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In this paper, a scaled unscented Kalman filter (SUKF) based on the quaternion concept is designed for determination of the attitude, velocity and position parameters in inertial navigation system (INS) under large attitude error conditions. In this feedback filter, only bias effects are considered to be independent states and are used to compensate for navigation errors. To preserve the nonlinear nature of unit quaternion, the weighted mean computation for quaternions is derived in rotational space as a barycentric mean with renormalization and a multiplicative quaternion-error is used for predicted covariance computation of the quaternion because it represents the distance from the predicted mean quaternion. The updates are performed using quaternion multiplication which guarantees that quaternion normalization is maintained in the filter. Since the quaternion process noise increases the uncertainty in attitude orientation, modeling it as a vector part of quaternion is considered. Simulation and experimental results indicate a satisfactory performance of the newly developed model.