# Accession Number:

## AD1031625

# Title:

## Initial Orbit Determination Based on Propagation of Admissible Regions with Differential Algebra

# Descriptive Note:

## Technical Report,15 Jun 2015,14 Jun 2018

# Corporate Author:

## POLITECNICO DI MILANO MILANO Italy

# Personal Author(s):

# Report Date:

## 2017-01-19

# Pagination or Media Count:

## 55.0

# Abstract:

This work contains the definition of the initial orbit determination IOD method with some first results, a literature review about the Manifold, the creation of the algorithms and architecture for the ADS and the initial merging of the ADS into the IOD technique. The IOD algorithm is explained, implemented and comparisons with results from literature are also outlined. In specific it takes as input optical observations and gives as output the state of the object at the central time of observation expanded with respect to perturbations on the observations. Since one expansion is not accurate enough to describe the full initial domain, the ADS tool is introduced. This tool is constructed on the mathematical definition of the manifold. The initial state vector is then defined as a set of Charts and the propagator integrates in time this initial manifold while the ADS manages the convergence radius of manifold, or rather the convergence radius of every single Chart. Thus, when a single truncated power series TPS is not sufficient to represent the whole manifold, that is when the estimation error of a chart is bigger than the threshold, the ADS splits the manifold and goes ahead with the propagation.

# Descriptors:

# Subject Categories:

- Theoretical Mathematics