Geometric Integration: Difference between revisions

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In summary, the problem is that
In summary, the problem is that
*there are an increasing number of space objects to track
**there are an increasing number of space objects to track
*sensor time per object is limited
**sensor time per object is limited
*many objects yield infrequent pass opportunities
**many objects yield infrequent pass opportunities


Advanced estimation techniques require accurate integration during extended propagation intervals when limited observation data is available.
Advanced estimation techniques require accurate integration during extended propagation intervals when limited observation data is available.

Revision as of 18:37, 13 November 2012

What is Geometric Integration?

Motivation

Space Object Cloud

One prevailing field in which this research is very pertinent is Space Situational Awareness (SSA). The U.S. Air Force is collecting data in order to catalogue Earth orbiting satellites, objects and debris. Accurate tracking of all Earth-orbiting objects is important since their presence can be extremely hazardous to current space missions as well as disruptive for any future mission. This danger can either be passive in the case of debris or active intentional threats. However, the data necessary to estimate the attitude of such objects is sparse as a result of the number of sensors available and the large number of objects in orbit. In particular, for objects in low-Earth orbit (LEO), observation windows may last only a few minutes and opportunities to obtain data are infrequent. As a result, an object's attitude may often need to be propagated very accurately over long time intervals before an update is possible.

Truncation and Roundoff Error Tradeoff

In summary, the problem is that

    • there are an increasing number of space objects to track
    • sensor time per object is limited
    • many objects yield infrequent pass opportunities

Advanced estimation techniques require accurate integration during extended propagation intervals when limited observation data is available.

Objective: Employ a Lie group method developed by Crouch and Grossman for the numerical integration of a quaternion parameterized attitude. Its inherent ability to integrate along the unit hypersphere helps to minimize truncation errors while maintaining the quaternion unit norm constraint.

Findings

Applications

  • Shape Estimation