TRIAD method is useful when we have only two vector measurements. If we need better accuracy and have more than two vector measurements, we need to use a more general algorithm. Before developing an algorithm, we need to make our problem statement more precise.

Say we have N unit vectors v_k, k = 1,2...N. We have a sensor measurement in the body frame for each vector, v_{kb}, and a mathematical model of the components in the inertial frame, v_{ki}. Our aim is to find a rotation matrix R_{bi}, such that<br \>

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 R_{bi} 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 \>

In this expression, J is the loss function that has to be minimized, k is the counter for the

N observations, w_k is weight assigned to the kth measurement, v_{kb} is the matrix consisting of the measured