CN-121435513-B - Track extrapolation method based on longitude and altitude coordinate system

CN121435513BCN 121435513 BCN121435513 BCN 121435513BCN-121435513-B

Abstract

The invention discloses a track extrapolation method based on a longitude and altitude coordinate system, which solves the problem of insufficient numerical value propagation efficiency and belongs to the field of track extrapolation; the method comprises the steps of constructing an under-satellite point longitude model based on orbit root numbers, obtaining a true near point angle model through calculation, obtaining a preferred true near point angle according to latitude amplitude iteration parameters, obtaining a first derivative and a second derivative of the true near point angle based on the preferred true near point angle, forming derivative parameters with the preferred true near point angle, introducing the derivative parameters to obtain the first derivative and the second derivative of the under-satellite point longitude, constructing an orbit height model through the difference between the ground center distance of a spacecraft and the earth radius, introducing the derivative parameters to obtain the first derivative and the second derivative of the orbit height, constructing a state space equation with the first derivative and the second derivative of the under-satellite point longitude, integrating the state space equation through a numerical integrator, and extrapolating a four-dimensional space state vector to obtain a longitude height propagation model.

Inventors

XUE JINYAN
MA ZHIHAO
ZHANG YASHENG
TAO XUEFENG
ZHANG QINGCHEN
ZHAO SHUAILONG
TONG FEI
YANG MINGQI
YAO JING
HAN LEI

Assignees

中国人民解放军军事航天部队航天工程大学

Dates

Publication Date: 20260508
Application Date: 20251031

Claims (6)

1. A method of track extrapolation based on a longitude-altitude coordinate system, the method comprising: the method comprises the steps of firstly, constructing a longitude model of an undersea point by considering earth rotation based on the number of tracks, resolving the longitude model of the undersea point to obtain a true near point angle model, iterating parameters in the true near point angle model according to quadrants of latitude amplitude angles to obtain a converged optimal true near point angle; Obtaining a first derivative of the real near point angle based on the optimal real near point angle, deriving the first derivative of the real near point angle, and obtaining a second derivative of the real near point angle; step three, introducing a derivative parameter to derive a model of the longitude of the point below the satellite, and obtaining a first derivative and a second derivative of the longitude of the point below the satellite; Step four, constructing an orbit height model according to the difference between the ground center distance and the earth radius of the spacecraft, introducing a derivative parameter to derive the orbit height model, and obtaining a first derivative and a second derivative of the orbit height; constructing a state space equation of a four-dimensional space state vector by using a first derivative and a second derivative of the longitude of the point below the satellite and a first derivative and a second derivative of the orbit height; In the first step, the longitude model of the satellite lower point is: ; in the formula, Is the longitude of the point under the satellite, In order to raise the right-hand meridian of the intersection point, Is an integer of the number of the times, According to the latitude amplitude angle Quadrant determination of (1) when When k=1, when Or (b) When k=0; Is the amplitude angle of the near-place, For a true angle of the near point, In order to achieve a peripheral rate of the material, For the inclination angle of the track, When the spacecraft passes through the Greennizhiping star at the moment of the ascending intersection point, Is the rotational angular velocity of the earth, Is a time variable; The true near point angle model is: ; Iterating parameters in the true and near point angle model according to quadrants of the latitude amplitude angle to obtain a converged optimal true and near point angle, wherein the method comprises the following steps: s11, when k=0, calculating the true near point angle in the true near point angle model Initial value of (1) ; S12, will Amplitude angle with near-spot Adding to obtain an iteration latitude argument ; S13, according to Quadrant adjustment k of (1) when When k=1, when Or (b) When k=0; s14, substituting the adjusted k into the true near point angle model to obtain an iteration value of the true near point angle ; S15, the iteration value of the true near point angle Replacing initial value of true near point angle in S12 Repeating steps S12-S14 until convergence to obtain the preferable true near point angle after convergence ; In the second step, the first derivative of the true near point angle is: ; the second derivative of the true near point angle is: ; in the formula, As the first derivative of the true near point angle, As the second derivative of the true near point angle, Is the gravitational constant of the celestial body, Is in the shape of a half-diameter, In order to achieve the eccentricity ratio, For a true angle of the near point, The first derivative is represented, the two points above the parameter are represented.
2. The method of claim 1 wherein in step three, the first derivative of the longitude of the undersea point is: ; The second derivative of the longitude of the undersea point is: ; in the formula, Is the first derivative of the longitude of the point below the satellite, Is the second derivative of the longitude of the point below the satellite; To raise the first derivative of the right ascension of the intersection points, Is the first derivative of the latitude argument, Is the first derivative of the near-place argument.
3. The method of claim 2, wherein in step four, the orbit height model is: ; in the formula, The height of the track is defined as the track height, For the ground center distance of the spacecraft, Is the earth radius.
4. A method according to claim 3, wherein in step four, the first derivative of the track height The method comprises the following steps: ; Second derivative of track height The method comprises the following steps: 。
5. the method of claim 4, wherein in step five, the state space equation is: ; in the formula, Is a four-dimensional spatial state vector.
6. The method of claim 5, wherein in the fifth step, the state space equation is integrated by a numerical integrator, and the method for extrapolating the four-dimensional space state vector required by the task is as follows: s21, starting from a four-dimensional space state vector at an initial moment by adopting a numerical integrator, integrating a state space equation, and reversely calculating a first derivative and a second derivative of the longitude of the point below the satellite and a first derivative and a second derivative of the altitude within the time step of an integration process; S22, returning the first derivative and the second derivative of the longitude of the point below the satellite and the first derivative and the second derivative of the altitude to the numerical integrator, updating the four-dimensional space state vector, pushing the updated four-dimensional space state vector to the next moment, repeating the steps S21 to S22 until the moment of termination, and stopping extrapolation to obtain the four-dimensional space state vector required by the task.

Description

Track extrapolation method based on longitude and altitude coordinate system Technical Field The invention belongs to the technical field of space dynamics and orbit determination, and relates to an orbit extrapolation method based on a longitude and altitude coordinate system. Background The orbit extrapolation is the basis for task planning and on-orbit control, and the state information of the spacecraft at any moment needs to be accurately and rapidly forecasted. However, for any inclination of spacecraft orbit, the existing methods mostly use state quantitiesHigh-precision orbit propagation is carried out, wherein,Is the position corresponding to the geocentric inertial rectangular coordinate system,The high-dimensional description mode is theoretically complete, but faces serious challenges in engineering practice: One is that the computational efficiency is not particularly pronounced, especially when calculating large eccentricity tracks, very small steps must be employed to capture the large changes in state, directly resulting in reduced computational efficiency. For example Zhang Haocheng spacecraft orbit dynamics modeling and control based on quaternion [ D ]. Harbine university of industry, 2014. And secondly, the state quantity cannot intuitively reflect geometric information of the orbit, and engineers must convert Cartesian coordinates into the longitude of the point below the satellite and the orbit height directly required by the task layer through complex mathematical conversion. The prior art lacks a state vector capable of being directly in four-dimensional spaceWithin the framework of complete dynamics modeling, which limits the ability to directly conduct control designs and rapid analysis within an intuitive parameter space. Therefore, the orbit dynamics description is reduced from six dimensions to visual four dimensions, and a complete system is established, so that the orbit dynamics description becomes a key breakthrough point for improving the efficiency of the space mission. Disclosure of Invention In order to solve the problem of how to improve the efficiency of space missions, the invention provides an orbit extrapolation method based on a longitude-altitude coordinate system, wherein a closed state space equation is constructed by establishing an accurate dynamic relation among the longitude of a point below the satellite, the orbit altitude and the change rate thereof, so that the orbit propagation efficiency is improved, the calculation time is reduced, and the high-precision numerical propagation in the state space concerned by the missions is realized. The aim of the invention is realized by the following technical scheme: The invention discloses a track extrapolation method based on a longitude and altitude coordinate system, which comprises the following steps: the method comprises the steps of firstly, constructing a longitude model of an undersea point by considering earth rotation based on the number of tracks, resolving the longitude model of the undersea point to obtain a true near point angle model, iterating parameters in the true near point angle model according to quadrants of latitude amplitude angles to obtain a converged optimal true near point angle; Obtaining a first derivative of the real near point angle based on the optimal real near point angle, deriving the first derivative of the real near point angle, and obtaining a second derivative of the real near point angle; step three, introducing a derivative parameter to derive a model of the longitude of the point below the satellite, and obtaining a first derivative and a second derivative of the longitude of the point below the satellite; Step four, constructing an orbit height model according to the difference between the ground center distance and the earth radius of the spacecraft, introducing a derivative parameter to derive the orbit height model, and obtaining a first derivative and a second derivative of the orbit height; And fifthly, constructing a state space equation of a four-dimensional space state vector by using a first derivative and a second derivative of the longitude of the point below the satellite and a first derivative and a second derivative of the orbit height, and adopting a numerical integrator to integrate the state space equation to extrapolate the four-dimensional space state vector required by the task to obtain a longitude height propagation model. In the first step, the longitude model of the satellite lower point is: ; in the formula, Is the longitude of the point under the satellite,In order to raise the right-hand meridian of the intersection point,Is an integer of the number of the times,According to the latitude amplitude angleQuadrant determination of (1) whenWhen k=1, whenOr (b)When k=0; Is the amplitude angle of the near-place, For a true angle of the near point,In order to achieve a peripheral rate of the material,For the inclination angle of the track,When the sp