## Study of a Homotopy Continuation Method for Early Orbit Determination with the Tracking and Data Relay Satellite System, (TDRSS)National Aeronautics and Space Administration, Scientific and Technical Information Branch, 1986 - Artificial satellites - 138 pages |

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### Contents

Formulation of the Basic Homotopy Method | 3-1 |

Numerical Examples of the Basic Homotopy | 4-1 |

Prototype Algorithm for TDRSS Early Orbit | 4-5 |

2 other sections not shown

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### Common terms and phrases

angle errors angular antenna beam angles antenna pointing approximation arc length Azimuth bifurcation points calculation computed correct solution corrector critical hypersurface critical points curve point defined Doppler measurements early orbit algorithm early orbit determination ECCENTRIC ORBIT Equa Equations 3-3 example extremum Figure geometric homotopy continuation method homotopy method hyperplane interpolated kilometers level 1 loops Level Level Level light-time Low-Inclination Newton-Raphson iteration Newton-Raphson method observation partials matrix orbit determination problem Orbit Elements ORBIT POSITION VECTORS orbit solutions orbit state vector parameters partial derivatives polynomial position vector predicted priori estimate procedure R. L. Smith range and Doppler range and/or Doppler range measurements Rank Rank Rank refinement Relay RTDRS Schematic Diagram selected six-level algorithm six-observation solu solution curve solution loop Solution Solution specified tolerance step subalgorithm tangent vector TDRS Antenna Beam TDRS orbit plane TDRSS tracking tracking data trajectory transponder delay true anomaly two-body two-level algorithm