Abstract: The convergence speed of Kalman filter is slow and the accuracy of initialization is low if the ambiguities are taken parameters estimated in dynamic precise point positioning. The accuracy of Kalman filter will degrade if the spectral density of the dynamic model is not accurate. So fixing single difference ambiguities are used to improve the speed of convergence. Firstly, the ambiguities of ionosphere-free observations are estimated with the sequential least squares, and the ambiguities of wide lane are fixed. Then, the ambiguities of narrow lane are fixed. At last, the ambiguities of ionosphere-free observations are fixed. For errors of the spectral density affect covariance matrix of the predicted state vector, adaptive filtering is used to control outliers. Adaptive factor on the basis of current information can adjust the scale between covariance matrix of predicted state and covariance matrix of observations noise, so that the contribution of dynamic state to results of Kalman filter is more efficient. In the processing of data of air, the adaptive Kalman filter in which single difference ambiguities fixing are used, can improve the speed of convergence and accuracy of positioning. The stability of adaptive Kalman filter is better when the spectral density has different numerical value.