Observability of a Geosynchronous Spacecraft Attitude Determination System

Abstract

The observability is examined of a standard geosynchronous spacecraft attitude determination system that uses Earth and sun sensor measurements. The results show that the attitude determination error state, including the attitude and gyro bias errors, is entirely observable over the portion of the orbit where both sun and Earth sensor measurements are available. However, when the sun is outside the sun sensor window, the system is unobservable with a one-dimensional unobservable subspace. It is shown that the eigenvalue associated with this unobservable subspaceiszero and thatthecorresponding eigenvectorisanequilibrium lineoftheattitudedetermination system. The state vector converges to this equilibrium line from any initial state. This result has practical importance in spacecraftattitudecontrolandmaybeusedtospeedtherecoveryfromattitudedeterminationanomalies.Numerical simulations and actual spacecraft e ight data are included to illustrate the theory.