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for each of the N vectors. It is clear that this set of equations will be overdetermined for N > 2,
and hence the equation, in general, cannot be satisfied for each k = 1,2..N. Hence,
we wish to find a solution for <math>R_{bi} </math> that in some way minimizes the overall error for
the N vectors. <ref>http://www.dept.aoe.vt.edu/~cdhall/courses/aoe4140/attde.pdf</ref><br \>
[[File:Equation72.png|frame|center]]
In this expression, J is the loss function that has to be minimized, k is the counter for the
N observations, <math<w_k </math> is weight assigned to the kth measurement, <math>v_{kb} </math> is the matrix consisting of the measuredcomponents in the body frame, and <math>v_{ki} </math> is the matrix consisting of components in the inertial
frame as determined using appropriate mathematical models. This loss function is a
sum of the squared errors for each vector measurement. If the measurements and
mathematical models are perfect, then J = 0, since the first equation on this page will be satisfied for all N vectors. If there are any errors or noisy measurements, then J > 0. The smaller
we make J, the better the approximation of <math>R_{bi}</math>.
== Q-Method ==