Time correlations always exist in modern geodetic data, and ignoring these time correlations will affect the precision and reliability of solutions. In this paper, several methods for processing kinematic time-correlated observations are studied. Firstly, the method for processing the time-correlated observations is expanded and unified. Based on the theory of maximum a posteriori estimation, the third idea is proposed after the decorrelation transformation and differential transformation. Two types of situations with and without common parameters are both investigated by using the decorrelation transformation, differential transformation and maximum a posteriori estimation solutions. Besides, the characteristics and equivalence of above three methods are studied. Secondly, in order to balance the computational efficiency in real applications and meantime effectively capture the time correlations, the corresponding reduced forms based on the autocorrelation function are deduced. Finally, with GPS real data, the correctness and practicability of derived formulae are evaluated.