Space target short-arc orbit determination configuration design method based on space-based cooperative angle measurement

Abstract

The application discloses a space target short-arc orbit determination observation configuration design method based on space-based cooperative angle measurement, and belongs to the technical field of spaceflight measurement and control. The steps comprise the following steps. Firstly, a nonlinear orbit determination system is constructed by fusing a perturbation dynamics state model and a space-based multi-point cooperative inertial angle measurement observation model. Secondly, time updating and observation updating are performed through a nonlinear Kalman filter, and orbit estimation values are obtained by accumulating preset short-arc segment time. Thirdly, multiple observation configurations covering coplanar, non-coplanar and different scales are designed, and corresponding orbit estimation values are obtained. Finally, the optimal configuration is selected through error comparison. The application can effectively overcome the geometric defects of suboptimal observation configurations, improve the precision and robustness of short-arc segment space target orbit determination, and provide reliable support for high-dynamic space target monitoring.

Description

Technical Field

[0001] This invention relates to the field of aerospace telemetry and control technology, and in particular to a method for designing short-arc orbit determination observation configurations for space targets based on space-based collaborative angle measurement. Background Technology

[0002] Addressing the needs of space security and orbital resource maintenance, and focusing on the determination of non-cooperative space target orbits, this technology leverages the advantages of space-based optical observation—its all-weather, all-time capability and resistance to environmental interference—to develop single-satellite observation and multi-satellite collaborative angle measurement orbit determination technology. This technology integrates observation data from multiple platforms and enhances observability through multi-dimensional geometric constraints to determine the orbits of space targets. Specific implementation methods include relative orbit determination using only angle measurement from two satellites and precise orbit determination through collaborative efforts from two platforms. This technology is a key technology supporting the orderly conduct of space activities.

[0003] Current space target orbit determination technology based on space-based angle measurement has a certain research foundation. The dual-satellite and dual-platform collaborative observation scheme can effectively improve observability under angle measurement conditions alone, and significantly improve orbit determination accuracy compared with single-satellite observation, verifying the application value of multi-line-of-sight collaborative observation in orbit determination. However, existing technologies have not carried out systematic and multi-dimensional design of observation configurations for short-arc orbit determination, which is highly dependent on observation conditions. They have not formed a multi-type observation configuration system covering different spatial distributions and different baseline scales. Under short-arc observation scenarios, the orbit estimation accuracy is low and the stability is insufficient, making it difficult to meet the practical application requirements of rapid and high-precision short-arc orbit determination of space targets. Summary of the Invention

[0004] The purpose of this invention is to provide a design method for short-arc orbit determination observation configuration of space targets based on space-based collaborative angle measurement, thereby solving the above-mentioned technical problems.

[0005] To achieve the above objectives, this invention provides a method for designing short-arc orbit determination observation configurations for space targets based on space-based collaborative angle measurement, comprising the following steps: S1. Based on the application requirements of short-arc precision orbit determination of space targets, a nonlinear space-based collaborative angle measurement and orbit determination system is constructed that integrates the perturbation dynamic state model and the space-based multi-point collaborative inertial angle measurement and observation model. S2. Based on the state model and observation model of the space-based collaborative angle measurement and orbit determination system, the time update and observation update operations are repeatedly executed by nonlinear Kalman filtering and the preset short arc time is accumulated to obtain the estimated value of the short arc orbit of the space target. S3. Based on the space-based multi-point collaborative angle measurement observation constraints of the space-based collaborative angle measurement and orbit determination system, design multiple sets of observation configurations between observation satellites and space targets, covering coplanar configurations, non-coplanar configurations and configurations of different scales, and obtain multiple sets of observation configurations and corresponding short arc orbit estimates of space targets; S4. Based on the set of nominal values ​​of the space target's orbital state within a preset short arc time and the set of estimated values ​​of the space target's short arc orbit corresponding to multiple observation configurations, the space target orbital estimation error is calculated through error comparison analysis and the optimal configuration is selected to obtain the optimal observation configuration suitable for the short arc orbit determination of the space target.

[0006] Preferably, the specific steps of S1 include: S11. The state variables of the space-based collaborative angle measurement and orbit determination system are obtained by defining the orbital position and velocity of the space target using a geocentric inertial coordinate system. Specifically: ; S12. Based on the constraints of geocentric gravity, the second-order zonal harmonics of Earth's oblateness, and the gravitational perturbations of the Sun, Moon, and other third bodies, by establishing a perturbation-containing acceleration... With Gaussian distributed process noise The nonlinear state function is: To obtain the perturbation dynamic state model of the space-based collaborative angle measurement and orbit determination system; S13. Based on the principle of space-based multi-point cooperative inertial angle measurement, the satellite position vector is observed in the geocentric inertial coordinate system. Constructing a structure with pitch angle Azimuth Observations and Gaussian distribution observation noise The nonlinear observation function is given by the formula: To obtain the space-based multi-point collaborative inertial angle measurement observation model of the space-based collaborative angle measurement and orbit determination system; S14. Based on the state variables, perturbation dynamics state model, and space-based multi-point collaborative inertial angle measurement observation model of the space-based collaborative angle measurement and orbit determination system, a nonlinear system architecture is constructed through system integration and fusion to obtain a nonlinear space-based collaborative angle measurement and orbit determination system that integrates the perturbation dynamics state model and the space-based multi-point collaborative inertial angle measurement observation model.

[0007] Preferably, the Gaussian distributed process noise in S1 Gaussian distribution observation noise All are zero-mean Gaussian white noise.

[0008] Preferably, the specific steps of S2 include: S21, based on the first Estimates of state variables of the orbit determination system at specific times Covariance Matrix The time update operation of nonlinear Kalman filtering is used to obtain the first... One-step prediction estimate of the state variables of the orbit determination system at a given time. And one-step prediction of covariance matrix ; S22, based on the first One-step prediction estimate of the state variables of the orbit determination system at a given time. And one-step prediction of covariance matrix The observation update operation through nonlinear Kalman filtering is used to obtain the first... Optimal estimates of state variables of the orbit determination system at a given time. and the optimal covariance matrix ; S23. Based on the optimal estimates of the state variables of the orbit determination system at each moment obtained from a single iteration, the estimated short-arc orbit of the space target is obtained by repeatedly executing the time update and observation update operations of the nonlinear Kalman filter and accumulating the preset short arc time.

[0009] Preferably, the nonlinear Kalman filter in S2 is an extended Kalman filter; the extended Kalman filter achieves a linear approximation of the nonlinear space-based collaborative angle measurement and orbit determination system by performing Taylor expansion on the nonlinear state function and the nonlinear observation function respectively, so as to complete the optimal estimation of the state variables.

[0010] Preferably, the nonlinear Kalman filter repeatedly performs time updates and observation updates according to a preset short arc observation time and observation sampling interval; and when the state correction or state estimation difference is less than a preset threshold, the filter estimation is determined to be stable.

[0011] Preferably, the specific steps of S3 include: S31. Constraints for space-based multi-point collaborative angle measurement observation based on space-based collaborative angle measurement and orbit determination system: By planning the spatial distribution topology relationship between observation satellites and space targets, three basic observation configurations are obtained: coplanar configuration, non-coplanar configuration, and configurations at different scales. S32. Based on the three basic observation configurations, by refining the horizontal / vertical arrangement of the observation satellites relative to the space target and the baseline scale parameters, multiple subdivided observation configurations corresponding to the coplanar configuration group, the non-coplanar configuration group, and the configuration groups of different scales are obtained. S33. Based on the space-based multi-point collaborative inertial angle measurement data corresponding to each subdivided observation configuration, the estimated short-arc orbit of the space target corresponding to each subdivided observation configuration is obtained through nonlinear Kalman filter iterative update and short arc time accumulation method. S34. Based on each set of subdivided observation configurations and the corresponding short-arc orbit estimates of space targets, through a one-to-one mapping and association operation between configuration parameters and orbit estimation results, multiple sets of observation configurations between observation satellites and space targets, covering coplanar configurations, non-coplanar configurations and configurations of different scales, and the corresponding short-arc orbit estimates of space targets are obtained.

[0012] Preferably, the coplanar configurations in S31 include coplanar horizontally aligned distribution, coplanar horizontally advanced distribution, coplanar horizontally lagging distribution, and coplanar longitudinally opposite-sided distribution; the non-coplanar configurations include non-coplanar horizontally aligned distribution, non-coplanar horizontally advanced distribution, non-coplanar horizontally lagging distribution, and non-coplanar longitudinally opposite-sided distribution; the different scale configurations include medium-scale coplanar horizontally aligned distribution and large-scale coplanar horizontally aligned distribution.

[0013] Preferably, the specific steps of S4 include: S41. The set of nominal values ​​of the orbital state of the space target within a preset short arc segment and the set of estimated values ​​of the short arc orbit of the space target corresponding to multiple observation configurations are matched and aligned one-to-one with the orbital state data at each time point to obtain the matching dataset of nominal values ​​and estimated values ​​of the orbital state of the space target at each time point and each observation configuration within the preset short arc segment. S42. Based on the matching dataset of nominal and estimated values ​​of the space target orbit state at each moment and for each observation configuration within a preset short arc segment time, the estimated error of the space target orbit for each observation configuration is obtained through moment-by-moment orbit position calculation, velocity difference calculation, and error statistics. S43. Based on the space target orbit estimation error corresponding to each set of observation configurations, the optimal observation configuration suitable for short-arc orbit determination of space targets is obtained through a comprehensive comparison and screening operation of error magnitude, stability and short-arc orbit determination accuracy.

[0014] Preferably, the space target orbit estimation error in S4 includes position errors in three directions: x-axis, y-axis, and z-axis. The difference between the nominal value and the estimated value of the position component at each moment within a preset short arc segment is calculated. The mean, standard deviation, and root mean square error of the position errors in each direction are statistically analyzed. The core evaluation indicators are the smaller mean of the three-axis position errors, the smaller the error dispersion, and the smaller the error fluctuation over time. The optimal observation configuration is selected to meet the requirements of short-arc precision orbit determination of the space target.

[0015] Therefore, the present invention adopts the above-mentioned space target short-arc orbit determination observation configuration design method based on space-based collaborative angle measurement, which has the following beneficial effects: 1. By clearly defining the state variables of the orbit determination system using a geocentric inertial coordinate system, a dynamic state model is constructed that integrates the perturbations of geocentric gravity, the second-order zonal harmonics of Earth's oblateness, and the gravitational perturbations of the Sun, Moon, and other third bodies. Combined with the principle of space-based multi-point collaborative inertial angle measurement, an observation model including pitch and azimuth angles is established, and the process noise and observation noise are limited to zero-mean Gaussian white noise. The integration of the nonlinear space-based collaborative angle measurement orbit determination system is completed, comprehensively characterizing the perturbation characteristics of the actual motion of the space target and the nonlinear mapping relationship between space-based angle measurement observations. It accurately represents the uncertainty of the model and observations, eliminates the system bias caused by the simplification of traditional single-star orbit determination models and the fuzziness of noise assumptions, and provides a high-precision and high-reliability basic model support for subsequent short-arc orbit estimation and observation configuration design, significantly improving the adaptability of the orbit determination system to complex space environments.

[0016] 2. An extended Kalman filter is used to linearize the nonlinear orbit determination system. The state variables are estimated step by step through time updates and observation updates. The short arc time and the termination condition of the difference between three consecutive iterations being less than a preset threshold are limited to achieve short arc orbit estimation of space targets. This is suitable for scenarios where the observation time of space targets is limited and the orbit changes rapidly. The linearization of the extended Kalman filter balances the nonlinear estimation accuracy and engineering computational complexity. The short arc time setting is close to the actual observation capability. The iteration termination condition takes into account the orbit estimation accuracy and computational efficiency. It solves the problems of slow convergence and low accuracy of traditional filtering methods in short arc scenarios, and improves the stability and accuracy of space target orbit estimation under short arc conditions.

[0017] 3. Based on the constraints of space-based collaborative angle measurement observation, three basic configurations are designed: coplanar, non-coplanar, and different scales. The horizontal / vertical arrangement and baseline scale parameters are refined to form multiple subdivided observation configurations and obtain corresponding orbit estimates one by one. This covers the full-dimensional spatial distribution topology of observation satellites and space targets, breaking through the limitations of traditional single configuration design. It takes into account both the diversity of observation geometry and engineering feasibility. The parallel design of multiple configurations can comprehensively characterize the impact of observation geometry on short-arc orbit determination performance, providing sufficient and differentiated candidate schemes for optimal configuration selection, and enhancing the versatility and adaptability of the method under different observation scenarios.

[0018] 4. By matching and aligning the nominal and estimated orbit values, the three-axis position errors are calculated at each time step, and the mean and variance are statistically analyzed. The optimal observation configuration is selected based on the minimum mean error and the most stable variance. Through the above process, a quantitative evaluation system for the orbit determination performance of the observation configuration is established. This system accurately quantifies the differences in accuracy and stability of different configurations in short-arc orbit determination, avoiding the blindness of traditional subjective selection. It accurately matches the core requirements of high stability and high accuracy for short-arc precision orbit determination of space targets, optimizes orbit determination accuracy from the perspective of observation geometry, provides the optimal observation configuration basis for the engineering application of space-based collaborative angle measurement short-arc orbit determination, and ensures the reliability and efficiency of space target orbit determination.

[0019] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0020] Figure 1 A flowchart of the space target short-arc orbit determination observation configuration design method based on space-based collaborative angle measurement provided by the present invention; Figure 2 A diagram showing the coplanar lateral alignment of two observation satellites and a space target in a coplanar configuration provided by this invention; Figure 3 A diagram showing the coplanar lateral advance distribution of two observation satellites and a space target in a coplanar configuration provided by this invention; Figure 4 A diagram showing the coplanar lateral hysteresis distribution in a coplanar configuration of two observation satellites and a space target, provided by this invention. Figure 5 A diagram showing the coplanar longitudinal opposite-side distribution of two observation satellites and a space target in a coplanar configuration provided by this invention; Figure 6 A diagram showing the non-coplanar lateral alignment distribution of two observation satellites and a space target in a non-coplanar configuration provided by this invention. Figure 7 This invention provides a diagram showing the non-coplanar lateral advance distribution of two observation satellites and a space target in a non-coplanar configuration. Figure 8 A diagram showing the non-coplanar lateral hysteresis distribution in a non-coplanar configuration of two observation satellites and a space target, provided by this invention. Figure 9 This invention provides a diagram showing the non-coplanar longitudinal opposite-side distribution of two observation satellites and a space target in a non-coplanar configuration. Figure 10 A mid-scale coplanar lateral alignment distribution diagram of two observation satellites and a space target in different scale configurations provided by this invention; Figure 11 Large-scale coplanar lateral alignment distribution diagrams of two observation satellites and space targets in different scale configurations provided by this invention; Figure 12 A diagram showing the position estimation error of coplanar, laterally aligned spatial targets in the coplanar configuration provided by this invention. Figure 13 A diagram showing the position estimation error of spatial targets with pre-distributed coplanar lateral distribution in the coplanar configuration provided by the present invention. Figure 14 A spatial target position estimation error diagram for the coplanar lateral hysteresis distribution in the coplanar configuration provided by the present invention; Figure 15A diagram illustrating the position estimation error of spatial targets distributed longitudinally on opposite sides in a coplanar configuration provided by the present invention. Figure 16 A diagram illustrating the position estimation error of spatial targets with non-coplanar lateral alignment in a non-coplanar configuration provided by the present invention. Figure 17 A diagram illustrating the position estimation error of spatial targets with non-coplanar lateral pre-distribution in the non-coplanar configuration provided by this invention. Figure 18 A diagram illustrating the spatial target position estimation error in the non-coplanar lateral hysteresis distribution of the non-coplanar configuration provided by this invention. Figure 19 A diagram illustrating the position estimation error of spatial targets distributed longitudinally on opposite sides in a non-coplanar configuration provided by the present invention. Figure 20 This invention provides a diagram showing the position estimation error of spatial targets with coplanar and horizontally aligned distributions at different scales in the present invention. Figure 21 This is a diagram showing the position estimation error of large-scale coplanar laterally aligned spatial targets in different scale configurations provided by the present invention. Detailed Implementation

[0021] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0022] While existing space-based angle measurement-based orbit determination technology can improve observability and orbit determination accuracy through multi-satellite collaboration, angle measurement-based orbit determination systems are highly sensitive to observation configurations. Furthermore, current research has not conducted multi-dimensional and systematic design of observation configurations for the demanding scenario of short-arc orbit determination, resulting in low orbit estimation accuracy and insufficient stability under short-arc observation conditions. This makes it difficult to meet the practical application requirements of rapid, high-precision, short-arc precise orbit determination for space targets.

[0023] Based on the above analysis, this invention is designed. (See appendix.) Figures 1-21 The design method for short-arc orbit determination observation configuration of space targets based on space-based collaborative angle measurement includes the following steps: S1. Based on the application requirements of short-arc precision orbit determination of space targets, a nonlinear space-based collaborative angle measurement and orbit determination system is constructed, which integrates the perturbation dynamic state model and the space-based multi-point collaborative inertial angle measurement and observation model.

[0024] Specifically, in one embodiment of the present invention, the space target and the observation satellite are located near Earth's orbit, the state variables are position and velocity in a geocentric inertial coordinate system, and the dynamic model considers Earth's gravity and the Earth's orbital forces. Perturbation and gravitational perturbation by the Sun, Moon, and other third bodies; each observation satellite provides elevation and azimuth observations of space targets, and multiple observation satellites form a multi-line-of-sight collaborative angle measurement constraint; the specific steps of S1 include: S11. The state variables of the space-based collaborative angle measurement and orbit determination system are obtained by defining the orbital position and velocity of the space target using a geocentric inertial coordinate system. Specifically: ; in, Let be the position components of the spatial target in the geocentric inertial coordinate system, and ; Let be the velocity components of the space target in the geocentric inertial coordinate system, and ; S12. Based on the constraints of geocentric gravity, the second-order zonal harmonics of Earth's oblateness, and the gravitational perturbations of the Sun, Moon, and other third bodies, by establishing a perturbation-containing acceleration... With Gaussian distributed process noise The nonlinear state function is: ; in, For the time derivative vector of the state variable of the space-based collaborative angle measurement and orbit determination system; This is a constraint established based on the second-order zonal harmonics of Earth's oblateness and the gravitational perturbations of the Sun, Moon, and other third bodies. The nonlinear orbital dynamics state function is used to obtain the perturbation dynamics state model of the space-based collaborative angle measurement and orbit determination system; specifically, the nonlinear orbital dynamics state function is: ; The algorithm process is as follows: 1) Considering only the gravitational pull of Earth as the central celestial body, the equation of motion for a space target is: ; in, , , for , , The first derivative, i.e., the velocity components of the space target in the geocentric inertial coordinate system, corresponds to the following: , , ; , , for , , The second derivative of is the acceleration component of the space target in the geocentric inertial coordinate system; It is the gravitational constant; The geocentric distance of the spatial target; 2) Based on the gravitational force of the central celestial body, and considering the perturbation acceleration of the Earth's oblateness, i.e., the second-order zonal harmonic term, the formula is: ; in, is the second-order band harmonic coefficient of Earth, a core dimensionless constant used to describe the non-spherical gravitational field of Earth; The perturbation acceleration vector generated by the second-order zonal harmonics of Earth's oblateness is used to correct the deviations in the ideal spherical gravitational field model of Earth. , , for Components along the x, y, and z axes; The average radius of the Earth; The strength coefficient; , and These are the direction correction terms; 3) Considering the perturbation acceleration caused by the gravitational pull of third bodies such as the Sun and Moon, the formula is: ; in, The perturbation acceleration vector generated by the gravitational pull of the Sun, Moon, and other third bodies; , , These are the components of the third-body perturbation acceleration in the x, y, and z axes, corresponding to the perturbation acceleration values ​​in the three coordinate axes of the geocentric inertial coordinate system, respectively. The gravitational constant of the third body (the Sun or the Moon); The distance from the Earth's center to the third body (the Sun or the Moon); The relative distance between a space target and a third body (the sun or the moon); 4) Based on the principle of linear superposition of Newton's second law, the three types of accelerations mentioned above are summed along the x, y, and z coordinate axes respectively to obtain the total acceleration components of the target, i.e. ,in, Let be the total perturbation acceleration vector of the space target in the geocentric inertial coordinate system. The total perturbation acceleration vector The components along the x, y, and z axes in the geocentric inertial coordinate system correspond to the perturbation acceleration values ​​experienced by the target along the three coordinate axes, respectively. 5) Combining the first derivative of the position with the total acceleration components yields the complete 6-dimensional state function, i.e. .

[0025] S13. Based on the principle of space-based multi-point cooperative inertial angle measurement, the satellite position vector is observed in the geocentric inertial coordinate system. Constructing a structure with pitch angle Azimuth Observations and Gaussian distribution observation noise The nonlinear observation function is given by the formula: ; in, The measurement vector; For objective function With the observed satellite position vector The constructed theoretical observation model, and the observation function of a single observation satellite, is: ; and , which is the position vector of the observed satellite in the geocentric inertial frame; To obtain the space-based multi-point cooperative inertial angle measurement observation model of the space-based cooperative angle measurement and orbit determination system; wherein, Gaussian distributed process noise Gaussian distribution observation noise All are zero-mean Gaussian white noise.

[0026] S14. Based on the state variables, perturbation dynamics state model, and space-based multi-point collaborative inertial angle measurement observation model of the space-based collaborative angle measurement and orbit determination system, a nonlinear system architecture is constructed through system integration and fusion to obtain a nonlinear space-based collaborative angle measurement and orbit determination system that integrates the perturbation dynamics state model and the space-based multi-point collaborative inertial angle measurement observation model.

[0027] S2. Based on the state model and observation model of the space-based collaborative angle measurement and orbit determination system, the time update and observation update operations are repeatedly executed through nonlinear Kalman filtering, and a preset short arc time is accumulated to obtain the estimated short arc orbit of the space target. The preset short arc time can be an observation duration of 10 seconds. The specific steps of S2 include: S21, based on the first Estimates of state variables of the orbit determination system at specific times Covariance Matrix The time update operation of nonlinear Kalman filtering is used to obtain the first... One-step prediction estimate of the state variables of the orbit determination system at a given time. And one-step prediction of covariance matrix ; S22, based on the first One-step prediction estimate of the state variables of the orbit determination system at a given time. And one-step prediction of covariance matrix The observation update operation through nonlinear Kalman filtering is used to obtain the first... Optimal estimates of state variables of the orbit determination system at a given time. and the optimal covariance matrix The specific algorithm process includes: 1) Discretize the nonlinear state function into discrete-time state equations: ; in, For the first State variables at discrete moments; For the first State variables at discrete moments; This is the discretized state transition function; This refers to the discretized process noise. 2) Transform the nonlinear state function exist Performing a Taylor expansion at this point, the formula is: ; in, For nonlinear state functions in Real state variables at any given time Output value at; for The real state variables of the spatial target in the geocentric inertial coordinate system at any given time; for Estimates of the time-space target state variables; Nonlinear state function At the point of expansion Jacobian matrix at the location; For higher-order infinitesimal remainder terms in Taylor expansion, including second-order and higher expansion terms, used to represent the deviation of nonlinear functions from first-order linear approximations; 3) Substituting the Taylor expansion into the discrete state equations and neglecting higher-order infinitesimal terms, we obtain the following formula: ; 4) The estimated values ​​and covariances of the one-step state prediction are as follows: ; ; in, For the first The one-step predicted state estimate at time t; For mathematical expectation operators; For the first The one-step prediction covariance matrix of the state variables at time step; For the first The posterior optimal covariance matrix of the state variables at time step; The state Jacobian matrix The transpose of the matrix; This is the discretized process noise covariance matrix; 5) Perform measurement updates, updating the nonlinear observation function. In one-step state prediction Performing a Taylor expansion at this point, the formula is: ; in, For the nonlinear observation function, by the first Time-space target true state variables The theoretical observations obtained through calculation; For the first One-step prediction estimate of the time-space target state variable; To observe the Jacobian matrix; For higher-order infinitesimal remainder terms in Taylor expansion; 6) Ignore higher-order terms The formula for the subsequent observation model is: ; in, For the first The actual observed value at time; For observed and predicted values; This refers to the discretized observation noise; 7) The estimated values ​​and covariances of the one-step observation predictions are as follows: ; ; ; in, For the first One-step observation prediction estimate at time; For the first The covariance matrix of the time-time observation prediction; For the first The cross-covariance matrix between the state variables at time points and the observed values; For the first The covariance matrix of the noise observed at any given time; 8) The state gain matrix is ​​calculated as follows: ; in, For the first The state gain matrix at time step; 9) Obtain the estimated values ​​of the state variables and covariance matrix of the orbit determination system at time i, using the following formula: ; ; in, For the first The posterior optimal estimate of the state variables of the orbit determination system at a given time; For the first The posterior optimal covariance matrix at time step 1; It is an identity matrix.

[0028] S23. Based on the optimal estimates of the state variables of the orbit determination system at each moment obtained from a single iteration, the estimated short-arc orbit of the space target is obtained by repeatedly executing the time update and observation update operations of the nonlinear Kalman filter and accumulating the preset short arc time.

[0029] Among them, the nonlinear Kalman filter is the extended Kalman filter; the extended Kalman filter realizes the linear approximation of the nonlinear space-based coordinated angle measurement and orbit determination system by performing Taylor expansion on the nonlinear state function and the nonlinear observation function respectively, so as to complete the optimal estimation of the state variables.

[0030] The nonlinear Kalman filter repeatedly performs time updates and observation updates according to the preset short arc observation time and observation sampling interval; and when the state correction or state estimation difference is less than the preset threshold, the filter estimation is judged to be stable.

[0031] Specifically, the preset short arc time in S23 is 10~300s, and the iteration termination condition of the nonlinear Kalman filter is: the difference between the estimated values ​​of the state variables in three consecutive iterations is less than a preset threshold. , Including position component thresholds and velocity component threshold .

[0032] S3. Based on the constraints of space-based multi-point collaborative angle measurement and orbit determination systems, design multiple sets of observation configurations between observation satellites and space targets, covering coplanar configurations, non-coplanar configurations, and configurations at different scales, to obtain multiple sets of observation configurations and corresponding short-arc orbit estimates for the space targets. The specific steps of S3 include: S31. Constraints for space-based multi-point collaborative angle measurement observation based on space-based collaborative angle measurement and orbit determination system: By planning the spatial distribution topology relationship between observation satellites and space targets, three basic observation configurations are obtained: coplanar configuration, non-coplanar configuration, and configurations at different scales. Among them, the coplanar configurations in S31 include coplanar horizontal alignment, coplanar horizontal advance, coplanar horizontal lag, and coplanar longitudinal opposite-sided distribution; the non-coplanar configurations include non-coplanar horizontal alignment, non-coplanar horizontal advance, non-coplanar horizontal lag, and non-coplanar longitudinal opposite-sided distribution; the different scale configurations include mesoscale coplanar horizontal alignment and large-scale coplanar horizontal alignment, wherein the relative distance or observation baseline scale between the observation satellite and the space target corresponding to the large-scale configuration is larger than that of the mesoscale configuration. Specifically, the baseline length of the large-scale configuration is 1.5-2 times that of the mesoscale configuration.

[0033] S32. Based on the three basic observation configurations, by refining the horizontal / vertical arrangement of the observation satellites relative to the space target and the baseline scale parameters, multiple subdivided observation configurations corresponding to the coplanar configuration group, the non-coplanar configuration group, and the configuration groups of different scales are obtained. S33. Based on the space-based multi-point collaborative inertial angle measurement data corresponding to each subdivided observation configuration, the estimated short-arc orbit of the space target corresponding to each subdivided observation configuration is obtained through nonlinear Kalman filter iterative update and short arc time accumulation method. S34. Based on each set of subdivided observation configurations and the corresponding short-arc orbit estimates of space targets, through a one-to-one mapping and association operation between configuration parameters and orbit estimation results, multiple sets of observation configurations between observation satellites and space targets, covering coplanar configurations, non-coplanar configurations and configurations of different scales, and the corresponding short-arc orbit estimates of space targets are obtained.

[0034] S4. Based on the set of nominal values ​​of the orbital state of the space target within a preset short arc segment time. Set of short-arc orbit estimates for space targets corresponding to m observation configurations By comparing and analyzing errors, the orbit estimation error of the space target is calculated and the optimal configuration is selected to obtain the optimal observation configuration suitable for short-arc orbit determination of the space target.

[0035] The formula for calculating the orbit estimation error of a space target is as follows: ; in, For the first The orbit estimation error vector under various observation configurations. The specific steps of S4 include: S41. The set of nominal values ​​of the orbital state of the space target within a preset short arc segment and the set of estimated values ​​of the short arc orbit of the space target corresponding to multiple observation configurations are matched and aligned one-to-one with the orbital state data at each time point to obtain the matching dataset of nominal values ​​and estimated values ​​of the orbital state of the space target at each time point and each observation configuration within the preset short arc segment. S42. Based on the matching dataset of nominal and estimated values ​​of the space target orbit state at each moment and for each observation configuration within a preset short arc segment time, the estimated error of the space target orbit for each observation configuration is obtained through moment-by-moment orbit position calculation, velocity difference calculation, and error statistics. S43. Based on the space target orbit estimation error corresponding to each set of observation configurations, the optimal observation configuration suitable for short-arc orbit determination of space targets is obtained through a comprehensive comparison and screening operation of error magnitude, stability and short-arc orbit determination accuracy.

[0036] After statistical analysis of the orbit estimation errors of space targets across multiple observation configurations, non-coplanar small-scale observation configurations are prioritized. When the observation satellite and the space target must be in a coplanar configuration, lateral distribution configurations with relative phase differences relative to the space target are prioritized. For short-arc observation scenarios, prioritizing non-coplanar small-scale observation configurations avoids the geometric degradation problem that easily occurs in traditional coplanar configurations, adapts to short-arc observation constraints, and reduces orbit estimation errors. When coplanar, prioritizing lateral distribution configurations with relative phase differences increases the diversity of observation baselines, avoids information redundancy, and effectively improves the accuracy and stability of space target orbit estimation. This addresses the technical shortcomings of existing observation configurations in short-arc scenarios, such as insufficient accuracy and poor robustness, and significantly enhances the adaptability of observation configurations to complex short-arc observation conditions.

[0037] The orbit estimation error of the space target in S4 includes the position error in the three directions of x-axis, y-axis and z-axis. The difference between the nominal value and the estimated value of the position component at each moment within the preset short arc segment time is calculated. The mean, standard deviation and root mean square error of the position error in each direction are statistically analyzed. The core evaluation indicators are the small mean of the three-axis position error, the small degree of error dispersion and the small fluctuation of error over time. The optimal observation configuration is selected to meet the requirements of short arc precision orbit determination of the space target.

[0038] In summary, this invention constructs a system incorporating Earth's central gravity, A high-precision orbital dynamics model perturbed by non-spherical gravity and the gravitational forces of the Sun, Moon, and other third bodies was developed. By combining extended Kalman filtering with first-order Taylor expansion linearization of the nonlinear state / observation model, unbiased recursive estimation of the orbital state of space targets was achieved. Simultaneously, by designing multiple sets of different observation configurations and quantifying the orbital estimation errors under each configuration, the correlation between observation geometry and orbit determination accuracy was established. The optimal observation configuration can be selected, overcoming the observation geometry defects of suboptimal configurations, improving the accuracy and robustness of orbit determination for space targets in short arc segments, and providing reliable technical support for high-precision orbit monitoring of highly dynamic space targets.

Claims

1. A method for designing short-arc orbit determination observation configurations for space targets based on space-based collaborative angle measurement, characterized in that: Includes the following steps: S1. Based on the application requirements of short-arc precision orbit determination of space targets, a nonlinear space-based collaborative angle measurement and orbit determination system is constructed that integrates the perturbation dynamic state model and the space-based multi-point collaborative inertial angle measurement and observation model. S2. Based on the state model and observation model of the space-based collaborative angle measurement and orbit determination system, the time update and observation update operations are repeatedly executed by nonlinear Kalman filtering and the preset short arc time is accumulated to obtain the estimated value of the short arc orbit of the space target. S3. Based on the space-based multi-point collaborative angle measurement observation constraints of the space-based collaborative angle measurement and orbit determination system, design multiple sets of observation configurations between observation satellites and space targets, covering coplanar configurations, non-coplanar configurations and configurations of different scales, and obtain multiple sets of observation configurations and corresponding short arc orbit estimates of space targets; S4. Based on the set of nominal values ​​of the space target's orbital state within a preset short arc time and the set of estimated values ​​of the space target's short arc orbit corresponding to multiple observation configurations, the space target orbital estimation error is calculated through error comparison analysis and the optimal configuration is selected to obtain the optimal observation configuration suitable for the short arc orbit determination of the space target.

2. The space target short-arc orbit determination observation configuration design method based on space-based collaborative angle measurement according to claim 1, characterized in that: The specific steps of S1 include: S11. The state variables of the space-based collaborative angle measurement and orbit determination system are obtained by defining the orbital position and velocity of the space target using a geocentric inertial coordinate system. Specifically: ； in, This represents the position components of a spatial target in the geocentric inertial coordinate system. The velocity components of the space target in the geocentric inertial coordinate system; S12. Based on the constraints of geocentric gravity, the second-order zonal harmonics of Earth's oblateness, and the gravitational perturbations of the Sun, Moon, and other third bodies, by establishing a perturbation-containing acceleration... With Gaussian distributed process noise The nonlinear state function is: ； in, For the time derivative vector of the state variable of the space-based collaborative angle measurement and orbit determination system; This is a constraint established based on the second-order zonal harmonics of Earth's oblateness and the gravitational perturbations of the Sun, Moon, and other third bodies. The nonlinear orbital dynamics state function; To obtain the perturbation dynamic state model of the space-based collaborative angle measurement and orbit determination system; S13. Based on the principle of space-based multi-point cooperative inertial angle measurement, the satellite position vector is observed in the geocentric inertial coordinate system. Constructing a structure with pitch angle Azimuth Observations and Gaussian distribution observation noise The nonlinear observation function is given by the formula: ； in, The measurement vector; For objective function With the observed satellite position vector The constructed theoretical observation model, and the observation function of a single observation satellite, is: ； and , where is the position vector of the observed satellite in the geocentric inertial frame; thus, the space-based multi-point collaborative inertial angle measurement observation model of the space-based collaborative angle measurement and orbit determination system is obtained; S14. Based on the state variables, perturbation dynamics state model, and space-based multi-point collaborative inertial angle measurement observation model of the space-based collaborative angle measurement and orbit determination system, a nonlinear system architecture is constructed through system integration and fusion to obtain a nonlinear space-based collaborative angle measurement and orbit determination system that integrates the perturbation dynamics state model and the space-based multi-point collaborative inertial angle measurement observation model.

3. The space target short-arc orbit determination observation configuration design method based on space-based collaborative angle measurement according to claim 2, characterized in that: Gaussian distributed process noise in S1 Gaussian distribution observation noise All are zero-mean Gaussian white noise.

4. The space target short-arc orbit determination observation configuration design method based on space-based collaborative angle measurement according to claim 3, characterized in that: The specific steps of S2 include: S21, based on the first Estimates of state variables of the orbit determination system at specific times Covariance Matrix The time update operation of nonlinear Kalman filtering is used to obtain the first... One-step prediction estimate of the state variables of the orbit determination system at a given time. And one-step prediction of covariance matrix ; S22, based on the first One-step prediction estimate of the state variables of the orbit determination system at a given time. And one-step prediction of covariance matrix The observation update operation through nonlinear Kalman filtering is used to obtain the first... Optimal estimates of state variables of the orbit determination system at a given time. and the optimal covariance matrix ; S23. Based on the optimal estimates of the state variables of the orbit determination system at each moment obtained from a single iteration, the estimated short-arc orbit of the space target is obtained by repeatedly executing the time update and observation update operations of the nonlinear Kalman filter and accumulating the preset short arc time.

5. The space target short-arc orbit determination observation configuration design method based on space-based collaborative angle measurement according to claim 4, characterized in that: The nonlinear Kalman filter in S2 is an extended Kalman filter; the extended Kalman filter achieves a linear approximation of the nonlinear space-based collaborative angle measurement and orbit determination system by performing Taylor expansion on the nonlinear state function and the nonlinear observation function respectively, so as to complete the optimal estimation of the state variables.

6. The space target short-arc orbit determination observation configuration design method based on space-based collaborative angle measurement according to claim 5, characterized in that: The nonlinear Kalman filter repeatedly performs time updates and observation updates according to the preset short arc observation time and observation sampling interval; and when the state correction or state estimation difference is less than the preset threshold, the filter estimation is judged to be stable.

7. The space target short-arc orbit determination observation configuration design method based on space-based collaborative angle measurement according to claim 6, characterized in that: The specific steps of S3 include: S31. Constraints for space-based multi-point collaborative angle measurement observation based on space-based collaborative angle measurement and orbit determination system: By planning the spatial distribution topology relationship between observation satellites and space targets, three basic observation configurations are obtained: coplanar configuration, non-coplanar configuration, and configurations at different scales. S32. Based on the three basic observation configurations, by refining the horizontal / vertical arrangement of the observation satellites relative to the space target and the baseline scale parameters, multiple subdivided observation configurations corresponding to the coplanar configuration group, the non-coplanar configuration group, and the configuration groups of different scales are obtained. S33. Based on the space-based multi-point collaborative inertial angle measurement data corresponding to each subdivided observation configuration, the estimated short-arc orbit of the space target corresponding to each subdivided observation configuration is obtained through nonlinear Kalman filter iterative update and short arc time accumulation method. S34. Based on each set of subdivided observation configurations and the corresponding short-arc orbit estimates of space targets, through a one-to-one mapping and association operation between configuration parameters and orbit estimation results, multiple sets of observation configurations between observation satellites and space targets, covering coplanar configurations, non-coplanar configurations and configurations of different scales, and the corresponding short-arc orbit estimates of space targets are obtained.

8. The space target short-arc orbit determination observation configuration design method based on space-based collaborative angle measurement according to claim 7, characterized in that: The coplanar configurations in S31 include coplanar horizontal alignment, coplanar lateral advance distribution, coplanar lateral lag distribution, and coplanar longitudinal opposite-sided distribution; the non-coplanar configurations include non-coplanar horizontal alignment, non-coplanar lateral advance distribution, non-coplanar lateral lag distribution, and non-coplanar longitudinal opposite-sided distribution; the different scale configurations include medium-scale coplanar horizontal alignment and large-scale coplanar horizontal alignment.

9. The space target short-arc orbit determination observation configuration design method based on space-based collaborative angle measurement according to claim 8, characterized in that: The specific steps of S4 include: S41. The set of nominal values ​​of the orbital state of the space target within a preset short arc segment and the set of estimated values ​​of the short arc orbit of the space target corresponding to multiple observation configurations are matched and aligned one-to-one with the orbital state data at each time point to obtain the matching dataset of nominal values ​​and estimated values ​​of the orbital state of the space target at each time point and each observation configuration within the preset short arc segment. S42. Based on the matching dataset of nominal and estimated values ​​of the space target orbit state at each moment and for each observation configuration within a preset short arc segment time, the estimated error of the space target orbit for each observation configuration is obtained through moment-by-moment orbit position calculation, velocity difference calculation, and error statistics. S43. Based on the space target orbit estimation error corresponding to each set of observation configurations, the optimal observation configuration suitable for short-arc orbit determination of space targets is obtained through a comprehensive comparison and screening operation of error magnitude, stability and short-arc orbit determination accuracy.

10. The space target short-arc orbit determination observation configuration design method based on space-based collaborative angle measurement according to claim 9, characterized in that: The orbit estimation error of the space target in S4 includes the position error in the three directions of x-axis, y-axis and z-axis. The difference between the nominal value and the estimated value of the position component at each moment within the preset short arc segment time is calculated. The mean, standard deviation and root mean square error of the position error in each direction are statistically analyzed. The core evaluation indicators are the small mean of the three-axis position error, the small degree of error dispersion and the small fluctuation of error over time. The optimal observation configuration is selected to meet the requirements of short arc precision orbit determination of the space target.

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