Estimation of orthogonal transformations in strapdown inertial systems

One advantage of strapdown inertial systems is the feasibility of automatic computation of alignment transformations between two or more attitude reference systems rigidly fixed to some common rigid body. The essential analytical problem involved reduces to the problem of finding some optimal estimate of an orthogonal transformation given a sequence of pairs of observation vectors that are linearly related by the orthogonal transformation. Several solutions to the problem are presented using a least squares cost function. These solutions include optimal but generally nonorthogonal estimates and an optimal estimate constrained to he orthogonal. In addition, a procedure is presented to orthogonalize a generally nonorthogonal estimate in a least squares sense.