In moving object positioning and tracking, the GPS positioning error is colored noise with time correlations. According to the results of time sequential analyses, the model of the positioning error can be described as a AR(10) model. In order to decrease the computations and realize the real-time positioning and tracking of the moving objects, the AR(10) model is fit to be a 2-order Markov process. The positioning data act as the measurements, the system equations are built, in which the measuring noises have time-correlation. Subtracting the adjacent measurements, the correlated portions of measurements are eliminated, and the differences of the measurements are considered to be the new measurements. The new system equations are rebuilt and the recursive state evaluation algorithm is given, in which the measuring noise is white noise. It avoids higher-order matrix inverse calculations and fewer memories are needed. The simulation results show that the 2-order Markov process can effectively fit to the GPS error model and the precision of the moving object positioning is increased.