Short arc initial orbit determining method based on gauss solution cluster

Patent metadata

Field	Value
Publication number	US-11662209-B2
Application number	US-201916762505-A
Country	US
Kind code	B2
Filing date	Sep 23, 2019
Priority date	Mar 19, 2019
Publication date	May 30, 2023
Grant date	May 30, 2023

Abstract

The invention discloses a preferable short arc initial orbit determining method based on Gauss solution cluster, and belongs to the astrodynamics field, including: grouping the observation data, using Gauss method to obtain the target state vector at the corresponding time point for each group of data, forming a solution set of preliminary estimation; dividing the solution set of preliminary estimation into a position component vector solution set and a velocity component vector solution set for clustering to obtain a position component vector solution cluster and a velocity component vector solution cluster; based on the position component vector solution cluster and the velocity component vector solution cluster, generating a two-dimensional trajectory solution set; evaluating each of the two-dimensional trajectories by using a trajectory optimal method, calculating the number of root of orbits corresponding to the optimal two-dimensional trajectory, thereby completing determination of initial orbit.

First claim

What is claimed is:

1. A short arc initial orbit determining method for single space-based imaging observation platform based on Gauss solution cluster, wherein the method comprises the following steps:
S 1 . dividing an observation data, which are captured by an observation camera, into groups, wherein for each group of data, Gauss method is adopted to find a target state vector for a corresponding time point to form a solution set of preliminary estimation;
S 2 . dividing a solution set of preliminary estimation into a position component vector solution set and a velocity component vector solution set, which are respectively clustered to obtain a position component vector solution cluster and a velocity component vector solution cluster;
S 3 . generating a two-dimensional trajectory solution set based on the position component vector solution cluster and the velocity component vector solution cluster;
S 4 . using a trajectory optimization method to evaluate each two-dimensional trajectory, calculate the number of roots of orbit corresponding to the optimal two-dimensional trajectory, and complete determination of the short arc initial orbit;
wherein step S 2 comprises the following sub-steps:
S 201 . eliminating non-reasonable solutions from the solution set of preliminary estimation;
S 202 . dividing the remaining state vector solution set into a position component vector solution set and a velocity component vector solution set, and clustering being performed respectively so correct solutions are gathered in the same cluster as many as possible, thereby obtaining a position component vector solution cluster and a velocity component vector solution cluster;
S 203 . performing noise reduction preprocessing on the position component vector solution cluster and the velocity component vector solution cluster, respectively.

2. The short arc initial orbit determining method according to claim 1 , wherein step S 1 comprises the following sub-steps:
S 101 . dividing the observation data into groups, and vector data corresponding to every 3 time points being sorted into a group;
S 102 . for each group of vector data, using the conventional Gauss method to find a target state vector at the corresponding time point to form a solution set of preliminary estimation.

3. The short arc initial orbit determining method according to claim 2 , wherein it is assumed that an observation time point is [t 0 ,t k ], and k+1≥3, and for input data [t 0 ,t k ] of a total of k+1 time points, the interval parameter Nrate=└rate*k┘ is taken, wherein └•┘ represents the rounding down, rate is the interval rate, and the grouped observation data is expressed as {{right arrow over (L)} t s1 , {right arrow over (L)} t s2 , {right arrow over (L)} t s3 , {right arrow over (R)} t s1 , {right arrow over (R)} t s2 , {right arrow over (R)} t s3 }, wherein {right arrow over (R)} t s represents a satellite observation position vector, {right arrow over (L)} t s represents an observation angle vector

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4. The short arc initial orbit determining method according to claim 1 , wherein position data and velocity data satisfying any one of conditions |{right arrow over (r)} t s |<6378.14 km or |{right arrow over (r)} t s |>42378 km or |{right arrow over (v)} t s |>11.2 km/s are excluded, wherein {right arrow over (r)} t s represents the target position vector at time point t s , and {right arrow over (v)} t s represents the target velocity vector at the time point t s .

5. The short arc initial orbit determining method according to claim 1 , wherein in step S 202 , a k-means clustering method is used for clustering and Chauvenet's—criterion discriminating method is adopted to eliminate abnormal data.

6. The short arc initial orbit determining method according to claim 1 , wherein step S 3 comprises the following sub-steps:
S 301 . performing fitting on the position component vector solution cluster and the velocity component vector solution cluster after noise reduction to construct a state vector combination at various time points;
S 302 . generating a three-dimensional trajectory solution set of the target orbit according to the state vector combination corresponding to various time points;
S 303 . projecting the 3D trajectory solution set of the target orbit onto an instantaneous observation image plane according to a measurement status of an observation platform to obtain a 2D trajectory solution set.

7. The short arc initial orbit determining method according to claim 1 , wherein step S 4 comprises the following sub-steps:
S 401 . calculating a derivative error and a position error for each two-dimensional trajectory;
wherein the formula for calculating the derivative error of the m-th two-dimensional trajectory is as follows:
Δ ⁢ uv ′ ⁢ m = ∑ n = 0 k [ ❘ "\[LeftBracketingBar]" ( 2 ⁢ t n × U ^ ″ ⁢ m + U ^ ′ ⁢ m ) - ( 2 ⁢ t n × U ″ * + U ′ * ) ❘ "\[RightBracketingBar]" + ❘ "\[LeftBracketingBar]" ( 2 ⁢ t n × V ^ ″ ⁢ m + V ^ ′ ⁢ m ) - ( 2 ⁢ t n × V ″ * + V ′ * ) ❘ "\[RightBracketingBar]"

Assignees

• Univ Huazhong Science Tech

Inventors

• Hu Jing
• Li Binzhe
• Fang Li
• Xiong Tao
• Gao Xiang
• Kang Susu
• Jiang Kan

Classifications

• B64G1/242

  Orbits and trajectories · CPC title

• G01C21/24

  specially adapted for cosmonautical navigation · CPC title

• G01C21/20 Primary

  Instruments for performing navigational calculations (G01C21/24, G01C21/26 take precedence) · CPC title

• G01C21/02 Primary

  by astronomical means (G01C21/24, G01C21/26 take precedence) · CPC title

• B64G3/00

  Observing or tracking cosmonautic vehicles · CPC title