This brief concerns model and noise design relevant to drag-free and attitude control of the European satellite gravity field and steady-state ocean circulation explorer (GOCE) under different control modes. As the model must include accurate dynamics of disturbance and measurement drifts to be rejected/estimated, noise design aims to select, and to mark with the Boolean variables of the control modes, the necessary and sufficient feedback channels (noise estimator) connecting model error to noise, which are the paths through which model state variables can be updated in real-time. Noise design is applied to a generic model encompassing position and attitude control, fed by position, rate, attitude, and acceleration sensors. The resulting closed-loop becomes a state predictor, providing controllable and disturbance states to drag-free and attitude control law, switching smoothly from mode to mode. Noise estimator gains are tuned to robust performance and stability by properly assigning closed-loop eigenvalues. Tuning details and simulated results illustrating the different modes are provided.