Extended Kalman Filter (EKF) is a well-known technique in GPS based orbit estimation studies. Pseudoranges, which are established by spaceborne onboard satellite GPS receiver data, are directly used in these classical approaches as nonlinear measurements. On the other hand, the position vector components can be extracted from pseudoranges with an acceptable error tolerance via utilization of a preprocessing block before the EKF algorithm. In this way, these coarse position values can be employed as linear measurements in the EKF algorithm which might be called modern approach. In this paper, the linear and nonlinear measurements based orbit estimation EKF algorithms are developed and analyzed. The Multivariate Newton-Raphson Method (NRM) is used in the modern EKF as preprocessing block. The Auto-Assignment block is implemented for setting up initial state vector in the proposed modern EKF algorithm. The Low Earth Orbit (LEO) satellite's orbital motion is simulated via the J(2) perturbative orbit model. Statistical analysis shows that better results can be obtained by using linear measurements in the GPS based orbit estimation EKF algorithm, compared to traditional approach. By contrast, the classical approach is required less computational time. The design complexity of the filter is considerably reduced in the modern approach because of the preprocessing block application.