When quaternions are used for representing the attitude of a spinning spacecraft in an attitude estimation filter, several problems appear due to their rapid variations. These problems include numerical integration errors and violation of the linear approximations for the filter. In this study, we propose representing the attitude of a spinning spacecraft using a set of spin parameters. These parameters consist of the spin-axis orientation unit vector in the inertial frame and the spin phase angle. This representation is advantageous as the spin axis direction components in the inertial frame do not change rapidly and the phase angle changes with a constant rate in the absence of a torque. The attitude matrix and the kinematics equations are derived in terms of spin parameters. As the equations are highly nonlinear an Unscented Kalman Filter (UKF) is implemented to estimate the spacecraft's attitude in spin parameters. The estimation results are compared with those of a quaternion based UKF in different scenarios using the simulated data for JAXA's ERG spacecraft.