of the statistics in the three-dimensional spatial structure, so that the predicted state has a more accurate reference basis in subsequent searches.

[0043] Second, by constructing the envelope region based on eigenvalues ​​and eigenvectors, the direction of error extension in space is clearly characterized, and the shape of the envelope is more in line with the distribution trend of the predicted state. This gives the search area a higher geometric matching capability, enabling the radar to focus on a more reasonable spatial range during the initial search and reducing the resource consumption caused by invalid search areas.

[0044] Third, by using a three-dimensional envelope region constructed around the predicted state, the search process can maintain a good fit to the predicted trajectory even under dynamic conditions, thereby enhancing the search efficiency in a multi-radar cooperative environment and making the initial tracking phase more stable. This provides a coherent spatial basis for subsequent correlation calculations and state updates, making the interception process more reliable.

[0045] As a preferred embodiment, the steps for constructing the test statistic based on the forecast state, forecast error covariance information, candidate state, and candidate covariance information include: constructing a state difference vector from the difference between the forecast state and the candidate state; constructing a joint covariance matrix by adding the forecast error covariance information and the candidate covariance information; and performing matrix multiplication operations using the transpose of the state difference vector, the inverse of the joint covariance matrix, and the state difference vector to obtain the test statistic.

[0046] This test statistic construction technique achieves the following technical effects by measuring state differences within a unified error framework:

[0047] First, by using the state difference vector as the core comparison basis, the difference between cross-radar candidate states and predicted states is clearly expressed in high-dimensional space, so that the trend of position and velocity change maintains clear directionality in the comparison process, and the association judgment has a more sensitive recognition ability when the state difference is small, making cross-radar state matching more reasonable.

[0048] Second, by adopting the construction method of joint covariance matrix, error information can be consistently presented under additive structure, and prediction error and candidate error can form a comparable relationship under a unified statistical framework. This enables an effective trade-off between state differences and error scale, keeps the test results stable under different error levels, and makes cross-radar judgment more reliable under complex conditions.

[0049] Third, by using matrix multiplication to form test statistics, the measurement results can simultaneously reflect the magnitude of state differences and the directionality of error distribution, giving the association judgment a more complete statistical basis and demonstrating stronger robustness under multidimensional data processing conditions. This provides reliable input for subsequent association quality evaluation and makes the cross-radar association process more robust.

[0050] As a preferred option, the steps for determining the cross-radar association results by combining multi-time-time association quality evaluation include: calculating a test statistic for each pair of forecast states and candidate states; updating the association quality function based on the comparison result between the test statistic and the preset limit; adding a predetermined increment to the association quality function when the association is judged to be successful; keeping the association quality function unchanged when the association is judged to be unsuccessful; normalizing the association quality function based on the quantitative relationship between the number of successful associations and the number of association judgments within a set of continuous sampling times; and determining the cross-radar association results based on the normalized results.

[0051] This correlation quality assessment technology achieves the following technical effects by accumulating correlation information from multiple time points during continuous sampling to form a stable criterion:

[0052] First, by using the statistical calculation results of each pair of forecast states and candidate states as evaluation input, the judgment process has the ability to accumulate over time beyond a single comparison, and the correlation quality function can reflect the continuous impact of historical judgments on the current trend. This allows for a more robust expression under conditions of trajectory fluctuations or uneven measurement quality, and enables the correlation evaluation to have a higher adaptability in dynamic environments.

[0053] Second, a normalization method based on the relationship between the number of successful judgments and the total number of judgments is adopted so that the quality function can reflect the importance of the success rate to the overall judgment, and the evaluation results can still have a uniform scale under different sampling lengths. This makes the function change trend after multiple time-accumulation more reflective of the actual correlation tendency, makes the cross-radar correlation criteria present a clearer direction in a statistical sense, and makes the judgment results maintain higher reliability in complex scenarios.

[0054] Third, by using the method of distinguishing between success and failure in the sampling sequence, the correlation evaluation can reflect the continuous changes in state differences over time, so that short-term anomalies do not have an excessive impact on the final judgment, and the evaluation mechanism can still maintain sufficient resistance to disturbances in the event of multiple error propagation or temporary obstruction. Thus, under the evaluation framework with time accumulation properties, it provides a more stable statistical basis for the final correlation judgment.

[0055] As a preferred approach, when updating the association quality function, weight values ​​related to the test statistic are assigned to the successfully associated records based on the magnitude of the test statistic at the corresponding sampling time. The weight values ​​decrease as the test statistic increases, and the weight values ​​at earlier sampling times are attenuated during continuous sampling to construct an association quality function that is sensitive to recent association results.

[0056] This weighted quality function technique achieves the following technical effects by introducing a dynamic weight structure based on statistical changes during the evaluation process:

[0057] First, by utilizing weights that vary with the size of the test statistic, the successful association records can obtain a stronger contribution expression under conditions of small differences, the quality function can be significantly enhanced when candidate states that approximate the predicted trend appear, and the evaluation process can be made more sensitive to the state performance near the true trajectory, thereby making the evaluation results exhibit higher identification accuracy in complex state distributions.

[0058] Second, by attenuating the weight values ​​of early sampling moments, the evaluation focus is more concentrated on recent judgment results, enabling the quality function to reflect rapid changes in the target's movement trend in a timely manner. This ensures good timeliness even when there are sudden changes in the trajectory, changes in measurement, or changes in related environmental conditions, making the evaluation system more adaptable to dynamic changes and giving the final evaluation a stronger realistic correspondence.

[0059] Third, by using a dynamic weighting structure, the impact of judgments at different times on the overall evaluation is differentiated, allowing the quality function to maintain a clear statistical relationship even when the data volume is large or the error fluctuation is strong. This enables the recording structure to emphasize effective judgments and suppress the impact of noise, thereby forming a more robust evaluation curve in the continuous sampling sequence and providing a more reliable statistical basis for subsequent related decisions.

[0060] As a preferred embodiment, when the second radar generates multiple candidate states and candidate covariance information at the same sampling time, the test statistic is calculated for each candidate state. Among the candidate states that meet the preset limit, the candidate state with the smallest test statistic is selected as the associated object at the current sampling time, and the association quality function is updated based on the associated object.

[0061] This multi-candidate state screening technique achieves the following technical effects by optimizing the candidate states and updating the evaluation structure at the same sampling time:

[0062] First, by directly comparing the statistics corresponding to each candidate state, the judgment process obtains a clear selection basis when there are multiple trajectory possibilities, enabling the optimal candidate to show a stronger advantage in the state difference measurement, thus making the association judgment maintain a clear direction under the condition of many branches, and making the cross-radar matching results more accurate.

[0063] Second, by adopting the method of selecting associated objects based on the principle of minimum statistics, the screening process can take into account both the trend of the predicted state and the distribution of the error structure, so that the selection results are closer to the position and velocity direction of the real target in a statistical sense, thereby maintaining a more coherent association link in the subsequent sampling process, and making cross-radar tracking have a more stable connection performance in the continuous time dimension.

[0064] Third, by using the optimal candidate to update the quality function, the correlation evaluation can reflect the best matching situation at the current moment in real time, and the quality function can continue to change with the selection results under different sampling conditions. This enables the evaluation system to have better discrimination ability when facing complex candidate sets, thereby forming a more reliable correlation trend in the statistical sense accumulated over multiple future moments, and laying a more stable judgment foundation for the complete cross-radar handover process.

[0065] The beneficial effect of this invention is that by constructing a continuous state extrapolation and error expression link among multiple radars, it achieves consistent processing of state and covariance information across coordinate systems, which enables the predicted trajectory to exhibit higher consistency, error statistics to maintain stronger uniformity, and correlation judgment to have better stability, thus meeting the requirements of high trajectory consistency, strong error consistency, and high correlation reliability in space target handover.

[0066] Furthermore, the design principle of this invention is reliable, the structure is simple, and it has a very wide range of application prospects.

[0067] Therefore, it is evident that the present invention has outstanding substantive features and significant progress compared with the prior art, and the beneficial effects of its implementation are also obvious. Attached Figure Description

[0068] 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 embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0069] Figure 1 This is a flowchart of the space target multi-radar handover tracking method based on prediction error covariance propagation provided by the present invention. Detailed Implementation

[0070] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. The following embodiments are explanations of the present invention, but the present invention is not limited to the following implementation methods.

[0071] like Figure 1 As shown in the figure, this embodiment provides a multi-radar handover tracking method for space targets based on prediction error covariance propagation, which includes the following steps:

[0072] Step S1: Filter and track the space target in the northeast-north-sky coordinate system of the first radar to obtain the first position, first velocity, and first covariance information including the first position covariance, the first velocity covariance, and the first position-velocity cross-covariance at the last observation time;

[0073] Step S2: Transform the first position, first velocity, and first covariance information to the geocentric inertial coordinate system to obtain the second position, second velocity, and second covariance information;

[0074] Step S3: Construct the initial forecast state and initial forecast error covariance information using the second position, second velocity, and second covariance information, and perform forecast extrapolation to obtain the forecast state and forecast error covariance information for future times;

[0075] Step S4: Determine the entry time of the space target into the coverage airspace of the second radar based on the forecast status and forecast error covariance information, and send the forecast status and forecast error covariance information corresponding to the entry time to the second radar.

[0076] Step S5: The second radar plans the interception position and interception area based on the forecast state and forecast error covariance information and performs tracking to obtain candidate state and candidate covariance information;

[0077] Step S6: Based on the forecast state, forecast error covariance information, candidate state and candidate covariance information, construct the test statistic, and combine it with the multi-time correlation quality evaluation to determine the cross-radar correlation result and complete the handover tracking of space targets.

[0078] By adopting the above technical solution, and by constructing a continuous state extrapolation and error expression link among multiple radars, consistent processing of state and covariance information under cross-coordinate system can be achieved. This enables the predicted trajectory to exhibit higher consistency, error statistics to maintain stronger uniformity, and correlation judgment to have better stability, thus meeting the requirements of high trajectory consistency, strong error consistency, and high correlation reliability in space target handover.

[0079] Specifically, after the first radar obtains the target's position, velocity, and covariance information, the state and error basis are made continuous from the source and can be used for subsequent calculations. After the state is transformed to the geocentric inertial coordinate system, it obtains a unified form under an independent coordinate system, establishing a consistent reference framework for subsequent extrapolation. When performing forecast extrapolation based on this state, the evolution of the trajectory at future moments maintains a consistent trend under unified dynamic conditions, and the evolution of the error is consistent with the state. When determining the time to enter the airspace covered by the second radar based on the forecast state and forecast error covariance information, the selection of the handover node is based on the spatiotemporal extrapolation results of the previous radar to form a coordinated entry basis. When the second radar conducts interception and tracking based on this, it can perform initial search and state acquisition based on the forecast state and error expression. When constructing test statistics and combining them with multi-time correlation quality evaluation, cross-radar correlation is carried out under a unified state difference metric and error structure, thereby forming a more stable correlation result. Overall, the handover performance of space targets is more continuous, consistent, and has a more reliable trend.

[0080] Hereinafter, steps S1 to S6 will be specifically described according to embodiments of this application.

[0081] In step S1, the core task is to continuously track the space target in the local coordinate system using the first radar before the space target enters the multi-radar relay monitoring link. By filtering, a consistent trajectory result with dynamic constraints is obtained, thereby filtering and tracking the space target in the ENU (East North Up) coordinate system of the first radar. At the end of the continuous observation, the target position, velocity, and covariance information related to position and velocity are extracted. This forms the first position, first velocity, and first covariance information including the first position covariance, first velocity covariance, and first position-velocity cross-covariance at the last observation time. This provides a high-confidence initial state basis for subsequent forecast extrapolation and multi-radar handover in a unified reference system.

[0082] Specifically, in the embodiments of this application, the first radar is deployed at a predetermined geographical location, and the ENU coordinate system with the center of the radar station as the origin is used as the local spatial reference. Its east axis is used to represent the component pointing due east along the local horizontal plane, the north axis is used to represent the component pointing due north along the local horizontal plane, and the celestial axis is used to represent the component perpendicular to the local horizontal plane and pointing upward. Under this coordinate system, the geometric relationship of the spatial target relative to the radar station can be uniquely represented, which facilitates the establishment of a clear geometric mapping relationship with the geocentric inertial coordinate system.

[0083] In the ENU coordinate system, in order to uniformly model the motion state of spatial targets, the first radar constructs a state vector structure for the tracked target at the sampling time. The positional components of the target in the east, north, and sky directions are denoted as follows: , , The velocity components of the target in the three directions are denoted as follows: , , In the ENU coordinate system, the target position vector and velocity vector obtained by filtering can be expressed as follows:

[0084]

[0085] in, Indicates at the sampling time The position vector obtained by the first radar filter estimation Indicates at the sampling time The velocity vector estimated by the first radar filter is used when the target is continuously observed and tracked until the last observation time. At that time, the target position vector in the ENU coordinate system That is, the first position, and the corresponding velocity vector. That is, the first velocity.

[0086] To give the aforementioned position and velocity estimates a clear statistical meaning, the first radar, while constructing the state model, establishes a covariance structure for the target that includes the statistics of position and velocity errors. In the ENU coordinate system, the covariance matrix of the position estimation error is denoted as... Let the covariance matrix of the velocity estimation error be denoted as Let the cross-covariance matrix between the position estimation error and the velocity estimation error be denoted as... and ,in It can be defined by the following formula:

[0087]

[0088] Then it can be defined by the second-order statistics of the velocity vector. and Used to describe the correlation between position error and velocity error, where Greek letters Represents the mathematical expectation operator. The matrix transpose operation is represented by the above definition, which allows for the construction of a complete structure of the first position covariance, the first velocity covariance, and the first position-velocity cross-covariance in the ENU coordinate system.

[0089] Furthermore, at the implementation level of the trajectory tracking process, the first radar continuously observes the space target in the ENU coordinate system. The observation information can include measurements such as slant range, azimuth angle, and elevation angle. The first radar records the actual received measurements as measurement vectors. The measurement vector and the state vector are connected through a nonlinear measurement relationship function. Establish a mapping relationship for the first... Each sampling time can be represented as:

[0090]

[0091] in, The target state vector in the ENU coordinate system can be formed by concatenating position and velocity to create a six-dimensional vector. This represents the measurement noise vector, which can be modeled as random noise with zero mean in engineering implementation to characterize random errors in radar measurements.

[0092] In some embodiments of this application, in order to fully incorporate the dynamic characteristics of the space target during mid-course flight, the first radar selects a dynamic model adapted to the mid-course trajectory motion in the ENU coordinate system to model the temporal evolution of the target state. The continuous-time dynamic equations are discretized to form state update equations, and at discrete time intervals... and The space between can be written as:

[0093]

[0094] in, This represents the discrete state transition matrix in the ENU coordinate system, used to represent the motion relationship of the target within the current sampling interval. The process noise vector is used to characterize the influence of factors such as unmodeled perturbation and modeling error on the target's motion. In practical implementation, the process noise can be regarded as a random vector with zero mean, and its covariance is represented by the process noise covariance matrix. The predicted state can be obtained at each sampling time through the state update equation.

[0095] Furthermore, the state estimate can be corrected using a filtering algorithm between the predicted state and the actual measurement. In engineering implementation, Kalman filtering, extended Kalman filtering, or filter structures suitable for the mid-course trajectory characteristics of space targets can be used. At each sampling time, the filtering process updates the state estimate and covariance estimate based on the state prediction results of the previous time and the current measurement, so that the state estimate output by the filter reflects the evolution of the real trajectory based on the dynamic model and observation information. During continuous observation, the filtering process is repeated at a fixed sampling interval until the space target leaves the effective coverage area of ​​the first radar.

[0096] As the filtering process iterates, estimates of the current position and velocity, along with their corresponding covariance and cross-covariance, can be obtained at each sampling moment. This information is then applied at the tracking termination moment, i.e., the last observation moment. At that time, by reading the state estimation and error covariance results from the filtered output, the target position vector in the ENU coordinate system is obtained. Specify the first position and set the velocity vector Specify it as the first speed, and set the corresponding , , and The overall error statistic formed by the first position covariance, the first velocity covariance, and the first position-velocity cross-covariance information constitutes the first covariance information.

[0097] In some embodiments of this application, in actual engineering deployment, the first radar can be configured with a suitable sampling period, beam pointing strategy and measurement noise model according to the typical trajectory characteristics of the space target. This enables the filter constructed in the ENU coordinate system to maintain stable tracking quality during the target's flight across the coverage area of ​​the first radar. After continuous tracking is completed, the first position, first velocity and first covariance information obtained through filtering output can be regarded as the comprehensive tracking result of the space target in the first radar monitoring stage, which directly constrains the accuracy of subsequent coordinate transformation, prediction extrapolation and handover association links.

[0098] Thus, step S1 constructs a dynamic model and measurement model for the mid-course trajectory of a space target in the ENU coordinate system of the first radar, and outputs the first position, first velocity and first covariance information by combining continuous filtering operations. This provides a high-confidence initial state and error statistics basis for subsequent processing links, enabling multi-radar handover tracking to be established on unified and quantifiable source information.

[0099] In step S2, the core task is to transform the first position, first velocity, and first covariance information in the first radar northeast-sky coordinate system obtained in step S1 to the geocentric inertial coordinate system to obtain the second position, second velocity, and second covariance information. This transformation enables the state variables and error statistics of the space target to be consistently mapped from the local reference system to the global inertial reference system, providing a unified state starting point for subsequent trajectory prediction and multi-radar handover tracking in the geocentric inertial coordinate system.

[0100] Specifically, in some embodiments of this application, a coordinate transformation matrix can be constructed based on the geodetic longitude, geodetic latitude, geodetic elevation, and Earth's rotation angular velocity of the location of the first radar station, and the geodetic latitude of the center of the first radar station is denoted as... Longitude is recorded as Earth's elevation is denoted as The Earth's equatorial radius is denoted as . The Earth's rotational angular velocity is denoted as . At a given discrete time Below, through angular measurement Describe the ECI (Earth-Centered Inertial) coordinate system and its coordinates based on longitude. The rotation relationship is based on, where These parameters are used to characterize the rotation angle from the reference time to the current time, and a direction cosine matrix is ​​constructed based on these parameters to represent the ENU coordinate system to the ECI coordinate system. and the angular velocity matrix related to rotation This forms a complete coordinate transformation matrix system.

[0101] Based on the above station parameters, the direction cosine matrix from the ENU coordinate system to the ECI coordinate system It can be written as:

[0102]

[0103] In this matrix, the first row of three items represents the projection of the three axes of the ENU coordinate system onto the first axis of the ECI coordinate system; the second row of three items represents the projection onto the second axis; and the third row of three items represents the projection onto the third axis. The matrix elements are directly correlated with the geodetic longitude and latitude of the station location through trigonometric functions, ensuring that the spatial relationship between the directions of the ENU coordinate system and the ECI coordinate system can be determined at every moment. and The only certainty.

[0104] In addition, to characterize the angular velocity effect introduced by rotation, it is also necessary to introduce a time-varying matrix. :

[0105]

[0106] This matrix is ​​derived from the Earth's rotational angular velocity. and , The combination gives the rate of change of the ENU coordinate system basis vectors with time in the ECI coordinate system, enabling the additional velocity term caused by rotation to be explicitly considered in subsequent velocity transformation and covariance propagation.

[0107] After constructing the direction cosine matrix and its time derivative matrix, the position and velocity of the radar station center need to be projected from the ENU coordinate system to the ECI coordinate system to form position and velocity offsets. These offsets are used to add the radar station's own motion components in the ECI coordinate system to the initial position and velocity of the space target relative to the radar. The position offset vector can be expressed as:

[0108]

[0109] Where vector In the ENU coordinate system, the distance of the radar station center relative to the Earth's center along the celestial direction is equal to the sum of the Earth's equatorial radius and the station's elevation. This distance is obtained by relating it to the matrix... Multiplying transforms this geometric quantity into its three-axis component form in the ECI coordinate system.

[0110] The velocity offset vector can be represented as:

[0111]

[0112] This expression shows that the linear velocity of the radar station center caused by the Earth's rotation can be obtained by applying the angular velocity matrix from the ENU coordinate system to the ECI coordinate system to the station position vector. In the ECI coordinate system, it is manifested as the tangential velocity component of the rotation around the Earth's axis.

[0113] Based on the aforementioned matrix and offset vector, the coordinate transformation matrix can be used to perform a linear transformation on the first position, first velocity, and first covariance information to obtain the second position, second velocity, and second covariance information.

[0114] It should be noted that, for the convenience of describing the following steps, in step S2 and subsequent steps, the first position output in step S1 will be used. Recorded as First speed Recorded as and the corresponding , , and They are respectively denoted as , , and The second position corresponding to this in the ECI coordinate system Second speed It can be written as:

[0115]

[0116]

[0117] The first equation maps the first position vector relative to the radar to the ECI coordinate system using the direction cosine matrix, and superimposes the station center position offset vector to obtain the geometric position of the space target in the ECI coordinate system. The second equation introduces a velocity partial derivative term caused by rotation and a station position velocity offset on the basis of the first velocity transformation, so that the second velocity in the ECI coordinate system includes both the motion component of the space target relative to the radar and the motion component of the radar station relative to the Earth's center.

[0118] After obtaining the second position and the second velocity, it is necessary to further convert the first covariance information into the second covariance information, that is, to map the position covariance, velocity covariance and position-velocity cross-covariance in the ENU coordinate system to the ECI coordinate system to form the second covariance information, including the second position covariance, the second velocity covariance and the second position-velocity cross-covariance.

[0119] Specifically, let the position covariance in the ENU coordinate system be... The velocity covariance is The position-velocity cross-covariance is , The corresponding position covariance in the ECI coordinate system is The velocity covariance is The position-velocity cross-covariance is , The position covariance in the ECI coordinate system It can be represented as:

[0120]

[0121] in, The mathematical expectation operator is represented by the Greek letter in step S1. ,Will Substituting and expanding the linear expression, we get:

[0122]

[0123] This expression indicates that the position covariance in the ECI coordinate system is obtained by multiplying the position covariance in the ENU coordinate system by the direction cosine matrix and its transpose on both sides, ensuring that the statistical structure of the position error remains consistent in different coordinate systems.

[0124] Similarly, the velocity covariance in the ECI coordinate system can be expressed as:

[0125]

[0126] Will Substituting and expanding the linear expression, we get:

[0127]

[0128] This structure shows that the velocity covariance is related not only to the velocity covariance in the ENU coordinate system, but also to the position-velocity cross-covariance and the combination of position covariance under the influence of the angular velocity matrix. The additional linear term introduced by rotation is expressed through the matrix. This is reflected in their participation.

[0129] Similarly, the position-velocity cross-covariance in the ECI coordinate system can be expressed as:

[0130]

[0131] After unfolding, we get:

[0132]

[0133] Similarly, the cross-variance of velocity and position:

[0134]

[0135] It can be written as:

[0136]

[0137] The above set of matrix relationships together completes the mapping from the first covariance information to the second covariance information, so that the second position covariance, the second velocity covariance and the second position-velocity cross-covariance completely retain the error statistical structure in the ENU coordinate system in the ECI coordinate system, while explicitly reflecting the influence of Earth's rotation and station offset on error propagation.

[0138] This technical solution achieves the following technical effects by constructing a continuous geographic and physical parameter framework using a single reference station during coordinate transformation:

[0139] First, by uniformly expressing the state information derived from the local observation environment into a coordinate form suitable for three-dimensional spatial dynamics, the directional relationship between position and velocity in the spatial reference system can be kept more stable, thereby maintaining good geometric consistency in subsequent state extrapolation. This improves the accuracy of subsequent extrapolation calculations in expressing state changes and provides a structurally complete input basis for error propagation, enabling the state to be expressed coherently under different reference frames.

[0140] Second, by utilizing the structural characteristics of linear transformation, various statistical quantities formed by radar measurements can maintain their intrinsic correlation during the transformation process, thereby strengthening the correspondence between error components and ensuring that the statistical characteristics of velocity and position directions remain consistent in the spatial reference system. This lays a unified statistical structure for subsequent covariance derivation and also ensures that the distribution characteristics of errors in high-dimensional state space maintain good orthogonality and consistency, which is beneficial for subsequent dynamic models to handle error distribution.

[0141] Third, by reconstructing covariance information in a geocentric inertial coordinate system, each error component can obtain a structure that can be directly used in the prediction model under a global reference frame. This gives the state variables a stronger consistency basis when they are involved in perturbations, long-arc motions, or cross-radar links. Consequently, it maintains a more robust numerical performance in subsequent trajectory calculations, error extrapolation, and handover node determination, forming a more coordinated error and state expression system for continuous tracking of space targets.

[0142] Thus, step S2 explicitly constructs a coordinate transformation matrix system determined by the geodetic longitude, geodetic latitude, geodetic elevation, and Earth's rotation angular velocity of the first radar station, and uses this matrix and its time derivative to perform linear transformations to form the second position, second velocity, and second covariance information in the ECI coordinate system. This provides a complete and consistent state and error statistics basis for subsequent trajectory prediction and multi-radar handover correlation in the ECI coordinate system.

[0143] In step S3, the core task is to construct the initial forecast state and the initial forecast error covariance information in the ECI coordinate system using the second position, the second velocity, and the second covariance information, and to perform forecast extrapolation to obtain the forecast state and forecast error covariance information at future times.

[0144] Specifically, when constructing the initial forecast quantities, the second position vector and the second velocity vector obtained in step S2 need to be concatenated in the ECI coordinate system to form a six-dimensional initial forecast state vector:

[0145]

[0146] in, For the second position, For the second velocity, the second position covariance, the second velocity covariance, and the second position-velocity cross-covariance obtained in step S2 are combined to form the initial covariance information of the prediction error:

[0147]

[0148] in, The second position covariance, For the second velocity covariance, and The second position-velocity covariance is used to characterize the uncertainty of position and velocity and their correlation at the initial moment.

[0149] In this embodiment of the application, during the state extrapolation process, a discrete-time spatial dynamics model is used to update the predicted state, changing the predicted state from time [time value missing]. Advance to the moment It can be written as:

[0150]

[0151] in, and The coefficient matrix used for forecasting is denoted as . Based on the time distance from the walk, it is constructed as follows:

[0152]

[0153] Among them, matrix By introducing time intervals in position sub-blocks Incorporating velocity into position updates, matrix Introduced into velocity components And introduce into the position component Together with the acceleration vector, they form a state propulsion structure in the form of a second-order integral.

[0154] In this embodiment, the acceleration vector of the space target in the ECI coordinate system is calculated using the Earth's gravitational field parameters and the predicted initial state through a space dynamics model including the Earth's non-spherical gravity term, and the predicted state is updated with the predicted initial state and the acceleration vector.

[0155] Wherein, the acceleration vector in the ECI coordinate system is the dynamic function. Written as:

[0156]

[0157] Expanding and substituting, we get:

[0158]

[0159] in, , , For a moment Predict the position elements in the initial state vector. Let the position modulus of the space target in the ECI coordinate system be denoted as . The gravitational constant is... , It represents the second-order zone harmonic coefficient of the Earth. Let be the equatorial radius of the Earth. The above expression is based on the gravitational model and superimposes zonal harmonic terms related to latitudinal and altitude terms to correct the acceleration of the space target in the ECI coordinate system.

[0160] This forecast extrapolation technique achieves the following technical effects by continuously predicting the target motion within a unified dynamics framework:

[0161] First, by utilizing the structural features of the space dynamics model, the motion state of the target in the geocentric inertial coordinate system is made more consistent with the actual trajectory evolution trend, thereby maintaining higher trajectory coherence in the state prediction at future moments and maintaining stable evolution accuracy in long arc motion affected by perturbation, so that the prediction results have more reliable temporal consistency in subsequent use.

[0162] Second, by adopting an acceleration construction method based on gravitational field parameters, the state update process can fully reflect the influence of the Earth's non-spherical gravity on the target trajectory, effectively suppressing the deviation between the future state trend and the real dynamic environment, and maintaining stronger coordination of the dynamic model's performance in different altitude regions. This gives the extrapolated trajectory a more complete physical logic basis and provides consistent state input for subsequent prediction links.

[0163] Third, by combining the initial state with the acceleration vector for state updates, the state evolution can reflect the coupling relationship between velocity changes and gravitational perturbations, making the trajectory evolution exhibit a smoother change pattern in the high-dimensional state space, and making the future trajectory estimation based on dynamic conditions maintain a more robust extensibility over time, thus forming a state extrapolation capability suitable for cross-time domain prediction in multi-radar environments.

[0164] Furthermore, after defining the state progression, it is necessary to propagate the forecast error. A linearized error propagation relationship can be constructed based on the Jacobian matrix of the space dynamics model. The initial covariance information of the forecast error is propagated in the form of a combination of the Jacobian matrix and the state transition matrix. Process noise covariance information is introduced during the propagation process, so as to finally obtain the forecast error covariance information at future times.

[0165] Specifically, for the forecast model, the nonlinear function Taking the partial derivatives of each component of the predicted initial state vector, we construct the Jacobian matrix. The matrix structure is written as:

[0166]

[0167] The first three columns of the matrix reflect the first-order sensitivity of the acceleration vector to the position component, while the last three columns give the first-order sensitivity of the acceleration vector to the velocity component. In the current dynamic model, acceleration does not explicitly contain velocity, so the last three columns are zero and can be directly treated as a zero matrix during implementation.

[0168] After the Jacobian matrix is ​​constructed, the initial covariance matrix of the forecast error is advanced by combining the state transition matrix and the Jacobian matrix. The error propagation relation is written as:

[0169]

[0170] in, The covariance matrix of the zero-mean Gaussian white process noise is used to characterize the stochastic uncertainties introduced by truncating higher-order terms, unmodeled perturbations, and external disturbances in the space dynamics model. This is achieved through continuous superposition during propagation. This allows the forecast error covariance to reflect the diffusion characteristics of the cumulative uncertainty over time during the dynamic prediction process.

[0171] For example, in a specific implementation, an appropriate sampling interval can be selected based on the type of space target and the orbital altitude. Based on engineering experience, the process noise covariance matrix is ​​given. The diagonal element order of magnitude ensures that the prediction error covariance matches the actual tracking accuracy after multiple sampling periods. During operation, the consistency between the predicted and measured trajectories can be compared to... Adjustments will be made.

[0172] This error propagation technique utilizes the locally linearized structure of the dynamic model to construct an error inference link, achieving the following technical effects:

[0173] First, by using an error expansion method based on the Jacobi matrix, the propagation path of the error during the state change process presents a more explicit linear structure, thereby maintaining a high degree of evolution consistency in the error prediction at future moments, and maintaining the structural stability of the error information in scenarios where the state dimension increases or the trajectory changes rapidly, so that the propagation trend of the error is coordinated with the spatial dynamics environment.

[0174] Second, by using the Jacobian matrix in conjunction with the state transition matrix, the error change can simultaneously reflect the local dynamic influence and the overall state update law, so that the covariance maintains the continuous expression of correlation in matrix operations and exhibits a higher positive definite preservation ability in the error evolution process. Thus, the error structure in the future time step still has a clear statistical relationship under high-dimensional operations, providing a stable error input basis for subsequent state deduction and correlation judgment.

[0175] Third, by introducing process noise covariance information during error propagation, the model becomes more resistant to external disturbances, trajectory deviations, or small model uncertainties. This allows the error estimate for future moments to maintain a more robust expression in a dynamically changing environment and forms an adaptive error structure when there are model approximations or perturbation fluctuations. The resulting forecast error covariance information is more closely aligned with the actual state distribution, thus providing a more reliable error description system for subsequent processing links.

[0176] Thus, step S3 constructs the initial covariance matrix of the forecast initial state and forecast error in the ECI coordinate system using the second position, second velocity, and second covariance information. It then combines the space dynamics model containing the Earth's non-spherical gravity term and its Jacobian matrix, using a combination of the state transition matrix and the Jacobian matrix to advance the state and error covariance. In addition, process noise covariance information is explicitly introduced during propagation, realizing the continuous extrapolation of the forecast state and forecast error covariance in time. This lays a complete predictive foundation for estimating the time and position of subsequent space targets entering the subsequent radar airspace and for handover tracking between multiple radars.

[0177] In step S4, the core task is to use the predicted state and prediction error covariance information of the future time obtained in step S3 to analyze the predicted trajectory of the space target time by time, thereby determining the entry time of the space target into the coverage airspace of the second radar based on the predicted state and prediction error covariance information, and sending the predicted state and prediction error covariance information corresponding to the entry time to the second radar.

[0178] In some embodiments of this application, it is necessary to convert a series of future discrete time forecast states into coordinate representations based on the second radar, compare the coverage airspace conditions of the second radar, filter the forecast times that satisfy the coverage airspace constraints, and identify the time when the second radar first detects the target among these candidate times. This time is taken as the entry time, so that the second radar can receive the forecast state and forecast error covariance information from the first radar at the moment when the space target has just entered the coverage boundary and can be effectively detected.

[0179] Specifically, when constructing the criteria for determining the entry time, the future time forecast state sequence obtained in step S3 is denoted as:

[0180]

[0181] The corresponding future time prediction error covariance is denoted as Together, these two constitute the motion prediction information and error statistics information of space targets on the future time axis.

[0182] Simultaneously, in order for the second radar to determine coverage relationships under a unified reference, it is necessary to convert the forecast states at multiple future times into coordinate representations based on the second radar, denoted as... This transformation is accomplished through the location and attitude of the second radar, as well as the geometric relationship between its ENU coordinate system and ECI coordinate system, enabling the second radar to assess whether a space target falls within its coverage area in its own working coordinate system.

[0183] In the converted trajectory, the airspace covered by the second radar can be described by a set of constraints, including its field of view, elevation limit, azimuth limit, lower bound of the measured elevation angle, and upper bound of the maximum observation distance, denoted as . Next, the predicted states for multiple future times need to be compared with the airspace covered by the second radar. The comparison rules can be as follows: The decision is made to retain only future times that satisfy the coverage space constraints, thus forming a set of candidate times for entry. Each of the sets These could all be effective time points for space targets to enter the coverage area of ​​the second radar.

[0184] Based on this, in order to give a clear definition of the entry time in the candidate time set, the "earliest detectable time" is adopted as the selection criterion. Specifically, for the set... Arranged chronologically, and verified one by one based on the minimum elevation angle requirement, maximum range constraint, and preset detection conditions of the second radar (such as the target echo signal-to-noise ratio reaching the operating threshold, the target not being obstructed by the ground, etc.). The moment when the second radar first achieves detection capability under these conditions is marked as the entry time. Formally, it can be written as:

[0185]

[0186] Once the entry time is obtained The forecast status corresponding to that moment. and forecast error covariance The signal is sent to the second radar as the initial input for its follow-up tracking, ensuring that the follow-up process unfolds around the moment when the second radar is first able to effectively detect space targets.

[0187] For example, in a typical long-distance rendezvous scenario, several future discrete sampling periods can be set as candidate time windows. After each forecast state is converted to the second radar reference coordinates, coverage determination is performed one by one. Among the times when the elevation angle, azimuth angle and range constraints are met and the estimated detection conditions meet the working requirements, the earliest time is selected as the final entry time.

[0188] This entry time determination technology achieves the following technical effects by selecting the optimal entry time from the unified prediction link:

[0189] First, by using a coordinate representation method based on the second radar, the state at future moments has a consistent basis for expression in subsequent judgments, thereby maintaining a clearer geometric correspondence under different spatial location conditions and making the spatial relationship between radars present a more stable matching effect, thus enhancing the ability to interpret position changes in dynamic environments.

[0190] Second, by adopting a screening method based on coverage spatial constraints, the adaptability of each candidate time in terms of geometric conditions is improved, the relationship between the predicted state and the effective detection area is more determinable, and a more coordinated entry basis is formed in the comparison of multiple times, so that the selection of the handover node has higher spatial adaptability and the predicted time corresponds well with the actual detectable conditions.

[0191] Third, by using the covariance of the prediction error in the position direction, the selection of the entry time can take into account both the spatiotemporal relationship and the error distribution trend, and reflect the constraint of error information in the time series extrapolation, so that the final selected entry time can maintain more reliable stability in the future state extrapolation, thereby providing a clearer time reference for the subsequent interception and correlation process.

[0192] Thus, step S4 performs time-by-time coordinate transformation and coverage judgment on the predicted state formed by the second position and the second velocity advancement on the future time axis, and selects the moment when the second radar first detects the target from the candidate moments that meet the coverage and detection conditions as the entry time. This establishes an entry time selection mechanism based on the constraint of the coverage airspace and the earliest detectable moment as the criterion, enabling the second radar to obtain the state input in a timely manner when the space target reaches the coverage boundary and meets the detection conditions, providing stable support for the continuity and reliability of subsequent follow-up tracking.

[0193] In step S5, the core task is that after obtaining the predicted state and prediction error covariance information corresponding to the entry time, the second radar needs to plan the interception position and interception area suitable for its own measurement method based on the prediction result, and conduct space target search and initial tracking within the interception area to obtain candidate state and candidate covariance information. The overall goal in this process is to enable the second radar to use the prediction center point and uncertainty range to lock the possible target landing area in its own observation coordinate system, and to establish a preliminary state estimate of the space target after acquiring actual measurement data, forming a candidate state in the ECI coordinate system. With candidate covariance information This serves as the candidate state and candidate covariance information required for subsequent association judgment.

[0194] It should be noted that in this step and subsequent steps, the following will still be used: This indicates the entry time into the airspace covered by the second radar, obtained in step S4. .

[0195] Specifically, the second radar will first enter the time-corresponding forecast state. and forecast error covariance information As input, the forecast state is mapped to the measurement space used by the second radar to conform to the observation dimension of the second radar, so that the interception position can be planned according to the forecast state; then, the forecast error covariance information is transformed into coordinates through the linearization relationship of the measurement space to form the covariance matrix in the measurement space. ,in The partial derivative matrix of the measurement space is used to describe the local projection of the ECI coordinate system error vector in the second radar measurement dimension, so that the error distribution can be characterized under the second radar working system, and thus the interception area can be planned.

[0196] Simultaneously, to enable the second radar to focus on the most probable target impact area during the subsequent search phase, a three-dimensional envelope region surrounding the predicted state needs to be constructed based on the eigenvectors and eigenvalues ​​of the transformed covariance matrix. For this purpose, it is necessary to... Eigenvalues ​​and eigenvectors are extracted, and the three sets of eigenvectors are used as the principal directions of the uncertainty distribution in the measurement space, with the square root of the eigenvalues ​​used as the extension scale along each principal direction. Based on this, the mapping position of the predicted state in the measurement space is used as the basis for the calculation. Construct a three-dimensional envelope region centered on the target area. ,in, This is the adjustment amount of the envelope area. By adjusting this parameter, the range of the intercept space can be controlled, so as to maintain a balance between search efficiency and coverage. This envelope area is used to constrain the beam pointing and scanning strategy of the second radar, so that the search process always revolves around the high probability area of ​​possible locations.

[0197] The interception area planning technology solution achieves the following technical effects by constructing a three-dimensional envelope based on an error structure within the measurement space:

[0198] First, by utilizing the coordinate transformation of the forecast error covariance information, the error information can be consistently expressed in the second radar measurement space, so that the error distribution maintains the continuity of directional characteristics in the new coordinate system and reflects the integrity of the statistics in the three-dimensional spatial structure, so that the predicted state has a more accurate reference basis in subsequent searches.

[0199] Second, by constructing the envelope region based on eigenvalues ​​and eigenvectors, the direction of error extension in space is clearly characterized, and the shape of the envelope is more in line with the distribution trend of the predicted state. This gives the search area a higher geometric matching capability, enabling the radar to focus on a more reasonable spatial range during the initial search and reducing the resource consumption caused by invalid search areas.

[0200] Third, by using a three-dimensional envelope region constructed around the predicted state, the search process can maintain a good fit to the predicted trajectory even under dynamic conditions, thereby enhancing the search efficiency in a multi-radar cooperative environment and making the initial tracking phase more stable. This provides a coherent spatial basis for subsequent correlation calculations and state updates, making the interception process more reliable.

[0201] After the three-dimensional envelope region is constructed, the second radar enters the interception and search phase. It performs a comprehensive scan of the space within the envelope region using detection methods such as beam scheduling, scanning sequences, or fixed directions. After obtaining valid measurements, the second radar uses these measurements, combined with predicted positions near the envelope center, to perform initial filtering on the spatial target, thus obtaining the target state expressed in the ECI coordinate system. and the corresponding error covariance These two items are the candidate states and candidate covariance information of the space target after being intercepted by the second radar, which provide basic data for subsequent cross-radar information association.

[0202] For example, in a scenario involving long-range detection and airspace intersection, parameters can be adjusted. By controlling the probability quality covered by the envelope, we can avoid the search efficiency from being too large and the detection from being too small, thus ensuring that the second radar can acquire stable measurements and complete the initial tracking start as soon as the target enters its field of view.

[0203] Thus, step S5 maps the forecast state and forecast error covariance information to the second radar measurement space, constructs a three-dimensional envelope region based on the covariance feature structure, and performs interception search within the envelope region, enabling the second radar to form candidate states in the geocentric inertial coordinate system after the target enters the coverage airspace. With candidate covariance This provides a continuous and reliable initial data foundation for subsequent association judgments.

[0204] In step S6, the core task is to construct a test statistic based on the predicted state, prediction error covariance information, and candidate state and candidate covariance information output by the second radar, obtained in the previous steps. This statistic, combined with multi-time-step correlation quality evaluation, determines the cross-radar correlation result, ultimately completing the handover tracking of the space target. During this process, it is necessary to construct a statistic based on the state differences between the predicted trajectory and the intercepted trajectory, cumulatively evaluate the success or failure of correlation at multiple time steps, and filter candidates when multiple candidate tracks exist to obtain cross-radar correlation results that meet statistical constraints.

[0205] In the embodiments of this application, when performing correlation testing, it is necessary to perform the same sampling time... The forecast information and candidate information are paired. Specifically, for the first radar, the forecast information is paired with the candidate information. The trajectory, and its predicted state in the ECI coordinate system, is denoted as... The forecast error covariance information is denoted as The second radar The trajectory, and its candidate states in the ECI coordinate system are denoted as follows: Candidate covariance information is denoted as These four items together constitute a set of data to be tested at this sampling time, which are used to construct test statistics and assess whether the radars are pointing to the same spatial target.

[0206] In some embodiments of this application, in order to characterize the geometric deviation between the predicted state and the candidate state, the difference between the predicted state and the candidate state can be used to construct a state difference vector, defined as follows: This vector, in six dimensions within the ECI coordinate system, represents the difference between position and velocity, characterizing the degree of offset between the two trajectories at the current moment. Simultaneously, the prediction error covariance information and the candidate covariance information are added to form a joint covariance matrix, written as... , where the matrix It comprehensively reflects the joint distribution of forecast uncertainty and interception uncertainty at the current moment, and is used to weight the state difference vector.

[0207] After obtaining the state difference vector and the joint covariance matrix, matrix multiplication is performed using the transpose of the state difference vector, the inverse of the joint covariance matrix, and the state difference vector to obtain the test statistic, defined as: This quantity is essentially a distance metric with joint covariance weighting, used to characterize the degree of matching between the forecast state and the candidate state. The smaller the value, the closer the two trajectories are under the current covariance structure.

[0208] This test statistic construction technique achieves the following technical effects by measuring state differences within a unified error framework:

[0209] First, by using the state difference vector as the core comparison basis, the difference between cross-radar candidate states and predicted states is clearly expressed in high-dimensional space, so that the trend of position and velocity change maintains clear directionality in the comparison process, and the association judgment has a more sensitive recognition ability when the state difference is small, making cross-radar state matching more reasonable.

[0210] Second, by adopting the construction method of joint covariance matrix, error information can be consistently presented under additive structure, and prediction error and candidate error can form a comparable relationship under a unified statistical framework. This enables an effective trade-off between state differences and error scale, keeps the test results stable under different error levels, and makes cross-radar judgment more reliable under complex conditions.

[0211] Third, by using matrix multiplication to form test statistics, the measurement results can simultaneously reflect the magnitude of state differences and the directionality of error distribution, giving the association judgment a more complete statistical basis and demonstrating stronger robustness under multidimensional data processing conditions. This provides reliable input for subsequent association quality evaluation and makes the cross-radar association process more robust.

[0212] Based on a single test, limit constraints need to be introduced to form decision conditions. Therefore, limit values ​​are preset. ,when At that time, determine the current sampling time. The predicted trajectory and the first If the candidate trajectories are statistically compatible, it can be considered a "successful association" result; when If this occurs, it is considered a "correlation failure". Additionally, if the second radar has more than one track in the aforementioned single test... If the test requirements are met, then the test statistic is taken. To achieve the minimum trajectory As the associated track at that moment.

[0213] Furthermore, in order to reduce the impact of momentary misjudgments on the final results in complex environments, it is necessary not only to make judgments based on test statistics at a single moment, but also to conduct cumulative evaluations of the associated results at multiple moments.

[0214] In the embodiments of this application, a correlation quality function is introduced in the multi-time cumulative evaluation. Used to record the correlation performance from the start time to the current time. Specifically, let... Indicates the sampling time, the initial time is defined. For each pair of predicted and candidate states, a test statistic is calculated and compared. After each test, the incremental term in the correlation quality function is updated based on the comparison between the current test statistic and the preset limit. It can be written as:

[0215]

[0216] And through recursive relations This forms a cumulative association quality record over time. When an association is determined to be successful, a predetermined increment is added to the association quality function. When an association is determined to be unsuccessful, the association quality function remains unchanged.

[0217] Furthermore, if in a segment of length... There are a total of If the association is successful, then:

[0218]

[0219] At this point, the association quality function can be normalized based on the quantitative relationship between the number of successful associations and the number of association judgments, and the cross-radar association result can be determined based on the normalized result. and The ratio gives the association quality level within that time period. For example, in some application scenarios, a specific value can be selected. A value close to 0.5 is used as a dividing line to distinguish between stable and unstable correlations.

[0220] This correlation quality assessment technology achieves the following technical effects by accumulating correlation information from multiple time points during continuous sampling to form a stable criterion:

[0221] First, by using the statistical calculation results of each pair of forecast states and candidate states as evaluation input, the judgment process has the ability to accumulate over time beyond a single comparison, and the correlation quality function can reflect the continuous impact of historical judgments on the current trend. This allows for a more robust expression under conditions of trajectory fluctuations or uneven measurement quality, and enables the correlation evaluation to have a higher adaptability in dynamic environments.

[0222] Second, a normalization method based on the relationship between the number of successful judgments and the total number of judgments is adopted so that the quality function can reflect the importance of the success rate to the overall judgment, and the evaluation results can still have a uniform scale under different sampling lengths. This makes the function change trend after multiple time-accumulation more reflective of the actual correlation tendency, makes the cross-radar correlation criteria present a clearer direction in a statistical sense, and makes the judgment results maintain higher reliability in complex scenarios.

[0223] Third, by using the method of distinguishing between success and failure in the sampling sequence, the correlation evaluation can reflect the continuous changes in state differences over time, so that short-term anomalies do not have an excessive impact on the final judgment, and the evaluation mechanism can still maintain sufficient resistance to disturbances in the event of multiple error propagation or temporary obstruction. Thus, under the evaluation framework with time accumulation properties, it provides a more stable statistical basis for the final correlation judgment.

[0224] Furthermore, based on the aforementioned infrastructure, to more precisely differentiate the contributions of different successful associations, a weight design related to the test statistic can be introduced when updating the association quality function, for each sampling time determined as a successful association. Based on the magnitude of the test statistic at the corresponding sampling time, assign weight values ​​related to the test statistic. Introducing weights based on And adjust the update relationship of the correlation quality function as follows:

[0225]

[0226] Among them, weight The value decreases as the test statistic at the corresponding time point increases, reflecting that a smaller test statistic indicates a higher degree of matching and a greater contribution to the overall association quality. Simultaneously, to enhance the sensitivity to association results at recent sampling times, it is possible to... A time decay factor is introduced to attenuate the weight values ​​at earlier sampling times, gradually reducing the contribution of earlier times during continuous sampling. This allows for a higher quality function level to be achieved for the same number of successful associations in recent periods, ultimately constructing an association quality function sensitive to recent association results. Simultaneously, during normalization, a length of [missing information] can be used. Within the time window The ratio of the ratio to the corresponding cumulative weight is used to obtain the normalized association quality index.

[0227] This weighted quality function technique achieves the following technical effects by introducing a dynamic weight structure based on statistical changes during the evaluation process:

[0228] First, by utilizing weights that vary with the size of the test statistic, the successful association records can obtain a stronger contribution expression under conditions of small differences, the quality function can be significantly enhanced when candidate states that approximate the predicted trend appear, and the evaluation process can be made more sensitive to the state performance near the true trajectory, thereby making the evaluation results exhibit higher identification accuracy in complex state distributions.

[0229] Second, by attenuating the weight values ​​of early sampling moments, the evaluation focus is more concentrated on recent judgment results, enabling the quality function to reflect rapid changes in the target's movement trend in a timely manner. This ensures good timeliness even when there are sudden changes in the trajectory, changes in measurement, or changes in related environmental conditions, making the evaluation system more adaptable to dynamic changes and giving the final evaluation a stronger realistic correspondence.

[0230] Third, by using a dynamic weighting structure, the impact of judgments at different times on the overall evaluation is differentiated, allowing the quality function to maintain a clear statistical relationship even when the data volume is large or the error fluctuation is strong. This enables the recording structure to emphasize effective judgments and suppress the impact of noise, thereby forming a more robust evaluation curve in the continuous sampling sequence and providing a more reliable statistical basis for subsequent related decisions.

[0231] In some embodiments of this application, the determination of cross-radar correlation results can employ a combination of multi-time quality evaluation and single-time decision. For a given time window length, after calculating the test statistics and updating the quality function for all sampling times within that time window, the final cross-radar correlation result is given based on the comparison between the normalized correlation quality index and a preset quality threshold. If the normalized index exceeds the preset quality threshold, the first radar is considered to have passed the first radar correlation test. The trajectory and the second radar's first If the trajectories exhibit stable and consistent correlation characteristics within the time window, it can be determined that the two correspond to the same spatial target, and the handover tracking of the spatial target is completed in terms of time sequence; if the normalization index is lower than the quality threshold, it is considered that the consistency between the trajectory pairs is insufficient and is not judged as a valid handover.

[0232] In some embodiments of this application, when the second radar generates multiple candidate trajectories at the same sampling time, corresponding to multiple candidate states and candidate covariance information, further filtering is required from the candidate set. Specifically, for the same... The predicted trajectory and all the second radar at the same time Calculate the test statistic for each candidate trajectory. , will satisfy The candidate set is used as the set of optional associated objects. Within this set, the candidate trajectory number with the smallest test statistic is selected. ,Right now:

[0233]

[0234] Only this trajectory is used as the associated object at the current sampling time to participate in the update of the association quality function. If none of the candidate trajectories meet the preset limit at the current time, it is determined that there is no successful association record at the current time. The process remains unchanged, recording only one instance of association failure. This approach avoids duplicate weighting of the same predicted trajectory by multiple candidate trajectories at the same time, thus ensuring the uniqueness of the association logic.

[0235] This multi-candidate state screening technique achieves the following technical effects by optimizing the candidate states and updating the evaluation structure at the same sampling time:

[0236] First, by directly comparing the statistics corresponding to each candidate state, the judgment process obtains a clear selection basis when there are multiple trajectory possibilities, enabling the optimal candidate to show a stronger advantage in the state difference measurement, thus making the association judgment maintain a clear direction under the condition of many branches, and making the cross-radar matching results more accurate.

[0237] Second, by adopting the method of selecting associated objects based on the principle of minimum statistics, the screening process can take into account both the trend of the predicted state and the distribution of the error structure, so that the selection results are closer to the position and velocity direction of the real target in a statistical sense, thereby maintaining a more coherent association link in the subsequent sampling process, and making cross-radar tracking have a more stable connection performance in the continuous time dimension.

[0238] Third, by using the optimal candidate to update the quality function, the correlation evaluation can reflect the best matching situation at the current moment in real time, and the quality function can continue to change with the selection results under different sampling conditions. This enables the evaluation system to have better discrimination ability when facing complex candidate sets, thereby forming a more reliable correlation trend in the statistical sense accumulated over multiple future moments, and laying a more stable judgment foundation for the complete cross-radar handover process.

[0239] Furthermore, while considering multi-timeframe behavior, at the end of each time window, the normalized association quality index can be combined with the distribution of test statistics over the duration for auxiliary judgment. For example, when a pair of trajectories corresponds to low test statistics at most sampling times and the normalized quality index exceeds a preset threshold, the cross-radar continuity relationship between the two trajectory pairs can be considered stable. When the test statistics frequently approach the preset limit boundary or there are many instances of exceeding the limit, even if the normalized index reaches the threshold in a few windows, the risk of false association can be suppressed by adjusting the quality threshold or the window length.

[0240] Thus, step S6 constructs a test statistic using the state difference vector and joint covariance matrix between the predicted state and the candidate state, and uses weighted accumulation and normalization at multiple time points to form a correlation quality evaluation. At the same time, when there are multiple candidate trajectories, a unique correlation object is selected based on the threshold and minimum criterion of the test statistic, thus completing the determination of the correlation results between radars and the final confirmation of the handover tracking of space targets.

[0241] In summary, this method achieves continuous estimation and handover association of space targets within the coverage area of ​​multiple radars by establishing a unified geocentric inertial coordinate framework between the first and second radars, constructing a space trajectory prediction mechanism that includes state covariance propagation, forming a precise interception area planning based on three-dimensional envelope, and introducing a test statistic composed of state difference vector and joint covariance matrix. This enables the continuous estimation and handover association of space targets within the coverage area of ​​multiple radars. It can maintain the consistency of target state expression under large-scale, high-dynamic, and cross-site observation conditions, making the trajectory connection between multiple radars more stable and the association decision more reliable. Furthermore, it maintains high association robustness and handover success rate in long-distance observation scenarios where errors grow rapidly.

[0242] It should be noted that, although the embodiments in this application are based on... Figure 1 Steps S1 to S6 are described sequentially, but this does not mean that steps S1 to S6 must be performed in a strict order. The reason this embodiment follows this order is... Figure 1The order in which steps S1 to S6 are described is provided to facilitate understanding of the technical solutions of the embodiments of this application by those skilled in the art. In other words, in the embodiments of this application, the order of steps S1 to S6 can be appropriately adjusted according to actual needs.

[0243] The above-disclosed embodiments are merely preferred embodiments of the present invention, but the present invention is not limited thereto. Any non-creative variations that can be conceived by those skilled in the art, as well as any improvements and modifications made without departing from the principles of the present invention, should fall within the protection scope of the present invention.

Claims

1. A multi-radar handover tracking method for space targets based on forecast error covariance propagation, characterized in that, Includes the following steps: The space target is filtered and tracked in the northeast-sky coordinate system of the first radar to obtain the first position, first velocity, and first covariance information including the first position covariance, the first velocity covariance, and the first position-velocity cross-covariance at the last observation time. The first position, first velocity, and first covariance information are transformed to the geocentric inertial coordinate system to obtain the second position, second velocity, and second covariance information; The initial state and initial covariance of the forecast error are constructed using the second position, second velocity, and second covariance information, and the forecast is extrapolated to obtain the forecast state and forecast error covariance information for future times. The entry time of a space target into the airspace covered by the second radar is determined based on the forecast status and forecast error covariance information, and the forecast status and forecast error covariance information corresponding to the entry time are sent to the second radar. The second radar plans the interception position and interception area based on the forecast state and forecast error covariance information, and performs tracking to obtain candidate state and candidate covariance information. Based on the forecast state, forecast error covariance information, candidate state and candidate covariance information, a test statistic is constructed, and combined with multi-time-time correlation quality evaluation, the cross-radar correlation result is determined to complete the handover tracking of space targets.

2. The space target multi-radar handover tracking method based on prediction error covariance propagation as described in claim 1, characterized in that, The steps of transforming the first position, first velocity, and first covariance information to the geocentric inertial coordinate system to obtain the second position, second velocity, and second covariance information include: A coordinate transformation matrix is ​​constructed based on the geodetic longitude, geodetic latitude, geodetic elevation, and Earth's rotation angular velocity of the location of the first radar station; The first position, first velocity, and first covariance information are linearly transformed using a coordinate transformation matrix to obtain the second position, second velocity, and second covariance information. The second covariance information includes the second position covariance, the second velocity covariance, and the cross-covariance between the second position and velocity.

3. The space target multi-radar handover tracking method based on prediction error covariance propagation as described in claim 1, characterized in that, The forecast extrapolation includes: using a space dynamics model to calculate the acceleration vector of the space target in the geocentric inertial coordinate system based on the Earth's gravitational field parameters and the forecast initial state, and updating the forecast state with the forecast initial state and the acceleration vector. The space dynamics model includes the Earth's non-spherical gravity term.

4. The space target multi-radar handover tracking method based on prediction error covariance propagation as described in claim 3, characterized in that, The forecast extrapolation further includes: constructing a linearized error propagation relationship based on the Jacobian matrix of the space dynamics model, propagating the initial covariance information of the forecast error in the form of a combination of the Jacobian matrix and the state transition matrix, and introducing process noise covariance information during the propagation process to obtain the forecast error covariance information at future times.

5. The space target multi-radar handover tracking method based on prediction error covariance propagation as described in claim 1, characterized in that, The steps for determining the entry time of a space target into the airspace covered by the second radar based on the forecast state and forecast error covariance information include: converting the forecast state of multiple future times into a coordinate representation based on the second radar, comparing it with the airspace covered by the second radar, and selecting the earliest time when the second radar detects the target from the forecast times that satisfy the airspace coverage constraints as the entry time.

6. The space target multi-radar handover tracking method based on prediction error covariance propagation as described in claim 1, characterized in that, The steps of the second radar to plan the interception position and interception area based on the forecast state and forecast error covariance information include: transforming the forecast error covariance information into coordinates in the measurement space of the second radar, constructing a three-dimensional envelope region around the forecast state based on the eigenvectors and eigenvalues ​​of the transformed covariance matrix, and performing an interception search within the three-dimensional envelope region.

7. The space target multi-radar handover tracking method based on prediction error covariance propagation as described in claim 1, characterized in that, The steps for constructing a test statistic based on the forecast state, forecast error covariance information, candidate state, and candidate covariance information include: constructing a state difference vector from the difference between the forecast state and the candidate state; constructing a joint covariance matrix by adding the forecast error covariance information and the candidate covariance information; and performing matrix multiplication operations using the transpose of the state difference vector, the inverse of the joint covariance matrix, and the state difference vector to obtain the test statistic.

8. The space target multi-radar handover tracking method based on prediction error covariance propagation as described in claim 1, characterized in that, The steps for determining cross-radar association results by combining multi-time-time association quality evaluation include: calculating a test statistic for each pair of forecast states and candidate states; updating the association quality function based on the comparison between the test statistic and a preset limit; adding a predetermined increment to the association quality function when the association is judged to be successful; keeping the association quality function unchanged when the association is judged to be unsuccessful; normalizing the association quality function based on the quantitative relationship between the number of successful associations and the number of association judgments within a set of continuous sampling times; and determining the cross-radar association results based on the normalized results.

9. The space target multi-radar handover tracking method based on prediction error covariance propagation as described in claim 8, characterized in that, When updating the association quality function, a weight value related to the test statistic is assigned to the successfully associated records based on the magnitude of the test statistic at the corresponding sampling time. The weight value decreases as the test statistic increases, and the weight value of the earlier sampling time is decayed during continuous sampling to construct an association quality function that is sensitive to recent association results.

10. The space target multi-radar handover tracking method based on prediction error covariance propagation as described in claim 8, characterized in that, When the second radar generates multiple candidate states and candidate covariance information at the same sampling time, the test statistic is calculated for each candidate state. Among the candidate states that meet the preset limit, the candidate state with the smallest test statistic is selected as the associated object at the current sampling time, and the association quality function is updated based on the associated object.

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