With the increase of human polar activities, polar integrated navigation has gradually become a hot topic of concern. The traditional navigation scheme in the geographic coordinate system has inherent singular points in polar regions. Polar navigation coordinate systems such as the grid coordinate system or the transverse coordinate system also have the same limitations in low-latitude regions. A single coordinate system cannot meet the requirements of global integrated navigation. In additional, the state spaces of the integrated navigation system under different coordinate systems are inconsistent, and seamless switching of navigation poses a huge challenge. This paper proposes a Kalman state transformation algorithm. By deriving the transformation matrix, it realizes the mutual mapping of different state spaces. Furthermore, considering the influence of the state space on the parameters of the Kalman system, it achieves smooth switching of the Kalman filter parameters. Finally, both simulation experiment and Monte Carlo trials demonstrate that the proposed algorithm can effectively reduce oscillatory errors and enhance the stability of the integrated navigation system, for the realization of global integrated navigation.