This paper presents the OCIT2 and OCITn algorithms which optimally estimate a pointing direction (e.g. the spin axis) without computing the spacecraft attitude and by using n=2 and n>2 observed vectors, respectively. OCIT2, which fully complies with Wahba optimality criterion, optimally estimates the intersection of two cones in a closed-form. Speed tests show OCIT2 faster than the presently fastest optimal attitude estimator (ESOQ-2). Therefore, OCIT2 is suitable when a fast and optimal estimation of a pointing direction is required. OCITn provides the solution as a weighted sum of OCIT2 solutions. The OCITn accuracy is, on average, just a little less than that provided by optimal ESOQ-2, while it presents a speed gain, compared to ESOQ-2, for n<5.
