Abstract To solve the problem of divergence of Sage-Husa adaptive filtering algorithm in the integrated navigation system, we propose an improved Sage-Husa adaptive filtering algorithm. Firstly, we apply the compensation feedback correction algorithm to the linear Kalman filter algorithm to obtain the optimal estimation and simplify the innovation vector of filter. Then, we propose an improved, simple to implement, Sage-Husa adaptive filtering algorithm, avoiding divergence of state estimation. Finally, a GNSS/SINS integrated navigation experiment based on this algorithm shows that this algorithm can accurately track not only the variance of sudden change but also the variance of slow change of measurement noise, and the estimation accuracy of variance is equivalent to that of variational Bayesian method. Compared with the standard KF algorithm, the position accuracy and velocity accuracy can be improved by 20% and 21% respectively when the variance of measurement noise changes, thus effectively reducing the influence of unknown statistical characteristics of measurement noise on filtering accuracy.