In this paper, the error investigation of a 3-dimensional GPS attitude determination system using the error covariance analysis is given. New efficient formulas for computing the Euler Angle Dilution of Precision (EADOP) are also derived. The formulas are easy to compute and represent the attitude error as a function of the nominal attitude of a vehicle, the baseline configuration and the receiver noise. Using the formula, the accuracy of the Euler angle can be analytically predicted without the use of computer simulations. Applications to some configurations reveal the effectiveness of the proposed method.