Abstract: The reasons of the instability of Kalman filter were analyzed from the stability of Kalman filter. A new group of adaptive estimation methods of Kalman filter fading factor were developed and simulated in GPS/SINS(global position system and strapdown inertial navigation system) integrated navigation system. The characteristic that the filter residuals were zero-mean Gaussian white noise vectors was used and a chi-square distribution variable was made while computing the fading factor. The fading factor was computed by testing each element of the filter residual vector. The result shows that the proposed algorithms can estimate the fading factor adaptively, restrain filtering divergence and has the less computation burden than other algorithms.