To use Kalman filtering for kinematic navigation and positioning, we have to deal with function model and stochastic model. The precision and reliability of kinematic Kalman filtering are affected remarkably from the function model and stochastic model errors. Adaptive fitting of both colored noise and covariance matrices by using moving windows are presented based on the assumption that the observation and dynamic model noises mainly include the colored noises with first order self-correlation character. The expressions to calculate the colored noise estimators and covariance matrices of the modified observations and predicted states are obtained. Feasibility and practicability of the model and algorithm are tested by an example. It is shown that the Kalman filtering, based on the adaptive fittings of the colored noises and covariance matrices, can be effective in resisting the influence of the colored noises on the navigation results.