A numerical algorithm as an observer for spacecraft attitude determination

This paper studies a nonlinear discrete-time state observer design problem for rigid spacecraft, particularly for spacecraft attitude estimation. The observer is a partial state observer, and it is constructed based on a numerical algorithm that preserves the orthogonality of a matrix function. Orthogonality preservation is important as the attitude matrix to be estimated is orthogonal, whereas in general orthogonality is destroyed under sampling. We prove that the proposed construction yields a semiglobal practical asymptotic observer. We also show that the separation principle holds for our problem, and hence stabilization using output feedback is possible. Two examples are provided to illustrate the usefulness of our results in a sampled-data implementation.