Energy Approach Algorithm for Attitude Determination from Vector Observations

Abstract

This paper presents a new mathematical approach to the Wahba’s problem of optimal estimation of spacecraft attitude based on vector observations. The Wahba’s problem is demonstrated here to be equivalent to the problem of finding the static equilibrium of a rigid body constrained by a set of spherical springs. The equilibrium attitude of such a body is therefore derived by either setting to zero the overall torque, or by minimizing the spring stored energy. Both of these mathematical procedures lead to the same second-order matrix equation, the R -equation, which relates attitude matrix and data. From the R -equation several solution forms, which compute the same optimal attitude matrix, are derived. These solution forms do not present ambiguities and/or singularities; and they are easy to code and equivalent in accuracy. Finally, a numerical comparison of the fastest Energy Approach Algorithm (EAA) solution form with known optimal algorithms highlights its computational speed.