The Extended Kalman Filter (EKF), is an estimation method for nonlinear systems. GPS-based Satellite localization problem is such a nonlinear problem which has nonlinear state and measurement vectors, and the researchers in this area are frequently utilizing the EKF as standard solution technique. The traditional EKF requires some definitions at the initialization step of the filter algorithm. Measurement noise covariance matrix (R) is one of them and should be introduced into the algorithm either using sensor data sheets or statistical offline error calculations. In the proposed study, we used a Single Measurement Noise Scale Factor (SMNSF) to update the R matrix, which defined in the identity matrix form at the beginning. Thus, we developed an innovation-based Robust Kalman Filter (RKF) with Single Measurement Noise Scale Factor established over the EKF process. Also, we implemented a preprocessing block to convert measurements into linear form and feed the measurement channel of the Kalman filter. The preprocessing block of the algorithm has a soft-switch, and Newton-Raphson Method (NRM) based solver. We used J(2) perturbative orbit model for the Low Earth Orbit (LEO) satellite's orbital motion for 90 minutes. We had remarkable statistical results at the end of the simulation phase.