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«2. may sense. Furthermore, the methods are not easily applied to star trackers or combinations of sensors which provide many simultaneous vector measurements. Given a set of n > 2 vector measurements, u'a, in the body system, one choice for an optimal attitude matrix. A, is that which minimizes the loss function

i where w, is the weight of the <th vector measurement and u'A is the vector in the reference coordinate system. The loss function is the weighted sum squared of the difference between the measured and transformed vectors.

The attitude matrix may be computed by an elegant algorithm derived by Davenport [1968] and based in part on earlier work by Wahba [1965] and Stuelpnagel [1966]. This algorithm was used for the HEAO-1 attitude determination system [Keat, 1977].

The loss function may be rewritten as n

i= i where the unnormalized vectors W, and V, are defined as

The loss function J(A) is clearly a minimum when

is a maximum, where the (3 x n) matrices W and V are defined by

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