A comparable analysis is made on calculating the usual least squares and total least squares (TLS) solution of an over-determined system, which deals with uncertainties on the sensitivity matrix and the erroneous perturbation in the transformation and back-substitution. In this paper the TLS method provides a clearer understanding of the problems and provides a solution expressed in closed form. The objective of this research is to improve reliability and positioning accuracy standalone GPS receiver. According to security feature of receiver autonomous integrity monitoring (RAIM) and fault detection and exclusion (FDE), the improved algorithm is used to compute the GPS position estimates from pseudo-range and delta range measurements in order to detect and exclude erroneous measurements.