ENERGY APPROACH ALGORITHM FOR ATTITUDE DETERMINATION FROM VECTOR OBSERVATIONS

This paper presents a new mathematical approach to the Wahba's problem of optimal estimation of spacecraft attitude based on vector observat ions. 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 bod y is therefore derived by either setting to zero the overall torque, o r by minimizing the spring stored energy. Both of these mathematical p rocedures lead to the same second-order matrix equation, the R-equatio n, which relates attitude matrix and data. From the R-equation several solution forms, which compute the same optimal attitude matrix, are d erived. These solution forms do not present ambiguities and/or singula rities; 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 computatio nal speed.