Abstract: Three optimal linear attitude estimators are proposed for single-point real-time estimation of spacecraft attitude using a geometric approach. The final optimal attitude is represented by modified Rodrigues parameters (MRPs). After introducing incidental right-hand orthogonal coordinates for each pair of measured values, three error vectors are obtained by the use of dot or/and cross products. Corresponding optimality criteria are rigorously quadratic and unconstrained, which do not coincide with Wahba’s constrained criterion. The singularity, which occurs when the principal angle is close to π, can be easily avoided by one proper rotation. Numerical simulations show that the proposed three optimal linear estimators can provide a precision comparable with those complying with the Wahba optimality definition, and have faster computational speed than the famous quaternion estimator (QUEST).

Key words: Linear attitude determination, Geometric analysis, Gibbs vector, Singularity avoidance

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