Characteristic polynomial of the QUEST algorithm

QUEST is a widely-used attitude estimation algorithm that determines three-axis attitude from vector observations. A key step in QUEST as well as many other fast attitude estimation algorithms involves solving the characteristic equation of a four-dimensional symmetric real matrix for the maximum eigenvalue of the matrix using an iterative root-finding method, for example, the Newton-Raphson method. When the attitude is only marginally observable, the form of the characteristic polynomial play a bigger role in the calculation of the maximum eigenvalue. The partially-factorized form of the characteristic polynomial leads to higher accuracy in the calculation of maximum eigenvalue than the expanded form of the characteristic polynomial.