== Introduction ==Obtaining quaternion information from q-method involves solving We had begun with the eigenvalue problem of overdetermination because we had more equations than the unknown variables. Now, with sensor errors it becomes impossible to solve for a 4X4 Matrix. This can be done on MATLAB or other computer tools. But these variables such that it satisfies all the solution is numerically intensiveequations (remember, these equations are superfluous). On-board computing is So Wahba’s problem gives us a serious concern for any satellite designer and hence a better algorithm way to solve , if not circumvent, at least rationally deal with this problem using less computing is required. <br \>The QuEST algorithm provides It defines a less efficient but a ‘faster’ way weighted error function (i.e errors from each of the sensors are given weightage based on reliability) which is to solve the eigenvalue problembe minimised.
== The Algorithm ==Recall from [[Q Method and Wahba's Problem]] that the optimal attitude minimizes the loss function,[[File:Equation40Equation74.JPGpng|frame|center]]And maximizes The error function J can be simplified to a summation involving w_k (the weights, which are constants set by us) and the gain function, g as defined below[[File:Equation41Equation75.png|frame|center]]ThusIt is easy to see that minimising J is equivalent to maximising g. <br \>This expression when written in terms of quaternions becomes very compact. And qmethod showed that maximising g involved solving an eigenvalue problem. This can be done on MATLAB or other computer tools. But the solution is numerically intensive.<ref>http://www.dept.aoe.vt.edu/~cdhall/courses/aoe4140/attde.pdf</ref> Satellite makers need a better algorithm than [[Q Method and Wahba's Problem| Q-method]] to determine the attitude with minimal compromise in the accuracy. The QuEST algorithm provides a less efficient but a ‘faster’ way to solve the eigenvalue problem.<br \>QuEST starts with the assumption that sensor errors are minimal so that J can be minimised to a very low value. Rewriting J in terms of g,
[[File:Equation42.png|frame|center]]
[[File:Equation43.png]] where [[File:Equation44.png]] is the maximum eigenvalue of the K matrix defined in [[Q Method and Wahba's Problem]].