In this paper, a general non-linear psi-angle approach is presented that does not require coarse alignment. In the psi-angle model, The SINS error models (position, velocity and attitude angles) with large misalignment angles are derived. This error model uses Euler angles to describe the misalignment of platform frame to navigation frame, but the derived error models are only valid under condition that the heading uncertainty is large and the two leveling misalignment angles
are small the three misalignment angles are assumed all large. We simulate SINS large azimuth misalignment angle on the stationary base (fixed position and multi-position) alignment also on the movable base (In-flight) alignment in two cases (straight level flight and turn level maneuver) based on the trajectory generator data. All these simulations are done using different Kalman filter techniques (nonlinear discrete equations, Standard extended Kalman filter EKF, and iterative filtering IKF) to solve the non-linear system problems.