Space target initial orbit determination method based on Gauss algorithm

Abstract

The invention belongs to the technical field of aerospace orbit determination, and aims to solve the problem that in an existing Gauss algorithm, singularity can be displayed under observation data with relatively strong coplane characteristics mainly depending on a vector geometrical relationship among position vectors of input visual right ascension, visual declination and an observation station center. According to the Gauss algorithm-based space target initial orbit determination method, the cosine theorem is used for improving the algorithm, after improvement, the Gauss algorithm-based space target initial orbit determination method only depends on a vector geometrical relationship between an observation station point at the middle moment and the target and an iterative initial value of an octagonal equation at the moment with respect to the geocentric distance, errors are reduced, and the calculation accuracy is improved. Therefore, the error propagation phenomenon is reduced.

Description

Technical Field

[0001] This invention belongs to the field of aerospace trajectory determination technology. Background Technology

[0002] In response to the threat of space object collisions and the needs of space defense security, the Space Object Surveillance System (SOSS) provides information support and security assurance for the development of space technology. Determining the orbit of space objects is a crucial part of SOSS. Based on the calculated target orbit data, cataloging, identification, and orbit prediction can be performed. Furthermore, it can be combined with other subsystems of the Space Object Surveillance System (SOSS) to avoid or warn of potential collisions and attacks, possessing significant military application value and providing a fundamental guarantee for the rational utilization of future space resources.

[0003] Initial orbit determination utilizes short-segment observation data and a relatively simple dynamic model (typically a two-body model). Based on the available observation data, a suitable method is used to quickly calculate the initial orbit of the spacecraft, making an initial guess about the orbit. This is often done without prior information. The initial orbit determination result serves two purposes: first, it provides initial values ​​for orbit improvement; second, it provides rapid and accurate orbit insertion parameters for real-time orbital monitoring to determine whether the spacecraft has entered its designed orbit. The orbit is primarily represented by the orbital root numbers, and there is also a state vector to represent the orbit's state in space. Existing initial orbit determination methods are generally deterministic methods that directly calculate the orbital root numbers under conditions of scarce observation data. The observation data is usually limited to a maximum of three sets, the most classic being the Gauss method based on three sets of angular observations.

[0004] like Figure 1 As shown, the following theoretical model is the Gaussian orbital model. , , For the target at three different epochs in the target orbit , , The geocentric position vector (in the J2000 coordinate system). , , This represents the position vector of the observation platform at the corresponding moment. , , This represents the distance from the target to the observation platform at the corresponding time. , , Let be its corresponding unit vector, where .

[0005] The known trajectory of the observation platform ( , , Given the target's right ascension and declination from the observation platform, the position vector of the target at a certain moment is determined, and then the target's orbit is initially estimated. The basic relationship is as follows:  ,  ,  , At the same time, it can be seen from the above model that, , , Within the same orbital plane, we have:  ,  , , The conversion can be performed using the right ascension and declination at the corresponding time, as shown in the following formula:  , Among them, , and For the right ascension and declination at the corresponding epoch.

[0006] By combining the above equations and performing vector operations, the solution can be obtained. , , Algorithm factors:  ,  , The following is given , , The calculation formula.

[0007]  ,  ,  , Among them,  ,  , To obtain the unknown parameters in the above formula By iteratively solving the following eighth-degree equation, we can give... Initial guess: .

[0008] in, , , , Substitution , , The calculation formula is obtained , , Substitute , , The calculation formula can be used to determine the target at three different epochs. , , The geocentric position vector. The velocity vector at a given moment can be calculated using methods such as the f- and g-series iteration method or the Gibbs algorithm. Then, based on the formula for calculating the six orbital elements, the orbital information of the space target can be obtained.

[0009] The mathematical model analysis above shows that three sets of apparent right ascension and apparent declination at different observation times are needed to obtain the orbital root numbers, which also have six degrees of freedom. To better fit the algorithm model, the three sets of input data must possess spatial depth, meaning their angular information must have sufficient differences to represent orbital information in three-dimensional space. Based on this, the Gauss method, in coplanar... Singularity can be observed in observational data with strong characteristics, which, from a mathematical model perspective, mainly depends on... The calculation formula, , As can be seen from the formula, where , To have greater weight It is relatively large, with a semi-major axis of its near-Earth orbit exceeding 6500 km. Therefore, its negative cubic power has a relatively small weight. The value mainly depends on the vector geometric relationship between the input right ascension, apparent declination, and the position vector of the observation station center. , Its advantage lies in reducing the impact of errors such as noise and decreasing sensitivity to noise. Its disadvantage is that when… When the error is very small, , value pairs It played a decisive role and did not conform to the characteristics of the algorithm. , On the contrary, it will amplify the error, which is especially true for smaller errors. That would have the opposite effect. Summary of the Invention

[0010] To address the issues in the existing Gaussian algorithm, This mainly depends on the vector geometric relationship between the input apparent right ascension, apparent declination, and the position vector of the observation station center. Singularity issues may appear in observation data with strong coplanar characteristics. Initially, error propagation occurs. This invention proposes an improvement method using the law of cosines. The algorithm's "method for determining the initial orbit of a space target based on the Gauss algorithm" includes the following steps: like Figure 2 As shown, three observation times were collected. , , Angle measurement data of space targets and location information of observation stations, , , This represents the position vector of the observation platform at the corresponding moment. , , The distance from the target to the observation platform at the corresponding time. , , This represents the target's geocentric position vector at the corresponding moment. Iterative solution Earth-center distance of the target at any given time: ; Solve , , At any given moment, the distance from the observation platform to the target. , , : , , , Finally, find the solution. , , The geocentric position vector of the target at any given time is used to calculate the initial orbit information of the space target using the orbital root formula.

[0011] Technical effects: This invention addresses the problem that existing Gaussian algorithms exhibit singularities in observation data with strong coplanar characteristics. In such cases, existing Gaussian algorithms suffer from computational limitations. This process amplifies errors, thus affecting subsequent calculations. This process causes error propagation. The present invention calculates... The algorithm removes the factors affecting the coplanarity problem. , Only the iteration result of the eighth-degree equation Regarding, in When the error is small, it can be reduced. This reduces the error propagation phenomenon.

[0012] To better illustrate the technical effects of the present invention, through comparison... as well as The error was used to verify the effectiveness of this method on measurement data with strong coplanar characteristics. The accuracy improvement effect is shown. First, the space-based observation target and its orbital data are simulated using STK simulation software. The simulation model is a two-body model with the coordinate system J2000.0 (the same below). Experimental data shows that, with an iteration error of 0.8km in the eighth equation, the present invention improves accuracy compared to the existing Gauss algorithm. The error was reduced by 45km. Attached Figure Description

[0013] Figure 1 This is a schematic diagram of the three-position vector principle of the existing Gauss algorithm.

[0014] Figure 2 For the present invention A schematic diagram of the algorithm's geometric relationship. Detailed Implementation

[0015] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. All other embodiments obtained by those skilled in the art without creative effort using the embodiments of the present invention are within the scope of protection of the present invention.

[0016] This embodiment proposes a method for determining the initial orbit of a space target based on the Gaussian algorithm, collecting data at three observation times. , , Angle measurement data of space targets and location information of observation stations, , , This represents the position vector of the observation platform at the corresponding moment. , , The distance from the target to the observation platform at the corresponding time. , , This is the target's geocentric position vector at the corresponding moment.

[0017] Will , , Convert the apparent right ascension and apparent declination to unit vectors: , In the formula, , and For the right ascension and declination at the corresponding epoch.

[0018] Iterative solution of octet equations Earth-center distance of the target at any given time: .

[0019] in: , , , , , , , , Then solve , , At any given moment, the distance from the observation platform to the target. , , : , , , in, , , .

[0020] Calculate using the geometric triangle cosine theorem at the intermediate time.

[0021] Finally, the triangle rule of vector geometry is used to calculate... , , Position vectors of the target at three observation times (J2000.0 coordinate system): , , .

[0022] The input data of this invention is the apparent right ascension and apparent declination of the space target in the J2000 coordinate system. Any apparent right ascension and apparent declination that can be obtained through calculation or observation equipment can be used to determine the initial orbit using the method described in this invention. At the same time, this invention is not limited to the specific details in the above embodiments. Within the scope of the technical concept of this invention, various simple modifications can be made to the technical solution of this invention, and these simple modifications all fall within the protection scope of this invention.

Claims

1. A method for determining the initial orbit of a space target based on the Gauss algorithm, comprising the following steps: Collect three observation times , , Angle measurement data of space targets and location information of observation stations, , , This represents the position vector of the observation platform at the corresponding moment. , , The distance from the target to the observation platform at the corresponding time. , , This represents the target's geocentric position vector at the corresponding moment. Iterative solution Earth-center distance of the target at any given time: ; Solve , , At any given moment, the distance from the observation platform to the target. , , : ， ， Its features are, ， Solve , , The geocentric position vector of the target at any given time is used to calculate the initial orbit information of the space target using the orbital root formula.

2. The method for determining the initial orbit of a space target based on the Gauss algorithm according to claim 1, characterized in that, The The specific derivation process is as follows: First calculate time The included angle ; Using the Law of Cosines, we can derive The included angle : ， ， calculate The included angle ; Calculate using the Law of Cosines : ， 。 3. The method for determining the initial orbit of a space target based on the Gauss algorithm according to claim 1, characterized in that, Solve Distance from the Earth's center to the target at any given time , in: , , , , ， ， ， 。 4. The method for determining the initial orbit of a space target based on the Gaussian algorithm according to claim 1, characterized in that, Solve , , The position vector of the target in the J2000.0 coordinate system at any given time: ， ， 。

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