This paper studies a nonlinear discrete-time partial state observer design problem for rigid spacecraft systems, particularly for spacecraft attitude estimation. The construction is inspired by an orthogonality-preserving numerical algorithm, and it yields a semiglobal practical asymptotic observer. We show that the separation principle holds, and hence stabilization using output feedback is possible. An example is provided to illustrate the usefulness of our results in a sampled-data implementation of an attitude control for a rigid spacecraft using output feedback and to illustrate the advantages of the proposed observer design, especially compared to a sample and hold version of a similar type observer designed in continuous-time. (C) 2011 Elsevier Ltd. All rights reserved.