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An Optimal Linear Attitude Estimator (OLAE), is presented for the case of a singlepoint real-time estimation of spacecraft attitude using the minimum-element attitude parametrization: Rodrigues (or Gibbs) vector g. The optimality criterion, which does not coincide with the Wahba's constrained criterion, is rigorously quadratic and unconstrained. The singularity, which occurs when the principal angle is π, can easily be avoided by one rotation. The attitude accuracy tests show that the proposeddoi:10.2514/1.29568 fatcat:qluc3ei5mzaq3lddrom2omdcla