Improvement to the Implementation of the QUEST Algorithm

QUEST has supported hundreds of missions, both in Earth orbit and at the far reaches of the solar system, without an anomaly. Recently, however, a robustness issue of QUEST was raised. Specifically, it was shown that the Newton Raphson iteration, employed by the QUEST algorithm to solve the characteristic equation for the maximum eigenvalue of the Davenport matrix, did not converge in an extreme case. It should be pointed out that the issue was about the implementation detail of the characteristic polynomial, not the mathematical procedure of the algorithm. The values of the components have been chosen so that each column vector has exactly unit norm. The robustness issue of the QUEST characteristic polynomial is not due to errors in the coefficients used in the polynomial, but due to the order in which the terms are combined.