Space debris radar observation segmental arc initial orbit determination method and system

Abstract

The invention provides a space debris radar observation segmental arc initial orbit determination method and system. Radar observation segmental arc data of space debris are acquired. And obtaining a distance measurement error and an angle measurement error of radar observation equipment. And calculating the sight line vector of the space debris relative to the observation station in the geocentric inertial coordinate system and the position coordinate of the observation station in the geocentric inertial coordinate system. And calculating an orbit position speed initial value. And calculating a target function corresponding to the current track position. And calculating partial derivatives of the relative position and speed of the target function. And comparing the current target function with the minimum value of the historical target function, and recording according to a comparison result. And judging whether a convergence condition is met or not, and if yes, outputting the position and speed corresponding to the minimum value of the historical target function. Otherwise, updating the track position and the speed value. The method is easy to implement and can be effectively applied to determining the initial orbit of the space debris radar observation arc section.

Description

Technical Field

[0001] The present invention relates to the technical field of space situation awareness, and specifically, to a method and system for determining the initial orbit of a space debris radar observation arc segment. Background Art

[0002] Currently, space debris monitoring equipment mainly relies on ground-based monitoring equipment, including radars and telescopes. Radars use an active detection method and can break through limitations such as atmospheric conditions and sunlight, and are widely used in the field of space debris monitoring. The greater the transmitting power of a radar and the higher the antenna gain, the smaller the space debris that can be detected.

[0003] When a radar discovers new space debris, it is usually necessary to determine the initial orbit of the observed data. Since a radar can obtain relatively high ranging data and can also get angle measurement information, compared with telescope equipment, the angle measurement error of a radar is relatively large. For radar observation data containing ranging and angle measurement, the initial orbit methods that can be adopted include: Lambert method, Gibbs method, Gooding method, Laplace method, etc. Literature 1 (Initial Orbit Calculation Method Considering the Influence of Earth Flattening Perturbation, Acta Astronomica Sinica, 2003, Vol. 44, No. 2) presents a Laplace-type initial orbit determination method considering the influence of flattening perturbation. Literature 2 (Spacecraft Initial Orbit Determination Algorithm Using Double-Satellite Positioning System and Radar Altimeter, Navigation and Space Vehicle Technology, 2006, No. 3) uses the domestic double-satellite positioning system and radar altimeter to form a space-based TT&C system to determine the initial orbit of a spacecraft and designs an initial orbit calculation algorithm based on series. Literature 3 (Research on the Method of Determining the Initial Orbit of a Single-Station and Single-Orbit Satellite, Fire Control & Command Control, 2014, Vol. 39, No. 12) studies the problem of satellite initial orbit determination and orbit prediction based on the measurement data of a single-station and single-orbit radar station using genetic algorithm and least square method. Literature 4 (Research on Initial Orbit Calculation Based on Phased Array Radar Data, Modern Radar, 2014, Vol. 36, No. 11) proposes to calculate the state values (position and velocity) of a space target at the initial moment based on the ground measurement data of a phased array radar using the method of multi-phase fitting and iteration. The iteration is based on the approximation of the FG series in the orbit. Literature 5 (Error Analysis of the Gibbs Problem in Space Target Initial Orbit Determination, Chinese Journal of Inertial Technology, 2019, Vol. 24, No. 2) based on the orbit determination model of the Gibbs method, uses the method of vector differentiation to derive in detail the sensitivity matrix of the orbital elements to the observed position error, and gives the relationship between the orbital element error and the observed position error, clarifying the determination accuracy and error propagation law of the initial orbit. Literature 6 (Error Analysis of Initial Orbit Determination in Low Earth Orbit, Space Debris Research, 2019, Vol. 19, No. 2) studies the improved Laplace method considering the influence of the J2 term and conducts research on the initial orbit determination problem using the positioning data of low-orbit near-circular orbits. Literature 7 (Initial Orbit Determination of Generalized Laplace Method Based on Differential Correction and Circular Orbit Constraint, Science China: Physics, Mechanics & Astronomy, 2022, Vol. 52, No. 6) on the basis of the existing generalized Laplace method, uses differential correction to solve the normal equation to improve the convergence stability. At the same time, for a clear circular orbit target, additional constraints are introduced to improve the convergence.Patent 1 (A method for determining the initial relative state of a satellite with given boundaries under a circular reference orbit, CN104200030A) discloses a method for determining the initial relative state of a satellite with given boundaries under a circular reference orbit, gives optimization models applicable to periodic relative motion and fly-around relative motion respectively, and then uses a certain optimization algorithm to solve the established optimization model to obtain the numerical solution of the initial relative state with given boundaries. Patent 2 (A method for determining the initial orbit of a low-earth orbit target satellite based on space-based satellite angle measurement data, CN103927289A) discloses a method for determining the initial orbit of a low-earth orbit target satellite based on space-based satellite angle measurement data.

[0004] Traditional radar orbit determination has the problem of large velocity errors, which will have a certain impact on subsequent arc segment association and orbit improvement. The present invention combines the perturbed orbit dynamics model with the system parameters of radar equipment and gives a new method for determining the initial orbit of a radar observation arc segment. Summary of the Invention

[0005] Aiming at the defects in the prior art, the purpose of the present invention is to provide a method and system for determining the initial orbit of a space debris radar observation arc segment.

[0006] A method for determining the initial orbit of a space debris radar observation arc segment according to the present invention includes:

[0007] Step S1, obtaining the radar observation arc segment data of the space debris, including: the time t at multiple sampling moments i , the distance l between the space debris and the observation station i , the azimuth angle A in the instantaneous true horizon coordinate system of the observation station i , the altitude angle h i , the coordinates of the observation station in the Earth-fixed coordinate system, i = 1, 2,..., M, where M is the number of sampling points;

[0008] Step S2, obtaining the system parameters of the radar observation equipment, including the ranging error σ range , the angle measurement error σ angle ;

[0009] Step S3, calculating the line-of-sight vector of the space debris relative to the observation station in the geocentric inertial coordinate system The position coordinates of the observation station in the geocentric inertial coordinate system

[0010] Step S4, calculating the initial value of the orbit position corresponding to the moment t0 The initial value of the velocity

[0011] Step S5, calculating the objective function corresponding to the current orbit position

[0012] Step S6, calculate the partial derivatives of the current orbital position objective function with respect to the orbital position and velocity at time t0

[0013] Step S7, compare the current objective function with the minimum value of the historical objective function, and record according to the comparison result;

[0014] Step S8, determine whether the convergence condition is satisfied. If it is satisfied, output the position and velocity corresponding to the minimum value of the historical objective function. Otherwise, update the orbital position and velocity values;

[0015] Among them, steps S5 to S8 are repeatedly triggered until the convergence condition is reached.

[0016] Furthermore, step S4 includes:

[0017] Step S4.1, calculate the rough position of the space debris in the geocentric inertial coordinate system

[0018]

[0019] Step 4.2, calculate the initial values of the orbital position The initial value of the velocity

[0020]

[0021] Step 4.3, initialize the initial value of the first momentum vector And the initial value of the second momentum vector To be all-zero vectors.

[0022] Furthermore, step S5 includes:

[0023] Step S5.1, from the orbital position at time t0 Velocity According to the perturbed orbit dynamics model, perform orbit recursion to obtain the guessed values of the orbital positions corresponding to the sampling times t i respectively

[0024] Step 5.2, calculate the guessed value l of the distance between the space debris and the observation station guess,i :

[0025]

[0026] Among them, || || represents the calculation of the 2-norm of the vector;

[0027] Step 5.3, calculate the guessed value of the line-of-sight vector of the space debris relative to the observation station

[0028]

[0029] Step 5.4, calculate the distance difference l Δ,i and the line-of-sight difference u Δ,i :

[0030]

[0031] where, <> represents the inner product calculation of two vectors;

[0032] Step 5.5, calculate the objective function

[0033]

[0034] Furthermore, in step S6, the calculation method of the partial derivative includes:

[0035]

[0036] The orbital position coordinates are (r x , r y , r z ), and the velocity coordinates are (v x , v y , v z ).

[0037] Furthermore, in step S8, the convergence conditions include any one of the following:

[0038] The number of iterations reaches the given maximum number of iterations;

[0039] The objective function is less than the given threshold;

[0040] The current objective function value is more than 10 times the minimum value of the objective function in the historical record.

[0041] Furthermore, in step S7, compare the current objective function with the minimum value of the historical objective function. If it is the 0th iteration currently, then the minimum value of the historical objective function is equal to the current objective function, and record the position and velocity corresponding to the minimum value of the objective function. Otherwise, only when the current objective function is less than the minimum value of the historical objective function, let the minimum value of the historical objective function be equal to the current objective function, and record the position and velocity corresponding to the minimum value of the objective function.

[0042] Furthermore, in step S8, the maximum number of iterations is taken as 200, and the convergence threshold of the objective function is taken as 1.0.

[0043] Furthermore, in step S8, the method for updating the orbital position and velocity when the convergence conditions are not met includes:

[0044] Step S8.1, calculate the learning rate η in the k-th iteration (k) :

[0045]

[0046] Step S8.2, calculate the first momentum vector at the k-th iteration and the second momentum vector at the k-th iteration

[0047]

[0048] Step S8.3, calculate the updated values of the orbital position and velocity

[0049]

[0050] where η is the learning rate factor, β1 and β2 are hyperparameters, λ is the regularization factor, and the vector represents the combined vector of the orbital position and velocity, that is The power series operation on the vector represents the operation on each element of the vector, ε is a constant, is the partial derivative of the objective function at the k-th iteration.

[0051] Furthermore, the learning rate factor η takes the value of 30, the hyperparameter β1 takes the value of 0.9, the hyperparameter β2 takes the value of 0.999, the regularization factor λ takes the value of 1×10 -6 and the constant ε takes the value of 1×10 -8 .

[0052] According to a system for determining the initial orbit of a space debris radar observation arc segment provided by the present invention, it includes:

[0053] Module M1, obtaining the radar observation arc segment data of the space debris, including: the time t at multiple sampling moments i , the distance l of the space debris relative to the observation station i , the azimuth angle A in the instantaneous true horizon coordinate system of the observation station i , the altitude angle h i , the coordinates of the observation station in the Earth-fixed coordinate system, i = 1, 2,..., M, and M is the number of sampling points;

[0054] Module M2, obtaining the system parameters of the radar observation equipment, including the ranging error σ range , the angle measurement error σ angle ;

[0055] Module M3, calculating the line-of-sight vector of the space debris relative to the observation station in the geocentric inertial coordinate system The position coordinates of the observatory station in the geocentric inertial coordinate system

[0056] Module M4, calculating the initial value of the orbital position corresponding to the moment t0 Initial velocity value

[0057] Module M5, calculating the objective function corresponding to the current orbital position

[0058] Module M6, calculating the partial derivatives of the objective function of the current orbital position with respect to the orbital position and velocity at the moment t0

[0059] Module M7, comparing the current objective function with the minimum value of the historical objective function and making records according to the comparison result;

[0060] Module M8, judging whether the convergence condition is satisfied. If satisfied, outputting the position and velocity corresponding to the minimum value of the historical objective function; otherwise, updating the orbital position and velocity values;

[0061] Among them, modules M5 to M8 are repeatedly triggered to work until the convergence condition is reached.

[0062] Compared with the prior art, the present invention has the following beneficial effects:

[0063] Aiming at the problem of large velocity error in the traditional initial orbit determination method for the radar observation arc of space debris, the present invention constructs a method considering the perturbed orbit dynamics model and radar system parameters, gives a definition of the objective function based on weighted operations on range measurement and angle measurement deviations respectively using radar system parameters, gives a process of position and velocity iterative operations using partial derivative information, and gives the convergence condition of the iteration. The method of the present invention is reasonable, simple in calculation and easy to implement, and can be effectively applied to the calculation of the initial orbit of the radar observation arc of space debris. Brief description of the drawings

[0064] By reading the detailed description of the non-limiting embodiments with reference to the following drawings, other features, objects and advantages of the present invention will become more obvious:

[0065] Figure 1 It is the flow chart of the present invention.

[0066] Figure 2 It is the statistical histogram of the observation duration corresponding to 1000 groups of arc data applied to the present invention.

[0067] Figure 3 It is the comparison of the initial orbit determination position accuracy of the present invention with the Laplace method.

[0068] Figure 4This is a comparison of the initial orbit determination speed accuracy of the present invention with the Laplace method. Detailed implementation manners

[0069] The present invention will be described in detail below with reference to specific embodiments. The following embodiments will help those skilled in the art to further understand the present invention, but do not limit the present invention in any form. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present invention, several changes and improvements can still be made. These all belong to the protection scope of the present invention.

[0070] As Figure 1 shown, the present invention provides a method for determining the initial orbit of a space debris radar observation arc segment, including:

[0071] Step S1: Obtain the radar observation arc segment data of the space debris, including: the time t at multiple sampling moments i , the distance l between the space debris and the observation station i , the azimuth angle A in the instantaneous true horizon coordinate system of the observation station i , the altitude angle h i , and the coordinates of the observation station in the Earth-fixed coordinate system, i = 1, 2,..., M, where M is the number of sampling points.

[0072] Step S2: Obtain the system parameters of the radar observation equipment, including the ranging error σ range , and the angle measurement error σ angle .

[0073] Step S3: Calculate the line-of-sight vector of the space debris relative to the observation station in the geocentric inertial coordinate system The position coordinates of the observation station in the geocentric inertial coordinate system

[0074] Step S4: Calculate the initial value of the orbital position corresponding to the moment t0 The initial value of the velocity

[0075] Step S5: Calculate the objective function corresponding to the current orbital position

[0076] Step S6: Calculate the partial derivatives of the objective function of the current orbital position with respect to the orbital position and velocity at the moment t0

[0077] Step S7: Compare the current objective function with the minimum value of the historical objective function, and record according to the comparison result.

[0078] Step S8: Determine whether the convergence condition is satisfied. If satisfied, output the position and velocity corresponding to the minimum value of the historical objective function; otherwise, update the orbital position and velocity values.

[0079] Among them, steps S5 to S8 are repeatedly triggered until the convergence condition is reached.

[0080] Generally, the data of a radar arc segment for observing space debris includes: the time t at multiple sampling moments i , the distance l of the space debris relative to the observation station i , the azimuth angle A in the instantaneous true horizon coordinate system of the observation station i , the altitude angle h i , where the subscript i ranges from 1, 2,..., M. M is the total number of sampling points of the observation data. The coordinates of the observation station in the Earth-fixed coordinate system and the system parameters of the radar observation equipment, including the ranging error σ range , the angle measurement error σ angle are known information.

[0081] To calculate the initial orbit, it is first necessary to determine the reference coordinate system selected for the orbit calculation. Usually, the geocentric inertial coordinate system is selected. Therefore, it is necessary to convert the observation data into the geocentric inertial coordinate system to generate the line-of-sight vector (unit vector) of the space debris relative to the observation station The position coordinates of the observation station in the geocentric inertial coordinate system In addition, it is also necessary to determine the moment corresponding to the solved orbit. In the present invention, the starting point of the arc segment is selected as the solution moment. Other moments can also be selected. Based on the dynamic model, the orbit state at one moment can be used to recursively deduce the orbit states at other moments.

[0082] To calculate the initial orbit, it is necessary to determine an evaluation criterion to evaluate whether the calculated orbit is close to the true value. In the absence of other prior information, it can only be judged based on the difference between the observation data and the estimated data. Since the radar observation data has the characteristics of high ranging accuracy and low angle measurement accuracy, the present invention defines the objective function by weighting the ranging and angle measurement deviations respectively. If the orbit position and velocity at time t0 According to the perturbed orbit dynamics model, the orbit is recursively deduced to obtain the guessed values of the orbit positions corresponding to the sampling moments t i respectively

[0083] Then calculate the guessed value l of the distance of the space debris relative to the observation station guess,i .

[0084]

[0085] Among them, ‖‖ represents the calculation of the 2-norm of the vector.

[0086] Further calculate the guessed value of the line-of-sight vector of the space debris relative to the observation station

[0087]

[0088] Finally, the distance difference l can be calculated. Δ,i and the line-of-sight difference u Δ,i .

[0089]

[0090] Among them, <> represents the inner product calculation of two vectors.

[0091] Based on the distance difference l Δ,i and the line-of-sight difference u Δ,i , using the radar ranging error σ range , the angle measurement error σ angle , calculate the objective function

[0092]

[0093] This objective function is equivalent to assigning different weights to the ranging data and the angle measurement data.

[0094] After determining the objective function, the problem of determining the initial orbit of the space debris radar observation arc is transformed into an unconstrained optimization problem. Optimization usually requires iteration based on an initial value. Iteration requires determining the iteration direction and the iteration step size. The present invention integrates the first-order momentum and the second-order momentum and adopts the dynamic adaptive AdamW update method. To calculate the initial orbit, the observation data of an arc should be no less than 2, that is, M≥2. According to the starting two points of the arc, the rough position of the space debris in the geocentric inertial coordinate system can be calculated However, usually the error is large.

[0095]

[0096] The position initial value calculated on this basis The velocity initial value has a large error.

[0097]

[0098] AdamW needs to first set the learning rate factor to η, the two hyperparameters to β1 and β2 respectively, and the regularization factor to λ,

[0099] Calculate the learning rate η in the kth (k≥1) iteration (k) .

[0100]

[0101] The first momentum vector in the kth (k≥1) iteration and the second momentum vector

[0102]

[0103] Among them, represents the partial derivative value of the objective function at the k-th iteration. Initially, the first momentum vector and the second momentum vector (k = 0) are both zero vectors. If the position coordinates are (r x , r y , r z ), and the velocity coordinates are (v x , v y , v z ), then the calculation method of the partial derivative is

[0104]

[0105] Based on the momentum, the updated values of the position and velocity are calculated according to the dynamic adaptive step size

[0106]

[0107] Among them, the vector represents the combined vector of the position and velocity, that is, The power series operation on the vector represents the operation on each element of the vector. The parameter ε is the constant 1×10 -8 , to avoid division by zero in the operation.

[0108] According to the initial orbit determination problem of the radar observation data and the selected initial values in the present invention, the learning rate factor η can take the value of 30, the hyperparameter β1 can take the value of 0.9, β2 can take the value of 0.999, and the regularization factor λ takes the value of 1×10 -6 .

[0109] During the iteration process, it cannot be ensured that each iteration is in the direction of the smaller objective function. Therefore, in each iteration step, the current objective function is compared with the minimum value of the historical objective function. If it is the 0th iteration currently, the minimum value of the historical objective function is equal to the current objective function, and the position and velocity corresponding to the minimum value of the objective function are recorded. Otherwise, only when the current objective function is less than the minimum value of the historical objective function, the minimum value of the historical objective function is set equal to the current objective function, and the position and velocity corresponding to the minimum value of the objective function are recorded. By recording the minimum value of the historical objective function and the corresponding position and velocity values, the optimal value on the entire iteration path can be output during the final output.

[0110] The judgment of iterative convergence is set as follows: (1) The number of iterations reaches the given maximum number of iterations; (2) The objective function is less than the given threshold; (3) The current objective function value is more than 10 times the minimum value of the objective function in the historical record. Any one of the convergence conditions is satisfied. Without loss of generality, the maximum number of iterations can be taken as 200, and the convergence threshold of the objective function can be taken as 1.0.

[0111] The following combines data to verify the effectiveness of the method of the present invention. For 1000 sets of arc segment data of different space debris observed by multiple radars, the method of the present invention is respectively executed to calculate the initial orbit, and the results are compared with the results of the traditional Laplace method. The duration distribution of the 1000 sets of arc segments is as shown in the appendix Figure 2 As shown. The reference orbit for true value comparison comes from the precise orbit determination result. The appendix Figure 3 And the appendix Figure 4 Are respectively the statistical histograms of the position deviation and velocity deviation of the method proposed by the present invention and the Laplace initial orbit determination method. It can be seen from the figure that the position accuracy of the initial orbit determination of the method of the present invention is comparable to that of the Laplace method, while the velocity accuracy is significantly better than that of the Laplace method.

[0112] The present invention also provides a system for determining the initial orbit of a space debris radar observation arc segment. The system for determining the initial orbit of a space debris radar observation arc segment can be implemented by executing the process steps of the method for determining the initial orbit of a space debris radar observation arc segment. That is, those skilled in the art can understand the method for determining the initial orbit of a space debris radar observation arc segment as the preferred implementation manner of the system for determining the initial orbit of a space debris radar observation arc segment. The system includes:

[0113] Module M1, which obtains the radar observation arc segment data of the space debris, including: the time t at multiple sampling moments i , the distance l of the space debris relative to the observation station i , the azimuth angle A in the instantaneous true horizon coordinate system of the observation station i , the altitude angle h i , and the coordinates of the observation station in the Earth-fixed coordinate system, i = 1, 2,..., M, where M is the number of sampling points.

[0114] Module M2, which obtains the system parameters of the radar observation equipment, including the ranging error σ range , and the angle measurement error σ angle .

[0115] Module M3, which calculates the line-of-sight vector of the space debris relative to the observation station in the geocentric inertial coordinate system The position coordinates of the observation station in the geocentric inertial coordinate system

[0116] Module M4, which calculates the initial value of the orbit position corresponding to the moment t0 Initial velocity value

[0117] Module M5, calculating the objective function corresponding to the current orbital position

[0118] Module M6, calculating the partial derivatives of the objective function at the current orbital position with respect to the orbital position and velocity at time t0

[0119] Module M7, comparing the current objective function with the minimum value of the historical objective function and recording according to the comparison result

[0120] Module M8, determining whether the convergence condition is satisfied. If satisfied, outputting the position and velocity corresponding to the minimum value of the historical objective function; otherwise, updating the orbital position and velocity values

[0121] Among them, modules M5 to M8 are repeatedly triggered to work until the convergence condition is reached

[0122] Those skilled in the art know that in addition to implementing the system and its various devices, modules, and units provided by the present invention in the form of pure computer-readable program code, the method steps can be logically programmed to enable the system and its various devices, modules, and units provided by the present invention to be implemented in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers, etc., to achieve the same functions. Therefore, the system and its various devices, modules, and units provided by the present invention can be regarded as a kind of hardware component, and the devices, modules, and units included therein for implementing various functions can also be regarded as the structures within the hardware component; the devices, modules, and units for implementing various functions can also be regarded as both software modules for implementing the method and the structures within the hardware component

[0123] The specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the above specific embodiments, and those skilled in the art can make various changes or modifications within the scope of the claims, which does not affect the essence of the present invention. Without conflict, the embodiments of the present application and the features in the embodiments can be combined arbitrarily

Claims

1. A method for determining the initial orbit of a space debris radar observation arc, characterized in that Including: Step S1, obtain the radar observation arc data of space debris, including: time t at multiple sampling moments i , the distance l between the space debris and the observation station i , the azimuth angle A in the instantaneous true horizon coordinate system of the observation station i , the altitude angle h i , the coordinates of the observation station in the Earth-fixed coordinate system, i = 1, 2, …… M, where M is the number of sampling points; Step S2, obtain the system parameters of the radar observation device, including the ranging error σ range , the angle measurement error σ angle ; Step S3, calculate the line-of-sight vector of the space debris relative to the observation station in the geocentric inertial coordinate system The position coordinates of the observation station in the geocentric inertial coordinate system Step S4, calculate the initial value of the orbital position corresponding to the moment t0 Initial value of velocity Step S5, calculate the objective function corresponding to the current orbital position Step S6, calculate the partial derivatives of the objective function of the current orbital position with respect to the orbital position and velocity at time t0 Step S7: Compare the current objective function with the minimum value of the historical objective function and record according to the comparison result; Step S8: Determine whether the convergence condition is satisfied. If it is satisfied, output the position and velocity corresponding to the minimum value of the historical objective function; otherwise, update the orbital position and velocity values; Among them, steps S5 - S8 are repeatedly triggered until the convergence condition is reached.

2. The method for determining the initial orbit of the space debris radar observation arc according to claim 1, characterized in that Step S4 includes: Step S4.1, calculate the approximate position of the space debris in the geocentric inertial coordinate system Step 4.2, calculate the initial orbital position Initial velocity Step 4.3, initialize the initial values of the first momentum vector and the initial values of the second momentum vector to all-zero vectors.

3. The method for determining the initial orbit of the space debris radar observation arc according to claim 1, characterized in that Step S5 includes: Step S5.1, from the orbital position at time t0 speed According to the perturbed orbit dynamics model, perform orbit recurrence to obtain the guessed values of the orbital positions corresponding to the sampling times t i respectively Step 5.2, calculate the estimated distance value l of the space debris relative to the observation station guess,i : Among them, || || represents the calculation of the 2 - norm of a vector; Step 5.3, calculate the guessed value of the line-of-sight vector of the space debris relative to the observation station Step 5.4, calculate the distance difference l Δ,i and the line-of-sight difference u Δ,i : Among them, < > represents the calculation of the inner product of two vectors; Step 5.5, calculate the objective function 4. The method for determining the initial orbit of the space debris radar observation arc according to claim 1, wherein In step S6, the partial derivative is calculated by the following method: Orbital position The coordinates are (r x , r y , r z ), and the velocity The coordinates are (v x , v y , v z ).

5. The method for determining the initial orbit of the space debris radar observation arc according to claim 1, characterized in that The convergence conditions in step S8 include any one of the following: The number of iterations reaches the given maximum number of iterations; The objective function is less than the given threshold; The current objective function value is more than 10 times greater than the minimum value of the objective function in the historical record.

6. The method for determining the initial orbit of the space debris radar observation arc according to claim 1, wherein In step S7, when comparing the current objective function with the minimum value of the historical objective function, if it is the 0th iteration currently, the minimum value of the historical objective function is equal to the current objective function, and record the position and velocity corresponding to the minimum value of the objective function; otherwise, only when the current objective function is less than the minimum value of the historical objective function, make the minimum value of the historical objective function equal to the current objective function, and record the position and velocity corresponding to the minimum value of the objective function.

7. The method for determining the initial orbit of the space debris radar observation arc according to claim 1, wherein In step S8, the maximum number of iterations is taken as 200, and the convergence threshold of the objective function is taken as 1.

0.

8. The method for determining the initial orbit of the space debris radar observation arc according to claim 1, wherein In step S8, the method for updating the orbital position and velocity when the convergence condition is not satisfied includes: Step S8.1, calculate the learning rate η in the k-th iteration (k) :[[-END]] Step S8.2, calculate the first momentum vector at the k-th iteration and the second momentum vector at the k-th iteration Step S8.3, calculate the updated values of the orbital position and velocity where η is the learning rate factor, β1 and β2 are hyperparameters, λ is the regularization factor, and the vector represents the combined vector of the orbital position and velocity, i.e., The power series operation on the vector represents the operation on each element of the vector. ε is a constant, is the partial derivative of the objective function at the k-th iteration.

9. The method for determining the initial orbit of the space debris radar observation arc according to claim 8, characterized in that The learning rate factor η takes the value of 30, the hyperparameter β1 takes the value of 0.9, the hyperparameter β2 takes the value of 0.999, and the regularization factor λ takes the value of 1×10 -6 and the constant ε takes the value of 1×10 -8 .

10. A system for determining the initial orbit of a space debris radar observation arc, characterized in that, Including: Module M1, which acquires the radar observation arc data of space debris, including: the time t at multiple sampling moments i , the distance l of the space debris relative to the observation station i , the azimuth angle A in the instantaneous true horizon coordinate system of the observation station i , the altitude angle h i , the coordinates of the observation station in the Earth-fixed coordinate system, i = 1, 2,..., M, where M is the number of sampling points; Module M2, which obtains the system parameters of the radar observation device, including the ranging error σ range , the angle measurement error σ angle ; Module M3 calculates the line-of-sight vector of the space debris relative to the observation station in the geocentric inertial coordinate system The position coordinates of the observation station in the geocentric inertial coordinate system Module M4, calculating the initial value of the orbital position corresponding to the moment t0 Initial velocity value Module M5, which calculates the objective function corresponding to the current orbital position Module M6, calculating the partial derivatives of the current orbital position objective function with respect to the orbital position and velocity at time t0 Module M7: Compare the current objective function with the minimum value of the historical objective function and record according to the comparison result; Module M8: Determine whether the convergence condition is satisfied. If it is satisfied, output the position and velocity corresponding to the minimum value of the historical objective function; otherwise, update the orbital position and velocity values; Among them, modules M5 - M8 are repeatedly triggered to work until the convergence condition is reached.

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