In this paper, a dynamic modeling for the velocity and position information of a single frequency stand-alone GPS(Global Positioning System) receiver is described. In static condition, the position error dynamic model is identified as a first/second order transfer function, and the velocity error model is identified as a band-limited Gaussian white noise via non-parametric method of a PSD(Power Spectrum Density) estimation in continuous time domain. A Kalman filter is proposed considering both correlated/white measurements noise based on identified GPS error model. The performance of the proposed Kalman filtering method is verified via numerical simulation.