The Journal of the Astronautical Sciences

, Volume 63, Issue 1, pp 60–80 | Cite as

Nonlinear Observability for Relative Orbit Determination with Angles-Only Measurements



This paper presents nonlinear observability criteria for the relative orbital dynamics represented by the solutions of the two-body problem. It is assumed that a chief is on a circular orbit with a prescribed orbital radius, and it measures lines-of-sight toward a deputy only. A differential geometric method, based on the Lie derivatives, is used to derive sufficient conditions for observability of the orbital properties of the deputy. It is shown that under certain geometric conditions on the relative configuration between the chief and the deputy, the nonlinear relative motion is observable from angles-only measurements. The second part of this paper presents a quantitative measure of observability for the relative orbits, and it is formulated by generalizing the observability Gramian of linear dynamic systems. An extended Kalman filter is also developed to numerically illustrate the observability of nonlinear relative orbits with angles-only measurements and to show correspondence between the proposed observability measure and filtered solution accuracy.


Nonlinear observability Relative orbit determination Angles-Only measurements 


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Copyright information

© American Astronautical Society 2015

Authors and Affiliations

  1. 1.Department of Mechanical and Aerospace EngineeringThe George Washington UniversityWashingtonUSA
  2. 2.Air Force Research LaboratorySpace Vehicles DirectorateKirtland AFBUSA

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