This paper proposes a new constrained attitude estimation method for a satellite to reduce the influence of non-Gaussian measurement noise. A conventional constrained filter, the Receding-Horizon Nonlinear Kaiman Filter (RNKF), propagates the state value with a model in the prediction step, and minimizes the cost function with a constraint in the filtering step. The cost function is desired to be a quadratic program problem, whose constraint is linear, in terms of computational complexity. If the RNKF is applied to the attitude estimation problem, the appropriate attitude representation is the quaternion, which does not have a singular point, in the prediction step. However, the quaternion does not define a quadratic program in the filtering step because the quaternion needs to satisfy a single constraint of a unit norm. Therefore, this paper proposes the Receding-Horizon Unscented Kaiman Filter (RUKF) as an improvement of the RNKF to deal with appropriate attitude representation in each step. In the RUKF. the attitude is represented by the Rodrigues parameter in the filtering step owing to the Unscented Transformation. The Rodrigues parameter is an attitude representation with no constraint. It was confirmed from Monte Carlo simulation that the RUKF with a constraint is more accurate than the Extended Kaiman Filter.