With the rapid development of modern science and technology, navigation technology plays a crucial role in transportation, aerospace, military and other fields. At present, a single navigation technology has been difficult to meet the complex navigation needs of high mobility carriers or special environments. Aiming at the above problems, this paper carries out an in-depth study on the tightly coupled navigation system of Strapdown Inertial Navigation System (SINS) and Global Navigation Satellite System (GNSS), and introduces the square-root information Kalman filtering algorithm. The algorithm takes the information matrix (the inverse of the mean square error matrix) as the updating object, which effectively avoids the numerical instability and non-positive characterization problems that may occur in the iterative process of the mean square error matrix. Compared with the traditional extended Kalman filter, the square-root information Kalman filter has higher numerical stability and computational efficiency in dealing with nonlinear systems, which is especially suitable for multi-sensor fusion scenarios.