Space target initial orbit determination method suitable for space-based ultra-short arc optical observation

Abstract

The invention discloses a space target initial orbit determination method suitable for space-based ultra-short arc optical observation, and the method comprises the steps: employing short arc optical observation data, based on the assumption that a measurement residual error weighted square sum meets chi-square distribution, combining an L-M nonlinear optimization function and a Lanbert problem, and carrying out the initial orbit determination of a space target. And carrying out adaptive fitting on the distance from the initial epoch observation platform to the target and the corresponding minimum measurement residual weighted sum of squares to realize the initial orbit determination of the target. According to the method, high-precision pointing information of a target is required to be provided, position information of an observation platform is required to be known, initial orbit determination of short-arc optical observation can be completed by utilizing a simple algorithm on the basis, and the method is a simple and efficient short-arc initial orbit determination method.

Description

Technical Field

[0001] The present invention relates to a method for initially determining the orbit of a space target applicable to space-based single-line-of-sight ultra-short arc optical observation. It involves using space-based single-line-of-sight ultra-short arc optical observation information to complete the initial orbit determination of a non-cooperative target through a space search method and a Lambert orbit determination method. It belongs to the field of space technology. Background Art

[0002] With the continuous development of microsatellite technology, the number of near-Earth space spacecraft has increased exponentially.

[0003] The effective cataloging and monitoring of space targets are prerequisite conditions for ensuring the safe in-orbit operation of our spacecraft and for performing operations such as collision warning and avoidance. Orbit determination technology is the core technology for space target cataloging. According to the required information and processing flow, it can be divided into initial orbit determination technology and orbit improvement technology, and the latter is also called precise orbit determination. Initial orbit determination technology is to quickly determine the orbit of a target using a segment of observed data without any prior information, obtaining a rough estimate of the target orbit parameters, so as to provide necessary prior information for subsequent precise orbit determination. The accuracy of initial orbit determination directly determines the convergence accuracy and speed of precise orbit determination. Therefore, it is crucial to study efficient initial orbit determination technology.

[0004] When using a space-based scanning mode for observation, the obtained target observation arc is usually very short, often less than 60 s. Such observation data is called ultra-short arc data. This part of the data accounts for a large proportion in the observation data. Especially with the rapid development of current commercial space technology, commercial satellites will generate a large amount of short arc optical observation data during their in-orbit operation. In order to effectively utilize this observation data, further provide necessary prior information for space target orbit improvement and cataloging, and improve the cataloging efficiency of targets, thereby better enhancing China's space situation awareness ability, it is very necessary to study an efficient initial orbit determination technology for ultra-short arc space targets based on angle-only measurement. This invention can provide a solid theoretical basis for the development of China's space-based surveillance system.

[0005] Traditional methods for orbit determination based on angle measurement information include the Laplace method, the Gauss method, the double R iteration algorithm, and the Gooding method. The Laplace method is only applicable to the determination of heliocentric planetary orbits and cannot be used for the determination of orbits of near-Earth space targets. The Gauss method is sensitive to the interval of observables. Both too large and too small intervals will lead to orbit determination failure. For ultra-short arc observation data, the Gauss method has serious ill-conditioning, making the method completely ineffective. The double R iteration algorithm is applicable to orbit determination with a long observation time interval. The disadvantage is that it requires the initial distance values at the beginning and end epochs. It is difficult to converge to the true value under ultra-short arc observation conditions. The Gooding method is sensitive to measurement errors and easily converges to wrong solutions under ultra-short arc data. Different from traditional methods, in order to improve the accuracy of ultra-short arc initial orbit determination, scholars at home and abroad have introduced the concept of allowable domain. This method uses prior information to restrict the solution space of the target, and then represents the solution space in the form of discretization or Gaussian sum. Compared with traditional methods, this method can provide multiple solutions, which is more conducive to the convergence of the filter during subsequent orbit improvement. The disadvantage is that it requires artificial provision of constraint information and is greatly affected by subjective factors.

[0006] The present invention proposes a method for directly using actual ultra-short arc observation data for initial orbit determination, which effectively utilizes all observation data, does not require fitting operations on the observation data, and does not require artificial provision of constraint information. Based on the assumption that the weighted sum of squared residuals (WSSR) of measurements satisfies the chi-square distribution, the boundary of the solution space is directly determined through an adaptive fitting method, and then the solution space is represented through discretized sampling, efficiently solving the problem of initial orbit determination for ultra-short arc optical observations. Summary of the Invention

[0007] In response to the current demand for effective utilization of a large amount of short arc optical observation data in space situation awareness, the present invention designs a method for initial orbit determination of space targets suitable for space-based ultra-short arc optical observations. The advantages of the present invention are as follows: The initial orbit determination of space targets can be completed using single-satellite platform single-line-of-sight ultra-short arc optical observations. The algorithm is simple. At the same time, during the initial orbit determination process, the angle measurement information at the initial and end epochs is considered to have errors and is optimized. It greatly improves the utilization rate of the observation data of space-based optical payloads and further enhances China's space situation awareness ability.

[0008] The main technical solution of the present invention is as follows: Using a short arc of optical observation data, based on the assumption that the weighted sum of squared residuals (WSSR) of measurements satisfies the chi-square distribution, by adaptively searching for the distance ρ1 from the observation platform to the target at the initial epoch, the range of ρ1 corresponding to the solution space is determined. The main steps are as follows:

[0009] (1) Obtain a short arc of optical observation data and determine the degrees of freedom of the chi-square distribution satisfied by the weighted sum of squared residuals of the measurements and the lower limit ρ of the search for ρ1 1min ;

[0010] (2) Take the 95% chi-square distribution as the test criterion, and determine the critical value ε by referring to the chi-square distribution table.

[0011] (3) Given ρ1, use the L-M nonlinear optimization function to optimize the distance ρ2 from the observation platform at the final epoch to the target and the two sets of angle measurement data at the initial and final epochs by solving the Lambert problem. The objective function is WSSR, that is, given a ρ1, the minimum WSSR corresponding to this ρ1 and a corresponding set of optimized variables can be obtained through optimization, which can be expressed in functional form as:

[0012] WSSR min = f(ρ1) (1)

[0013] (4) Starting from ρ1, update the fitting interval by using the method of adaptive interpolation fitting. Step (3) is a sub-step of the adaptive interpolation fitting. At the same time, perform a root-finding operation on the fitting function within the new fitting interval:

[0014] F fit (ρ1) = ε (2)

[0015] (5) Determine whether there is a positive real root in step (4). If there is, save the root and execute step (6); if not, return to step (4);

[0016] (6) Determine whether two roots have been found. If so, end the operation; otherwise, return to step (4).

[0017] The two roots obtained above are the upper and lower bounds of ρ1 corresponding to the solution space that satisfies the 95% chi-square distribution test.

[0018] As can be seen from the above steps, given ρ1, there is a unique WSSR min corresponding to it, that is, WSSR min is a function of ρ1, but this function has no analytical solution. Therefore, it is fitted by the method of adaptive interpolation. The advantage of adaptive fitting is that it can not only adaptively adjust the length of the fitting interval according to the given fitting accuracy requirements, but also perform a root-finding operation on the fitted function, which is convenient for programmed operation. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 is a flow chart of an initial orbit determination method for space targets applicable to space-based ultra-short arc optical observations. DETAILED DESCRIPTION OF THE INVENTION

[0020] The technical solution of the present invention will be described in detail and completely below in conjunction with the accompanying drawings.

[0021] The present invention discloses an initial orbit determination method for space targets applicable to space-based ultra-short arc optical observations. AsFigure 1 As shown in the figure, the core idea of the present invention is as follows: for optical observation data, the angular information of each epoch is known, while the distance information from the observation platform to the target is unknown. Based on the assumption that the weighted sum of squared measurement residuals follows a chi-square distribution, given the initial and final epoch distance initial values from the observation platform to the target, and combined with the two sets of angular information at the initial and final epochs, a predicted orbit is obtained by solving the Lambert problem, thereby obtaining the corresponding weighted sum of squared measurement residuals. In the present invention, after giving ρ1, taking ρ2 and the two sets of angular information at the initial and final epochs as optimization variables, the minimum weighted sum of squared measurement residuals WSSR corresponding to this ρ1 is obtained through the L-M nonlinear optimization algorithm min , that is, given ρ1, there is a unique WSSR min corresponding to it; the ultimate goal is to find the range of ρ1 for which WSSR min satisfies the chi-square distribution test of 95%. This range is a continuous interval, and it is only necessary to find the upper and lower bounds of ρ1 that meet the conditions; on this basis, an adaptive interpolation fitting is performed on the relationship between WSSR min and ρ1. The advantage of adaptive interpolation fitting is that: the fitting interval is adaptively adjusted according to the given fitting accuracy; a root-finding operation is performed on the fitting function, which is convenient for programmed operation. The adaptive fitting operation is continuously repeated until two roots that meet the conditions are found. Thus, the initial orbit determination of space-based ultra-short arc optical observation is completed. The solution provided by the present invention is multiple solutions rather than a single solution, and all those that meet the conditions may be the target solutions. The advantage of multiple solutions is that it can provide necessary prior information for subsequent multi-initial value filtering or Gaussian sum filtering

[0022] Specifically, it includes the following steps:

[0023] (1) Data preparation: Obtain a short arc of optical observation data. Assume that this section of data has passed the previous image processing, determine the epochs corresponding to this section of data, and thus determine the degrees of freedom of the chi-square distribution satisfied by the weighted sum of squared measurement residuals; determine the threshold ε corresponding to the 95% chi-square distribution under this degree of freedom by referring to the chi-square distribution table; at the same time, give the starting value of the adaptive interpolation fitting, that is, the minimum value ρ of ε 1min ;

[0024] (2) Adaptive interpolation fitting: After the data preparation is completed, start the adaptive interpolation fitting. Starting from ρ 1min , both the L-M nonlinear optimization function and the Lambert problem are intermediate steps in the adaptive interpolation fitting;

[0025] (3) Root-finding of the fitting function: After each interval of fitting is completed, use the root-finding formula to perform a root-finding operation on the following formula:

[0026] F fit (ρ1) = ε (3)

[0027] (4) Judgment: Check whether a positive real root appears in the root-finding operation. If a positive real root appears, save the root; otherwise, do not save it. Check whether the cumulative number of positive real roots has reached 2. If not, return to the adaptive interpolation fitting step to perform fitting for a new interval. If it has reached 2, end the operation.

Claims

1. A method for initial orbit determination of space targets suitable for space-based ultra-short arc optical observation, characterized in that: Using a section of ultra-short arc optical observation data, based on the assumption that the weighted sum of squares of the measurement residuals satisfies the chi-square distribution, combined with the LM nonlinear optimization function and the Lambert problem, by performing adaptive interpolation fitting on the distance ρ1 from the initial epoch observation platform to the target and the minimum weighted sum of squares of the measurement residuals corresponding to ρ1, the critical ρ1 corresponding to the measurement residual satisfying the 95% chi-square distribution test is solved, thereby achieving the initial orbit determination of the target. The workflow of the space target initial orbit determination method for space-based ultra-short arc optical observation is as follows: First, data preparation is performed. Assuming that a short arc optical observation data has been obtained after image processing, the valid epoch and the corresponding valid measurement number are determined, so as to determine the degree of freedom of the chi-square distribution satisfied by the weighted sum of squares of the measurement residuals; the critical value corresponding to the chi-square test of 95% of the degree of freedom is determined by consulting the chi-square distribution table; Then determine the starting value of ρ1, that is, ρ 1min ; Next, adaptive interpolation fitting is performed. The principle is: given ρ1, the LM nonlinear optimization algorithm is used to optimize the distance ρ2 from the observation platform to the target at the last epoch and the two sets of angle measurement data at the first and last epochs. The objective function of the optimization is the weighted sum of squares of the measurement residual WSSR, and the minimum is the optimal. The orbit solution problem in the optimization process is the classic Lambert problem; that is, given ρ1, there is a unique WSSR min Correspondingly, there is a functional relationship between the two, and adaptive interpolation fitting is to perform segmented fitting on the relationship between the two to facilitate subsequent root-finding operations; Then, the root-finding operation is performed on the interval just fitted, with the aim of finding whether there is a critical ρ1 that satisfies the 95% chi-square test in the current fitting interval; Finally, the root-finding result is tested to see if there is a positive real root. If so, the root is saved, otherwise it is not saved. It is determined whether the cumulative number of positive real roots has reached 2. If not, the adaptive interpolation fitting step is returned to fit the new interval. If so, the operation is terminated. All the values ​​in the closed interval formed by the two ρ1s obtained at the end of the run are likely to be solutions to the target orbit, and the initial orbit determination of the target is completed.

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